]> matita.cs.unibo.it Git - helm.git/commitdiff
λδ-2B is released
authorFerruccio Guidi <fguidi@maelstrom.helm.cs.unibo.it>
Tue, 19 Nov 2019 19:45:15 +0000 (20:45 +0100)
committerFerruccio Guidi <fguidi@maelstrom.helm.cs.unibo.it>
Tue, 19 Nov 2019 19:45:15 +0000 (20:45 +0100)
+ some refactoring
+ extra spaces cleaned
+ web site update

124 files changed:
helm/www/lambdadelta/download/lambdadelta_2B.tar.bz2 [new file with mode: 0644]
helm/www/lambdadelta/web/home/documentation_2.tbl
helm/www/lambdadelta/web/home/news.ldw.xml
helm/www/lambdadelta/web/home/versions.tbl
matita/matita/contribs/lambdadelta/Makefile
matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snabstneg_1.ma [deleted file]
matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/sngref_2.ma [deleted file]
matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snitem1_2.ma [deleted file]
matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snlref_2.ma [deleted file]
matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snproj_3.ma [deleted file]
matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snprojneg_2.ma [deleted file]
matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snprojpos_2.ma [deleted file]
matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snstar_2.ma [deleted file]
matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snabstneg_1.ma [new file with mode: 0644]
matita/matita/contribs/lambdadelta/alpha_1/notation/functions/sngref_2.ma [new file with mode: 0644]
matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snitem1_2.ma [new file with mode: 0644]
matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snlref_2.ma [new file with mode: 0644]
matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snproj_3.ma [new file with mode: 0644]
matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snprojneg_2.ma [new file with mode: 0644]
matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snprojpos_2.ma [new file with mode: 0644]
matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snstar_2.ma [new file with mode: 0644]
matita/matita/contribs/lambdadelta/alpha_1/syntax/term.ma
matita/matita/contribs/lambdadelta/apps_2/models/li.ma
matita/matita/contribs/lambdadelta/apps_2/models/veq.ma
matita/matita/contribs/lambdadelta/apps_2/models/vpushs.ma
matita/matita/contribs/lambdadelta/apps_2/models/vpushs_fold.ma
matita/matita/contribs/lambdadelta/apps_2/web/apps_2_src.tbl
matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_conf.ma
matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpm_teqx_trans.ma
matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_cpms_teqx.ma
matita/matita/contribs/lambdadelta/basic_2/dynamic/cnv_fqus.ma
matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_fsb.ma
matita/matita/contribs/lambdadelta/basic_2/dynamic/nta_preserve.ma
matita/matita/contribs/lambdadelta/basic_2/i_dynamic/ntas_cpcs.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpms_cpms.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpts_drops.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_reqx.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_teqx.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_csx.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_simple.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbg.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_fqup.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/fpbs_lpxs.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_csx.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_feqx.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/fsb_fpbg.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx_csx.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/jsx_drops.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/lprs_ctc.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx.ma
matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_drops.ma
matita/matita/contribs/lambdadelta/basic_2/rt_transition/cnx.ma
matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpg.ma
matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpm.ma
matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpr.ma
matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt.ma
matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx.ma
matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_fqus.ma
matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_reqx.ma
matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpbq.ma
matita/matita/contribs/lambdadelta/basic_2/rt_transition/lpr_lpr.ma
matita/matita/contribs/lambdadelta/basic_2/rt_transition/rpx_reqx.ma
matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml
matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
matita/matita/contribs/lambdadelta/ground_2/lib/relations.ma
matita/matita/contribs/lambdadelta/ground_2/lib/stream_eq.ma
matita/matita/contribs/lambdadelta/ground_2/notation/functions/uparrow_1.ma
matita/matita/contribs/lambdadelta/ground_2/pull/pull_4.ma
matita/matita/contribs/lambdadelta/ground_2/relocation/nstream_coafter.ma
matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_after.ma
matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_at.ma
matita/matita/contribs/lambdadelta/ground_2/relocation/rtmap_fcla.ma
matita/matita/contribs/lambdadelta/ground_2/steps/rtc_plus.ma
matita/matita/contribs/lambdadelta/ground_2/web/ground_2_src.tbl
matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_le.ma
matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_lt.ma
matita/matita/contribs/lambdadelta/ground_2/ynat/ynat_plus.ma
matita/matita/contribs/lambdadelta/static_2/i_static/rexs.ma
matita/matita/contribs/lambdadelta/static_2/relocation/drops.ma
matita/matita/contribs/lambdadelta/static_2/relocation/drops_cext2.ma
matita/matita/contribs/lambdadelta/static_2/relocation/drops_drops.ma
matita/matita/contribs/lambdadelta/static_2/relocation/drops_length.ma
matita/matita/contribs/lambdadelta/static_2/relocation/drops_sex.ma
matita/matita/contribs/lambdadelta/static_2/relocation/lifts.ma
matita/matita/contribs/lambdadelta/static_2/relocation/lifts_teqo.ma
matita/matita/contribs/lambdadelta/static_2/relocation/lifts_tweq.ma
matita/matita/contribs/lambdadelta/static_2/relocation/sex.ma
matita/matita/contribs/lambdadelta/static_2/relocation/sex_tc.ma
matita/matita/contribs/lambdadelta/static_2/s_computation/fqus.ma
matita/matita/contribs/lambdadelta/static_2/s_computation/fqus_weight.ma
matita/matita/contribs/lambdadelta/static_2/s_transition/fqu_teqx.ma
matita/matita/contribs/lambdadelta/static_2/s_transition/fqu_weight.ma
matita/matita/contribs/lambdadelta/static_2/static/aaa_feqx.ma
matita/matita/contribs/lambdadelta/static_2/static/frees.ma
matita/matita/contribs/lambdadelta/static_2/static/frees_append.ma
matita/matita/contribs/lambdadelta/static_2/static/frees_drops.ma
matita/matita/contribs/lambdadelta/static_2/static/frees_fqup.ma
matita/matita/contribs/lambdadelta/static_2/static/fsle_fsle.ma
matita/matita/contribs/lambdadelta/static_2/static/gcp_cr.ma
matita/matita/contribs/lambdadelta/static_2/static/lsuba_drops.ma
matita/matita/contribs/lambdadelta/static_2/static/lsubf.ma
matita/matita/contribs/lambdadelta/static_2/static/lsubf_lsubr.ma
matita/matita/contribs/lambdadelta/static_2/static/lsubr.ma
matita/matita/contribs/lambdadelta/static_2/static/lsubr_drops.ma
matita/matita/contribs/lambdadelta/static_2/static/req.ma
matita/matita/contribs/lambdadelta/static_2/static/reqx_reqx.ma
matita/matita/contribs/lambdadelta/static_2/static/rex.ma
matita/matita/contribs/lambdadelta/static_2/static/rex_drops.ma
matita/matita/contribs/lambdadelta/static_2/syntax/append_length.ma
matita/matita/contribs/lambdadelta/static_2/syntax/ceq_ext.ma
matita/matita/contribs/lambdadelta/static_2/syntax/ceq_ext_ceq_ext.ma
matita/matita/contribs/lambdadelta/static_2/syntax/ext2_ext2.ma
matita/matita/contribs/lambdadelta/static_2/syntax/genv.ma
matita/matita/contribs/lambdadelta/static_2/syntax/lenv_length.ma
matita/matita/contribs/lambdadelta/static_2/syntax/lveq.ma
matita/matita/contribs/lambdadelta/static_2/syntax/lveq_length.ma
matita/matita/contribs/lambdadelta/static_2/syntax/sh_lt.ma
matita/matita/contribs/lambdadelta/static_2/syntax/teqx.ma
matita/matita/contribs/lambdadelta/static_2/syntax/tweq_teqx.ma
matita/matita/contribs/lambdadelta/static_2/web/static_2_src.tbl
matita/matita/contribs/lambdadelta/web/core.tbl

diff --git a/helm/www/lambdadelta/download/lambdadelta_2B.tar.bz2 b/helm/www/lambdadelta/download/lambdadelta_2B.tar.bz2
new file mode 100644 (file)
index 0000000..33786f9
Binary files /dev/null and b/helm/www/lambdadelta/download/lambdadelta_2B.tar.bz2 differ
index ee523fda4e2e4a7b59891b4a0de1ac10a2650223..2cd06743ecda3d7ddffca66f0c8c45f55546bfbb 100644 (file)
@@ -84,6 +84,14 @@ table {
      "Presentation at University of Bologna (slides)."
      * }
    ]
+   [ { name "ldV2b" "<span class=\"emph alpha\">V2b.</span>" "" } {
+     "F. Guidi:" +
+     @@("html/version_2.html" "lambdadelta_2B") +
+     "(revised <span class=\"emph gamma\">2019-11</span>)." +
+     "Formal specification for the proof assistant Matita 0.99.4 (scripts)." +
+     @@("html/documentation.html#bibtex" "BibTeX entry") ^ "."
+     * }
+   ]
    [ { name "ldV2a" "<span class=\"emph alpha\">V2a.</span>" "" } {
      "F. Guidi:" +
      @@("html/version_2.html" "lambdadelta_2A1") +
index 3f1c9f893e136452c8b5a1d3bbf6d47e80cb62e8..27e6dd4604e3671ff373df8c2c45ffa6e9366ce7 100644 (file)
 
    <section3 name="milestones">Milestones</section3>
 
+   <news class="gamma" date="November 2019.">
+      The specification of
+      <rlink to="html/documentation.html#ldV2b">λδ-2B</rlink>
+      is released.
+   </news>
+
    <news class="alpha" date="December 2015.">
       <rlink to="html/documentation.html#ldJ3a">Second journal paper on λδ</rlink>
       accepted for publication.
    </news>
 
    <news class="delta" date="August 2015.">
-      The specification of λδ version 2A1 is concluded.
+      The specification of λδ-2A is concluded.
    </news>
 
    <news class="gamma" date="June 2015.">
       The corrected specification of Landau's "Grundlagen der Analysis"
-      is validated in a λProlog implementation of λδ version 3.
+      is validated in a λProlog implementation of λδ-3.
    </news>
 
    <news class="delta" date="March 2015.">
-      The specification of λδ version 1 is validated by
+      The specification of λδ-1A is validated by
       <link to="http://matita.cs.unibo.it/">Matita 0.99.2</link>.
    </news>
 
    </news>
 
    <news class="delta" date="January 2015.">
-      The specification of <rlink to="html/specification.html#v1">λδ version 1</rlink>
-      is updated with backports from the abandoned specification of λδ version 2.
+      The specification of <rlink to="html/specification.html#v1">λδ-1A</rlink>
+      is updated with backports from the abandoned specification of λδ-2.
    </news>
 
    <news class="gamma" date="December 2014.">
       <rlink to="html/implementation.html#v2">"Helena 0.8.2"</rlink> is released.
       <list><item>
          The corrected specification of Landau's "Grundlagen der Analysis"
-         is validated in λδ version 3. 
+         is validated in λδ-3. 
       </item></list>
    </news>
 
    <news class="gamma" date="October 2014.">
-      <rlink to="html/documentation.html#ldJ2a">λδ version 2A1</rlink>
+      The specification of
+      <rlink to="html/documentation.html#ldR2c">λδ-2A</rlink>
       is released.
    </news>
 
@@ -66,7 +73,7 @@
    </news>
 
    <news class="beta" date="June 2014.">
-      <rlink to="html/documentation.html#ldP2c">First communication on λδ version 2.</rlink>
+      <rlink to="html/documentation.html#ldP2c">First communication on λδ-2.</rlink>
    </news>
 
    <news class="alpha" date="December 2012.">
    </news>
 
    <news class="alpha" date="April 2011.">
-      The specification of <rlink to="html/specification.html#v2">λδ version 2</rlink>
+      The specification of
+      <rlink to="html/specification.html#v2">λδ-2</rlink>
       and related topics is restarted in
       <link to="http://matita.cs.unibo.it/">Matita 0.5</link>.
    </news>
 
    <news class="delta" date="February 2011.">
-      The specification of λδ version 2 with Coq 7.3.1 is abandoned.
+      The specification of λδ-2 with Coq 7.3.1 is abandoned.
    </news>
 
    <news class="alpha" date="December 2010.">
    </news>
 
    <news class="alpha" date="June 2009.">
-      "Helena", a <rlink to="html/implementation.html#helena">validator for λδ version 2</rlink>,
+      "Helena", a <rlink to="html/implementation.html#helena">validator for λδ-2</rlink>,
       is available as a part of the <link to="http://helm.cs.unibo.it/">HELM</link> software. 
    </news>
 
    <news class="delta" date="July 2008.">
       First <link to="http://helm.cs.unibo.it/procedural/">procedural reconstruction</link>
       for <link to="http://matita.cs.unibo.it/">Matita 0.5</link>
-      of the λδ version 1 for Coq 7.3.1.
+      of the λδ-1A for Coq 7.3.1.
    </news>
 
    <news class="delta" date="June 2008.">
       The <rlink to="html/specification.html#static1">
-         HTML pages of the specification of λδ version 1 for Matita 0.5</rlink>
+         HTML pages of the specification of λδ-1A for Matita 0.5</rlink>
       are online.
    </news>
 
    <news class="delta" date="May 2008.">
-      The specification of λδ version 1 is concluded.
+      The specification of λδ-1A is concluded.
    </news>
 
    <news class="alpha" date="March 2008.">
-      The specification of λδ version 2 is started with Coq 7.3.1 (false start).
+      The specification of λδ-2 is started with Coq 7.3.1 (false start).
    </news>
 
    <news class="gamma" date="September 2007.">
       The <rlink to="html/specification.html#dynamic1">
-         specification of λδ version 1 for Matita 0.4</rlink>
+         specification of λδ-1A for Matita 0.4</rlink>
       is online.
    </news>
 
    <news class="gamma" date="November 2006.">
-      <rlink to="html/documentation.html#ldR1b">λδ version 1</rlink>
+      The specification of
+      <rlink to="html/documentation.html#ldR1b">λδ-1A</rlink>
       is released.
    </news>
 
    <news class="beta" date="December 2005.">
-      <rlink to="html/documentation.html#ldP1a">First communication on λδ version 1</rlink>.
+      <rlink to="html/documentation.html#ldP1a">First communication on λδ-1</rlink>.
    </news>
 
    <news class="alpha" date="May 2004.">
-      The specification of <rlink to="html/specification.html#v1">λδ version 1</rlink>
+      The specification of <rlink to="html/specification.html#v1">λδ-1</rlink>
       is started with Coq 7.3.1.
    </news>
 
index 0d84b3b1fae7483d479236e6d50ea04a4f41600a..fa16e06671b3ce3c29111ef0cb9a0608af14f811 100644 (file)
@@ -16,9 +16,9 @@ table {
    class "orange" {
       [ { @@("html/specification#v2" "Version 2") * }
         { "\"basic_2\"" * }
-        { [ "\"B\"" @("http://matita.cs.unibo.it/" "Matita 0.99.3")
-            "October 2015" "November 2018" "" ""
-            ""  *
+        { [ "\"B\"" @("http://matita.cs.unibo.it/" "Matita 0.99.4")
+            "October 2015" "November 2018" "November 2019" ""
+            @@("html/documentation#ldV2b" "V2b")  *
           ]
           [ "\"A\"" @("http://matita.cs.unibo.it/" "Matita 0.99.2")
             "April 2011" "June 2014" "October 2014" "August 2015" 
index 3e0228cb086305ca98911fea26b7ec66d432698f..e22b7ec42cbf59aba516a2299af4666adda02fb0 100644 (file)
@@ -25,7 +25,7 @@ PRB_OPTS     := $(XOA_OPTS) -g -i
 ORIG         := . ./orig.sh 
 ORIGS        := basic_2/basic_1.orig
 
-CONTRIB      := lambdadelta_2
+CONTRIB      := lambdadelta_2B
 
 WWW          := ../../../../helm/www/lambdadelta
 
@@ -260,8 +260,8 @@ trim: $(TRIMS:%=%.trimmed)
 # contrib ####################################################################
 
 contrib:
-       @echo "  TAR -czf $(CONTRIB).tar.gz root $(XPACKAGES)"
-       $(H)tar -czf $(CONTRIB).tar.gz root $(XMAS)
+       @echo "  TAR -cjf $(CONTRIB).tar.bz2 root $(XPACKAGES)"
+       $(H)tar -cjf $(CONTRIB).tar.bz2 root $(XMAS)
 
 # clean ######################################################################
 
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snabstneg_1.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snabstneg_1.ma
deleted file mode 100644 (file)
index a82ce46..0000000
+++ /dev/null
@@ -1,19 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
-
-notation "hvbox( - 𝛌 . break term 55 T )"
- non associative with precedence 55
- for @{ 'SnAbstNeg $T }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/sngref_2.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/sngref_2.ma
deleted file mode 100644 (file)
index f28b669..0000000
+++ /dev/null
@@ -1,19 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
-
-notation "hvbox( § term 90 p . break term 55 T )"
- non associative with precedence 55
- for @{ 'SnGRef $p $T }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snitem1_2.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snitem1_2.ma
deleted file mode 100644 (file)
index cef7a31..0000000
+++ /dev/null
@@ -1,19 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
-
-notation "hvbox( ① { term 46 I } . break term 55 T )"
- non associative with precedence 55
- for @{ 'SnItem1 $I $T }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snlref_2.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snlref_2.ma
deleted file mode 100644 (file)
index 4f9311f..0000000
+++ /dev/null
@@ -1,19 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
-
-notation "hvbox( # term 90 i . break term 55 T )"
- non associative with precedence 55
- for @{ 'SnLRef $i $T }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snproj_3.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snproj_3.ma
deleted file mode 100644 (file)
index 3e985c3..0000000
+++ /dev/null
@@ -1,19 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
-
-notation "hvbox( 𝛑 { term 46 a } break term 55 T1 . break term 55 T2 )"
- non associative with precedence 55
- for @{ 'SnProj $a $T1 $T2 }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snprojneg_2.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snprojneg_2.ma
deleted file mode 100644 (file)
index c29417e..0000000
+++ /dev/null
@@ -1,19 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
-
-notation "hvbox( - 𝛑 term 55 T1 . break term 55 T2 )"
- non associative with precedence 55
- for @{ 'SnProjNeg $T1 $T2 }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snprojpos_2.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snprojpos_2.ma
deleted file mode 100644 (file)
index 74a573d..0000000
+++ /dev/null
@@ -1,19 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
-
-notation "hvbox( + 𝛑 term 55 T1 . break term 55 T2 )"
- non associative with precedence 55
- for @{ 'SnProjPos $T1 $T2 }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snstar_2.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/constructors/snstar_2.ma
deleted file mode 100644 (file)
index b4e1e0d..0000000
+++ /dev/null
@@ -1,19 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||M||                                                             *)
-(*      ||A||       A project by Andrea Asperti                           *)
-(*      ||T||                                                             *)
-(*      ||I||       Developers:                                           *)
-(*      ||T||         The HELM team.                                      *)
-(*      ||A||         http://helm.cs.unibo.it                             *)
-(*      \   /                                                             *)
-(*       \ /        This file is distributed under the terms of the       *)
-(*        v         GNU General Public License Version 2                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
-
-notation "hvbox( ⋆ term 90 k . break term 55 T )"
- non associative with precedence 55
- for @{ 'SnStar $k $T }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snabstneg_1.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snabstneg_1.ma
new file mode 100644 (file)
index 0000000..a82ce46
--- /dev/null
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
+
+notation "hvbox( - 𝛌 . break term 55 T )"
+ non associative with precedence 55
+ for @{ 'SnAbstNeg $T }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/sngref_2.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/sngref_2.ma
new file mode 100644 (file)
index 0000000..f28b669
--- /dev/null
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
+
+notation "hvbox( § term 90 p . break term 55 T )"
+ non associative with precedence 55
+ for @{ 'SnGRef $p $T }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snitem1_2.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snitem1_2.ma
new file mode 100644 (file)
index 0000000..cef7a31
--- /dev/null
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
+
+notation "hvbox( ① { term 46 I } . break term 55 T )"
+ non associative with precedence 55
+ for @{ 'SnItem1 $I $T }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snlref_2.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snlref_2.ma
new file mode 100644 (file)
index 0000000..4f9311f
--- /dev/null
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
+
+notation "hvbox( # term 90 i . break term 55 T )"
+ non associative with precedence 55
+ for @{ 'SnLRef $i $T }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snproj_3.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snproj_3.ma
new file mode 100644 (file)
index 0000000..3e985c3
--- /dev/null
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
+
+notation "hvbox( 𝛑 { term 46 a } break term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnProj $a $T1 $T2 }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snprojneg_2.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snprojneg_2.ma
new file mode 100644 (file)
index 0000000..c29417e
--- /dev/null
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
+
+notation "hvbox( - 𝛑 term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnProjNeg $T1 $T2 }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snprojpos_2.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snprojpos_2.ma
new file mode 100644 (file)
index 0000000..74a573d
--- /dev/null
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
+
+notation "hvbox( + 𝛑 term 55 T1 . break term 55 T2 )"
+ non associative with precedence 55
+ for @{ 'SnProjPos $T1 $T2 }.
diff --git a/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snstar_2.ma b/matita/matita/contribs/lambdadelta/alpha_1/notation/functions/snstar_2.ma
new file mode 100644 (file)
index 0000000..b4e1e0d
--- /dev/null
@@ -0,0 +1,19 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* NOTATION FOR THE FORMAL SYSTEM α *****************************************)
+
+notation "hvbox( ⋆ term 90 k . break term 55 T )"
+ non associative with precedence 55
+ for @{ 'SnStar $k $T }.
index 7b09c887df47aad954a767d4109d5cd42e14a860..4ba35edc6f5518fbb76a0d7ef52f03899dfd6ab3 100644 (file)
@@ -18,14 +18,14 @@ include "static_2/notation/functions/snabstpos_2.ma".
 include "static_2/notation/functions/snabbr_3.ma".
 include "static_2/notation/functions/snabbrpos_2.ma".
 include "static_2/notation/functions/snabbrneg_2.ma".
-include "alpha_1/notation/constructors/snitem1_2.ma".
-include "alpha_1/notation/constructors/snstar_2.ma".
-include "alpha_1/notation/constructors/snlref_2.ma".
-include "alpha_1/notation/constructors/sngref_2.ma".
-include "alpha_1/notation/constructors/snabstneg_1.ma".
-include "alpha_1/notation/constructors/snproj_3.ma".
-include "alpha_1/notation/constructors/snprojpos_2.ma".
-include "alpha_1/notation/constructors/snprojneg_2.ma".
+include "alpha_1/notation/functions/snitem1_2.ma".
+include "alpha_1/notation/functions/snstar_2.ma".
+include "alpha_1/notation/functions/snlref_2.ma".
+include "alpha_1/notation/functions/sngref_2.ma".
+include "alpha_1/notation/functions/snabstneg_1.ma".
+include "alpha_1/notation/functions/snproj_3.ma".
+include "alpha_1/notation/functions/snprojpos_2.ma".
+include "alpha_1/notation/functions/snprojneg_2.ma".
 include "alpha_1/syntax/item.ma".
 
 (* TERMS ********************************************************************)
index b3ad3915733a01f5e97978b1f0cd49ade8bc0292..6975017c595632d885aa7cf4c99997623153a54d 100644 (file)
@@ -31,7 +31,7 @@ interpretation "local environment interpretation (model)"
 
 (* Basic inversion lemmas ***************************************************)
 
-fact li_inv_abbr_aux (M) (gv): is_model M → 
+fact li_inv_abbr_aux (M) (gv): is_model M →
                                ∀v,Y. v ϵ ⟦Y⟧{M}[gv] → ∀L,V. Y = L.ⓓV →
                                ∃∃lv. lv ϵ ⟦L⟧[gv] & ⫯[0←⟦V⟧[gv,lv]]lv ≗ v.
 #M #gv #HM #v #Y #H elim H -v -Y
index 3d9e440a7f42980bf63ca0bd8e7aafae74927249..044866007346ddad0bc03a5d052d8e3aa381b316 100644 (file)
@@ -79,7 +79,7 @@ elim (lt_or_eq_or_gt j i) #Hij destruct
 ]
 qed-.
 
-(* Properies with term interpretation ***************************************) 
+(* Properies with term interpretation ***************************************)
 
 lemma ti_comp (M): is_model M →
                    ∀T,gv1,gv2. gv1 ≗ gv2 → ∀lv1,lv2. lv1 ≗ lv2 →
index 34e9de237d2cf58588e1857efe3afaba59363ba2..c401800d1974a8f5dcf9b4b480b96ed89ce82630 100644 (file)
@@ -40,7 +40,7 @@ fact vpushs_inv_atom_aux (M) (gv) (lv): is_model M →
 | #v #d #K #V #_ #_ #H destruct
 | #v #d #I #K #_ #_ #H destruct
 | #v1 #v2 #L #_ #Hv12 #IH #H destruct
-  /3 width=3 by veq_trans/ 
+  /3 width=3 by veq_trans/
 ]
 qed-.
 
index 8ac1699861e2c7751fcc34c38fd31e26d7bd645f..d017bc16a5950775b16fd35ef1c26ec2397736d5 100644 (file)
@@ -21,7 +21,7 @@ include "apps_2/models/vpushs.ma".
 
 lemma vpushs_fold (M): is_model M → is_extensional M →
                        ∀L,T1,T2,gv,lv.
-                       (∀v. L ⨁[gv] lv ≘ v → ⟦T1⟧[gv,v] ≗ ⟦T2⟧[gv,v]) → 
+                       (∀v. L ⨁[gv] lv ≘ v → ⟦T1⟧[gv,v] ≗ ⟦T2⟧[gv,v]) →
                        ⟦L+T1⟧[gv,lv] ≗{M} ⟦L+T2⟧[gv,lv].
 #M #H1M #H2M #L elim L -L [| #K * [| * ]]
 [ #T1 #T2 #gv #lv #H12
index 34cf9f85131e431061fa0c745673f5ffd8c9c15f..8499b43e359d22ff36b1a6f6fec006ab00e3d584 100644 (file)
@@ -82,12 +82,12 @@ class "capitalize italic" { 0 }
 
 class "italic"            { 1 }
 (*
-        [ { "evaluation drop" * } {        
+        [ { "evaluation drop" * } {
              [ "vdrop" + "( ⫰{?}? )" + "( ⫰{?}[?]? )" "vdrop_vlift" * ]
           }
         ]
         [ { "reduction and type machine" * } {
              [ "rtm" "rtm_step ( ? ⇨ ? )" * ]
           }
-        ]        
+        ]
 *)
index 683c57b1f99dbedcaeb1560a7df0b9d782dede12..ae42a21681562a42bf0d0144a36ad0a48285f1ad 100644 (file)
@@ -127,7 +127,7 @@ qed-.
 fact cnv_cpm_conf_lpr_bind_zeta_aux (h) (a) (G) (L) (V) (T):
      (∀G0,L0,T0. ⦃G,L,+ⓓV.T⦄ >[h] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
      ⦃G,L⦄ ⊢ +ⓓV.T ![h,a] →
-     ∀V1. ⦃G,L⦄ ⊢V ➡[h] V1 → ∀n1,T1. ⦃G,L.ⓓV⦄ ⊢ T ➡[n1,h] T1 → 
+     ∀V1. ⦃G,L⦄ ⊢V ➡[h] V1 → ∀n1,T1. ⦃G,L.ⓓV⦄ ⊢ T ➡[n1,h] T1 →
      ∀T2. ⇧*[1]T2 ≘ T → ∀n2,XT2. ⦃G,L⦄ ⊢ T2 ➡[n2,h] XT2 →
      ∀L1. ⦃G,L⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G,L⦄ ⊢ ➡[h] L2 →
      ∃∃T. ⦃G,L1⦄ ⊢ +ⓓV1.T1 ➡*[n2-n1,h] T & ⦃G,L2⦄ ⊢ XT2 ➡*[n1-n2,h] T.
@@ -136,7 +136,7 @@ fact cnv_cpm_conf_lpr_bind_zeta_aux (h) (a) (G) (L) (V) (T):
 #L1 #HL01 #L2 #HL02
 elim (cnv_inv_bind … H0) -H0 #_ #HT0
 lapply (cnv_inv_lifts … HT0 (Ⓣ) … L0 … HT20) -HT0
-[ /3 width=3 by drops_refl, drops_drop/ ] #HT2 
+[ /3 width=3 by drops_refl, drops_drop/ ] #HT2
 elim (cpm_inv_lifts_sn … HT01 (Ⓣ) … L0 … HT20) -HT01
 [| /3 width=1 by drops_refl, drops_drop/ ] #XT1 #HXT1 #HXT12
 elim (cnv_cpm_conf_lpr_sub … IH … HXT12 … HXT2 … HL01 … HL02)
@@ -225,7 +225,7 @@ elim (cpm_inv_abbr1 … HX) -HX *
   #T #HT1 #HT2 -L0 -V0 -W0 -T0
   /4 width=7 by cpms_theta_dx, cpms_appl_dx, cpms_bind_dx, ex2_intro/
 | #X0 #HXT0 #H1X0 #H destruct
-  lapply (cnv_inv_lifts … HT0 (Ⓣ) … L0 … HXT0) -HT0 [ /3 width=3 by drops_refl, drops_drop/ ] #H2X0 
+  lapply (cnv_inv_lifts … HT0 (Ⓣ) … L0 … HXT0) -HT0 [ /3 width=3 by drops_refl, drops_drop/ ] #H2X0
   elim (cpm_inv_lifts_sn … HT02 (Ⓣ) … L0 … HXT0) -HT02 [| /3 width=1 by drops_refl, drops_drop/ ] #X2 #HXT2 #HX02
   elim (cnv_cpm_conf_lpr_sub … IH … H1X0 … HX02 … HL01 … HL02)
   [|*: /4 width=5 by fqup_fpbg, fqup_strap1, fqu_drop/ ] #T #HT1 #HT2 -L0 -V0 -W0 -T0
@@ -423,7 +423,7 @@ fact cnv_cpm_conf_lpr_aux (h) (a):
     @(cnv_cpm_conf_lpr_delta_delta_aux … IH1) -IH1 /1 width=13 by/
   | #m2 #K2 #W2 #XW2 #i2 #HLK2 #_ #_ #H21 #H22 #K1 #V1 #XV1 #i1 #HLK1 #_ #_ #H11 destruct -a -XW2 -XV1 -HL2 -HL1
     elim cnv_cpm_conf_lpr_delta_ell_aux /1 width=8 by/
-  | #H21 #H22 #m1 #K1 #W1 #XW1 #i1 #HLK1 #HWX1 #HXW1 #H11 #H12 destruct -IH2 
+  | #H21 #H22 #m1 #K1 #W1 #XW1 #i1 #HLK1 #HWX1 #HXW1 #H11 #H12 destruct -IH2
     <minus_O_n <minus_n_O
     @ex2_commute @(cnv_cpm_conf_lpr_atom_ell_aux … IH1) -IH1 /1 width=6 by/
   | #s2 #H21 #H22 #H23 #m1 #K1 #W1 #XW1 #i1 #_ #_ #_ #H11 #H12 destruct
index e69ab2fae74c11fd9e6c53f52e89472e811603e2..1736148f785dc3a89dec6ad2a269d4c3e612dce4 100644 (file)
@@ -65,7 +65,7 @@ fact cnv_cpm_teqx_cpm_trans_sub (h) (a) (G0) (L0) (T0):
     lapply (cpm_teqx_free … HT0 … H1T02 H2T02 G (L.ⓓⓝW2.V2)) -H1T02 #H1T02
     /3 width=6 by cpm_beta, cpm_bind, teqx_pair, ex3_intro/
   | #p #V2 #V0 #W1 #W2 #T #T2 #HV12 #HV20 #HW12 #HT2 #H1 #H2 destruct
-    elim (cpm_teqx_inv_bind_dx … H0T1 … H1T1 H2T1) -H0T1 -H1T1 -H2T1 #T1 #_ #H0T1 #H1T1 #H2T1 #H destruct 
+    elim (cpm_teqx_inv_bind_dx … H0T1 … H1T1 H2T1) -H0T1 -H1T1 -H2T1 #T1 #_ #H0T1 #H1T1 #H2T1 #H destruct
     elim (IH1 … H0T1 … H1T1 H2T1 … HT2) -T -IH1 [| // ] #T0 #HT10 #H1T02 #H2T02
     lapply (IH2 … H0T1 … HT10 (L.ⓓW1) ?) -IH2 -H0T1 [3:|*: /2 width=1 by fqup_fpbg/ ] #HT0
     lapply (cpm_teqx_free … HT0 … H1T02 H2T02 G (L.ⓓW2)) -H1T02
index 7654a5eb89fc44fde53549f61fe2f124e957bf9b..ab676566fe76ac4e374459cb987e543ee132bce8 100644 (file)
@@ -47,7 +47,7 @@ fact cpms_teqx_ind_sn (h) (a) (G) (L) (T2) (Q:relation2 …):
      (∀n1,n2,T1,T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → ⦃G,L⦄ ⊢ T1 ![h,a] → T1 ≛ T → ⦃G,L⦄ ⊢ T ➡*[n2,h] T2 → ⦃G,L⦄ ⊢ T ![h,a] → T ≛ T2 → Q n2 T → Q (n1+n2) T1) →
      ∀n,T1. ⦃G,L⦄ ⊢ T1 ➡*[n,h] T2 → ⦃G,L⦄ ⊢ T1 ![h,a] → T1 ≛ T2 →
      (∀G0,L0,T0. ⦃G,L,T1⦄ >[h] ⦃G0,L0,T0⦄ → IH_cnv_cpms_conf_lpr h a G0 L0 T0) →
-     (∀G0,L0,T0. ⦃G,L,T1⦄ >[h] ⦃G0,L0,T0⦄ → IH_cnv_cpm_trans_lpr h a G0 L0 T0) → 
+     (∀G0,L0,T0. ⦃G,L,T1⦄ >[h] ⦃G0,L0,T0⦄ → IH_cnv_cpm_trans_lpr h a G0 L0 T0) →
      Q n T1.
 #h #a #G #L #T2 #Q #IB1 #IB2 #n #T1 #H
 @(cpms_ind_sn … H) -n -T1
index 50e4edbee00f04ccd9d58d09a0bdfcbea546ead6..7498e33c199b8fce1af06915ac4d869a780f65e7 100644 (file)
@@ -38,7 +38,7 @@ lemma cnv_fqu_conf (h) (a):
   [ elim (cnv_inv_appl … H) -H //
   | elim (cnv_inv_cast … H) -H //
   ]
-| #I1 #G1 #L1 #T1 #U1 #HTU1 #HU 
+| #I1 #G1 #L1 #T1 #U1 #HTU1 #HU
   /4 width=7 by cnv_inv_lifts, drops_refl, drops_drop/
 ]
 qed-.
index 5aea50a665c3a15abf396c569fb9b1460add4092..4d4cebd5e13074829a5af9ae5050cb82da6c31f3 100644 (file)
@@ -29,4 +29,4 @@ theorem nta_fwd_fsb (h) (a) (G) (L):
 #h #a #G #L #T #U #H
 elim (cnv_inv_cast … H) #X #HU #HT #_ #_ -X
 /3 width=2 by cnv_fwd_fsb, conj/
-qed-. 
+qed-.
index 44dac970e116e598f4c4c4fe13a309953588ce2f..20bb43faffc51222977602b3f4b8fe7b89ec24fc 100644 (file)
@@ -124,7 +124,7 @@ elim (cpms_inv_lref_sn … H2) -H2 *
 ]
 qed-.
 
-lemma nta_inv_lref_sn_drops_cnv (h) (a) (G) (L): 
+lemma nta_inv_lref_sn_drops_cnv (h) (a) (G) (L):
       ∀X2,i. ⦃G,L⦄ ⊢ #i :[h,a] X2 →
       ∨∨ ∃∃K,V,W,U. ⇩*[i] L ≘ K.ⓓV & ⦃G,K⦄ ⊢ V :[h,a] W & ⇧*[↑i] W ≘ U & ⦃G,L⦄ ⊢ U ⬌*[h] X2 & ⦃G,L⦄ ⊢ X2 ![h,a]
        | ∃∃K,W,U. ⇩*[i] L ≘ K. ⓛW & ⦃G,K⦄ ⊢ W ![h,a] & ⇧*[↑i] W ≘ U & ⦃G,L⦄ ⊢ U ⬌*[h] X2 & ⦃G,L⦄ ⊢ X2 ![h,a].
index 8438e030746076a61b6b0be1eca4188e4cd8544c..6adb6f7adedaad1d407e2eb131e2a8dabd4e6b28 100644 (file)
@@ -32,5 +32,5 @@ lemma ntas_inv_zero (h) (a) (G) (L):
       ∀T1,T2. ⦃G,L⦄ ⊢ T1 :*[h,a,0] T2 →
       ∧∧ ⦃G,L⦄ ⊢ T1 ![h,a] & ⦃G,L⦄ ⊢ T2 ![h,a] & ⦃G,L⦄ ⊢ T1 ⬌*[h] T2.
 #h #a #G #L #T1 #T2 * #T0 #HT1 #HT2 #HT20 #HT10
-/3 width=3 by cprs_div, and3_intro/ 
+/3 width=3 by cprs_div, and3_intro/
 qed-.
index 245d44f9ce1643d025ab721df604dd65459bcbe6..25a57d7468b6c35602cde1186152c2633e8b0bec 100644 (file)
@@ -87,7 +87,7 @@ qed.
 theorem cpms_theta (n) (h) (G) (L):
                    ∀V,V2. ⇧*[1] V ≘ V2 → ∀W1,W2. ⦃G,L⦄ ⊢ W1 ➡*[h] W2 →
                    ∀T1,T2. ⦃G,L.ⓓW1⦄ ⊢ T1 ➡*[n,h] T2 →
-                   ∀V1. ⦃G,L⦄ ⊢ V1 ➡*[h] V → 
+                   ∀V1. ⦃G,L⦄ ⊢ V1 ➡*[h] V →
                    ∀p. ⦃G,L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ➡*[n,h] ⓓ{p}W2.ⓐV2.T2.
 #n #h #G #L #V #V2 #HV2 #W1 #W2 #HW12 #T1 #T2 #HT12 #V1 #H @(cprs_ind_sn … H) -V1
 [ /2 width=3 by cpms_theta_rc/
index 66045be0e99912b9df193d2241f3274def2acdf6..cebbb8ed0b11ea65df0287f581ab502a353d7188 100644 (file)
@@ -24,7 +24,7 @@ lemma cpts_lifts_sn (h) (n) (G):
       d_liftable2_sn … lifts (λL. cpts h G L n).
 /3 width=6 by d2_liftable_sn_ltc, cpt_lifts_sn/ qed-.
 
-lemma cpts_lifts_bi (h) (n) (G): 
+lemma cpts_lifts_bi (h) (n) (G):
       d_liftable2_bi … lifts (λL. cpts h G L n).
 #h #n #G @d_liftable2_sn_bi
 /2 width=6 by cpts_lifts_sn, lifts_mono/
index 4a0550473950942927529804cca47a6cd0385d86..5081b65ec942c8f6d22864e70faa231b17c212c5 100644 (file)
@@ -127,7 +127,7 @@ qed.
 lemma cpxs_theta_dx: ∀h,p,G,L,V1,V,V2,W1,W2,T1,T2.
                      ⦃G,L⦄ ⊢ V1 ⬈[h] V → ⇧*[1] V ≘ V2 → ⦃G,L.ⓓW1⦄ ⊢ T1 ⬈*[h] T2 →
                      ⦃G,L⦄ ⊢ W1 ⬈[h] W2 → ⦃G,L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ⬈*[h] ⓓ{p}W2.ⓐV2.T2.
-#h #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 * -T2 
+#h #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 #HV1 #HV2 * -T2
 /4 width=9 by cpx_cpxs, cpxs_strap1, cpxs_bind_dx, cpxs_flat_dx, cpx_theta/
 qed.
 
index eb1444b26f69ccddd91a3e0e7d9f6203c4762bea..64be00b99ccc3150af51ecf8aa0a16bb103b3964 100644 (file)
@@ -19,7 +19,7 @@ include "basic_2/rt_computation/cpxs_teqx.ma".
 
 (* Properties with sort-irrelevant equivalence for local environments *******)
 
-(* Basic_2A1: was just: lleq_cpxs_trans *) 
+(* Basic_2A1: was just: lleq_cpxs_trans *)
 lemma reqx_cpxs_trans: ∀h,G,L0,T0,T1. ⦃G,L0⦄ ⊢ T0 ⬈*[h] T1 →
                        ∀L2. L2 ≛[T0] L0 →
                        ∃∃T. ⦃G,L2⦄ ⊢ T0 ⬈*[h] T & T ≛ T1.
@@ -31,19 +31,19 @@ elim (teqx_cpxs_trans … H2 … H3) -T #U0 #H2 #H3
 /3 width=5 by cpxs_strap2, teqx_trans, ex2_intro/
 qed-.
 
-(* Basic_2A1: was just: cpxs_lleq_conf *) 
+(* Basic_2A1: was just: cpxs_lleq_conf *)
 lemma cpxs_reqx_conf: ∀h,G,L0,T0,T1. ⦃G,L0⦄ ⊢ T0 ⬈*[h] T1 →
                       ∀L2. L0 ≛[T0] L2 →
                       ∃∃T. ⦃G,L2⦄ ⊢ T0 ⬈*[h] T & T ≛ T1.
 /3 width=3 by reqx_cpxs_trans, reqx_sym/ qed-.
 
-(* Basic_2A1: was just: cpxs_lleq_conf_dx *) 
+(* Basic_2A1: was just: cpxs_lleq_conf_dx *)
 lemma cpxs_reqx_conf_dx: ∀h,G,L2,T1,T2. ⦃G,L2⦄ ⊢ T1 ⬈*[h] T2 →
                          ∀L1. L1 ≛[T1] L2 → L1 ≛[T2] L2.
 #h #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_reqx_conf_dx/
 qed-.
 
-(* Basic_2A1: was just: lleq_conf_sn *) 
+(* Basic_2A1: was just: lleq_conf_sn *)
 lemma cpxs_reqx_conf_sn: ∀h,G,L1,T1,T2. ⦃G,L1⦄ ⊢ T1 ⬈*[h] T2 →
                          ∀L2. L1 ≛[T1] L2 → L1 ≛[T2] L2.
 /4 width=6 by cpxs_reqx_conf_dx, reqx_sym/ qed-.
index 7af7b41b8aef9be884f43f5a5560a1e20d11cc20..178a2c440e8e29c742db8e99e30efe37bcd6606a 100644 (file)
@@ -19,7 +19,7 @@ include "basic_2/rt_computation/cpxs.ma".
 
 (* Properties with sort-irrelevant equivalence for terms ********************)
 
-lemma teqx_cpxs_trans: ∀h,U1,T1. U1 ≛ T1 → ∀G,L,T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → 
+lemma teqx_cpxs_trans: ∀h,U1,T1. U1 ≛ T1 → ∀G,L,T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 →
                        ∃∃U2. ⦃G,L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≛ T2.
 #h #U1 #T1 #HUT1 #G #L #T2 #HT12 @(cpxs_ind … HT12) -T2 /2 width=3 by ex2_intro/
 #T #T2 #_ #HT2 * #U #HU1 #HUT elim (teqx_cpx_trans … HUT … HT2) -T -T1
index 31ebb2c771013868994633d252550d2ea7fc482b..d162f660a984b37fbadc4e8b274881d8207ed719 100644 (file)
@@ -98,6 +98,6 @@ lemma csx_fwd_flat: ∀h,I,G,L,V,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃ⓕ{I}V.T⦄ 
             sn3_appl_appls sn3_bind sn3_appl_bind sn3_appls_bind
 *)
 (* Basic_2A1: removed theorems 6:
-              csxa_ind csxa_intro csxa_cpxs_trans csxa_intro_cpx 
+              csxa_ind csxa_intro csxa_cpxs_trans csxa_intro_cpx
               csx_csxa csxa_csx
 *)
index 915866a229682a56311abdc5f0e64fd1726ec096..4a5330d1e7326a1d60f7077ba41a7b37bc1aeb91 100644 (file)
@@ -54,7 +54,7 @@ qed.
 
 (* Basic_1: was just: sn3_abbr *)
 (* Basic_2A1: was: csx_lref_bind *)
-lemma csx_lref_pair_drops (h) (G): 
+lemma csx_lref_pair_drops (h) (G):
       ∀I,L,K,V,i. ⇩*[i] L ≘ K.ⓑ{I}V →
       ⦃G,K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ → ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃#i⦄.
 #h #G #I #L #K #V #i #HLK #HV
index 7253cdb50d10f3c30abdf64738c2b40df937a398..50e525ec4f3155fbdce3ead33d4ca193e515d053 100644 (file)
@@ -30,7 +30,7 @@ elim (cpx_inv_appl1_simple … H1) // -H1
 elim (tneqx_inv_pair … H2) -H2
 [ #H elim H -H //
 | #HV0 @(csx_cpx_trans … (ⓐV0.T1)) /2 width=1 by cpx_flat/ -HLT10
-  @(IHV … HLV0 … HV0) -HV0 /4 width=5 by csx_cpx_trans, cpx_pair_sn/ (**) (* full auto too slow *) 
+  @(IHV … HLV0 … HV0) -HV0 /4 width=5 by csx_cpx_trans, cpx_pair_sn/ (**) (* full auto too slow *)
 | -IHV -HT1 /4 width=3 by csx_cpx_trans, cpx_pair_sn/
 ]
 qed.
index 258ba510785ae758cae25eabc9f40e8b8a273baf..696fee8ef78dbc23ac7387b64c7369c19eb44e16 100644 (file)
@@ -61,4 +61,4 @@ lemma fpbg_feqx_trans: ∀h,G1,G,L1,L,T1,T. ⦃G1,L1,T1⦄ >[h] ⦃G,L,T⦄ →
 lemma cpm_tneqx_cpm_fpbg (h) (G) (L):
                          ∀n1,T1,T. ⦃G,L⦄ ⊢ T1 ➡[n1,h] T → (T1 ≛ T → ⊥) →
                          ∀n2,T2. ⦃G,L⦄ ⊢ T ➡[n2,h] T2 → ⦃G,L,T1⦄ >[h] ⦃G,L,T2⦄.
-/4 width=5 by fpbq_fpbs, cpm_fpbq, cpm_fpb, ex2_3_intro/ qed. 
+/4 width=5 by fpbq_fpbs, cpm_fpbq, cpm_fpb, ex2_3_intro/ qed.
index 25f0a3ffb55292315731b2c32120f1a64175f8be..4fcd971bb397d5416718a7a5fc0d4b016cf339fe 100644 (file)
@@ -32,7 +32,7 @@ lemma fpbs_teqx_trans: ∀h,G1,G2,L1,L2,T1,T. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T
 
 lemma fqup_fpbs: ∀h,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂+ ⦃G2,L2,T2⦄ →
                  ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄.
-#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2 
+#h #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind … H) -G2 -L2 -T2
 /4 width=5 by fqu_fquq, fpbq_fquq, tri_step/
 qed.
 
index 3ab294cf9735b8bd3d44884b0f445e615577c247..f01561bc24af4902c9bc26026bf5196e66da383b 100644 (file)
@@ -66,7 +66,7 @@ lemma fpbs_cpxs_teqx_fqup_lpx_trans: ∀h,G1,G3,L1,L3,T1,T3. ⦃G1,L1,T1⦄ ≥
                                      ∀T4. ⦃G3,L3⦄ ⊢ T3 ⬈*[h] T4 → ∀T5. T4 ≛ T5 →
                                      ∀G2,L4,T2. ⦃G3,L3,T5⦄ ⬂+ ⦃G2,L4,T2⦄ →
                                      ∀L2. ⦃G2,L4⦄ ⊢ ⬈[h] L2 → ⦃G1,L1,T1⦄ ≥ [h] ⦃G2,L2,T2⦄.
-#h #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42  
+#h #G1 #G3 #L1 #L3 #T1 #T3 #H13 #T4 #HT34 #T5 #HT45 #G2 #L4 #T2 #H34 #L2 #HL42
 @(fpbs_lpx_trans … HL42) -L2 (**) (* full auto too slow *)
 @(fpbs_fqup_trans … H34) -G2 -L4 -T2
 /3 width=3 by fpbs_cpxs_trans, fpbs_teqx_trans/
index 5b383e05d131faf75e85fd897e49f5d0762a65da..98bed39de105e13dd752c4e238326093503e849f 100644 (file)
@@ -31,7 +31,7 @@ lemma csx_fsb_fpbs: ∀h,G1,L1,T1. ⦃G1,L1⦄ ⊢ ⬈*[h] 𝐒⦃T1⦄ →
                     ∀G2,L2,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄ → ≥[h] 𝐒⦃G2,L2,T2⦄.
 #h #G1 #L1 #T1 #H @(csx_ind … H) -T1
 #T1 #HT1 #IHc #G2 #L2 #T2 @(fqup_wf_ind (Ⓣ) … G2 L2 T2) -G2 -L2 -T2
-#G0 #L0 #T0 #IHu #H10 
+#G0 #L0 #T0 #IHu #H10
 lapply (fpbs_csx_conf … H10) // -HT1 #HT0
 generalize in match IHu; -IHu generalize in match H10; -H10
 @(rsx_ind … (csx_rsx … HT0)) -L0
index b55d1907377335457450606b473d0e945d783c2f..918adc2aad1e53e420a68342a450fc9650a04a7c 100644 (file)
@@ -21,7 +21,7 @@ include "basic_2/rt_computation/fsb.ma".
 
 lemma fsb_feqx_trans: ∀h,G1,L1,T1. ≥[h] 𝐒⦃G1,L1,T1⦄ →
                       ∀G2,L2,T2. ⦃G1,L1,T1⦄ ≛ ⦃G2,L2,T2⦄ → ≥[h] 𝐒⦃G2,L2,T2⦄.
-#h #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1 
+#h #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
 #G1 #L1 #T1 #_ #IH #G2 #L2 #T2 #H12
 @fsb_intro #G #L #T #H2
 elim (feqx_fpb_trans … H12 … H2) -G2 -L2 -T2
index 1d8e0eb7d608fe1af0bca3a4d9e5f4b1e034a56c..1fd7ea36b6f77dc068d3e3ad073880d69522774d 100644 (file)
@@ -43,7 +43,7 @@ lemma fsb_ind_fpbg_fpbs: ∀h. ∀Q:relation3 genv lenv term.
                                      (∀G2,L2,T2. ⦃G1,L1,T1⦄ >[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
                                      Q G1 L1 T1
                          ) →
-                         ∀G1,L1,T1. ≥[h] 𝐒⦃G1,L1,T1⦄ → 
+                         ∀G1,L1,T1. ≥[h] 𝐒⦃G1,L1,T1⦄ →
                          ∀G2,L2,T2. ⦃G1,L1,T1⦄ ≥[h] ⦃G2,L2,T2⦄ → Q G2 L2 T2.
 #h #Q #IH1 #G1 #L1 #T1 #H @(fsb_ind_alt … H) -G1 -L1 -T1
 #G1 #L1 #T1 #H1 #IH #G2 #L2 #T2 #H12
index 9521a9b27d932915d530e24ceed3928fdf979940..05292539f92f0fb191b3e266cd2189ea700e756e 100644 (file)
@@ -72,7 +72,7 @@ lemma jsx_inv_pair_sn (h) (G):
        | ∃∃K2. G ⊢ K1 ⊒[h] K2 & G ⊢ ⬈*[h,V] 𝐒⦃K2⦄ & L2 = K2.ⓧ.
 #h #G #I #K1 #L2 #V #H elim (jsx_inv_bind_sn … H) -H *
 [ /3 width=3 by ex2_intro, or_introl/
-| #J #K2 #X #HK12 #HX #H1 #H2 destruct /3 width=4 by ex3_intro, or_intror/ 
+| #J #K2 #X #HK12 #HX #H1 #H2 destruct /3 width=4 by ex3_intro, or_intror/
 ]
 qed-.
 
index b8e919b738cc635d1b8cd26a6ecddc9666468845..adeaa3f882be30565e34efa719b754c6c7dd9e91 100644 (file)
@@ -27,7 +27,7 @@ lemma jsx_csx_conf (h) (G):
 
 (* Properties with strongly rt-normalizing referred local environments ******)
 
-(* Note: Try by induction on the 2nd premise by generalizing V with f *) 
+(* Note: Try by induction on the 2nd premise by generalizing V with f *)
 lemma rsx_jsx_trans (h) (G):
       ∀L1,V. G ⊢ ⬈*[h,V] 𝐒⦃L1⦄ →
       ∀L2. G ⊢ L1 ⊒[h] L2 → G ⊢ ⬈*[h,V] 𝐒⦃L2⦄.
index 7ac21a90d5d142b1254813193005e9bf2e38b567..74eb68212c40253d3b039426a4bd7ac60f29d7f3 100644 (file)
@@ -47,7 +47,7 @@ elim (drops_inv_bind1_isuni … H) -H [3,6: // |*: * -Hf ]
 [1,3: #Hf #H destruct -IH /3 width=3 by drops_refl, ex2_intro/
 |2,4:
   #g #Hg #HK1 #H destruct
-  elim (IH … Hg … HK1) -K1 -Hg #Y2 #HY12 #HKY2 
+  elim (IH … Hg … HK1) -K1 -Hg #Y2 #HY12 #HKY2
   /3 width=3 by drops_drop, ex2_intro/
 ]
 qed-.
index 742a0038ae51cea23edcfed2dc832b8adfd7dd1e..c3e72888bb0996373d49d7cbe6d50456adacd33c 100644 (file)
@@ -20,7 +20,7 @@ include "basic_2/rt_computation/lprs.ma".
 (* Properties with contextual transitive closure ****************************)
 
 lemma lprs_CTC (h) (G):
-               ∀L1,L2. L1⪤[CTC … (λL. cpm h G L 0)] L2 → ⦃G,L1⦄⊢ ➡*[h] L2. 
+               ∀L1,L2. L1⪤[CTC … (λL. cpm h G L 0)] L2 → ⦃G,L1⦄⊢ ➡*[h] L2.
 /3 width=3 by cprs_CTC, lex_co/ qed.
 
 (* Inversion lemmas with contextual transitive closure **********************)
index 06500ddc957c4e009eaaf67a08f519164eb90708..2671597f13eca7211c17021b3b598766fd8f0b56 100644 (file)
@@ -63,7 +63,7 @@ qed-.
 lemma rsx_fwd_flat_dx (h) (G):
       ∀I,L,V,T. G ⊢ ⬈*[h,ⓕ{I}V.T] 𝐒⦃L⦄ →
       G ⊢ ⬈*[h,T] 𝐒⦃L⦄.
-#h #G #I #L #V #T #H 
+#h #G #I #L #V #T #H
 @(rsx_ind … H) -L #L1 #_ #IHL1
 @rsx_intro #L2 #HL12 #HnL12
 /4 width=3 by reqx_fwd_flat_dx/
index 7abac34cd89a9d55f6d60820b4b953878024f853..5a4dd983ca7ffae3d6fcb26b5393b3403b12c82e 100644 (file)
@@ -26,7 +26,7 @@ include "basic_2/rt_computation/rsx_fqup.ma".
 lemma rsx_lifts (h) (G): d_liftable1_isuni … (λL,T. G ⊢ ⬈*[h,T] 𝐒⦃L⦄).
 #h #G #K #T #H @(rsx_ind … H) -K
 #K1 #_ #IH #b #f #L1 #HLK1 #Hf #U #HTU @rsx_intro
-#L2 #HL12 #HnL12 elim (lpx_drops_conf … HLK1 … HL12) 
+#L2 #HL12 #HnL12 elim (lpx_drops_conf … HLK1 … HL12)
 /5 width=9 by reqx_lifts_bi, lpx_fwd_length/
 qed-.
 
index 70681cf76ee0a57c0304e03a5ad0cc2e171d574d..0f45712626b3851ad7a6558089fd38632613cd75 100644 (file)
@@ -40,7 +40,7 @@ qed-.
 lemma cnx_inv_abbr_neg: ∀h,G,L,V,T. ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃-ⓓV.T⦄ →
                         ⦃G,L⦄ ⊢ ⬈[h] 𝐍⦃V⦄ ∧ ⦃G,L.ⓓV⦄ ⊢ ⬈[h] 𝐍⦃T⦄.
 #h #G #L #V1 #T1 #HVT1 @conj
-[ #V2 #HV2 lapply (HVT1 (-ⓓV2.T1) ?) -HVT1 /2 width=2 by cpx_pair_sn/ -HV2 
+[ #V2 #HV2 lapply (HVT1 (-ⓓV2.T1) ?) -HVT1 /2 width=2 by cpx_pair_sn/ -HV2
 | #T2 #HT2 lapply (HVT1 (-ⓓV1.T2) ?) -HVT1 /2 width=2 by cpx_bind/ -HT2
 ]
 #H elim (teqx_inv_pair … H) -H //
index 75e0211d51bee3c1110521459098a47ce492a9d5..8c9c5f5ef534deb536f344a9918dcbe6594d5516 100644 (file)
@@ -30,7 +30,7 @@ inductive cpg (Rt:relation rtc) (h): rtc → relation4 genv lenv term term ≝
              ⇧*[1] V2 ≘ W2 → cpg Rt h c G (L.ⓓV1) (#0) W2
 | cpg_ell  : ∀c,G,L,V1,V2,W2. cpg Rt h c G L V1 V2 →
              ⇧*[1] V2 ≘ W2 → cpg Rt h (c+𝟘𝟙) G (L.ⓛV1) (#0) W2
-| cpg_lref : ∀c,I,G,L,T,U,i. cpg Rt h c G L (#i) T → 
+| cpg_lref : ∀c,I,G,L,T,U,i. cpg Rt h c G L (#i) T →
              ⇧*[1] T ≘ U → cpg Rt h c G (L.ⓘ{I}) (#↑i) U
 | cpg_bind : ∀cV,cT,p,I,G,L,V1,V2,T1,T2.
              cpg Rt h cV G L V1 V2 → cpg Rt h cT G (L.ⓑ{I}V1) T1 T2 →
@@ -69,7 +69,7 @@ qed.
 (* Basic inversion lemmas ***************************************************)
 
 fact cpg_inv_atom1_aux: ∀Rt,c,h,G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈[Rt,c,h] T2 → ∀J. T1 = ⓪{J} →
-                        ∨∨ T2 = ⓪{J} ∧ c = 𝟘𝟘 
+                        ∨∨ T2 = ⓪{J} ∧ c = 𝟘𝟘
                          | ∃∃s. J = Sort s & T2 = ⋆(⫯[h]s) & c = 𝟘𝟙
                          | ∃∃cV,K,V1,V2. ⦃G,K⦄ ⊢ V1 ⬈[Rt,cV,h] V2 & ⇧*[1] V2 ≘ T2 &
                                          L = K.ⓓV1 & J = LRef 0 & c = cV
@@ -95,7 +95,7 @@ fact cpg_inv_atom1_aux: ∀Rt,c,h,G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈[Rt,c,h] T2 →
 qed-.
 
 lemma cpg_inv_atom1: ∀Rt,c,h,J,G,L,T2. ⦃G,L⦄ ⊢ ⓪{J} ⬈[Rt,c,h] T2 →
-                     ∨∨ T2 = ⓪{J} ∧ c = 𝟘𝟘 
+                     ∨∨ T2 = ⓪{J} ∧ c = 𝟘𝟘
                       | ∃∃s. J = Sort s & T2 = ⋆(⫯[h]s) & c = 𝟘𝟙
                       | ∃∃cV,K,V1,V2. ⦃G,K⦄ ⊢ V1 ⬈[Rt,cV,h] V2 & ⇧*[1] V2 ≘ T2 &
                                       L = K.ⓓV1 & J = LRef 0 & c = cV
@@ -153,7 +153,7 @@ fact cpg_inv_bind1_aux: ∀Rt,c,h,G,L,U,U2. ⦃G,L⦄ ⊢ U ⬈[Rt,c,h] U2 →
                         ∀p,J,V1,U1. U = ⓑ{p,J}V1.U1 →
                         ∨∨ ∃∃cV,cT,V2,T2. ⦃G,L⦄ ⊢ V1 ⬈[Rt,cV,h] V2 & ⦃G,L.ⓑ{J}V1⦄ ⊢ U1 ⬈[Rt,cT,h] T2 &
                                           U2 = ⓑ{p,J}V2.T2 & c = ((↕*cV)∨cT)
-                         | ∃∃cT,T. ⇧*[1] T ≘ U1 & ⦃G,L⦄ ⊢ T ⬈[Rt,cT,h] U2 & 
+                         | ∃∃cT,T. ⇧*[1] T ≘ U1 & ⦃G,L⦄ ⊢ T ⬈[Rt,cT,h] U2 &
                                    p = true & J = Abbr & c = cT+𝟙𝟘.
 #Rt #c #h #G #L #U #U2 * -c -G -L -U -U2
 [ #I #G #L #q #J #W #U1 #H destruct
@@ -191,7 +191,7 @@ qed-.
 lemma cpg_inv_abst1: ∀Rt,c,h,p,G,L,V1,T1,U2. ⦃G,L⦄ ⊢ ⓛ{p}V1.T1 ⬈[Rt,c,h] U2 →
                      ∃∃cV,cT,V2,T2. ⦃G,L⦄ ⊢ V1 ⬈[Rt,cV,h] V2 & ⦃G,L.ⓛV1⦄ ⊢ T1 ⬈[Rt,cT,h] T2 &
                                     U2 = ⓛ{p}V2.T2 & c = ((↕*cV)∨cT).
-#Rt #c #h #p #G #L #V1 #T1 #U2 #H elim (cpg_inv_bind1 … H) -H * 
+#Rt #c #h #p #G #L #V1 #T1 #U2 #H elim (cpg_inv_bind1 … H) -H *
 [ /3 width=8 by ex4_4_intro/
 | #c #T #_ #_ #_ #H destruct
 ]
index 4a937f119b5f8b1cbd7700a0e0e4df8890ec5153..6893cf19e6ef4ca8ae4e4a85c0c38fdf5161db58 100644 (file)
@@ -212,14 +212,14 @@ qed.
 
 lemma cpm_inv_gref1: ∀n,h,G,L,T2,l. ⦃G,L⦄ ⊢ §l ➡[n,h] T2 → T2 = §l ∧ n = 0.
 #n #h #G #L #T2 #l * #c #Hc #H elim (cpg_inv_gref1 … H) -H
-#H1 #H2 destruct /3 width=1 by isrt_inv_00, conj/ 
+#H1 #H2 destruct /3 width=1 by isrt_inv_00, conj/
 qed-.
 
 (* Basic_2A1: includes: cpr_inv_bind1 *)
 lemma cpm_inv_bind1: ∀n,h,p,I,G,L,V1,T1,U2. ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T1 ➡[n,h] U2 →
                      ∨∨ ∃∃V2,T2. ⦃G,L⦄ ⊢ V1 ➡[h] V2 & ⦃G,L.ⓑ{I}V1⦄ ⊢ T1 ➡[n,h] T2 &
                                  U2 = ⓑ{p,I}V2.T2
-                      | ∃∃T. ⇧*[1] T ≘ T1 & ⦃G,L⦄ ⊢ T ➡[n,h] U2 & 
+                      | ∃∃T. ⇧*[1] T ≘ T1 & ⦃G,L⦄ ⊢ T ➡[n,h] U2 &
                              p = true & I = Abbr.
 #n #h #p #I #G #L #V1 #T1 #U2 * #c #Hc #H elim (cpg_inv_bind1 … H) -H *
 [ #cV #cT #V2 #T2 #HV12 #HT12 #H1 #H2 destruct
@@ -252,7 +252,7 @@ lemma cpm_inv_abst1: ∀n,h,p,G,L,V1,T1,U2. ⦃G,L⦄ ⊢ ⓛ{p}V1.T1 ➡[n,h] U
 #n #h #p #G #L #V1 #T1 #U2 #H
 elim (cpm_inv_bind1 … H) -H
 [ /3 width=1 by or_introl/
-| * #T #_ #_ #_ #H destruct  
+| * #T #_ #_ #_ #H destruct
 ]
 qed-.
 
@@ -260,7 +260,7 @@ lemma cpm_inv_abst_bi: ∀n,h,p1,p2,G,L,V1,V2,T1,T2. ⦃G,L⦄ ⊢ ⓛ{p1}V1.T1
                        ∧∧ ⦃G,L⦄ ⊢ V1 ➡[h] V2 & ⦃G,L.ⓛV1⦄ ⊢ T1 ➡[n,h] T2 & p1 = p2.
 #n #h #p1 #p2 #G #L #V1 #V2 #T1 #T2 #H
 elim (cpm_inv_abst1 … H) -H #XV #XT #HV #HT #H destruct
-/2 width=1 by and3_intro/  
+/2 width=1 by and3_intro/
 qed-.
 
 (* Basic_1: includes: pr0_gen_appl pr2_gen_appl *)
index ee72b61494255856179fdec182ba022777e6cba2..e6555ec1800b85614d74224f62bc8778a0cf8699 100644 (file)
@@ -25,7 +25,7 @@ lemma cpr_flat: ∀h,I,G,L,V1,V2,T1,T2.
                 ⦃G,L⦄ ⊢ V1 ➡[h] V2 → ⦃G,L⦄ ⊢ T1 ➡[h] T2 →
                 ⦃G,L⦄ ⊢ ⓕ{I}V1.T1 ➡[h] ⓕ{I}V2.T2.
 #h * /2 width=1 by cpm_cast, cpm_appl/
-qed. 
+qed.
 
 (* Basic_1: was: pr2_head_1 *)
 lemma cpr_pair_sn: ∀h,I,G,L,V1,V2. ⦃G,L⦄ ⊢ V1 ➡[h] V2 →
@@ -45,7 +45,7 @@ lemma cpr_inv_atom1: ∀h,J,G,L,T2. ⦃G,L⦄ ⊢ ⓪{J} ➡[h] T2 →
 [2,4:|*: /3 width=8 by or3_intro0, or3_intro1, or3_intro2, ex4_4_intro, ex4_3_intro/ ]
 [ #n #_ #_ #H destruct
 | #n #K #V1 #V2 #_ #_ #_ #_ #H destruct
-]  
+]
 qed-.
 
 (* Basic_1: includes: pr0_gen_sort pr2_gen_sort *)
index 53f9d778d6ee580474db80b1fb81347ce937499d..fa110d8c43be5b41f895e77ceab88454268c7c99 100644 (file)
@@ -177,7 +177,7 @@ qed.
 lemma cpt_inv_gref_sn (h) (n) (G) (L) (l):
       ∀X2. ⦃G,L⦄ ⊢ §l ⬆[h,n] X2 → ∧∧ X2 = §l & n = 0.
 #h #n #G #L #l #X2 * #c #Hc #H elim (cpg_inv_gref1 … H) -H
-#H1 #H2 destruct /2 width=1 by conj/ 
+#H1 #H2 destruct /2 width=1 by conj/
 qed-.
 
 lemma cpt_inv_bind_sn (h) (n) (p) (I) (G) (L) (V1) (T1):
index f8978f460ca477121395de7024a3fe2bbbe42b48..7e1197873497abe570d25933719688530f33ddc6 100644 (file)
@@ -77,7 +77,7 @@ qed.
 lemma cpx_beta: ∀h,p,G,L,V1,V2,W1,W2,T1,T2.
                 ⦃G,L⦄ ⊢ V1 ⬈[h] V2 → ⦃G,L⦄ ⊢ W1 ⬈[h] W2 → ⦃G,L.ⓛW1⦄ ⊢ T1 ⬈[h] T2 →
                 ⦃G,L⦄ ⊢ ⓐV1.ⓛ{p}W1.T1 ⬈[h] ⓓ{p}ⓝW2.V2.T2.
-#h #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 * #cV #HV12 * #cW #HW12 * 
+#h #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 * #cV #HV12 * #cW #HW12 *
 /3 width=2 by cpg_beta, ex_intro/
 qed.
 
@@ -85,7 +85,7 @@ lemma cpx_theta: ∀h,p,G,L,V1,V,V2,W1,W2,T1,T2.
                  ⦃G,L⦄ ⊢ V1 ⬈[h] V → ⇧*[1] V ≘ V2 → ⦃G,L⦄ ⊢ W1 ⬈[h] W2 →
                  ⦃G,L.ⓓW1⦄ ⊢ T1 ⬈[h] T2 →
                  ⦃G,L⦄ ⊢ ⓐV1.ⓓ{p}W1.T1 ⬈[h] ⓓ{p}W2.ⓐV2.T2.
-#h #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 * #cV #HV1 #HV2 * #cW #HW12 * 
+#h #p #G #L #V1 #V #V2 #W1 #W2 #T1 #T2 * #cV #HV1 #HV2 * #cW #HW12 *
 /3 width=4 by cpg_theta, ex_intro/
 qed.
 
@@ -147,7 +147,7 @@ qed-.
 lemma cpx_inv_bind1: ∀h,p,I,G,L,V1,T1,U2. ⦃G,L⦄ ⊢ ⓑ{p,I}V1.T1 ⬈[h] U2 →
                      ∨∨ ∃∃V2,T2. ⦃G,L⦄ ⊢ V1 ⬈[h] V2 & ⦃G,L.ⓑ{I}V1⦄ ⊢ T1 ⬈[h] T2 &
                                  U2 = ⓑ{p,I}V2.T2
-                      | ∃∃T. ⇧*[1] T ≘ T1 & ⦃G,L⦄ ⊢ T ⬈[h] U2 & 
+                      | ∃∃T. ⇧*[1] T ≘ T1 & ⦃G,L⦄ ⊢ T ⬈[h] U2 &
                              p = true & I = Abbr.
 #h #p #I #G #L #V1 #T1 #U2 * #c #H elim (cpg_inv_bind1 … H) -H *
 /4 width=5 by ex4_intro, ex3_2_intro, ex_intro, or_introl, or_intror/
@@ -224,7 +224,7 @@ lemma cpx_inv_flat1: ∀h,I,G,L,V1,U1,U2. ⦃G,L⦄ ⊢ ⓕ{I}V1.U1 ⬈[h] U2 
   /3 width=14 by or5_intro0, or5_intro3, or5_intro4, ex7_7_intro, ex6_6_intro, ex3_2_intro/
 | elim (cpx_inv_cast1 … H) -H [ * ]
   /3 width=14 by or5_intro0, or5_intro1, or5_intro2, ex3_2_intro, conj/
-] 
+]
 qed-.
 
 (* Basic forward lemmas *****************************************************)
index 6c1d31e771457cb2537f876cb8f19e89c9e3f5ce..3be9277cdc9d4427bf9da43b0f023ad22c9286ee 100644 (file)
@@ -101,7 +101,7 @@ qed-.
 lemma fquq_cpx_trans_tneqx: ∀h,b,G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ⬂⸮[b] ⦃G2,L2,T2⦄ →
                             ∀U2. ⦃G2,L2⦄ ⊢ T2 ⬈[h] U2 → (T2 ≛ U2 → ⊥) →
                             ∃∃U1. ⦃G1,L1⦄ ⊢ T1 ⬈[h] U1 & T1 ≛ U1 → ⊥ & ⦃G1,L1,U1⦄ ⬂⸮[b] ⦃G2,L2,U2⦄.
-#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 elim H12 -H12 
+#h #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 elim H12 -H12
 [ #H12 #U2 #HTU2 #H elim (fqu_cpx_trans_tneqx … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fquq, ex3_intro/
 | * #HG #HL #HT destruct /3 width=4 by ex3_intro/
index de168279c11e69bd2ae9b4d07e1110ebfd38a98f..6dea95295ba979225a32429302580193a77d1d14 100644 (file)
@@ -22,7 +22,7 @@ include "basic_2/rt_transition/fpb.ma".
 (* Properties with sort-irrelevant equivalence for local environments *******)
 
 lemma teqx_fpb_trans: ∀h,U2,U1. U2 ≛ U1 →
-                      ∀G1,G2,L1,L2,T1. ⦃G1,L1,U1⦄ ≻[h] ⦃G2,L2,T1⦄ → 
+                      ∀G1,G2,L1,L2,T1. ⦃G1,L1,U1⦄ ≻[h] ⦃G2,L2,T1⦄ →
                       ∃∃L,T2. ⦃G1,L1,U2⦄ ≻[h] ⦃G2,L,T2⦄ & T2 ≛ T1 & L ≛[T1] L2.
 #h #U2 #U1 #HU21 #G1 #G2 #L1 #L2 #T1 * -G2 -L2 -T1
 [ #G2 #L2 #T1 #H
index e875cac283b9cb0ece3b8c387ff4884132358d59..e8e183cb8168c91008954cc50c03c23bff6a265d 100644 (file)
@@ -37,7 +37,7 @@ lemma fpbq_refl (h): tri_reflexive … (fpbq h).
 /2 width=1 by fpbq_cpx/ qed.
 
 (* Basic_2A1: includes: cpr_fpbq *)
-lemma cpm_fpbq (n) (h) (G) (L): ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 → ⦃G,L,T1⦄ ≽[h] ⦃G,L,T2⦄. 
+lemma cpm_fpbq (n) (h) (G) (L): ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 → ⦃G,L,T1⦄ ≽[h] ⦃G,L,T2⦄.
 /3 width=2 by fpbq_cpx, cpm_fwd_cpx/ qed.
 
 lemma lpr_fpbq (h) (G) (T): ∀L1,L2. ⦃G,L1⦄ ⊢ ➡[h] L2 → ⦃G,L1,T⦄ ≽[h] ⦃G,L2,T⦄.
index 184d914067d5f21154e10facc365fa84ac60fb48..dcbe44401f1a76ba9f3f7c41e0b80c30ea7b4948 100644 (file)
@@ -97,7 +97,7 @@ fact cpr_conf_lpr_bind_zeta (h):
       ∀G,L,T. ⦃G0,L0,+ⓓV0.T0⦄ ⬂+ ⦃G,L,T⦄ → IH_cpr_conf_lpr h G L T
    ) →
    ∀V1. ⦃G0,L0⦄ ⊢ V0 ➡[h] V1 → ∀T1. ⦃G0,L0.ⓓV0⦄ ⊢ T0 ➡[h] T1 →
-   ∀T2. ⇧*[1]T2 ≘ T0 → ∀X2. ⦃G0,L0⦄ ⊢ T2 ➡[h] X2 →  
+   ∀T2. ⇧*[1]T2 ≘ T0 → ∀X2. ⦃G0,L0⦄ ⊢ T2 ➡[h] X2 →
    ∀L1. ⦃G0,L0⦄ ⊢ ➡[h] L1 → ∀L2. ⦃G0,L0⦄ ⊢ ➡[h] L2 →
    ∃∃T. ⦃G0,L1⦄ ⊢ +ⓓV1.T1 ➡[h] T & ⦃G0,L2⦄ ⊢ X2 ➡[h] T.
 #h #G0 #L0 #V0 #T0 #IH #V1 #HV01 #T1 #HT01
index b0b50cf3ac0df6f60f8d94b4d2fe09c66183a99e..61b24fdae03d8bf440c33ca30ae7eb9aae45d6b7 100644 (file)
@@ -134,7 +134,7 @@ elim (cpx_teqx_conf_rex … HT01 … HT02 L … L) -HT01 -HT02
 qed-.
 
 lemma teqx_cpx_trans: ∀h,G,L,T2. ∀T0:term. T2 ≛ T0 →
-                      ∀T1. ⦃G,L⦄ ⊢ T0 ⬈[h] T1 → 
+                      ∀T1. ⦃G,L⦄ ⊢ T0 ⬈[h] T1 →
                       ∃∃T. ⦃G,L⦄ ⊢ T2 ⬈[h] T & T ≛ T1.
 #h #G #L #T2 #T0 #HT20 #T1 #HT01
 elim (cpx_teqx_conf … HT01 T2) -HT01 /3 width=3 by teqx_sym, ex2_intro/
index 28575ff0ea587c7a0b377529bd7140048bd6c21e..74e37e0da517a4e683ead31fee09b2b4212e8922 100644 (file)
@@ -7,7 +7,7 @@
       head = "cic:/matita/lambdadelta/basic_2/ (core λδ version 2)"
 >
    <sitemap name="sitemap"/>
-<!--   
+<!--
    <section>System's Syntax and Behavior</section>
    <body>This is a summary of the "block structure"
          of the System's syntactic items and reductions.
@@ -27,6 +27,9 @@
    <table name="basic_2_sum"/>
 
    <subsection name="B">Stage "B"</subsection>
+   <news class="gamma" date="2019 November 19.">
+         λδ-2B is released.
+   </news>
    <news class="beta" date="2019 September 3.">
          Applicability condition is now parametrized
          with a generic subset of numbers.
    </news>
    <news class="alpha" date="2014 April 16.">
          Lazy equivalence on local environments
-        added as q-step to rst-computation on closures
+         added as q-step to rst-computation on closures
          (anniversary milestone).
    </news>
    <news class="alpha" date="2014 January 20.">
          Parametrized slicing on local environments
-        comprises both versions of this operation
-        (one from basic_1, the other used in basic_2 till now).
+         comprises both versions of this operation
+         (one from basic_1, the other used in basic_2 till now).
    </news>
    <news class="alpha" date="2013 August 7.">
          Passive support for global environments.
index 7636e65e897c376cba85330cf64c698611e1f170..f9d388a3cbd7d4f9760634172dd387344cb2f9fc 100644 (file)
@@ -31,7 +31,7 @@ table {
      }
    ]
    class "prune"
-   [ { "rt-equivalence" * } {        
+   [ { "rt-equivalence" * } {
         [ { "context-sensitive parallel r-equivalence" * } {
              [ [ "for terms" ] "cpcs ( ⦃?,?⦄ ⊢ ? ⬌*[?] ? )" "cpcs_drops" + "cpcs_lsubr" + "cpcs_aaa" + "cpcs_csx" + "cpcs_cprs" + "cpcs_lprs" + "cpcs_cpc" + "cpcs_cpcs" * ]
           }
@@ -91,7 +91,7 @@ table {
              [ [ "strongly normalizing for terms" ] "csx" + "( ⦃?,?⦄ ⊢ ⬈*[?] 𝐒⦃?⦄ )" "csx_simple" + "csx_simple_teqo" + "csx_drops" + "csx_fqus" + "csx_lsubr" + "csx_reqx" + "csx_feqx" + "csx_aaa" + "csx_gcp" + "csx_gcr" + "csx_lpx" + "csx_cnx" + "csx_fpbq" + "csx_cpxs" + "csx_lpxs" + "csx_csx" * ]
              [ [ "for lenvs on all entries" ] "lpxs" + "( ⦃?,?⦄ ⊢ ⬈*[?] ? )" "lpxs_length" + "lpxs_drops" + "lpxs_reqx" + "lpxs_feqx" + "lpxs_aaa" + "lpxs_lpx" + "lpxs_cpxs" + "lpxs_lpxs" * ]
              [ [ "for binders" ] "cpxs_ext" + "( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" * ]
-             [ [ "for terms" ] "cpxs" + "( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" "cpxs_teqx" + "cpxs_teqo" + "cpxs_teqo_vector" + "cpxs_drops" + "cpxs_fqus" + "cpxs_lsubr" + "cpxs_reqx" + "cpxs_feqx" + "cpxs_aaa" + "cpxs_lpx" + "cpxs_cnx" + "cpxs_cpxs" * ] 
+             [ [ "for terms" ] "cpxs" + "( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" "cpxs_teqx" + "cpxs_teqo" + "cpxs_teqo_vector" + "cpxs_drops" + "cpxs_fqus" + "cpxs_lsubr" + "cpxs_reqx" + "cpxs_feqx" + "cpxs_aaa" + "cpxs_lpx" + "cpxs_cnx" + "cpxs_cpxs" * ]
           }
         ]
      }
index d272c0dbee63dfdbb474d8e6fa64a8ec7d099a89..dbd8b678b1f7f5ab7a13fd564269d0eb2d1492d2 100644 (file)
@@ -42,7 +42,7 @@ definition relation5: Type[0] → Type[0] → Type[0] → Type[0] → Type[0] 
 definition relation6: Type[0] → Type[0] → Type[0] → Type[0] → Type[0] → Type[0] → Type[0] ≝
            λA,B,C,D,E,F.A→B→C→D→E→F→Prop.
 
-(**) (* we don't use "∀a. reflexive … (R a)" since auto seems to dislike repeatd δ-expansion *)  
+(**) (* we don't use "∀a. reflexive … (R a)" since auto seems to dislike repeatd δ-expansion *)
 definition c_reflexive (A) (B): predicate (relation3 A B B) ≝
            λR. ∀a,b. R a b b.
 
index cee2483f3e4068ad01aa560805f126f89a5cbf59..66338bdbce4a8c83a10d82d76c41ccc57a15ce3f 100644 (file)
@@ -68,4 +68,4 @@ theorem eq_stream_canc_sn: ∀A,t,t1,t2. t ≗ t1 → t ≗ t2 → t1 ≗{A} t2.
 /3 width=3 by eq_stream_trans, eq_stream_sym/ qed-.
 
 theorem eq_stream_canc_dx: ∀A,t,t1,t2. t1 ≗ t → t2 ≗ t → t1 ≗{A} t2.
-/3 width=3 by eq_stream_trans, eq_stream_sym/ qed-. 
+/3 width=3 by eq_stream_trans, eq_stream_sym/ qed-.
index 01bc8d1563b028060d4b802eb8cf42ce1ffbf735..1402237cd2c10a501ac8dd1fb2156dd4ac7966e8 100644 (file)
@@ -14,6 +14,6 @@
 
 (* GENERAL NOTATION USED BY THE FORMAL SYSTEM λδ ****************************)
 
-notation "hvbox( ↑ term 70 T )" 
+notation "hvbox( ↑ term 70 T )"
    non associative with precedence 70
    for @{ 'UpArrow $T }.
index 4bf66b56e3ea36c6982ca962c77340dc3b199d86..a2e0baffb2c5878e3da998fb9ee74ad53b247d00 100644 (file)
@@ -22,5 +22,5 @@ lemma pull_4 (A1:Type[0])
              (A4:Type[0])
              (A:∀x1:A1.∀x2:A2 x1.A3 x1 x2 → A4 → Type[0]):
              (∀x4,x1,x2,x3. A x1 x2 x3 x4) →
-             (∀x1,x2,x3,x4. A x1 x2 x3 x4). 
+             (∀x1,x2,x3,x4. A x1 x2 x3 x4).
 /2 width=1 by/ qed-.
index 7758003287dde4ed294fe85588d6a93d4b589aa9..f93a968b0f3a373adbe8947ee0db8df00ebc7306 100644 (file)
@@ -44,7 +44,7 @@ interpretation "functional co-composition (nstream)"
 
 (* Basic properties on funs *************************************************)
 
-(* Note: we need theese since matita blocks recursive δ when ι is blocked *)  
+(* Note: we need theese since matita blocks recursive δ when ι is blocked *)
 lemma fun0_xn: ∀f2,n1. 0 = fun0 n1 (↑f2).
 * #n2 #f2 * //
 qed.
index 97636d5d88d40d57f9ffcb8c5b7e881bbc1b1990..cc067a24d4284c57021d0c5231e88169b1d79f72 100644 (file)
@@ -166,7 +166,7 @@ corec lemma after_eq_repl_back2: ∀f1,f. eq_repl_back (λf2. f2 ⊚ f1 ≘ f).
 #f21 #f1 #f #g21 [1,2: #g1 ] #g #Hf #H21 [1,2: #H1 ] #H #g22 #H0
 [ cases (eq_inv_px …  H0 …  H21) -g21 /3 width=7 by after_refl/
 | cases (eq_inv_px …  H0 …  H21) -g21 /3 width=7 by after_push/
-| cases (eq_inv_nx …  H0 …  H21) -g21 /3 width=5 by after_next/ 
+| cases (eq_inv_nx …  H0 …  H21) -g21 /3 width=5 by after_next/
 ]
 qed-.
 
@@ -267,7 +267,7 @@ lemma after_mono_eq: ∀f1,f2,f. f1 ⊚ f2 ≘ f → ∀g1,g2,g. g1 ⊚ g2 ≘ g
 
 (* Properties on tls ********************************************************)
 
-lemma after_tls: ∀n,f1,f2,f. @⦃0, f1⦄ ≘ n → 
+lemma after_tls: ∀n,f1,f2,f. @⦃0, f1⦄ ≘ n →
                  f1 ⊚ f2 ≘ f → ⫱*[n]f1 ⊚ f2 ≘ ⫱*[n]f.
 #n elim n -n //
 #n #IH #f1 #f2 #f #Hf1 #Hf
index 93980c881f9f41b5b20d89592c7358f255c84c40..ef10a824149d672bc91fe91a79a070e8945006df 100644 (file)
@@ -18,7 +18,7 @@ include "ground_2/relocation/rtmap_uni.ma".
 (* RELOCATION MAP ***********************************************************)
 
 coinductive at: rtmap → relation nat ≝
-| at_refl: ∀f,g,j1,j2. ⫯f = g → 0 = j1 → 0 = j2 → at g j1 j2 
+| at_refl: ∀f,g,j1,j2. ⫯f = g → 0 = j1 → 0 = j2 → at g j1 j2
 | at_push: ∀f,i1,i2. at f i1 i2 → ∀g,j1,j2. ⫯f = g → ↑i1 = j1 → ↑i2 = j2 → at g j1 j2
 | at_next: ∀f,i1,i2. at f i1 i2 → ∀g,j2. ↑f = g → ↑i2 = j2 → at g i1 j2
 .
@@ -324,7 +324,7 @@ lemma at_tls: ∀i2,f. ⫯⫱*[↑i2]f ≡ ⫱*[i2]f → ∃i1. @⦃i1,f⦄ ≘
 [ /4 width=4 by at_eq_repl_back, at_refl, ex_intro/
 | #i2 #IH #f <tls_xn <tls_xn in ⊢ (??%→?); #H
   elim (IH … H) -IH -H #i1 #Hf
-  elim (pn_split f) * #g #Hg destruct /3 width=8 by at_push, at_next, ex_intro/  
+  elim (pn_split f) * #g #Hg destruct /3 width=8 by at_push, at_next, ex_intro/
 ]
 qed-.
 
index 31989789a7163fe096c4fa436a82b220634c0eb9..89460528d3684c688de3fbf66338402eee65ebc2 100644 (file)
@@ -60,7 +60,7 @@ qed-.
 
 lemma fcla_inv_isid: ∀f,n. 𝐂⦃f⦄ ≘ n → 𝐈⦃f⦄ → 0 = n.
 #f #n #H elim H -f -n /3 width=3 by isid_inv_push/
-#f #n #_ #_ #H elim (isid_inv_next … H) -H //  
+#f #n #_ #_ #H elim (isid_inv_next … H) -H //
 qed-.
 
 (* Main forward lemmas ******************************************************)
index a5237af26b17a96981bda3ef94c805f23a050002..253db1df8a5fb3b2cdc4e4095703ac15f3ed744d 100644 (file)
@@ -27,7 +27,7 @@ interpretation "plus (rtc)"
 
 (* Basic properties *********************************************************)
 
-(**) (* plus is not disambiguated parentheses *) 
+(**) (* plus is not disambiguated parentheses *)
 lemma plus_rew: ∀ri1,ri2,rs1,rs2,ti1,ti2,ts1,ts2.
                  〈ri1+ri2,rs1+rs2,ti1+ti2,ts1+ts2〉 =
                  (〈ri1,rs1,ti1,ts1〉) + (〈ri2,rs2,ti2,ts2〉).
index 474eb277820cfa2fefb47a77aeb874905a9f626b..0fcbd11553d9b27f5068157d050086c4a2326cd0 100644 (file)
@@ -12,7 +12,7 @@ table {
    class "water"
    [ { "generic rt-transition counter" * } {
         [ { "" * } {
-             [ "rtc_ist ( 𝐓⦃?,?⦄ )" "rtc_ist_shift" "rtc_ist_plus" "rtc_ist_max" * ]  
+             [ "rtc_ist ( 𝐓⦃?,?⦄ )" "rtc_ist_shift" "rtc_ist_plus" "rtc_ist_max" * ]
              [ "rtc ( 〈?,?,?,?〉 ) ( 𝟘𝟘 ) ( 𝟙𝟘 ) ( 𝟘𝟙 )" "rtc_isrc ( 𝐑𝐓⦃?,?⦄ )" "rtc_shift ( ↕*? )" "rtc_max ( ? ∨ ? )" "rtc_plus ( ? + ? )" * ]
           }
         ]
@@ -21,7 +21,7 @@ table {
    class "green"
    [ { "multiple relocation" * } {
         [ { "" * } {
-             [ "rtmap" "rtmap_eq ( ? ≡ ? )" "rtmap_pushs ( ⫯*[?]? )" "rtmap_nexts ( ↑*[?]? )" 
+             [ "rtmap" "rtmap_eq ( ? ≡ ? )" "rtmap_pushs ( ⫯*[?]? )" "rtmap_nexts ( ↑*[?]? )"
                "rtmap_tl ( ⫱? )" "rtmap_tls ( ⫱*[?]? )" "rtmap_isid ( 𝐈⦃?⦄ )" "rtmap_id" "rtmap_isdiv ( 𝛀⦃?⦄ )"
                "rtmap_fcla ( 𝐂⦃?⦄ ≘ ? )" "rtmap_isfin ( 𝐅⦃?⦄ )" "rtmap_isuni ( 𝐔⦃?⦄ )" "rtmap_uni ( 𝐔❴?❵ )"
                "rtmap_sle ( ? ⊆ ? )" "rtmap_sdj ( ? ∥ ? )" "rtmap_sand ( ? ⋒ ? ≘ ? )" "rtmap_sor ( ? ⋓ ? ≘ ? )"
index ee8331d2fff18aaad0f820d290f3bc9473c5c8a2..54e946e96ca40a4ace88868863b258d2ce282cd5 100644 (file)
@@ -46,7 +46,7 @@ fact yle_inv_O2_aux: ∀m:ynat. ∀x:ynat. m ≤ x → x = 0 → m = 0.
 #m #x * -m -x
 [ #m #n #Hmn #H destruct /3 width=1 by le_n_O_to_eq, eq_f/
 | #m #H destruct
-] 
+]
 qed-.
 
 lemma yle_inv_O2: ∀m:ynat. m ≤ 0 → m = 0.
@@ -152,4 +152,4 @@ theorem yle_trans: Transitive … yle.
   /3 width=3 by transitive_le, yle_inj/ (**) (* full auto too slow *)
 | #x #z #H lapply (yle_inv_Y1 … H) //
 ]
-qed-. 
+qed-.
index ab9cf4565cc365d28ff3d8d94b3a8b2359e91c02..846522994823d55ae31c4a6e56aea58cd343fffa 100644 (file)
@@ -199,7 +199,7 @@ lemma yle_ylt_trans: ∀x:ynat. ∀y:ynat. ∀z:ynat. y < z → x ≤ y → x <
 ]
 qed-.
 
-lemma le_ylt_trans (x) (y) (z): x ≤ y → yinj y < z → yinj x < z.  
+lemma le_ylt_trans (x) (y) (z): x ≤ y → yinj y < z → yinj x < z.
 /3 width=3 by yle_ylt_trans, yle_inj/
 qed-.
 
@@ -223,7 +223,7 @@ theorem ylt_trans: Transitive … ylt.
 ]
 qed-.
 
-lemma lt_ylt_trans (x) (y) (z): x < y → yinj y < z → yinj x < z.  
+lemma lt_ylt_trans (x) (y) (z): x < y → yinj y < z → yinj x < z.
 /3 width=3 by ylt_trans, ylt_inj/
 qed-.
 
index 8f1dacf6c3a7b570db1d8a38f272afeb6c4383eb..38b9ddf707f1920eeb1de9da13c139c20f63b625 100644 (file)
@@ -86,7 +86,7 @@ lemma yplus_comm_24: ∀x1,x2,x3,x4. x1 + x4 + x3 + x2 = x1 + x2 + x3 + x4.
 /2 width=1 by eq_f2/
 qed.
 
-lemma yplus_assoc_23: ∀x1,x2,x3,x4. x1 + x2 + (x3 + x4) = x1 + (x2 + x3) + x4.  
+lemma yplus_assoc_23: ∀x1,x2,x3,x4. x1 + x2 + (x3 + x4) = x1 + (x2 + x3) + x4.
 #x1 #x2 #x3 #x4 >yplus_assoc >yplus_assoc
 /2 width=1 by eq_f2/
 qed.
@@ -148,15 +148,15 @@ lemma yplus_inv_monotonic_dx_inj: ∀z,x,y. x + yinj z = y + yinj z → x = y.
 qed-.
 
 lemma yplus_inv_monotonic_dx: ∀z,x,y. z < ∞ → x + z = y + z → x = y.
-#z #x #y #H elim (ylt_inv_Y2 … H) -H /2 width=2 by yplus_inv_monotonic_dx_inj/ 
+#z #x #y #H elim (ylt_inv_Y2 … H) -H /2 width=2 by yplus_inv_monotonic_dx_inj/
 qed-.
 
 lemma yplus_inv_Y2: ∀x,y. x + y = ∞ → x = ∞ ∨ y = ∞.
-* /2 width=1 by or_introl/ #x * // #y >yplus_inj #H destruct 
+* /2 width=1 by or_introl/ #x * // #y >yplus_inj #H destruct
 qed-.
 
 lemma yplus_inv_monotonic_23: ∀z,x1,x2,y1,y2. z < ∞ →
-                              x1 + z + y1 = x2 + z + y2 → x1 + y1 = x2 + y2. 
+                              x1 + z + y1 = x2 + z + y2 → x1 + y1 = x2 + y2.
 #z #x1 #x2 #y1 #y2 #Hz #H @(yplus_inv_monotonic_dx z) //
 >yplus_comm_23 >H -H //
 qed-.
@@ -269,7 +269,7 @@ lemma monotonic_ylt_plus_sn_inj: ∀x,y. x < y → ∀z:nat. yinj z + x < yinj z
 lemma monotonic_ylt_plus_dx: ∀x,y. x < y → ∀z. z < ∞ → x + z < y + z.
 #x #y #Hxy #z #Hz elim (ylt_inv_Y2 … Hz) -Hz
 #m #H destruct /2 width=1 by monotonic_ylt_plus_dx_inj/
-qed.  
+qed.
 
 lemma monotonic_ylt_plus_sn: ∀x,y. x < y → ∀z. z < ∞ → z + x < z + y.
 /2 width=1 by monotonic_ylt_plus_dx/ qed.
index a53ee2c823636520601d31342a6210a725efc554..58b26cd7621c57bfd425958afe5488e2d2aafc6b 100644 (file)
@@ -101,7 +101,7 @@ lemma rexs_inv_sort: ∀R,Y1,Y2,s. Y1 ⪤*[R,⋆s] Y2 →
       /4 width=7 by ex3_4_intro, rexs_step_dx, or_intror/
     ]
   ]
-] 
+]
 qed-.
 
 lemma rexs_inv_gref: ∀R,Y1,Y2,l. Y1 ⪤*[R,§l] Y2 →
@@ -119,7 +119,7 @@ lemma rexs_inv_gref: ∀R,Y1,Y2,l. Y1 ⪤*[R,§l] Y2 →
       /4 width=7 by ex3_4_intro, rexs_step_dx, or_intror/
     ]
   ]
-] 
+]
 qed-.
 
 lemma rexs_inv_bind: ∀R. (∀L. reflexive … (R L)) →
index 801bbd059e62637b29cba6bef2d579d7950398d1..8700b67fe15797b579e0e49d4b939efda0f79ff2 100644 (file)
@@ -86,7 +86,7 @@ definition co_dropable_sn: predicate (rtmap → relation lenv) ≝
 definition co_dropable_dx: predicate (rtmap → relation lenv) ≝
                            λR. ∀f2,L1,L2. R f2 L1 L2 →
                            ∀b,f,K2. ⇩*[b,f] L2 ≘ K2 → 𝐔⦃f⦄ →
-                           ∀f1. f ~⊚ f1 ≘ f2 → 
+                           ∀f1. f ~⊚ f1 ≘ f2 →
                            ∃∃K1. ⇩*[b,f] L1 ≘ K1 & R f1 K1 K2.
 
 definition co_dedropable_sn: predicate (rtmap → relation lenv) ≝
@@ -261,7 +261,7 @@ qed-.
 
 lemma drops_isuni_ex: ∀f. 𝐔⦃f⦄ → ∀L. ∃K. ⇩*[Ⓕ,f] L ≘ K.
 #f #H elim H -f /4 width=2 by drops_refl, drops_TF, ex_intro/
-#f #_ #g #H #IH destruct * /2 width=2 by ex_intro/ 
+#f #_ #g #H #IH destruct * /2 width=2 by ex_intro/
 #L #I elim (IH L) -IH /3 width=2 by drops_drop, ex_intro/
 qed-.
 
index c55f9332fcd09107c6db5e6ae35441610697a238..082cbc824823c868f87119fb7e3ffc1dbb53f3ee 100644 (file)
@@ -26,4 +26,4 @@ lemma cext2_d_liftable2_sn: ∀R. d_liftable2_sn … lifts R →
 | lapply (liftsb_inv_pair_sn … H) * #U1 #HTU1
 ] -H #H destruct /3 width=3 by ext2_unit, ex2_intro/
 elim (HR … HT12 … HLK … HTU1) -HR -b -K -T1 /3 width=3 by ext2_pair, ex2_intro/
-qed-. 
+qed-.
index 0e57eb6aaa6e7f809f74f556340099bbca3d8440..f8a65c53638fd411f6c0506496939045416cfb4b 100644 (file)
@@ -38,7 +38,7 @@ theorem drops_conf: ∀b1,f1,L1,L. ⇩*[b1,f1] L1 ≘ L →
 qed-.
 
 (* Basic_1: was: drop1_trans *)
-(* Basic_2A1: includes: drop_trans_ge drop_trans_le drop_trans_ge_comm 
+(* Basic_2A1: includes: drop_trans_ge drop_trans_le drop_trans_ge_comm
                         drops_drop_trans
 *)
 theorem drops_trans: ∀b1,f1,L1,L. ⇩*[b1,f1] L1 ≘ L →
index 73760857e9e8a0f02cc891ade8f95d61d17b667b..7d53c39db77d4572a3c5837cdf73a395ffb5d82c 100644 (file)
@@ -39,7 +39,7 @@ theorem drops_fwd_length_eq1: ∀b1,b2,f,L1,K1. ⇩*[b1,f] L1 ≘ K1 →
   #I2 #K2 #HLK2 #_ #H destruct
   lapply (IH … HLK2 H12) -f >length_bind >length_bind /2 width=1 by/ (**) (* full auto fails *)
 ]
-qed-.  
+qed-.
 
 (* forward lemmas with finite colength assignment ***************************)
 
index 5fe9c362ea218cfb09319a366f619e2abc5040ed..129f950eb5cbf44dd036cf191775eb7c2e2689d1 100644 (file)
@@ -34,7 +34,7 @@ lemma sex_co_dropable_sn: ∀RN,RP. co_dropable_sn (sex RN RP).
   lapply (drops_fwd_isid … HLK … Hf) -HLK #H0 destruct
   lapply (liftsb_fwd_isid … HJI1 … Hf) -HJI1 #H0 destruct
   elim (coafter_inv_pxx … Hf2) -Hf2 [1,3:* |*: // ] #g1 #g2 #Hg2 #H1 #H2 destruct
-  [ elim (sex_inv_push1 … H) | elim (sex_inv_next1 … H) ] -H #I2 #L2 #HL12 #HI12 #H destruct 
+  [ elim (sex_inv_push1 … H) | elim (sex_inv_next1 … H) ] -H #I2 #L2 #HL12 #HI12 #H destruct
   elim (IH … HL12 … Hg2) -g2 -IH /2 width=1 by isuni_isid/ #K2 #HK12 #HLK2
   lapply (drops_fwd_isid … HLK2 … Hf) -HLK2 #H0 destruct
   /4 width=3 by drops_refl, sex_next, sex_push, isid_push, ex2_intro/
index 1b383569934c5ff49afe90c9b24b45705b723590..9116951c311d6da1f41ca06af4caad072b44c51b 100644 (file)
@@ -41,7 +41,7 @@ interpretation "generic relocation (term)"
    'RLiftStar f T1 T2 = (lifts f T1 T2).
 
 definition liftable2_sn: predicate (relation term) ≝
-                         λR. ∀T1,T2. R T1 T2 → ∀f,U1. ⇧*[f] T1 ≘ U1 → 
+                         λR. ∀T1,T2. R T1 T2 → ∀f,U1. ⇧*[f] T1 ≘ U1 →
                          ∃∃U2. ⇧*[f] T2 ≘ U2 & R U1 U2.
 
 definition deliftable2_sn: predicate (relation term) ≝
@@ -49,7 +49,7 @@ definition deliftable2_sn: predicate (relation term) ≝
                            ∃∃T2. ⇧*[f] T2 ≘ U2 & R T1 T2.
 
 definition liftable2_bi: predicate (relation term) ≝
-                         λR. ∀T1,T2. R T1 T2 → ∀f,U1. ⇧*[f] T1 ≘ U1 → 
+                         λR. ∀T1,T2. R T1 T2 → ∀f,U1. ⇧*[f] T1 ≘ U1 →
                          ∀U2. ⇧*[f] T2 ≘ U2 → R U1 U2.
 
 definition deliftable2_bi: predicate (relation term) ≝
@@ -486,8 +486,8 @@ lemma lifts_uni: ∀n1,n2,T,U. ⇧*[𝐔❴n1❵∘𝐔❴n2❵] T ≘ U → ⇧
               lift_lref_ge_minus lift_lref_ge_minus_eq
 *)
 (* Basic_1: removed theorems 8:
-            lift_lref_gt            
-            lift_head lift_gen_head 
+            lift_lref_gt
+            lift_head lift_gen_head
             lift_weight_map lift_weight lift_weight_add lift_weight_add_O
             lift_tlt_dx
 *)
index be94378433006db33182e900570d67ec2b752c22..0a6831c7211bc81078c195c651cc6adbb9842102 100644 (file)
@@ -21,7 +21,7 @@ include "static_2/relocation/lifts_lifts.ma".
 
 lemma teqo_lifts_sn: liftable2_sn teqo.
 #T1 #T2 #H elim H -T1 -T2 [||| * ]
-[ #s1 #s2 #f #X #H 
+[ #s1 #s2 #f #X #H
   >(lifts_inv_sort1 … H) -H
   /2 width=3 by teqo_sort, ex2_intro/
 | #i #f #X #H
index f314e2b81ccc0d13850772421a494f6d8d54c476..82f6e2a73b75031eee16efbaefe4e10e99157bfd 100644 (file)
@@ -48,7 +48,7 @@ lemma tweq_lifts_sn: liftable2_sn tweq.
 | #V1 #V2 #T1 #T2 #_ #_ #IHV #IHT #f #X #H
   elim (lifts_inv_flat1 … H) -H #W1 #U1 #HVW1 #HTU1 #H destruct
   elim (IHV … HVW1) -V1 #W2 #HVW2 #HW12
-  elim (IHT … HTU1) -T1 #U2 #HTU2 #HU12 
+  elim (IHT … HTU1) -T1 #U2 #HTU2 #HU12
   /3 width=5 by lifts_flat, tweq_cast, ex2_intro/
 ]
 qed-.
index 6247b8686c3b92c04ea24ab3b1a33ed24bbc3ca3..6eb1629fd8609d3416f2aa0f272d6a3b8048ed8b 100644 (file)
@@ -143,7 +143,7 @@ lemma sex_inv_push: ∀RN,RP,f,I1,I2,L1,L2.
 qed-.
 
 lemma sex_inv_tl: ∀RN,RP,f,I1,I2,L1,L2. L1 ⪤[RN,RP,⫱f] L2 →
-                  RN L1 I1 I2 → RP L1 I1 I2 → 
+                  RN L1 I1 I2 → RP L1 I1 I2 →
                   L1.ⓘ{I1} ⪤[RN,RP,f] L2.ⓘ{I2}.
 #RN #RP #f #I1 #I2 #L2 #L2 elim (pn_split f) *
 /2 width=1 by sex_next, sex_push/
@@ -151,7 +151,7 @@ qed-.
 
 (* Basic forward lemmas *****************************************************)
 
-lemma sex_fwd_bind: ∀RN,RP,f,I1,I2,L1,L2. 
+lemma sex_fwd_bind: ∀RN,RP,f,I1,I2,L1,L2.
                     L1.ⓘ{I1} ⪤[RN,RP,f] L2.ⓘ{I2} →
                     L1 ⪤[RN,RP,⫱f] L2.
 #RN #RP #f #I1 #I2 #L1 #L2 #Hf
index 8d1cf55389dfd0df2135d685a5fe8ee1a18138c9..c892868cbbff68842c0366b806b05d385339ae94 100644 (file)
@@ -27,7 +27,7 @@ lemma sex_tc_refl: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
 /3 width=1 by sex_refl, TC_reflexive/ qed.
 
 lemma sex_tc_next_sn: ∀RN,RP. c_reflexive … RN →
-                      ∀f,I2,L1,L2. TC … (sex RN RP f) L1 L2 → ∀I1. RN L1 I1 I2 → 
+                      ∀f,I2,L1,L2. TC … (sex RN RP f) L1 L2 → ∀I1. RN L1 I1 I2 →
                       TC … (sex RN RP (↑f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
 #RN #RP #HRN #f #I2 #L1 #L2 #H @(TC_ind_dx ??????? H) -L1
 /3 width=3 by sex_next, TC_strap, inj/
@@ -41,7 +41,7 @@ lemma sex_tc_next_dx: ∀RN,RP. c_reflexive … RN → c_reflexive … RP →
 qed.
 
 lemma sex_tc_push_sn: ∀RN,RP. c_reflexive … RP →
-                      ∀f,I2,L1,L2. TC … (sex RN RP f) L1 L2 → ∀I1. RP L1 I1 I2 → 
+                      ∀f,I2,L1,L2. TC … (sex RN RP f) L1 L2 → ∀I1. RP L1 I1 I2 →
                       TC … (sex RN RP (⫯f)) (L1.ⓘ{I1}) (L2.ⓘ{I2}).
 #RN #RP #HRP #f #I2 #L1 #L2 #H @(TC_ind_dx ??????? H) -L1
 /3 width=3 by sex_push, TC_strap, inj/
index cafcd5933d3a93be3326273ed69500c8d8608ece..7177448ce79a088be389d14363912e1bff68874e 100644 (file)
@@ -96,7 +96,7 @@ qed-.
 lemma fqus_inv_bind1: ∀b,p,I,G1,G2,L1,L2,V1,T1,T2. ⦃G1,L1,ⓑ{p,I}V1.T1⦄ ⬂*[b] ⦃G2,L2,T2⦄ →
                       ∨∨ ∧∧ G1 = G2 & L1 = L2 & ⓑ{p,I}V1.T1 = T2
                        | ⦃G1,L1,V1⦄ ⬂*[b] ⦃G2,L2,T2⦄
-                       | ∧∧ ⦃G1,L1.ⓑ{I}V1,T1⦄ ⬂*[b] ⦃G2,L2,T2⦄ & b = Ⓣ 
+                       | ∧∧ ⦃G1,L1.ⓑ{I}V1,T1⦄ ⬂*[b] ⦃G2,L2,T2⦄ & b = Ⓣ
                        | ∧∧ ⦃G1,L1.ⓧ,T1⦄ ⬂*[b] ⦃G2,L2,T2⦄ & b = Ⓕ
                        | ∃∃J,L,T. ⦃G1,L,T⦄ ⬂*[b] ⦃G2,L2,T2⦄ & ⇧*[1] T ≘ ⓑ{p,I}V1.T1 & L1 = L.ⓘ{J}.
 #b #p #I #G1 #G2 #L1 #L2 #V1 #T1 #T2 #H elim (fqus_inv_fqu_sn … H) -H * /3 width=1 by and3_intro, or5_intro0/
index 72c46008f1e9f68dabe5418e37b5eb36c64bd103..67ba92a4b7462c45135b2388772c4205ecbb7617 100644 (file)
@@ -32,4 +32,4 @@ lemma fqus_inv_refl_atom3: ∀b,I,G,L,X. ⦃G,L,⓪{I}⦄ ⬂*[b] ⦃G,L,X⦄ 
 #G0 #L0 #T0 #H1 #H2 lapply (fqu_fwd_fw … H1) lapply (fqus_fwd_fw … H2) -H2 -H1
 #H2 #H1 lapply (le_to_lt_to_lt … H2 H1) -G0 -L0 -T0
 #H elim (lt_le_false … H) -H /2 width=1 by monotonic_le_plus_r/
-qed-.  
+qed-.
index 8e94430e64d90aa5eea840cd5bd814bffc481da7..b7e77976ca9ff2500392d74492713a4e4e8ece46 100644 (file)
@@ -33,4 +33,4 @@ lemma fqu_inv_teqx: ∀b,G,L1,L2,T1,T2. ⦃G,L1,T1⦄ ⬂[b] ⦃G,L2,T2⦄ →
                     |L1| = |L2| → T1 ≛ T2 → ⊥.
 #b #G #L1 #L2 #T1 #T2 #H
 @(fqu_inv_teqx_aux … H) // (**) (* full auto fails *)
-qed-. 
+qed-.
index 3b9964b46ce54263e3fcf1f84b371a1e845771ed..6e2a7ffeca2d800e740aca74a582b0f418ada98f 100644 (file)
@@ -31,7 +31,7 @@ qed-.
 
 lemma fqu_wf_ind: ∀b. ∀Q:relation3 …. (
                      ∀G1,L1,T1. (∀G2,L2,T2. ⦃G1,L1,T1⦄ ⬂[b] ⦃G2,L2,T2⦄ → Q G2 L2 T2) →
-                                Q G1 L1 T1
-                             ) → ∀G1,L1,T1. Q G1 L1 T1.
+                                 Q G1 L1 T1
+                              ) → ∀G1,L1,T1. Q G1 L1 T1.
 #b #Q #HQ @(f3_ind … fw) #x #IHx #G1 #L1 #T1 #H destruct /4 width=2 by fqu_fwd_fw/
 qed-.
index 157aac35399b056a0a4447a5c73db435b00220a8..47fd35c021bc5636016f55f85bb7762ae7bb6d7f 100644 (file)
@@ -19,7 +19,7 @@ include "static_2/static/aaa_reqx.ma".
 
 (* Properties with sort-irrelevant equivalence on referred entries **********)
 
-lemma aaa_feqx_conf: ∀G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ≛ ⦃G2,L2,T2⦄ → 
+lemma aaa_feqx_conf: ∀G1,G2,L1,L2,T1,T2. ⦃G1,L1,T1⦄ ≛ ⦃G2,L2,T2⦄ →
                      ∀A. ⦃G1,L1⦄ ⊢ T1 ⁝ A → ⦃G2,L2⦄ ⊢ T2 ⁝ A.
 #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
 /2 width=5 by aaa_teqx_conf_reqx/ qed-.
index a312c25256552dbf99cd59ef32a61603f7a5cded..2a72515f43b41c1b7a3fc5646be71e8db39e7733 100644 (file)
@@ -227,7 +227,7 @@ qed-.
               frees_inv_bind frees_inv_flat frees_inv_bind_O
               frees_lref_eq frees_lref_be frees_weak
               frees_bind_sn frees_bind_dx frees_flat_sn frees_flat_dx
-              frees_lift_ge frees_inv_lift_be frees_inv_lift_ge 
+              frees_lift_ge frees_inv_lift_be frees_inv_lift_ge
               lreq_frees_trans frees_lreq_conf
               llor_atom llor_skip llor_total
               llor_tail_frees llor_tail_cofrees
index 42523bb395637591e9c0e89d191d2384241f50fe..8863fb15e972ae094dfaba49414cd75ceb8e8207 100644 (file)
@@ -39,7 +39,7 @@ fact frees_inv_append_void_aux:
      ∀K. L = ⓧ.K → K ⊢ 𝐅+⦃T⦄ ≘ f.
 #f #L #T #H elim H -f -L -T
 [ /2 width=1 by frees_sort/
-| #f #i #_ #K #H 
+| #f #i #_ #K #H
   elim (append_inv_atom3_sn … H) -H #H1 #H2 destruct
 | #f #I #L #V #_ #IH #K #H
   elim (append_inv_bind3_sn … H) -H * [ | #Y ] #H1 #H2 destruct
index 698427fee1c128d01cda3a9cef95264b05744cc2..bc5a7056babb2ba2b28e75aa6627e699554963f0 100644 (file)
@@ -20,7 +20,7 @@ include "static_2/static/frees_fqup.ma".
 
 (* Advanced properties ******************************************************)
 
-lemma frees_atom_drops: 
+lemma frees_atom_drops:
       ∀b,L,i. ⇩*[b,𝐔❴i❵] L ≘ ⋆ →
       ∀f. 𝐈⦃f⦄ → L ⊢ 𝐅+⦃#i⦄ ≘ ⫯*[i]↑f.
 #b #L elim L -L /2 width=1 by frees_atom/
@@ -31,7 +31,7 @@ lemma frees_atom_drops:
 qed.
 
 lemma frees_pair_drops:
-      ∀f,K,V. K ⊢ 𝐅+⦃V⦄ ≘ f → 
+      ∀f,K,V. K ⊢ 𝐅+⦃V⦄ ≘ f →
       ∀i,I,L. ⇩*[i] L ≘ K.ⓑ{I}V → L ⊢ 𝐅+⦃#i⦄ ≘ ⫯*[i] ↑f.
 #f #K #V #Hf #i elim i -i
 [ #I #L #H lapply (drops_fwd_isid … H ?) -H /2 width=1 by frees_pair/
index feb74eb263f4fc3d49639e1d98d91c8c9b114005..68544e7b0a0fea49bcb6df417a81f79a916786b3 100644 (file)
@@ -109,7 +109,7 @@ lemma frees_ind_void (Q:relation3 …):
         ∀f,i. 𝐈⦃f⦄ →  Q (⋆) (#i) (⫯*[i]↑f)
       ) → (
         ∀f,I,L,V.
-        L ⊢ 𝐅+⦃V⦄ ≘ f →  Q L V f→ Q (L.ⓑ{I}V) (#O) (↑f) 
+        L ⊢ 𝐅+⦃V⦄ ≘ f →  Q L V f→ Q (L.ⓑ{I}V) (#O) (↑f)
       ) → (
         ∀f,I,L. 𝐈⦃f⦄ →  Q (L.ⓤ{I}) (#O) (↑f)
       ) → (
index 588182317cdf7db2a2614bd0b2d76aac30b45061..e97d5e4c1c0c83279caf2d064b302e19e2474ab5 100644 (file)
@@ -19,7 +19,7 @@ include "static_2/static/fsle_fqup.ma".
 
 (* Advanced inversion lemmas ************************************************)
 
-lemma fsle_frees_trans: 
+lemma fsle_frees_trans:
       ∀L1,L2,T1,T2. ⦃L1,T1⦄ ⊆ ⦃L2,T2⦄ →
       ∀f2. L2 ⊢ 𝐅+⦃T2⦄ ≘ f2 →
       ∃∃n1,n2,f1. L1 ⊢ 𝐅+⦃T1⦄ ≘ f1 & L1 ≋ⓧ*[n1,n2] L2 & ⫱*[n1]f1 ⊆ ⫱*[n2]f2.
index e14ca2a6f9c18847776888afb83ef9aa4314a9bc..3a3d1eac8adf6a8175c1de88cf985f3dc410711d 100644 (file)
@@ -74,7 +74,7 @@ interpretation
 
 (* Basic properties *********************************************************)
 
-(* Note: this requires Ⓕ-slicing in cfun since b is unknown in d_liftable_1 *) 
+(* Note: this requires Ⓕ-slicing in cfun since b is unknown in d_liftable_1 *)
 (* Note: this requires multiple relocation *)
 (* Basic 1: includes: sc3_lift *)
 (* Basic 2A1: includes: gcr_lift *)
index efca71482a305d8b830a3bfd2a620c7a7fabaa13..6863c36e0b05a43399fb20f71153363fdc6088dd 100644 (file)
@@ -21,7 +21,7 @@ include "static_2/static/lsuba.ma".
 
 (* Note: the premise 𝐔⦃f⦄ cannot be removed *)
 (* Basic_2A1: includes: lsuba_drop_O1_conf *)
-lemma lsuba_drops_conf_isuni: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 → 
+lemma lsuba_drops_conf_isuni: ∀G,L1,L2. G ⊢ L1 ⫃⁝ L2 →
                               ∀b,f,K1. 𝐔⦃f⦄ → ⇩*[b,f] L1 ≘ K1 →
                               ∃∃K2. G ⊢ K1 ⫃⁝ K2 & ⇩*[b,f] L2 ≘ K2.
 #G #L1 #L2 #H elim H -L1 -L2
index 6c248d9d532bb8977ec271d9f873fff7061a1155..49d435b3c7f78002a085a44232bf766834333f6a 100644 (file)
@@ -74,10 +74,10 @@ fact lsubf_inv_pair1_aux:
      ∀f1,f2,L1,L2. ⦃L1,f1⦄ ⫃𝐅+ ⦃L2,f2⦄ →
      ∀g1,I,K1,X. f1 = ↑g1 → L1 = K1.ⓑ{I}X →
      ∨∨ ∃∃g2,K2. ⦃K1,g1⦄ ⫃𝐅+ ⦃K2,g2⦄ & f2 = ↑g2 & L2 = K2.ⓑ{I}X
-      | ∃∃g,g0,g2,K2,W,V. ⦃K1,g0⦄ ⫃𝐅+ ⦃K2,g2⦄ & 
+      | ∃∃g,g0,g2,K2,W,V. ⦃K1,g0⦄ ⫃𝐅+ ⦃K2,g2⦄ &
           K1 ⊢ 𝐅+⦃V⦄ ≘ g & g0 ⋓ g ≘ g1 & f2 = ↑g2 &
           I = Abbr & X = ⓝW.V & L2 = K2.ⓛW
-      | ∃∃g,g0,g2,J,K2. ⦃K1,g0⦄ ⫃𝐅+ ⦃K2,g2⦄ & 
+      | ∃∃g,g0,g2,J,K2. ⦃K1,g0⦄ ⫃𝐅+ ⦃K2,g2⦄ &
           K1 ⊢ 𝐅+⦃X⦄ ≘ g & g0 ⋓ g ≘ g1 & f2 = ↑g2 & L2 = K2.ⓤ{J}.
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g1 #J #K1 #X #_ #H destruct
@@ -94,10 +94,10 @@ qed-.
 lemma lsubf_inv_pair1:
       ∀g1,f2,I,K1,L2,X. ⦃K1.ⓑ{I}X,↑g1⦄ ⫃𝐅+ ⦃L2,f2⦄ →
       ∨∨ ∃∃g2,K2. ⦃K1,g1⦄ ⫃𝐅+ ⦃K2,g2⦄ & f2 = ↑g2 & L2 = K2.ⓑ{I}X
-       | ∃∃g,g0,g2,K2,W,V. ⦃K1,g0⦄ ⫃𝐅+ ⦃K2,g2⦄ & 
+       | ∃∃g,g0,g2,K2,W,V. ⦃K1,g0⦄ ⫃𝐅+ ⦃K2,g2⦄ &
            K1 ⊢ 𝐅+⦃V⦄ ≘ g & g0 ⋓ g ≘ g1 & f2 = ↑g2 &
            I = Abbr & X = ⓝW.V & L2 = K2.ⓛW
-       | ∃∃g,g0,g2,J,K2. ⦃K1,g0⦄ ⫃𝐅+ ⦃K2,g2⦄ & 
+       | ∃∃g,g0,g2,J,K2. ⦃K1,g0⦄ ⫃𝐅+ ⦃K2,g2⦄ &
            K1 ⊢ 𝐅+⦃X⦄ ≘ g & g0 ⋓ g ≘ g1 & f2 = ↑g2 & L2 = K2.ⓤ{J}.
 /2 width=5 by lsubf_inv_pair1_aux/ qed-.
 
@@ -184,7 +184,7 @@ fact lsubf_inv_unit2_aux:
      ∀f1,f2,L1,L2. ⦃L1,f1⦄ ⫃𝐅+ ⦃L2,f2⦄ →
      ∀g2,I,K2. f2 = ↑g2 → L2 = K2.ⓤ{I} →
      ∨∨ ∃∃g1,K1. ⦃K1,g1⦄ ⫃𝐅+ ⦃K2,g2⦄ & f1 = ↑g1 & L1 = K1.ⓤ{I}
-      | ∃∃g,g0,g1,J,K1,V. ⦃K1,g0⦄ ⫃𝐅+ ⦃K2,g2⦄ & 
+      | ∃∃g,g0,g1,J,K1,V. ⦃K1,g0⦄ ⫃𝐅+ ⦃K2,g2⦄ &
           K1 ⊢ 𝐅+⦃V⦄ ≘ g & g0 ⋓ g ≘ g1 & f1 = ↑g1 & L1 = K1.ⓑ{J}V.
 #f1 #f2 #L1 #L2 * -f1 -f2 -L1 -L2
 [ #f1 #f2 #_ #g2 #J #K2 #_ #H destruct
@@ -200,7 +200,7 @@ qed-.
 lemma lsubf_inv_unit2:
       ∀f1,g2,I,L1,K2. ⦃L1,f1⦄ ⫃𝐅+ ⦃K2.ⓤ{I},↑g2⦄ →
       ∨∨ ∃∃g1,K1. ⦃K1,g1⦄ ⫃𝐅+ ⦃K2,g2⦄ & f1 = ↑g1 & L1 = K1.ⓤ{I}
-       | ∃∃g,g0,g1,J,K1,V. ⦃K1,g0⦄ ⫃𝐅+ ⦃K2,g2⦄ & 
+       | ∃∃g,g0,g1,J,K1,V. ⦃K1,g0⦄ ⫃𝐅+ ⦃K2,g2⦄ &
            K1 ⊢ 𝐅+⦃V⦄ ≘ g & g0 ⋓ g ≘ g1 & f1 = ↑g1 & L1 = K1.ⓑ{J}V.
 /2 width=5 by lsubf_inv_unit2_aux/ qed-.
 
@@ -368,7 +368,7 @@ lemma lsubf_beta_tl_dx:
 #f #f0 #g1 #L1 #V #Hf #Hg1 #f2
 elim (pn_split f2) * #x2 #H2 #L2 #W #HL12 destruct
 [ /3 width=4 by lsubf_push, sor_inv_sle_sn, ex2_intro/
-| @(ex2_intro … (↑g1)) /2 width=5 by lsubf_beta/ (**) (* full auto fails *) 
+| @(ex2_intro … (↑g1)) /2 width=5 by lsubf_beta/ (**) (* full auto fails *)
 ]
 qed-.
 
index 88d2ad9ba4f2ce542d15ce0d2a4f1acae487c134..627bc17799f119d43f9356c27229b2f796d319a9 100644 (file)
@@ -19,7 +19,7 @@ include "static_2/static/lsubf_lsubf.ma".
 
 (* Forward lemmas with restricted refinement for local environments *********)
 
-lemma lsubf_fwd_lsubr_isdiv: 
+lemma lsubf_fwd_lsubr_isdiv:
       ∀f1,f2,L1,L2. ⦃L1,f1⦄ ⫃𝐅+ ⦃L2,f2⦄ → 𝛀⦃f1⦄ → 𝛀⦃f2⦄ → L1 ⫃ L2.
 #f1 #f2 #L1 #L2 #H elim H -f1 -f2 -L1 -L2
 /4 width=3 by lsubr_bind, isdiv_inv_next/
index 5ff763dcbe66125b8476a457ce297d4c059cac00..e1a4fbacd49420a8b88ea27b0ce576701e836d1c 100644 (file)
@@ -42,7 +42,7 @@ fact lsubr_inv_atom1_aux: ∀L1,L2. L1 ⫃ L2 → L1 = ⋆ → L2 = ⋆.
 #L1 #L2 * -L1 -L2 //
 [ #I #L1 #L2 #_ #H destruct
 | #L1 #L2 #V #W #_ #H destruct
-| #I1 #I2 #L1 #L2 #V #_ #H destruct  
+| #I1 #I2 #L1 #L2 #V #_ #H destruct
 ]
 qed-.
 
@@ -108,7 +108,7 @@ lemma lsubr_inv_abst1:
       ∨∨ ∃∃K2. K1 ⫃ K2 & L2 = K2.ⓛW
        | ∃∃I2,K2. K1 ⫃ K2 & L2 = K2.ⓤ{I2}.
 #K1 #L2 #W #H elim (lsubr_inv_bind1 … H) -H *
-/3 width=4 by ex2_2_intro, ex2_intro, or_introl, or_intror/ 
+/3 width=4 by ex2_2_intro, ex2_intro, or_introl, or_intror/
 #K2 #V2 #W2 #_ #_ #H destruct
 qed-.
 
@@ -129,7 +129,7 @@ lemma lsubr_inv_pair2:
 #I #L1 #K2 #W #H elim (lsubr_inv_bind2 … H) -H *
 [ /3 width=3 by ex2_intro, or_introl/
 | #K1 #X #V #HK12 #H1 #H2 destruct /3 width=4 by ex3_2_intro, or_intror/
-| #J1 #J1 #K1 #V #_ #_ #H destruct   
+| #J1 #J1 #K1 #V #_ #_ #H destruct
 ]
 qed-.
 
index 4bcba00a9bfd56fe8d7e346565704d077edabf8a..9876c8fd2dfce995d011343711fed4e3a789c794 100644 (file)
@@ -21,7 +21,7 @@ include "static_2/static/lsubr.ma".
 
 (* Basic_2A1: includes: lsubr_fwd_drop2_pair *)
 lemma lsubr_fwd_drops2_bind:
-      ∀L1,L2. L1 ⫃ L2 → 
+      ∀L1,L2. L1 ⫃ L2 →
       ∀b,f,I,K2. 𝐔⦃f⦄ → ⇩*[b,f] L2 ≘ K2.ⓘ{I} →
       ∨∨ ∃∃K1. K1 ⫃ K2 & ⇩*[b,f] L1 ≘ K1.ⓘ{I}
        | ∃∃K1,W,V. K1 ⫃ K2 & ⇩*[b,f] L1 ≘ K1.ⓓⓝW.V & I = BPair Abst W
index acfb6c4e8a4e9ea879edfee076d6d06225823844..58255521fabe9da38726b6f8bf39c7307de48fb0 100644 (file)
@@ -105,5 +105,5 @@ qed-.
               lleq_fwd_drop_sn lleq_fwd_drop_dx
               lleq_skip lleq_lref lleq_free
               lleq_Y lleq_ge_up lleq_ge
-               
+
 *)
index f190e907ad4bfcc67189c394ca7dc650f87d798a..f7322ee5e7247b93902e70180166b6a33b981400 100644 (file)
@@ -30,7 +30,7 @@ lemma reqx_dec: ∀L1,L2. ∀T:term. Decidable (L1 ≛[T] L2).
 
 (* Main properties **********************************************************)
 
-(* Basic_2A1: uses: lleq_bind lleq_bind_O *) 
+(* Basic_2A1: uses: lleq_bind lleq_bind_O *)
 theorem reqx_bind: ∀p,I,L1,L2,V1,V2,T.
                    L1 ≛[V1] L2 → L1.ⓑ{I}V1 ≛[T] L2.ⓑ{I}V2 →
                    L1 ≛[ⓑ{p,I}V1.T] L2.
@@ -67,7 +67,7 @@ theorem reqx_repl: ∀L1,L2. ∀T:term. L1 ≛[T] L2 →
 
 (* Negated properties *******************************************************)
 
-(* Note: auto works with /4 width=8/ so reqx_canc_sn is preferred **********) 
+(* Note: auto works with /4 width=8/ so reqx_canc_sn is preferred **********)
 (* Basic_2A1: uses: lleq_nlleq_trans *)
 lemma reqx_rneqx_trans: ∀T:term.∀L1,L. L1 ≛[T] L →
                         ∀L2. (L ≛[T] L2 → ⊥) → (L1 ≛[T] L2 → ⊥).
index 07ad9fe0587b434e67a5198c9ea22a2de3a7810b..904a7c5208fdb880ea13ad782a23408a85cf8bd7 100644 (file)
@@ -34,7 +34,7 @@ definition R_confluent2_rex: relation4 (relation3 lenv term term)
                              ∃∃T. R2 L1 T1 T & R1 L2 T2 T.
 
 definition rex_confluent: relation … ≝
-                          λR1,R2. 
+                          λR1,R2.
                           ∀K1,K,V1. K1 ⪤[R1,V1] K → ∀V. R1 K1 V1 V →
                           ∀K2. K ⪤[R2,V] K2 → K ⪤[R2,V1] K2.
 
@@ -319,7 +319,7 @@ lemma rex_isid (R1) (R2):
 /4 width=7 by sex_co_isid, ex2_intro/
 qed-.
 
-lemma rex_unit_sn (R1) (R2): 
+lemma rex_unit_sn (R1) (R2):
       ∀I,K1,L2. K1.ⓤ{I} ⪤[R1,#0] L2 → K1.ⓤ{I} ⪤[R2,#0] L2.
 #R1 #R2 #I #K1 #L2 #H
 elim (rex_inv_zero_unit_sn … H) -H #f #K2 #Hf #HK12 #H destruct
@@ -327,8 +327,8 @@ elim (rex_inv_zero_unit_sn … H) -H #f #K2 #Hf #HK12 #H destruct
 qed-.
 
 (* Basic_2A1: removed theorems 9:
-              llpx_sn_skip llpx_sn_lref llpx_sn_free 
+              llpx_sn_skip llpx_sn_lref llpx_sn_free
               llpx_sn_fwd_lref
-              llpx_sn_Y llpx_sn_ge_up llpx_sn_ge 
-              llpx_sn_fwd_drop_sn llpx_sn_fwd_drop_dx      
+              llpx_sn_Y llpx_sn_ge_up llpx_sn_ge
+              llpx_sn_fwd_drop_sn llpx_sn_fwd_drop_dx
 *)
index f2f47d3d0aa2aea5a7a79a29797cfc9bc4b49e95..9a9df172e0c2955b90293c20b7750a1f93eda46d 100644 (file)
@@ -90,7 +90,7 @@ qed-.
 
 (* Basic_2A1: uses: llpx_sn_inv_lift_O *)
 lemma rex_inv_lifts_bi (R):
-      ∀L1,L2,U. L1 ⪤[R,U] L2 → ∀b,f. 𝐔⦃f⦄ → 
+      ∀L1,L2,U. L1 ⪤[R,U] L2 → ∀b,f. 𝐔⦃f⦄ →
       ∀K1,K2. ⇩*[b,f] L1 ≘ K1 → ⇩*[b,f] L2 ≘ K2 →
       ∀T. ⇧*[f] T ≘ U → K1 ⪤[R,T] K2.
 #R #L1 #L2 #U #HL12 #b #f #Hf #K1 #K2 #HLK1 #HLK2 #T #HTU
index 1945bac9f0a9890126a5b1929b652099e628bb0a..a0906800cef796ac1e170bb89dc1cd48cc5019bf 100644 (file)
@@ -102,7 +102,7 @@ qed-.
 (* Basic eliminators ********************************************************)
 
 (* Basic_1: was: c_tail_ind *)
-(* Basic_2A1: was: lenv_ind_alt *) 
+(* Basic_2A1: was: lenv_ind_alt *)
 lemma lenv_ind_tail: ∀Q:predicate lenv.
                      Q (⋆) → (∀I,L. Q L → Q (ⓘ{I}.L)) → ∀L. Q L.
 #Q #IH1 #IH2 #L @(f_ind … length … L) -L #x #IHx * //
index 63b3e210256687b6f2d0908a23eecde8e0e83347..23a3a91891450d6e341e35421ab60089f82e8085 100644 (file)
@@ -28,4 +28,4 @@ lemma ceq_ext_refl (L): reflexive … (ceq_ext L).
 
 lemma ceq_ext_inv_eq: ∀L,I1,I2. ceq_ext L I1 I2 → I1 = I2.
 #L #I1 #I2 * -I1 -I2 //
-qed-.   
+qed-.
index 020230a93e0cb3da987c34606f29c9d0c4819298..be057f98cd99b86655df6b105ca24adefacbd607 100644 (file)
@@ -19,7 +19,7 @@ include "static_2/syntax/ceq_ext.ma".
 (* Main properties **********************************************************)
 
 theorem ceq_ext_trans: ∀L1,I1,I. ceq_ext L1 I1 I →
-                       ∀L2,I2. ceq_ext L2 I I2 → ∀L3. ceq_ext L3 I1 I2. 
+                       ∀L2,I2. ceq_ext L2 I I2 → ∀L3. ceq_ext L3 I1 I2.
 #L1 #I1 #I * -I1 -I //
 #I1 #V1 #V #HV1 #L2 #Z #H elim (ext2_inv_pair_sn … H) -H //
 qed-.
index ec71ed980b700c4f28ba5ce4d750bd6430b4a935..08a1dc99ebc30a4f5facdb2397ddef4b76adb191 100644 (file)
@@ -21,7 +21,7 @@ include "static_2/syntax/ext2.ma".
 theorem ext2_trans: ∀R. Transitive … R → Transitive … (ext2 R).
 #R #HR #I1 #I #H elim H -I1 -I
 [ #I1 #J #H >(ext2_inv_unit_sn … H) -J /2 width=1 by ext2_unit/
-| #I1 #V1 #V #HV1 #J #H elim (ext2_inv_pair_sn … H) -H 
+| #I1 #V1 #V #HV1 #J #H elim (ext2_inv_pair_sn … H) -H
   #V2 #HV2 #H destruct /3 width=3 by ext2_pair/
 ]
 qed-.
index 35365d802ca8d3d12a9007de834905e5d16ac715..890126130ba9f041cfb407ce38cb75a359fd11ca 100644 (file)
@@ -44,7 +44,7 @@ lemma eq_genv_dec: ∀G1,G2:genv. Decidable (G1 = G2).
 #G1 elim G1 -G1 [| #G1 #I1 #T1 #IHG1 ] * [2,4: #G2 #I2 #T2 ]
 [3: /2 width=1 by or_introl/
 |2: elim (eq_bind2_dec I1 I2) #HI
-    [ elim (IHG1 G2) -IHG1 #HG 
+    [ elim (IHG1 G2) -IHG1 #HG
       [ elim (eq_term_dec T1 T2) #HT /2 width=1 by or_introl/ ]
     ]
 ]
index 52dfc3516e8b355a9b86a70543b3c462a606f2c6..162b21fa059d2df9dec535a05447996b29754ed0 100644 (file)
@@ -54,7 +54,7 @@ qed-.
 (* Basic_2A1: was: length_inv_pos_sn *)
 lemma length_inv_succ_sn: ∀n,L. ↑n = |L| →
                           ∃∃I,K. n = |K| & L = K. ⓘ{I}.
-#n #L #H lapply (sym_eq ??? H) -H 
+#n #L #H lapply (sym_eq ??? H) -H
 #H elim (length_inv_succ_dx … H) -H /2 width=4 by ex2_2_intro/
 qed-.
 
index e6d2fcbfc37a30a8714ffa23f1451faf90f02da6..a81857aeb8a888c6af53346c1ed42c947adcbbdd 100644 (file)
@@ -98,7 +98,7 @@ lemma lveq_inv_bind: ∀I1,I2,K1,K2. K1.ⓘ{I1} ≋ⓧ*[0,0] K2.ⓘ{I2} → K1 
 #I1 #I2 #K1 #K2 #H
 elim (lveq_inv_zero … H) -H * [| #Z1 #Z2 #Y1 #Y2 #HY ] #H1 #H2 destruct //
 qed-.
-  
+
 lemma lveq_inv_atom_atom: ∀n1,n2. ⋆ ≋ⓧ*[n1,n2] ⋆ → ∧∧ 0 = n1 & 0 = n2.
 * [2: #n1 ] * [2,4: #n2 ] #H
 [ elim (lveq_inv_succ … H)
index 8ae0a99bec6b6407d8b6ff454012111427c3ed63..7f77340e77d8cdad5f3691b73373630967733587 100644 (file)
@@ -62,7 +62,7 @@ lemma lveq_inj_length: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →
                        |L1| = |L2| → ∧∧ 0 = n1 & 0 = n2.
 #L1 #L2 #n1 #n2 #H #HL
 elim (lveq_fwd_length … H) -H
->HL -HL /2 width=1 by conj/ 
+>HL -HL /2 width=1 by conj/
 qed-.
 
 lemma lveq_fwd_length_plus: ∀L1,L2,n1,n2. L1 ≋ⓧ*[n1,n2] L2 →
index b7e10f851883233aae42c87faa1966256653c025..d33515ef80dfb47e04a986bcdf781b1a77e1ebf3 100644 (file)
@@ -91,7 +91,7 @@ elim (lt_or_ge s2 s1) #Hs
     | /3 width=2 by ex_intro, or_introl/
     ]
   | -IH @or_introl @(ex_intro … 1) // (**) (* auto fails *)
-  | lapply (transitive_lt s1 ??? Hs21) [ /2 width=1 by next_lt/ ] -Hs12 #Hs12 
+  | lapply (transitive_lt s1 ??? Hs21) [ /2 width=1 by next_lt/ ] -Hs12 #Hs12
     elim (IH (s2-⫯[h]s1)) -IH
     [3: /3 width=1 by next_lt, monotonic_lt_minus_r/ ]
     >minus_minus_m_m [2,4: /2 width=1 by lt_to_le/ ] -Hs21
index 6c1ddd17efa049a5d101af6e7c78f1ab09faafb3..fe295148cdb6da866f2a5f259ff28c84ccee00f3 100644 (file)
@@ -173,7 +173,7 @@ qed-.
 (* Negated inversion lemmas *************************************************)
 
 lemma tneqx_inv_pair: ∀I1,I2,V1,V2,T1,T2.
-                      (②{I1}V1.T1 ≛ ②{I2}V2.T2 → ⊥) → 
+                      (②{I1}V1.T1 ≛ ②{I2}V2.T2 → ⊥) →
                       ∨∨ I1 = I2 → ⊥
                       |  (V1 ≛ V2 → ⊥)
                       |  (T1 ≛ T2 → ⊥).
index 1d29c33aa24856177bb4d3e671557c61ccf24822..39cf1e3538800bcdfb3c3ad3d0073f254664b3da 100644 (file)
@@ -24,7 +24,7 @@ lemma teqx_tweq: ∀T1,T2. T1 ≛ T2 → T1 ≅ T2.
 [ /1 width=1 by tweq_sort/
 | /1 width=1 by tweq_lref/
 | /1 width=1 by tweq_gref/
-| cases p -p /2 width=1 by tweq_abbr_pos, tweq_abbr_neg/  
+| cases p -p /2 width=1 by tweq_abbr_pos, tweq_abbr_neg/
 | /1 width=1 by tweq_abst/
 | /2 width=1 by tweq_appl/
 | /2 width=1 by tweq_cast/
index ac892add2adbccce95f491fb7412b56a1d6c13d3..83796e3520ba58d05b227036a59f827c59c805be 100644 (file)
@@ -22,7 +22,7 @@ table {
         [ { "generic reducibility" * } {
              [ [ "restricted refinement for lenvs" ] "lsubc" + "( ? ⊢ ? ⫃[?] ? )" "lsubc_drops" + "lsubc_lsubr" + "lsubc_lsuba" * ]
              [ [ "candidates" ] "gcp_cr" + "( ⦃?,?,?⦄ ϵ[?] 〚?〛 )" "gcp_aaa" * ]
-             [ [ "computation properties" ] "gcp" *] 
+             [ [ "computation properties" ] "gcp" *]
           }
         ]
         [ { "atomic arity assignment" * } {
@@ -106,7 +106,7 @@ table {
              [ [ "preorder" ] "acle" + "( ? ⊆ ? )"  "acle_acle" * ]
              [ [ "properties" ] "ac" + "( 𝟏 )" + "( 𝟐 )" + "( 𝛚 )" * ]
           }
-        ]   
+        ]
         [ { "equivalence up to exclusion binders" * } {
              [ [ "for lenvs" ] "lveq" + "( ? ≋ⓧ*[?,?] ? )" "lveq_length" + "lveq_lveq" * ]
           }
index 2a2800a88dcd8666e07f66096240dc91cf670ceb..99ea6775b0cf26ebf00422b3ebfe112a4dc0f1c8 100644 (file)
@@ -3,587 +3,587 @@ name "core"
 table {
   [ class "gray" [ "Version 2A1" ]             class "gray"    [ "Version 2A2" ] * ]
 
-  [ class "" [ "aarity" ]                     class "green"   [ "aarity" ]                     * ]
+  [ class "" [ "aarity" ]                      class "green"   [ "aarity" ]                     * ]
   [ class "" [ "destruct_apair_apair_aux" ]    class "green"   [ "destruct_apair_apair_aux" ]   * ]
-  [ class "" [ "discr_apair_xy_x" ]           class "green"   [ "discr_apair_xy_x" ]           * ]
-  [ class "" [ "discr_tpair_xy_y" ]           class "green"   [ "discr_apair_xy_y" ]           * ]
-  [ class "" [ "eq_aarity_dec" ]              class "green"   [ "eq_aarity_dec" ]              * ]
-  
+  [ class "" [ "discr_apair_xy_x" ]            class "green"   [ "discr_apair_xy_x" ]           * ]
+  [ class "" [ "discr_tpair_xy_y" ]            class "green"   [ "discr_apair_xy_y" ]           * ]
+  [ class "" [ "eq_aarity_dec" ]               class "green"   [ "eq_aarity_dec" ]              * ]
+
   [ class "" [ "item0" ]                       class "green"   [ "item0" ]                      * ]
-  [ class "" [ "bind2" ]                      class "green"   [ "bind2" ]                      * ]
-  [ class "" [ "flat2" ]                      class "green"   [ "flat2" ]                      * ]
-  [ class "" [ "item2" ]                      class "green"   [ "item2" ]                      * ]
+  [ class "" [ "bind2" ]                       class "green"   [ "bind2" ]                      * ]
+  [ class "" [ "flat2" ]                       class "green"   [ "flat2" ]                      * ]
+  [ class "" [ "item2" ]                       class "green"   [ "item2" ]                      * ]
   [ class "" [ "destruct_sort_sort_aux" ]      class "green"   [ "destruct_sort_sort_aux" ]     * ]
-  [ class "" [ "eq_item0_dec" ]                       class "green"   [ "eq_item0_dec" ]               * ]
-  [ class "" [ "eq_bind2_dec" ]                       class "green"   [ "eq_bind2_dec" ]               * ]
-  [ class "" [ "eq_flat2_dec" ]                       class "green"   [ "eq_flat2_dec" ]               * ]
-  [ class "" [ "eq_item2_dec" ]                       class "green"   [ "eq_item2_dec" ]               * ]
+  [ class "" [ "eq_item0_dec" ]                class "green"   [ "eq_item0_dec" ]               * ]
+  [ class "" [ "eq_bind2_dec" ]                class "green"   [ "eq_bind2_dec" ]               * ]
+  [ class "" [ "eq_flat2_dec" ]                class "green"   [ "eq_flat2_dec" ]               * ]
+  [ class "" [ "eq_item2_dec" ]                class "green"   [ "eq_item2_dec" ]               * ]
 
-  [ class "" [ "sh" ]                         class "green"   [ "sh" ]                         * ]
-  [ class "" [ "sh_N" ]                               class "green"   [ "sh_N" ]                       * ]
-  [ class "" [ "nexts_le" ]                   class "green"   [ "nexts_le" ]                   * ]
-  [ class "" [ "nexts_lt" ]                   class "green"   [ "nexts_lt" ]                   * ]
-  [ class "" [ "nexts_dec" ]                  class "green"   [ "nexts_dec" ]                  * ]
-  [ class "" [ "nexts_inj" ]                  class "green"   [ "nexts_inj" ]                  * ]
+  [ class "" [ "sh" ]                          class "green"   [ "sh" ]                         * ]
+  [ class "" [ "sh_N" ]                        class "green"   [ "sh_N" ]                       * ]
+  [ class "" [ "nexts_le" ]                    class "green"   [ "nexts_le" ]                   * ]
+  [ class "" [ "nexts_lt" ]                    class "green"   [ "nexts_lt" ]                   * ]
+  [ class "" [ "nexts_dec" ]                   class "green"   [ "nexts_dec" ]                  * ]
+  [ class "" [ "nexts_inj" ]                   class "green"   [ "nexts_inj" ]                  * ]
 
-  [ class "" [ "sd" ]                         class "green"   [ "sd" ]                         * ]
-  [ class "" [ "deg_O" ]                      class "green"   [ "deg_O" ]                      * ]
-  [ class "" [ "sd_O" ]                               class "green"   [ "sd_O" ]                       * ]
-  [ class "" [ "deg_SO" ]                     class "green"   [ "deg_SO" ]                     * ]
-  [ class "" [ "deg_SO_inv_pos_aux" ]         class "green"   [ "deg_SO_inv_succ_aux" ]        * ]
-  [ class "" [ "deg_SO_inv_pos" ]             class "green"   [ "deg_SO_inv_succ" ]            * ]
-  [ class "" [ "deg_SO_refl" ]                class "green"   [ "deg_SO_refl" ]                * ]
-  [ class "" [ "deg_SO_gt" ]                  class "green"   [ "deg_SO_gt" ]                  * ]
-  [ class "" [ "sd_SO" ]                      class "green"   [ "sd_SO" ]                      * ]
-  [ class "" [ "sd_d" ]                               class "green"   [ "sd_d" ]                       * ]
-  [ class "" [ "deg_inv_pred" ]                       class "green"   [ "deg_inv_pred" ]               * ]
-  [ class "" [ "deg_inv_prec" ]                       class "green"   [ "deg_inv_prec" ]               * ]
-  [ class "" [ "deg_iter" ]                   class "green"   [ "deg_iter" ]                   * ]
-  [ class "" [ "deg_next_SO" ]                class "green"   [ "deg_next_SO" ]                * ]
-  [ class "" [ "sd_d_SS" ]                    class "green"   [ "sd_d_SS" ]                    * ]
-  [ class "" [ "sd_d_correct" ]                       class "green"   [ "sd_d_correct" ]               * ]
+  [ class "" [ "sd" ]                          class "green"   [ "sd" ]                         * ]
+  [ class "" [ "deg_O" ]                       class "green"   [ "deg_O" ]                      * ]
+  [ class "" [ "sd_O" ]                        class "green"   [ "sd_O" ]                       * ]
+  [ class "" [ "deg_SO" ]                      class "green"   [ "deg_SO" ]                     * ]
+  [ class "" [ "deg_SO_inv_pos_aux" ]          class "green"   [ "deg_SO_inv_succ_aux" ]        * ]
+  [ class "" [ "deg_SO_inv_pos" ]              class "green"   [ "deg_SO_inv_succ" ]            * ]
+  [ class "" [ "deg_SO_refl" ]                 class "green"   [ "deg_SO_refl" ]                * ]
+  [ class "" [ "deg_SO_gt" ]                   class "green"   [ "deg_SO_gt" ]                  * ]
+  [ class "" [ "sd_SO" ]                       class "green"   [ "sd_SO" ]                      * ]
+  [ class "" [ "sd_d" ]                        class "green"   [ "sd_d" ]                       * ]
+  [ class "" [ "deg_inv_pred" ]                class "green"   [ "deg_inv_pred" ]               * ]
+  [ class "" [ "deg_inv_prec" ]                class "green"   [ "deg_inv_prec" ]               * ]
+  [ class "" [ "deg_iter" ]                    class "green"   [ "deg_iter" ]                   * ]
+  [ class "" [ "deg_next_SO" ]                 class "green"   [ "deg_next_SO" ]                * ]
+  [ class "" [ "sd_d_SS" ]                     class "green"   [ "sd_d_SS" ]                    * ]
+  [ class "" [ "sd_d_correct" ]                class "green"   [ "sd_d_correct" ]               * ]
 
-  [ class "" [ "term" ]                               class "green"   [ "term" ]                       * ]
-  [ class "" [ "eq_term_dec" ]                class "green"   [ "eq_term_dec" ]                * ]
+  [ class "" [ "term" ]                        class "green"   [ "term" ]                       * ]
+  [ class "" [ "eq_term_dec" ]                 class "green"   [ "eq_term_dec" ]                * ]
   [ class "" [ "destruct_tatom_tatom_aux" ]    class "green"   [ "destruct_tatom_tatom_aux" ]   * ]
   [ class "" [ "destruct_tpair_tpair_aux" ]    class "green"   [ "destruct_tpair_tpair_aux" ]   * ]
-  [ class "" [ "discr_tpair_xy_x" ]           class "green"   [ "discr_tpair_xy_x" ]           * ]
-  [ class "" [ "discr_tpair_xy_y" ]           class "green"   [ "discr_tpair_xy_y" ]           * ]
+  [ class "" [ "discr_tpair_xy_x" ]            class "green"   [ "discr_tpair_xy_x" ]           * ]
+  [ class "" [ "discr_tpair_xy_y" ]            class "green"   [ "discr_tpair_xy_y" ]           * ]
   [ class "" [ "eq_false_inv_tpair_sn" ]       class "green"   [ "eq_false_inv_tpair_sn" ]      * ]
   [ class "" [ "eq_false_inv_tpair_dx" ]       class "green"   [ "eq_false_inv_tpair_dx" ]      * ]
 
-  [ class "" [ "tw" ]                         class "green"   [ "tw" ]                         * ]
-  [ class "" [ "tw_pos" ]                     class "green"   [ "tw_pos" ]                     * ]
+  [ class "" [ "tw" ]                          class "green"   [ "tw" ]                         * ]
+  [ class "" [ "tw_pos" ]                      class "green"   [ "tw_pos" ]                     * ]
 
-  [ class "" [ "simple" ]                     class "green"   [ "simple" ]                     * ]
-  [ class "" [ "simple_inv_bind_aux" ]        class "green"   [ "simple_inv_bind_aux" ]        * ]
-  [ class "" [ "simple_inv_bind" ]            class "green"   [ "simple_inv_bind" ]            * ]
-  [ class "" [ "simple_inv_pair" ]            class "green"   [ "simple_inv_pair" ]            * ]
+  [ class "" [ "simple" ]                      class "green"   [ "simple" ]                     * ]
+  [ class "" [ "simple_inv_bind_aux" ]         class "green"   [ "simple_inv_bind_aux" ]        * ]
+  [ class "" [ "simple_inv_bind" ]             class "green"   [ "simple_inv_bind" ]            * ]
+  [ class "" [ "simple_inv_pair" ]             class "green"   [ "simple_inv_pair" ]            * ]
 
-  [ class "" [ "lenv" ]                               class "green"   [ "lenv" ]                       * ]
-  [ class "" [ "eq_lenv_dec" ]                class "green"   [ "eq_lenv_dec" ]                * ]
+  [ class "" [ "lenv" ]                        class "green"   [ "lenv" ]                       * ]
+  [ class "" [ "eq_lenv_dec" ]                 class "green"   [ "eq_lenv_dec" ]                * ]
   [ class "" [ "destruct_lpair_lpair_aux" ]    class "green"   [ "destruct_lpair_lpair_aux" ]   * ]
-  [ class "" [ "discr_lpair_x_xy" ]           class "green"   [ "discr_lpair_x_xy" ]           * ]
-  [ class "" [ "" ]                            class ""        [ "discr_lpair_xy_x" ]           * ] 
-  [ class "" [ "" ]                            class ""        [ "ceq" ]                        * ] 
-  [ class "" [ "" ]                            class ""        [ "cfull" ]                      * ] 
+  [ class "" [ "discr_lpair_x_xy" ]            class "green"   [ "discr_lpair_x_xy" ]           * ]
+  [ class "" [ "" ]                            class ""        [ "discr_lpair_xy_x" ]           * ]
+  [ class "" [ "" ]                            class ""        [ "ceq" ]                        * ]
+  [ class "" [ "" ]                            class ""        [ "cfull" ]                      * ]
 
-  [ class "" [ "lw" ]                         class "green"   [ "lw" ]                         * ]
-  [ class "" [ "lw_pair" ]                    class "green"   [ "lw_pair" ]                    * ]
+  [ class "" [ "lw" ]                          class "green"   [ "lw" ]                         * ]
+  [ class "" [ "lw_pair" ]                     class "green"   [ "lw_pair" ]                    * ]
 
-  [ class "" [ "length" ]                     class "green"   [ "length" ]                     * ]
-  [ class "" [ "length_inv_zero_dx" ]         class "green"   [ "length_inv_zero_dx" ]         * ]
-  [ class "" [ "length_inv_zero_sn" ]         class "green"   [ "length_inv_zero_sn" ]         * ]
-  [ class "" [ "length_inv_pos_dx" ]          class "green"   [ "length_inv_succ_dx" ]         * ]
-  [ class "" [ "length_inv_pos_sn" ]          class "green"   [ "length_inv_succ_sn" ]         * ]
-  [ class "" [ "" ]                            class ""        [ "length_atom" ]                * ] 
-  [ class "" [ "" ]                            class ""        [ "length_pair" ]                * ] 
+  [ class "" [ "length" ]                      class "green"   [ "length" ]                     * ]
+  [ class "" [ "length_inv_zero_dx" ]          class "green"   [ "length_inv_zero_dx" ]         * ]
+  [ class "" [ "length_inv_zero_sn" ]          class "green"   [ "length_inv_zero_sn" ]         * ]
+  [ class "" [ "length_inv_pos_dx" ]           class "green"   [ "length_inv_succ_dx" ]         * ]
+  [ class "" [ "length_inv_pos_sn" ]           class "green"   [ "length_inv_succ_sn" ]         * ]
+  [ class "" [ "" ]                            class ""        [ "length_atom" ]                * ]
+  [ class "" [ "" ]                            class ""        [ "length_pair" ]                * ]
 
-  [ class "" [ "genv" ]                               class "green"   [ "genv" ]                       * ]
-  [ class "" [ "eq_genv_dec" ]                class "green"   [ "eq_genv_dec" ]                * ]
+  [ class "" [ "genv" ]                        class "green"   [ "genv" ]                       * ]
+  [ class "" [ "eq_genv_dec" ]                 class "green"   [ "eq_genv_dec" ]                * ]
 
-  [ class "" [ "rfw" ]                        class "green"   [ "rfw" ]                        * ]
-  [ class "" [ "rfw_shift" ]                  class "green"   [ "rfw_shift" ]                  * ]
-  [ class "" [ "rfw_tpair_sn" ]                       class "green"   [ "rfw_tpair_sn" ]               * ]
-  [ class "" [ "rfw_tpair_dx" ]                       class "green"   [ "rfw_tpair_dx" ]               * ]
-  [ class "" [ "rfw_lpair_sn" ]                       class "green"   [ "rfw_lpair_sn" ]               * ]
-  [ class "" [ "rfw_lpair_dx" ]                       class "green"   [ "rfw_lpair_dx" ]               * ]
+  [ class "" [ "rfw" ]                         class "green"   [ "rfw" ]                        * ]
+  [ class "" [ "rfw_shift" ]                   class "green"   [ "rfw_shift" ]                  * ]
+  [ class "" [ "rfw_tpair_sn" ]                class "green"   [ "rfw_tpair_sn" ]               * ]
+  [ class "" [ "rfw_tpair_dx" ]                class "green"   [ "rfw_tpair_dx" ]               * ]
+  [ class "" [ "rfw_lpair_sn" ]                class "green"   [ "rfw_lpair_sn" ]               * ]
+  [ class "" [ "rfw_lpair_dx" ]                class "green"   [ "rfw_lpair_dx" ]               * ]
 
-  [ class "" [ "da" ]                         class "orange"  [ "da" ]                         * ]
-  [ class "" [ "da_inv_sort_aux" ]            class "orange"  [ "da_inv_sort_aux" ]            * ]
-  [ class "" [ "da_inv_sort" ]                class "orange"  [ "da_inv_sort" ]                * ]
-  [ class "" [ "da_inv_lref_aux" ]            class "orange"  [ "da_inv_lref_aux" ]            * ]
-  [ class "" [ "da_inv_lref" ]                class "orange"  [ "da_inv_lref" ]                * ]
-  [ class "" [ "da_inv_gref_aux" ]            class "orange"  [ "da_inv_gref_aux" ]            * ]
-  [ class "" [ "da_inv_gref" ]                class "orange"  [ "da_inv_gref" ]                * ]
-  [ class "" [ "da_inv_bind_aux" ]            class "orange"  [ "da_inv_bind_aux" ]            * ]
-  [ class "" [ "da_inv_bind" ]                class "orange"  [ "da_inv_bind" ]                * ]
-  [ class "" [ "da_inv_flat_aux" ]            class "orange"  [ "da_inv_flat_aux" ]            * ]
-  [ class "" [ "da_inv_flat" ]                class "orange"  [ "da_inv_flat" ]                * ]
+  [ class "" [ "da" ]                          class "orange"  [ "da" ]                         * ]
+  [ class "" [ "da_inv_sort_aux" ]             class "orange"  [ "da_inv_sort_aux" ]            * ]
+  [ class "" [ "da_inv_sort" ]                 class "orange"  [ "da_inv_sort" ]                * ]
+  [ class "" [ "da_inv_lref_aux" ]             class "orange"  [ "da_inv_lref_aux" ]            * ]
+  [ class "" [ "da_inv_lref" ]                 class "orange"  [ "da_inv_lref" ]                * ]
+  [ class "" [ "da_inv_gref_aux" ]             class "orange"  [ "da_inv_gref_aux" ]            * ]
+  [ class "" [ "da_inv_gref" ]                 class "orange"  [ "da_inv_gref" ]                * ]
+  [ class "" [ "da_inv_bind_aux" ]             class "orange"  [ "da_inv_bind_aux" ]            * ]
+  [ class "" [ "da_inv_bind" ]                 class "orange"  [ "da_inv_bind" ]                * ]
+  [ class "" [ "da_inv_flat_aux" ]             class "orange"  [ "da_inv_flat_aux" ]            * ]
+  [ class "" [ "da_inv_flat" ]                 class "orange"  [ "da_inv_flat" ]                * ]
 
-  [ class "" [ "lstas" ]                      class "orange"  [ "lstas" ]                      * ]
-  [ class "" [ "lstas_inv_sort1_aux" ]        class "orange"  [ "lstas_inv_sort1_aux" ]        * ]
-  [ class "" [ "lstas_inv_sort1" ]            class "orange"  [ "lstas_inv_sort1" ]            * ]
-  [ class "" [ "lstas_inv_lref1_aux" ]        class "orange"  [ "lstas_inv_lref1_aux" ]        * ]
-  [ class "" [ "lstas_inv_lref1" ]            class "orange"  [ "lstas_inv_lref1" ]            * ]
-  [ class "" [ "lstas_inv_lref1_O" ]          class "orange"  [ "lstas_inv_lref1_O" ]          * ]
-  [ class "" [ "lstas_inv_lref1_S" ]          class "orange"  [ "lstas_inv_lref1_S" ]          * ]
-  [ class "" [ "lstas_inv_gref1_aux" ]        class "orange"  [ "lstas_inv_gref1_aux" ]        * ]
-  [ class "" [ "lstas_inv_gref1" ]            class "orange"  [ "lstas_inv_gref1" ]            * ]
-  [ class "" [ "lstas_inv_bind1_aux" ]        class "orange"  [ "lstas_inv_bind1_aux" ]        * ]
-  [ class "" [ "lstas_inv_bind1" ]            class "orange"  [ "lstas_inv_bind1" ]            * ]
-  [ class "" [ "lstas_inv_appl1_aux" ]        class "orange"  [ "lstas_inv_appl1_aux" ]        * ]
-  [ class "" [ "lstas_inv_appl1" ]            class "orange"  [ "lstas_inv_appl1" ]            * ]
-  [ class "" [ "lstas_inv_cast1_aux" ]        class "orange"  [ "lstas_inv_cast1_aux" ]        * ]
-  [ class "" [ "lstas_inv_cast1" ]            class "orange"  [ "lstas_inv_cast1" ]            * ]
+  [ class "" [ "lstas" ]                       class "orange"  [ "lstas" ]                      * ]
+  [ class "" [ "lstas_inv_sort1_aux" ]         class "orange"  [ "lstas_inv_sort1_aux" ]        * ]
+  [ class "" [ "lstas_inv_sort1" ]             class "orange"  [ "lstas_inv_sort1" ]            * ]
+  [ class "" [ "lstas_inv_lref1_aux" ]         class "orange"  [ "lstas_inv_lref1_aux" ]        * ]
+  [ class "" [ "lstas_inv_lref1" ]             class "orange"  [ "lstas_inv_lref1" ]            * ]
+  [ class "" [ "lstas_inv_lref1_O" ]           class "orange"  [ "lstas_inv_lref1_O" ]          * ]
+  [ class "" [ "lstas_inv_lref1_S" ]           class "orange"  [ "lstas_inv_lref1_S" ]          * ]
+  [ class "" [ "lstas_inv_gref1_aux" ]         class "orange"  [ "lstas_inv_gref1_aux" ]        * ]
+  [ class "" [ "lstas_inv_gref1" ]             class "orange"  [ "lstas_inv_gref1" ]            * ]
+  [ class "" [ "lstas_inv_bind1_aux" ]         class "orange"  [ "lstas_inv_bind1_aux" ]        * ]
+  [ class "" [ "lstas_inv_bind1" ]             class "orange"  [ "lstas_inv_bind1" ]            * ]
+  [ class "" [ "lstas_inv_appl1_aux" ]         class "orange"  [ "lstas_inv_appl1_aux" ]        * ]
+  [ class "" [ "lstas_inv_appl1" ]             class "orange"  [ "lstas_inv_appl1" ]            * ]
+  [ class "" [ "lstas_inv_cast1_aux" ]         class "orange"  [ "lstas_inv_cast1_aux" ]        * ]
+  [ class "" [ "lstas_inv_cast1" ]             class "orange"  [ "lstas_inv_cast1" ]            * ]
 
-  [ class "" [ "" ]                            class "" [ "" ]                           * ] 
+  [ class "" [ "" ]                            class "" [ "" ]                           * ]
 
-  [ class "" [ "lift" ]                               class "" [ "lift" ]                       * ]
-  [ class "" [ "lift_inv_O2_aux" ]            class "" [ "lift_inv_O2_aux" ]            * ]
-  [ class "" [ "lift_inv_O2" ]                class "" [ "lift_inv_O2" ]                * ]
-  [ class "" [ "lift_inv_sort1_aux" ]         class "" [ "lift_inv_sort1_aux" ]         * ]
-  [ class "" [ "lift_inv_sort1" ]             class "" [ "lift_inv_sort1" ]             * ]
-  [ class "" [ "lift_inv_lref1_aux" ]         class "" [ "lift_inv_lref1_aux" ]         * ]
-  [ class "" [ "lift_inv_lref1" ]             class "" [ "lift_inv_lref1" ]             * ]
-  [ class "" [ "lift_inv_lref1_lt" ]          class "" [ "lift_inv_lref1_lt" ]          * ]
-  [ class "" [ "lift_inv_lref1_ge" ]          class "" [ "lift_inv_lref1_ge" ]          * ]
-  [ class "" [ "lift_inv_gref1_aux" ]         class "" [ "lift_inv_gref1_aux" ]         * ]
-  [ class "" [ "lift_inv_gref1" ]             class "" [ "lift_inv_gref1" ]             * ]
-  [ class "" [ "lift_inv_bind1_aux" ]         class "" [ "lift_inv_bind1_aux" ]         * ]
-  [ class "" [ "lift_inv_bind1" ]             class "" [ "lift_inv_bind1" ]             * ]
-  [ class "" [ "lift_inv_flat1_aux" ]         class "" [ "lift_inv_flat1_aux" ]         * ]
-  [ class "" [ "lift_inv_flat1" ]             class "" [ "lift_inv_flat1" ]             * ]
-  [ class "" [ "lift_inv_sort2_aux" ]         class "" [ "lift_inv_sort2_aux" ]         * ]
-  [ class "" [ "lift_inv_sort2" ]             class "" [ "lift_inv_sort2" ]             * ]
-  [ class "" [ "lift_inv_lref2_aux" ]         class "" [ "lift_inv_lref2_aux" ]         * ]
-  [ class "" [ "lift_inv_lref2" ]             class "" [ "lift_inv_lref2" ]             * ]
-  [ class "" [ "lift_inv_lref2_lt" ]          class "" [ "lift_inv_lref2_lt" ]          * ]
-  [ class "" [ "lift_inv_lref2_be" ]          class "" [ "lift_inv_lref2_be" ]          * ]
-  [ class "" [ "lift_inv_lref2_ge" ]          class "" [ "lift_inv_lref2_ge" ]          * ]
-  [ class "" [ "lift_inv_gref2_aux" ]         class "" [ "lift_inv_gref2_aux" ]         * ]
-  [ class "" [ "lift_inv_gref2" ]             class "" [ "lift_inv_gref2" ]             * ]
-  [ class "" [ "lift_inv_bind2_aux" ]         class "" [ "lift_inv_bind2_aux" ]         * ]
-  [ class "" [ "lift_inv_bind2" ]             class "" [ "lift_inv_bind2" ]             * ]
-  [ class "" [ "lift_inv_flat2_aux" ]         class "" [ "lift_inv_flat2_aux" ]         * ]
-  [ class "" [ "lift_inv_flat2" ]             class "" [ "lift_inv_flat2" ]             * ]
-  [ class "" [ "lift_inv_pair_xy_x" ]         class "" [ "lift_inv_pair_xy_x" ]         * ]
-  [ class "" [ "lift_inv_pair_xy_y" ]         class "" [ "lift_inv_pair_xy_y" ]         * ]
-  [ class "" [ "lift_fwd_pair1" ]             class "" [ "lift_fwd_pair1" ]             * ]
-  [ class "" [ "lift_fwd_pair2" ]             class "" [ "lift_fwd_pair2" ]             * ]
-  [ class "" [ "lift_fwd_tw" ]                class "" [ "lift_fwd_tw" ]                * ]
-  [ class "" [ "lift_simple_dx" ]             class "" [ "lift_simple_dx" ]             * ]
-  [ class "" [ "lift_simple_sn" ]             class "" [ "lift_simple_sn" ]             * ]
-  [ class "" [ "lift_lref_ge_minus" ]         class "" [ "lift_lref_ge_minus" ]         * ]
+  [ class "" [ "lift" ]                        class "" [ "lift" ]                       * ]
+  [ class "" [ "lift_inv_O2_aux" ]             class "" [ "lift_inv_O2_aux" ]            * ]
+  [ class "" [ "lift_inv_O2" ]                 class "" [ "lift_inv_O2" ]                * ]
+  [ class "" [ "lift_inv_sort1_aux" ]          class "" [ "lift_inv_sort1_aux" ]         * ]
+  [ class "" [ "lift_inv_sort1" ]              class "" [ "lift_inv_sort1" ]             * ]
+  [ class "" [ "lift_inv_lref1_aux" ]          class "" [ "lift_inv_lref1_aux" ]         * ]
+  [ class "" [ "lift_inv_lref1" ]              class "" [ "lift_inv_lref1" ]             * ]
+  [ class "" [ "lift_inv_lref1_lt" ]           class "" [ "lift_inv_lref1_lt" ]          * ]
+  [ class "" [ "lift_inv_lref1_ge" ]           class "" [ "lift_inv_lref1_ge" ]          * ]
+  [ class "" [ "lift_inv_gref1_aux" ]          class "" [ "lift_inv_gref1_aux" ]         * ]
+  [ class "" [ "lift_inv_gref1" ]              class "" [ "lift_inv_gref1" ]             * ]
+  [ class "" [ "lift_inv_bind1_aux" ]          class "" [ "lift_inv_bind1_aux" ]         * ]
+  [ class "" [ "lift_inv_bind1" ]              class "" [ "lift_inv_bind1" ]             * ]
+  [ class "" [ "lift_inv_flat1_aux" ]          class "" [ "lift_inv_flat1_aux" ]         * ]
+  [ class "" [ "lift_inv_flat1" ]              class "" [ "lift_inv_flat1" ]             * ]
+  [ class "" [ "lift_inv_sort2_aux" ]          class "" [ "lift_inv_sort2_aux" ]         * ]
+  [ class "" [ "lift_inv_sort2" ]              class "" [ "lift_inv_sort2" ]             * ]
+  [ class "" [ "lift_inv_lref2_aux" ]          class "" [ "lift_inv_lref2_aux" ]         * ]
+  [ class "" [ "lift_inv_lref2" ]              class "" [ "lift_inv_lref2" ]             * ]
+  [ class "" [ "lift_inv_lref2_lt" ]           class "" [ "lift_inv_lref2_lt" ]          * ]
+  [ class "" [ "lift_inv_lref2_be" ]           class "" [ "lift_inv_lref2_be" ]          * ]
+  [ class "" [ "lift_inv_lref2_ge" ]           class "" [ "lift_inv_lref2_ge" ]          * ]
+  [ class "" [ "lift_inv_gref2_aux" ]          class "" [ "lift_inv_gref2_aux" ]         * ]
+  [ class "" [ "lift_inv_gref2" ]              class "" [ "lift_inv_gref2" ]             * ]
+  [ class "" [ "lift_inv_bind2_aux" ]          class "" [ "lift_inv_bind2_aux" ]         * ]
+  [ class "" [ "lift_inv_bind2" ]              class "" [ "lift_inv_bind2" ]             * ]
+  [ class "" [ "lift_inv_flat2_aux" ]          class "" [ "lift_inv_flat2_aux" ]         * ]
+  [ class "" [ "lift_inv_flat2" ]              class "" [ "lift_inv_flat2" ]             * ]
+  [ class "" [ "lift_inv_pair_xy_x" ]          class "" [ "lift_inv_pair_xy_x" ]         * ]
+  [ class "" [ "lift_inv_pair_xy_y" ]          class "" [ "lift_inv_pair_xy_y" ]         * ]
+  [ class "" [ "lift_fwd_pair1" ]              class "" [ "lift_fwd_pair1" ]             * ]
+  [ class "" [ "lift_fwd_pair2" ]              class "" [ "lift_fwd_pair2" ]             * ]
+  [ class "" [ "lift_fwd_tw" ]                 class "" [ "lift_fwd_tw" ]                * ]
+  [ class "" [ "lift_simple_dx" ]              class "" [ "lift_simple_dx" ]             * ]
+  [ class "" [ "lift_simple_sn" ]              class "" [ "lift_simple_sn" ]             * ]
+  [ class "" [ "lift_lref_ge_minus" ]          class "" [ "lift_lref_ge_minus" ]         * ]
   [ class "" [ "lift_lref_ge_minus_eq" ]       class "" [ "lift_lref_ge_minus_eq" ]      * ]
-  [ class "" [ "lift_refl" ]                  class "" [ "lift_refl" ]                  * ]
-  [ class "" [ "lift_total" ]                 class "" [ "lift_total" ]                 * ]
-  [ class "" [ "lift_split" ]                 class "" [ "lift_split" ]                 * ]
-  [ class "" [ "is_lift_dec" ]                class "" [ "is_lift_dec" ]                * ]
-  [ class "" [ "drop" ]                               class "" [ "drop" ]                       * ]
-  [ class "" [ "d_liftable" ]                 class "" [ "d_liftable" ]                 * ]
-  [ class "" [ "d_deliftable_sn" ]            class "" [ "d_deliftable_sn" ]            * ]
-  [ class "" [ "dropable_sn" ]                class "" [ "dropable_sn" ]                * ]
-  [ class "" [ "dropable_dx" ]                class "" [ "dropable_dx" ]                * ]
-  [ class "" [ "drop_inv_atom1_aux" ]         class "" [ "drop_inv_atom1_aux" ]         * ]
-  [ class "" [ "drop_inv_atom1" ]             class "" [ "drop_inv_atom1" ]             * ]
+  [ class "" [ "lift_refl" ]                   class "" [ "lift_refl" ]                  * ]
+  [ class "" [ "lift_total" ]                  class "" [ "lift_total" ]                 * ]
+  [ class "" [ "lift_split" ]                  class "" [ "lift_split" ]                 * ]
+  [ class "" [ "is_lift_dec" ]                 class "" [ "is_lift_dec" ]                * ]
+  [ class "" [ "drop" ]                        class "" [ "drop" ]                       * ]
+  [ class "" [ "d_liftable" ]                  class "" [ "d_liftable" ]                 * ]
+  [ class "" [ "d_deliftable_sn" ]             class "" [ "d_deliftable_sn" ]            * ]
+  [ class "" [ "dropable_sn" ]                 class "" [ "dropable_sn" ]                * ]
+  [ class "" [ "dropable_dx" ]                 class "" [ "dropable_dx" ]                * ]
+  [ class "" [ "drop_inv_atom1_aux" ]          class "" [ "drop_inv_atom1_aux" ]         * ]
+  [ class "" [ "drop_inv_atom1" ]              class "" [ "drop_inv_atom1" ]             * ]
   [ class "" [ "drop_inv_O1_pair1_aux" ]       class "" [ "drop_inv_O1_pair1_aux" ]      * ]
-  [ class "" [ "drop_inv_O1_pair1" ]          class "" [ "drop_inv_O1_pair1" ]          * ]
-  [ class "" [ "drop_inv_pair1" ]             class "" [ "drop_inv_pair1" ]             * ]
-  [ class "" [ "drop_inv_drop1_lt" ]          class "" [ "drop_inv_drop1_lt" ]          * ]
-  [ class "" [ "drop_inv_drop1" ]             class "" [ "drop_inv_drop1" ]             * ]
-  [ class "" [ "drop_inv_skip1_aux" ]         class "" [ "drop_inv_skip1_aux" ]         * ]
-  [ class "" [ "drop_inv_skip1" ]             class "" [ "drop_inv_skip1" ]             * ]
-  [ class "" [ "drop_inv_O1_pair2" ]          class "" [ "drop_inv_O1_pair2" ]          * ]
-  [ class "" [ "drop_inv_skip2_aux" ]         class "" [ "drop_inv_skip2_aux" ]         * ]
-  [ class "" [ "drop_inv_skip2" ]             class "" [ "drop_inv_skip2" ]             * ]
-  [ class "" [ "drop_inv_O1_gt" ]             class "" [ "drop_inv_O1_gt" ]             * ]
-  [ class "" [ "drop_refl_atom_O2" ]          class "" [ "drop_refl_atom_O2" ]          * ]
-  [ class "" [ "drop_refl" ]                  class "" [ "drop_refl" ]                  * ]
-  [ class "" [ "drop_drop_lt" ]                       class "" [ "drop_drop_lt" ]               * ]
-  [ class "" [ "drop_skip_lt" ]                       class "" [ "drop_skip_lt" ]               * ]
-  [ class "" [ "drop_O1_le" ]                 class "" [ "drop_O1_le" ]                 * ]
-  [ class "" [ "drop_O1_lt" ]                 class "" [ "drop_O1_lt" ]                 * ]
-  [ class "" [ "drop_O1_pair" ]                       class "" [ "drop_O1_pair" ]               * ]
-  [ class "" [ "drop_O1_ge" ]                 class "" [ "drop_O1_ge" ]                 * ]
-  [ class "" [ "drop_O1_eq" ]                 class "" [ "drop_O1_eq" ]                 * ]
-  [ class "" [ "drop_split" ]                 class "" [ "drop_split" ]                 * ]
-  [ class "" [ "drop_FT" ]                    class "" [ "drop_FT" ]                    * ]
-  [ class "" [ "drop_gen" ]                   class "" [ "drop_gen" ]                   * ]
-  [ class "" [ "drop_T" ]                     class "" [ "drop_T" ]                     * ]
-  [ class "" [ "d_liftable_LTC" ]             class "" [ "d_liftable_LTC" ]             * ]
-  [ class "" [ "d_deliftable_sn_LTC" ]        class "" [ "d_deliftable_sn_LTC" ]        * ]
-  [ class "" [ "dropable_sn_TC" ]             class "" [ "dropable_sn_TC" ]             * ]
-  [ class "" [ "dropable_dx_TC" ]             class "" [ "dropable_dx_TC" ]             * ]
+  [ class "" [ "drop_inv_O1_pair1" ]           class "" [ "drop_inv_O1_pair1" ]          * ]
+  [ class "" [ "drop_inv_pair1" ]              class "" [ "drop_inv_pair1" ]             * ]
+  [ class "" [ "drop_inv_drop1_lt" ]           class "" [ "drop_inv_drop1_lt" ]          * ]
+  [ class "" [ "drop_inv_drop1" ]              class "" [ "drop_inv_drop1" ]             * ]
+  [ class "" [ "drop_inv_skip1_aux" ]          class "" [ "drop_inv_skip1_aux" ]         * ]
+  [ class "" [ "drop_inv_skip1" ]              class "" [ "drop_inv_skip1" ]             * ]
+  [ class "" [ "drop_inv_O1_pair2" ]           class "" [ "drop_inv_O1_pair2" ]          * ]
+  [ class "" [ "drop_inv_skip2_aux" ]          class "" [ "drop_inv_skip2_aux" ]         * ]
+  [ class "" [ "drop_inv_skip2" ]              class "" [ "drop_inv_skip2" ]             * ]
+  [ class "" [ "drop_inv_O1_gt" ]              class "" [ "drop_inv_O1_gt" ]             * ]
+  [ class "" [ "drop_refl_atom_O2" ]           class "" [ "drop_refl_atom_O2" ]          * ]
+  [ class "" [ "drop_refl" ]                   class "" [ "drop_refl" ]                  * ]
+  [ class "" [ "drop_drop_lt" ]                class "" [ "drop_drop_lt" ]               * ]
+  [ class "" [ "drop_skip_lt" ]                class "" [ "drop_skip_lt" ]               * ]
+  [ class "" [ "drop_O1_le" ]                  class "" [ "drop_O1_le" ]                 * ]
+  [ class "" [ "drop_O1_lt" ]                  class "" [ "drop_O1_lt" ]                 * ]
+  [ class "" [ "drop_O1_pair" ]                class "" [ "drop_O1_pair" ]               * ]
+  [ class "" [ "drop_O1_ge" ]                  class "" [ "drop_O1_ge" ]                 * ]
+  [ class "" [ "drop_O1_eq" ]                  class "" [ "drop_O1_eq" ]                 * ]
+  [ class "" [ "drop_split" ]                  class "" [ "drop_split" ]                 * ]
+  [ class "" [ "drop_FT" ]                     class "" [ "drop_FT" ]                    * ]
+  [ class "" [ "drop_gen" ]                    class "" [ "drop_gen" ]                   * ]
+  [ class "" [ "drop_T" ]                      class "" [ "drop_T" ]                     * ]
+  [ class "" [ "d_liftable_LTC" ]              class "" [ "d_liftable_LTC" ]             * ]
+  [ class "" [ "d_deliftable_sn_LTC" ]         class "" [ "d_deliftable_sn_LTC" ]        * ]
+  [ class "" [ "dropable_sn_TC" ]              class "" [ "dropable_sn_TC" ]             * ]
+  [ class "" [ "dropable_dx_TC" ]              class "" [ "dropable_dx_TC" ]             * ]
   [ class "" [ "d_deliftable_sn_llstar" ]      class "" [ "d_deliftable_sn_llstar" ]     * ]
-  [ class "" [ "drop_fwd_drop2" ]             class "" [ "drop_fwd_drop2" ]             * ]
-  [ class "" [ "drop_fwd_length_ge" ]         class "" [ "drop_fwd_length_ge" ]         * ]
+  [ class "" [ "drop_fwd_drop2" ]              class "" [ "drop_fwd_drop2" ]             * ]
+  [ class "" [ "drop_fwd_length_ge" ]          class "" [ "drop_fwd_length_ge" ]         * ]
   [ class "" [ "drop_fwd_length_le_le" ]       class "" [ "drop_fwd_length_le_le" ]      * ]
   [ class "" [ "drop_fwd_length_le_ge" ]       class "" [ "drop_fwd_length_le_ge" ]      * ]
-  [ class "" [ "drop_fwd_length" ]            class "" [ "drop_fwd_length" ]            * ]
+  [ class "" [ "drop_fwd_length" ]             class "" [ "drop_fwd_length" ]            * ]
   [ class "" [ "drop_fwd_length_minus2" ]      class "" [ "drop_fwd_length_minus2" ]     * ]
   [ class "" [ "drop_fwd_length_minus4" ]      class "" [ "drop_fwd_length_minus4" ]     * ]
-  [ class "" [ "drop_fwd_length_le2" ]        class "" [ "drop_fwd_length_le2" ]        * ]
-  [ class "" [ "drop_fwd_length_le4" ]        class "" [ "drop_fwd_length_le4" ]        * ]
-  [ class "" [ "drop_fwd_length_lt2" ]        class "" [ "drop_fwd_length_lt2" ]        * ]
-  [ class "" [ "drop_fwd_length_lt4" ]        class "" [ "drop_fwd_length_lt4" ]        * ]
-  [ class "" [ "drop_fwd_length_eq1" ]        class "" [ "drop_fwd_length_eq1" ]        * ]
-  [ class "" [ "drop_fwd_length_eq2" ]        class "" [ "drop_fwd_length_eq2" ]        * ]
-  [ class "" [ "drop_fwd_lw" ]                class "" [ "drop_fwd_lw" ]                * ]
-  [ class "" [ "drop_fwd_lw_lt" ]             class "" [ "drop_fwd_lw_lt" ]             * ]
-  [ class "" [ "drop_fwd_rfw" ]                       class "" [ "drop_fwd_rfw" ]               * ]
-  [ class "" [ "drop_inv_O2_aux" ]            class "" [ "drop_inv_O2_aux" ]            * ]
-  [ class "" [ "drop_inv_O2" ]                class "" [ "drop_inv_O2" ]                * ]
-  [ class "" [ "drop_inv_length_eq" ]         class "" [ "drop_inv_length_eq" ]         * ]
-  [ class "" [ "drop_inv_refl" ]              class "" [ "drop_inv_refl" ]              * ]
-  [ class "" [ "drop_inv_FT_aux" ]            class "" [ "drop_inv_FT_aux" ]            * ]
-  [ class "" [ "drop_inv_FT" ]                class "" [ "drop_inv_FT" ]                * ]
-  [ class "" [ "drop_inv_gen" ]                       class "" [ "drop_inv_gen" ]               * ]
-  [ class "" [ "drop_inv_T" ]                 class "" [ "drop_inv_T" ]                 * ]
+  [ class "" [ "drop_fwd_length_le2" ]         class "" [ "drop_fwd_length_le2" ]        * ]
+  [ class "" [ "drop_fwd_length_le4" ]         class "" [ "drop_fwd_length_le4" ]        * ]
+  [ class "" [ "drop_fwd_length_lt2" ]         class "" [ "drop_fwd_length_lt2" ]        * ]
+  [ class "" [ "drop_fwd_length_lt4" ]         class "" [ "drop_fwd_length_lt4" ]        * ]
+  [ class "" [ "drop_fwd_length_eq1" ]         class "" [ "drop_fwd_length_eq1" ]        * ]
+  [ class "" [ "drop_fwd_length_eq2" ]         class "" [ "drop_fwd_length_eq2" ]        * ]
+  [ class "" [ "drop_fwd_lw" ]                 class "" [ "drop_fwd_lw" ]                * ]
+  [ class "" [ "drop_fwd_lw_lt" ]              class "" [ "drop_fwd_lw_lt" ]             * ]
+  [ class "" [ "drop_fwd_rfw" ]                class "" [ "drop_fwd_rfw" ]               * ]
+  [ class "" [ "drop_inv_O2_aux" ]             class "" [ "drop_inv_O2_aux" ]            * ]
+  [ class "" [ "drop_inv_O2" ]                 class "" [ "drop_inv_O2" ]                * ]
+  [ class "" [ "drop_inv_length_eq" ]          class "" [ "drop_inv_length_eq" ]         * ]
+  [ class "" [ "drop_inv_refl" ]               class "" [ "drop_inv_refl" ]              * ]
+  [ class "" [ "drop_inv_FT_aux" ]             class "" [ "drop_inv_FT_aux" ]            * ]
+  [ class "" [ "drop_inv_FT" ]                 class "" [ "drop_inv_FT" ]                * ]
+  [ class "" [ "drop_inv_gen" ]                class "" [ "drop_inv_gen" ]               * ]
+  [ class "" [ "drop_inv_T" ]                  class "" [ "drop_inv_T" ]                 * ]
 
-  [ class "" [ "lsubr" ]                      class "" [ "lsubr" ]                      * ]
-  [ class "" [ "lsubr_refl" ]                 class "" [ "lsubr_refl" ]                 * ]
-  [ class "" [ "lsubr_inv_atom1_aux" ]        class "" [ "lsubr_inv_atom1_aux" ]        * ]
-  [ class "" [ "lsubr_inv_atom1" ]            class "" [ "lsubr_inv_atom1" ]            * ]
-  [ class "" [ "lsubr_inv_abst1_aux" ]        class "" [ "lsubr_inv_abst1_aux" ]        * ]
-  [ class "" [ "lsubr_inv_abst1" ]            class "" [ "lsubr_inv_abst1" ]            * ]
-  [ class "" [ "lsubr_inv_abbr2_aux" ]        class "" [ "lsubr_inv_abbr2_aux" ]        * ]
-  [ class "" [ "lsubr_inv_abbr2" ]            class "" [ "lsubr_inv_abbr2" ]            * ]
-  [ class "" [ "lsubr_fwd_length" ]           class "" [ "lsubr_fwd_length" ]           * ]
-  [ class "" [ "lsubr_fwd_drop2_pair" ]               class "" [ "lsubr_fwd_drop2_pair" ]       * ]
-  [ class "" [ "lsubr_fwd_drop2_abbr" ]               class "" [ "lsubr_fwd_drop2_abbr" ]       * ]
+  [ class "" [ "lsubr" ]                       class "" [ "lsubr" ]                      * ]
+  [ class "" [ "lsubr_refl" ]                  class "" [ "lsubr_refl" ]                 * ]
+  [ class "" [ "lsubr_inv_atom1_aux" ]         class "" [ "lsubr_inv_atom1_aux" ]        * ]
+  [ class "" [ "lsubr_inv_atom1" ]             class "" [ "lsubr_inv_atom1" ]            * ]
+  [ class "" [ "lsubr_inv_abst1_aux" ]         class "" [ "lsubr_inv_abst1_aux" ]        * ]
+  [ class "" [ "lsubr_inv_abst1" ]             class "" [ "lsubr_inv_abst1" ]            * ]
+  [ class "" [ "lsubr_inv_abbr2_aux" ]         class "" [ "lsubr_inv_abbr2_aux" ]        * ]
+  [ class "" [ "lsubr_inv_abbr2" ]             class "" [ "lsubr_inv_abbr2" ]            * ]
+  [ class "" [ "lsubr_fwd_length" ]            class "" [ "lsubr_fwd_length" ]           * ]
+  [ class "" [ "lsubr_fwd_drop2_pair" ]        class "" [ "lsubr_fwd_drop2_pair" ]       * ]
+  [ class "" [ "lsubr_fwd_drop2_abbr" ]        class "" [ "lsubr_fwd_drop2_abbr" ]       * ]
 
-  [ class "" [ "cpr" ]                        class "" [ "cpr" ]                        * ]
-  [ class "" [ "lsubr_cpr_trans" ]            class "" [ "lsubr_cpr_trans" ]            * ]
-  [ class "" [ "tpr_cpr" ]                    class "" [ "tpr_cpr" ]                    * ]
-  [ class "" [ "cpr_refl" ]                   class "" [ "cpr_refl" ]                   * ]
-  [ class "" [ "cpr_pair_sn" ]                class "" [ "cpr_pair_sn" ]                * ]
-  [ class "" [ "cpr_delift" ]                 class "" [ "cpr_delift" ]                 * ]
-  [ class "" [ "lstas_cpr_aux" ]              class "" [ "lstas_cpr_aux" ]              * ]
-  [ class "" [ "lstas_cpr" ]                  class "" [ "lstas_cpr" ]                  * ]
-  [ class "" [ "cpr_inv_atom1_aux" ]          class "" [ "cpr_inv_atom1_aux" ]          * ]
-  [ class "" [ "cpr_inv_atom1" ]              class "" [ "cpr_inv_atom1" ]              * ]
-  [ class "" [ "cpr_inv_sort1" ]              class "" [ "cpr_inv_sort1" ]              * ]
-  [ class "" [ "cpr_inv_lref1" ]              class "" [ "cpr_inv_lref1" ]              * ]
-  [ class "" [ "cpr_inv_gref1" ]              class "" [ "cpr_inv_gref1" ]              * ]
-  [ class "" [ "cpr_inv_bind1_aux" ]          class "" [ "cpr_inv_bind1_aux" ]          * ]
-  [ class "" [ "cpr_inv_bind1" ]              class "" [ "cpr_inv_bind1" ]              * ]
-  [ class "" [ "cpr_inv_abbr1" ]              class "" [ "cpr_inv_abbr1" ]              * ]
-  [ class "" [ "cpr_inv_abst1" ]              class "" [ "cpr_inv_abst1" ]              * ]
-  [ class "" [ "cpr_inv_flat1_aux" ]          class "" [ "cpr_inv_flat1_aux" ]          * ]
-  [ class "" [ "cpr_inv_flat1" ]              class "" [ "cpr_inv_flat1" ]              * ]
-  [ class "" [ "cpr_inv_appl1" ]              class "" [ "cpr_inv_appl1" ]              * ]
-  [ class "" [ "cpr_inv_appl1_simple" ]               class "" [ "cpr_inv_appl1_simple" ]       * ]
-  [ class "" [ "cpr_inv_cast1" ]              class "" [ "cpr_inv_cast1" ]              * ]
-  [ class "" [ "cpr_fwd_bind1_minus" ]        class "" [ "cpr_fwd_bind1_minus" ]        * ]
-  [ class "" [ "cnr" ]                        class "" [ "cnr" ]                        * ]
-  [ class "" [ "cnr_inv_delta" ]              class "" [ "cnr_inv_delta" ]              * ]
-  [ class "" [ "cnr_inv_abst" ]                       class "" [ "cnr_inv_abst" ]               * ]
-  [ class "" [ "cnr_inv_abbr" ]                       class "" [ "cnr_inv_abbr" ]               * ]
-  [ class "" [ "cnr_inv_zeta" ]                       class "" [ "cnr_inv_zeta" ]               * ]
-  [ class "" [ "cnr_inv_appl" ]                       class "" [ "cnr_inv_appl" ]               * ]
-  [ class "" [ "cnr_inv_eps" ]                class "" [ "cnr_inv_eps" ]                * ]
-  [ class "" [ "cnr_sort" ]                   class "" [ "cnr_sort" ]                   * ]
-  [ class "" [ "cnr_lref_free" ]              class "" [ "cnr_lref_free" ]              * ]
-  [ class "" [ "cnr_lref_atom" ]              class "" [ "cnr_lref_atom" ]              * ]
-  [ class "" [ "cnr_abst" ]                   class "" [ "cnr_abst" ]                   * ]
-  [ class "" [ "cnr_appl_simple" ]            class "" [ "cnr_appl_simple" ]            * ]
-  [ class "" [ "cnr_dec" ]                    class "" [ "cnr_dec" ]                    * ]
-  [ class "" [ "cprs" ]                               class "" [ "cprs" ]                       * ]
-  [ class "" [ "cprs_ind" ]                   class "" [ "cprs_ind" ]                   * ]
-  [ class "" [ "cprs_ind_dx" ]                class "" [ "cprs_ind_dx" ]                * ]
-  [ class "" [ "cpr_cprs" ]                   class "" [ "cpr_cprs" ]                   * ]
-  [ class "" [ "cprs_refl" ]                  class "" [ "cprs_refl" ]                  * ]
-  [ class "" [ "cprs_strap1" ]                class "" [ "cprs_strap1" ]                * ]
-  [ class "" [ "cprs_strap2" ]                class "" [ "cprs_strap2" ]                * ]
-  [ class "" [ "lsubr_cprs_trans" ]           class "" [ "lsubr_cprs_trans" ]           * ]
-  [ class "" [ "tprs_cprs" ]                  class "" [ "tprs_cprs" ]                  * ]
-  [ class "" [ "cprs_bind_dx" ]                       class "" [ "cprs_bind_dx" ]               * ]
-  [ class "" [ "cprs_flat_dx" ]                       class "" [ "cprs_flat_dx" ]               * ]
-  [ class "" [ "cprs_flat_sn" ]                       class "" [ "cprs_flat_sn" ]               * ]
-  [ class "" [ "cprs_zeta" ]                  class "" [ "cprs_zeta" ]                  * ]
-  [ class "" [ "cprs_eps" ]                   class "" [ "cprs_eps" ]                   * ]
-  [ class "" [ "cprs_beta_dx" ]                       class "" [ "cprs_beta_dx" ]               * ]
-  [ class "" [ "cprs_theta_dx" ]              class "" [ "cprs_theta_dx" ]              * ]
-  [ class "" [ "cprs_inv_sort1" ]             class "" [ "cprs_inv_sort1" ]             * ]
-  [ class "" [ "cprs_inv_cast1" ]             class "" [ "cprs_inv_cast1" ]             * ]
-  [ class "" [ "cprs_inv_cnr1" ]              class "" [ "cprs_inv_cnr1" ]              * ]
-  [ class "" [ "scpds" ]                      class "" [ "scpds" ]                      * ]
-  [ class "" [ "sta_cprs_scpds" ]             class "" [ "sta_cprs_scpds" ]             * ]
-  [ class "" [ "lstas_scpds" ]                class "" [ "lstas_scpds" ]                * ]
-  [ class "" [ "scpds_strap1" ]                       class "" [ "scpds_strap1" ]               * ]
-  [ class "" [ "scpds_fwd_cprs" ]             class "" [ "scpds_fwd_cprs" ]             * ]
-  [ class "" [ "scpes" ]                      class "" [ "scpes" ]                      * ]
-  [ class "" [ "scpds_div" ]                  class "" [ "scpds_div" ]                  * ]
-  [ class "" [ "scpes_sym" ]                  class "" [ "scpes_sym" ]                  * ]
-  [ class "" [ "lift_inj" ]                   class "" [ "lift_inj" ]                   * ]
-  [ class "" [ "lift_div_le" ]                class "" [ "lift_div_le" ]                * ]
-  [ class "" [ "lift_div_be" ]                class "" [ "lift_div_be" ]                * ]
-  [ class "" [ "lift_mono" ]                  class "" [ "lift_mono" ]                  * ]
-  [ class "" [ "lift_trans_be" ]              class "" [ "lift_trans_be" ]              * ]
-  [ class "" [ "lift_trans_le" ]              class "" [ "lift_trans_le" ]              * ]
-  [ class "" [ "lift_trans_ge" ]              class "" [ "lift_trans_ge" ]              * ]
-  [ class "" [ "lift_conf_O1" ]                       class "" [ "lift_conf_O1" ]               * ]
-  [ class "" [ "lift_conf_be" ]                       class "" [ "lift_conf_be" ]               * ]
-  [ class "" [ "drop_mono" ]                  class "" [ "drop_mono" ]                  * ]
-  [ class "" [ "drop_conf_ge" ]                       class "" [ "drop_conf_ge" ]               * ]
-  [ class "" [ "drop_conf_be" ]                       class "" [ "drop_conf_be" ]               * ]
-  [ class "" [ "drop_conf_le" ]                       class "" [ "drop_conf_le" ]               * ]
-  [ class "" [ "drop_trans_ge" ]              class "" [ "drop_trans_ge" ]              * ]
-  [ class "" [ "drop_trans_le" ]              class "" [ "drop_trans_le" ]              * ]
-  [ class "" [ "d_liftable_llstar" ]          class "" [ "d_liftable_llstar" ]          * ]
-  [ class "" [ "drop_conf_lt" ]                       class "" [ "drop_conf_lt" ]               * ]
-  [ class "" [ "drop_trans_lt" ]              class "" [ "drop_trans_lt" ]              * ]
-  [ class "" [ "drop_trans_ge_comm" ]         class "" [ "drop_trans_ge_comm" ]         * ]
-  [ class "" [ "drop_conf_div" ]              class "" [ "drop_conf_div" ]              * ]
-  [ class "" [ "drop_fwd_be" ]                class "" [ "drop_fwd_be" ]                * ]
+  [ class "" [ "cpr" ]                         class "" [ "cpr" ]                        * ]
+  [ class "" [ "lsubr_cpr_trans" ]             class "" [ "lsubr_cpr_trans" ]            * ]
+  [ class "" [ "tpr_cpr" ]                     class "" [ "tpr_cpr" ]                    * ]
+  [ class "" [ "cpr_refl" ]                    class "" [ "cpr_refl" ]                   * ]
+  [ class "" [ "cpr_pair_sn" ]                 class "" [ "cpr_pair_sn" ]                * ]
+  [ class "" [ "cpr_delift" ]                  class "" [ "cpr_delift" ]                 * ]
+  [ class "" [ "lstas_cpr_aux" ]               class "" [ "lstas_cpr_aux" ]              * ]
+  [ class "" [ "lstas_cpr" ]                   class "" [ "lstas_cpr" ]                  * ]
+  [ class "" [ "cpr_inv_atom1_aux" ]           class "" [ "cpr_inv_atom1_aux" ]          * ]
+  [ class "" [ "cpr_inv_atom1" ]               class "" [ "cpr_inv_atom1" ]              * ]
+  [ class "" [ "cpr_inv_sort1" ]               class "" [ "cpr_inv_sort1" ]              * ]
+  [ class "" [ "cpr_inv_lref1" ]               class "" [ "cpr_inv_lref1" ]              * ]
+  [ class "" [ "cpr_inv_gref1" ]               class "" [ "cpr_inv_gref1" ]              * ]
+  [ class "" [ "cpr_inv_bind1_aux" ]           class "" [ "cpr_inv_bind1_aux" ]          * ]
+  [ class "" [ "cpr_inv_bind1" ]               class "" [ "cpr_inv_bind1" ]              * ]
+  [ class "" [ "cpr_inv_abbr1" ]               class "" [ "cpr_inv_abbr1" ]              * ]
+  [ class "" [ "cpr_inv_abst1" ]               class "" [ "cpr_inv_abst1" ]              * ]
+  [ class "" [ "cpr_inv_flat1_aux" ]           class "" [ "cpr_inv_flat1_aux" ]          * ]
+  [ class "" [ "cpr_inv_flat1" ]               class "" [ "cpr_inv_flat1" ]              * ]
+  [ class "" [ "cpr_inv_appl1" ]               class "" [ "cpr_inv_appl1" ]              * ]
+  [ class "" [ "cpr_inv_appl1_simple" ]        class "" [ "cpr_inv_appl1_simple" ]       * ]
+  [ class "" [ "cpr_inv_cast1" ]               class "" [ "cpr_inv_cast1" ]              * ]
+  [ class "" [ "cpr_fwd_bind1_minus" ]         class "" [ "cpr_fwd_bind1_minus" ]        * ]
+  [ class "" [ "cnr" ]                         class "" [ "cnr" ]                        * ]
+  [ class "" [ "cnr_inv_delta" ]               class "" [ "cnr_inv_delta" ]              * ]
+  [ class "" [ "cnr_inv_abst" ]                class "" [ "cnr_inv_abst" ]               * ]
+  [ class "" [ "cnr_inv_abbr" ]                class "" [ "cnr_inv_abbr" ]               * ]
+  [ class "" [ "cnr_inv_zeta" ]                class "" [ "cnr_inv_zeta" ]               * ]
+  [ class "" [ "cnr_inv_appl" ]                class "" [ "cnr_inv_appl" ]               * ]
+  [ class "" [ "cnr_inv_eps" ]                 class "" [ "cnr_inv_eps" ]                * ]
+  [ class "" [ "cnr_sort" ]                    class "" [ "cnr_sort" ]                   * ]
+  [ class "" [ "cnr_lref_free" ]               class "" [ "cnr_lref_free" ]              * ]
+  [ class "" [ "cnr_lref_atom" ]               class "" [ "cnr_lref_atom" ]              * ]
+  [ class "" [ "cnr_abst" ]                    class "" [ "cnr_abst" ]                   * ]
+  [ class "" [ "cnr_appl_simple" ]             class "" [ "cnr_appl_simple" ]            * ]
+  [ class "" [ "cnr_dec" ]                     class "" [ "cnr_dec" ]                    * ]
+  [ class "" [ "cprs" ]                        class "" [ "cprs" ]                       * ]
+  [ class "" [ "cprs_ind" ]                    class "" [ "cprs_ind" ]                   * ]
+  [ class "" [ "cprs_ind_dx" ]                 class "" [ "cprs_ind_dx" ]                * ]
+  [ class "" [ "cpr_cprs" ]                    class "" [ "cpr_cprs" ]                   * ]
+  [ class "" [ "cprs_refl" ]                   class "" [ "cprs_refl" ]                  * ]
+  [ class "" [ "cprs_strap1" ]                 class "" [ "cprs_strap1" ]                * ]
+  [ class "" [ "cprs_strap2" ]                 class "" [ "cprs_strap2" ]                * ]
+  [ class "" [ "lsubr_cprs_trans" ]            class "" [ "lsubr_cprs_trans" ]           * ]
+  [ class "" [ "tprs_cprs" ]                   class "" [ "tprs_cprs" ]                  * ]
+  [ class "" [ "cprs_bind_dx" ]                class "" [ "cprs_bind_dx" ]               * ]
+  [ class "" [ "cprs_flat_dx" ]                class "" [ "cprs_flat_dx" ]               * ]
+  [ class "" [ "cprs_flat_sn" ]                class "" [ "cprs_flat_sn" ]               * ]
+  [ class "" [ "cprs_zeta" ]                   class "" [ "cprs_zeta" ]                  * ]
+  [ class "" [ "cprs_eps" ]                    class "" [ "cprs_eps" ]                   * ]
+  [ class "" [ "cprs_beta_dx" ]                class "" [ "cprs_beta_dx" ]               * ]
+  [ class "" [ "cprs_theta_dx" ]               class "" [ "cprs_theta_dx" ]              * ]
+  [ class "" [ "cprs_inv_sort1" ]              class "" [ "cprs_inv_sort1" ]             * ]
+  [ class "" [ "cprs_inv_cast1" ]              class "" [ "cprs_inv_cast1" ]             * ]
+  [ class "" [ "cprs_inv_cnr1" ]               class "" [ "cprs_inv_cnr1" ]              * ]
+  [ class "" [ "scpds" ]                       class "" [ "scpds" ]                      * ]
+  [ class "" [ "sta_cprs_scpds" ]              class "" [ "sta_cprs_scpds" ]             * ]
+  [ class "" [ "lstas_scpds" ]                 class "" [ "lstas_scpds" ]                * ]
+  [ class "" [ "scpds_strap1" ]                class "" [ "scpds_strap1" ]               * ]
+  [ class "" [ "scpds_fwd_cprs" ]              class "" [ "scpds_fwd_cprs" ]             * ]
+  [ class "" [ "scpes" ]                       class "" [ "scpes" ]                      * ]
+  [ class "" [ "scpds_div" ]                   class "" [ "scpds_div" ]                  * ]
+  [ class "" [ "scpes_sym" ]                   class "" [ "scpes_sym" ]                  * ]
+  [ class "" [ "lift_inj" ]                    class "" [ "lift_inj" ]                   * ]
+  [ class "" [ "lift_div_le" ]                 class "" [ "lift_div_le" ]                * ]
+  [ class "" [ "lift_div_be" ]                 class "" [ "lift_div_be" ]                * ]
+  [ class "" [ "lift_mono" ]                   class "" [ "lift_mono" ]                  * ]
+  [ class "" [ "lift_trans_be" ]               class "" [ "lift_trans_be" ]              * ]
+  [ class "" [ "lift_trans_le" ]               class "" [ "lift_trans_le" ]              * ]
+  [ class "" [ "lift_trans_ge" ]               class "" [ "lift_trans_ge" ]              * ]
+  [ class "" [ "lift_conf_O1" ]                class "" [ "lift_conf_O1" ]               * ]
+  [ class "" [ "lift_conf_be" ]                class "" [ "lift_conf_be" ]               * ]
+  [ class "" [ "drop_mono" ]                   class "" [ "drop_mono" ]                  * ]
+  [ class "" [ "drop_conf_ge" ]                class "" [ "drop_conf_ge" ]               * ]
+  [ class "" [ "drop_conf_be" ]                class "" [ "drop_conf_be" ]               * ]
+  [ class "" [ "drop_conf_le" ]                class "" [ "drop_conf_le" ]               * ]
+  [ class "" [ "drop_trans_ge" ]               class "" [ "drop_trans_ge" ]              * ]
+  [ class "" [ "drop_trans_le" ]               class "" [ "drop_trans_le" ]              * ]
+  [ class "" [ "d_liftable_llstar" ]           class "" [ "d_liftable_llstar" ]          * ]
+  [ class "" [ "drop_conf_lt" ]                class "" [ "drop_conf_lt" ]               * ]
+  [ class "" [ "drop_trans_lt" ]               class "" [ "drop_trans_lt" ]              * ]
+  [ class "" [ "drop_trans_ge_comm" ]          class "" [ "drop_trans_ge_comm" ]         * ]
+  [ class "" [ "drop_conf_div" ]               class "" [ "drop_conf_div" ]              * ]
+  [ class "" [ "drop_fwd_be" ]                 class "" [ "drop_fwd_be" ]                * ]
 
-  [ class "" [ "aaa" ]                        class "" [ "aaa" ]                        * ]
-  [ class "" [ "aaa_inv_sort_aux" ]           class "" [ "aaa_inv_sort_aux" ]           * ]
-  [ class "" [ "aaa_inv_sort" ]                       class "" [ "aaa_inv_sort" ]               * ]
-  [ class "" [ "aaa_inv_lref_aux" ]           class "" [ "aaa_inv_lref_aux" ]           * ]
-  [ class "" [ "aaa_inv_lref" ]                       class "" [ "aaa_inv_lref" ]               * ]
-  [ class "" [ "aaa_inv_gref_aux" ]           class "" [ "aaa_inv_gref_aux" ]           * ]
-  [ class "" [ "aaa_inv_gref" ]                       class "" [ "aaa_inv_gref" ]               * ]
-  [ class "" [ "aaa_inv_abbr_aux" ]           class "" [ "aaa_inv_abbr_aux" ]           * ]
-  [ class "" [ "aaa_inv_abbr" ]                       class "" [ "aaa_inv_abbr" ]               * ]
-  [ class "" [ "aaa_inv_abst_aux" ]           class "" [ "aaa_inv_abst_aux" ]           * ]
-  [ class "" [ "aaa_inv_abst" ]                       class "" [ "aaa_inv_abst" ]               * ]
-  [ class "" [ "aaa_inv_appl_aux" ]           class "" [ "aaa_inv_appl_aux" ]           * ]
-  [ class "" [ "aaa_inv_appl" ]                       class "" [ "aaa_inv_appl" ]               * ]
-  [ class "" [ "aaa_inv_cast_aux" ]           class "" [ "aaa_inv_cast_aux" ]           * ]
-  [ class "" [ "aaa_inv_cast" ]                       class "" [ "aaa_inv_cast" ]               * ]
-  [ class "" [ "aaa_lift" ]                   class "" [ "aaa_lift" ]                   * ]
-  [ class "" [ "aaa_inv_lift" ]                       class "" [ "aaa_inv_lift" ]               * ]
-  [ class "" [ "aaa_mono" ]                   class "" [ "aaa_mono" ]                   * ]
-  [ class "" [ "lsuba" ]                      class "" [ "lsuba" ]                      * ]
-  [ class "" [ "lsuba_inv_atom1_aux" ]        class "" [ "lsuba_inv_atom1_aux" ]        * ]
-  [ class "" [ "lsuba_inv_atom1" ]            class "" [ "lsuba_inv_atom1" ]            * ]
-  [ class "" [ "lsuba_inv_pair1_aux" ]        class "" [ "lsuba_inv_pair1_aux" ]        * ]
-  [ class "" [ "lsuba_inv_pair1" ]            class "" [ "lsuba_inv_pair1" ]            * ]
-  [ class "" [ "lsuba_inv_atom2_aux" ]        class "" [ "lsuba_inv_atom2_aux" ]        * ]
-  [ class "" [ "lsubc_inv_atom2" ]            class "" [ "lsubc_inv_atom2" ]            * ]
-  [ class "" [ "lsuba_inv_pair2_aux" ]        class "" [ "lsuba_inv_pair2_aux" ]        * ]
-  [ class "" [ "lsuba_inv_pair2" ]            class "" [ "lsuba_inv_pair2" ]            * ]
-  [ class "" [ "lsuba_fwd_lsubr" ]            class "" [ "lsuba_fwd_lsubr" ]            * ]
-  [ class "" [ "lsuba_refl" ]                 class "" [ "lsuba_refl" ]                 * ]
-  [ class "" [ "lsuba_drop_O1_conf" ]         class "" [ "lsuba_drop_O1_conf" ]         * ]
-  [ class "" [ "lsuba_drop_O1_trans" ]        class "" [ "lsuba_drop_O1_trans" ]        * ]
-  [ class "" [ "lsuba_aaa_conf" ]             class "" [ "lsuba_aaa_conf" ]             * ]
-  [ class "" [ "lsuba_aaa_trans" ]            class "" [ "lsuba_aaa_trans" ]            * ]
-  [ class "" [ "lreq" ]                               class "" [ "lreq" ]                       * ]
-  [ class "" [ "lreq_pair_lt" ]                       class "" [ "lreq_pair_lt" ]               * ]
-  [ class "" [ "lreq_succ_lt" ]                       class "" [ "lreq_succ_lt" ]               * ]
-  [ class "" [ "lreq_pair_O_Y" ]              class "" [ "lreq_pair_O_Y" ]              * ]
-  [ class "" [ "lreq_refl" ]                  class "" [ "lreq_refl" ]                  * ]
-  [ class "" [ "lreq_O2" ]                    class "" [ "lreq_O2" ]                    * ]
-  [ class "" [ "lreq_sym" ]                   class "" [ "lreq_sym" ]                   * ]
-  [ class "" [ "lreq_inv_atom1_aux" ]         class "" [ "lreq_inv_atom1_aux" ]         * ]
-  [ class "" [ "lreq_inv_atom1" ]             class "" [ "lreq_inv_atom1" ]             * ]
-  [ class "" [ "lreq_inv_zero1_aux" ]         class "" [ "lreq_inv_zero1_aux" ]         * ]
-  [ class "" [ "lreq_inv_zero1" ]             class "" [ "lreq_inv_zero1" ]             * ]
-  [ class "" [ "lreq_inv_pair1_aux" ]         class "" [ "lreq_inv_pair1_aux" ]         * ]
-  [ class "" [ "lreq_inv_pair1" ]             class "" [ "lreq_inv_pair1" ]             * ]
-  [ class "" [ "lreq_inv_pair" ]              class "" [ "lreq_inv_pair" ]              * ]
-  [ class "" [ "lreq_inv_succ1_aux" ]         class "" [ "lreq_inv_succ1_aux" ]         * ]
-  [ class "" [ "lreq_inv_succ1" ]             class "" [ "lreq_inv_succ1" ]             * ]
-  [ class "" [ "lreq_inv_atom2" ]             class "" [ "lreq_inv_atom2" ]             * ]
-  [ class "" [ "lreq_inv_succ" ]              class "" [ "lreq_inv_succ" ]              * ]
-  [ class "" [ "lreq_inv_zero2" ]             class "" [ "lreq_inv_zero2" ]             * ]
-  [ class "" [ "lreq_inv_pair2" ]             class "" [ "lreq_inv_pair2" ]             * ]
-  [ class "" [ "lreq_inv_succ2" ]             class "" [ "lreq_inv_succ2" ]             * ]
-  [ class "" [ "lreq_fwd_length" ]            class "" [ "lreq_fwd_length" ]            * ]
-  [ class "" [ "lreq_inv_O_Y_aux" ]           class "" [ "lreq_inv_O_Y_aux" ]           * ]
-  [ class "" [ "lreq_inv_O_Y" ]                       class "" [ "lreq_inv_O_Y" ]               * ]
-  [ class "" [ "lreq_trans" ]                 class "" [ "lreq_trans" ]                 * ]
-  [ class "" [ "lreq_canc_sn" ]                       class "" [ "lreq_canc_sn" ]               * ]
-  [ class "" [ "lreq_canc_dx" ]                       class "" [ "lreq_canc_dx" ]               * ]
-  [ class "" [ "lreq_join" ]                  class "" [ "lreq_join" ]                  * ]
-  [ class "" [ "dedropable_sn" ]              class "" [ "dedropable_sn" ]              * ]
-  [ class "" [ "lreq_drop_trans_be" ]         class "" [ "lreq_drop_trans_be" ]         * ]
-  [ class "" [ "lreq_drop_conf_be" ]          class "" [ "lreq_drop_conf_be" ]          * ]
-  [ class "" [ "drop_O1_ex" ]                 class "" [ "drop_O1_ex" ]                 * ]
-  [ class "" [ "dedropable_sn_TC" ]           class "" [ "dedropable_sn_TC" ]           * ]
-  [ class "" [ "drop_O1_inj" ]                class "" [ "drop_O1_inj" ]                * ]
-  [ class "" [ "lpx_sn" ]                     class "" [ "lpx_sn" ]                     * ]
-  [ class "" [ "lpx_sn_refl" ]                class "" [ "lpx_sn_refl" ]                * ]
-  [ class "" [ "lpx_sn_inv_atom1_aux" ]               class "" [ "lpx_sn_inv_atom1_aux" ]       * ]
-  [ class "" [ "lpx_sn_inv_atom1" ]           class "" [ "lpx_sn_inv_atom1" ]           * ]
-  [ class "" [ "lpx_sn_inv_pair1_aux" ]               class "" [ "lpx_sn_inv_pair1_aux" ]       * ]
-  [ class "" [ "lpx_sn_inv_pair1" ]           class "" [ "lpx_sn_inv_pair1" ]           * ]
-  [ class "" [ "lpx_sn_inv_atom2_aux" ]               class "" [ "lpx_sn_inv_atom2_aux" ]       * ]
-  [ class "" [ "lpx_sn_inv_atom2" ]           class "" [ "lpx_sn_inv_atom2" ]           * ]
-  [ class "" [ "lpx_sn_inv_pair2_aux" ]               class "" [ "lpx_sn_inv_pair2_aux" ]       * ]
-  [ class "" [ "lpx_sn_inv_pair2" ]           class "" [ "lpx_sn_inv_pair2" ]           * ]
-  [ class "" [ "lpx_sn_inv_pair" ]            class "" [ "lpx_sn_inv_pair" ]            * ]
-  [ class "" [ "lpx_sn_fwd_length" ]          class "" [ "lpx_sn_fwd_length" ]          * ]
-  [ class "" [ "lpx_sn_drop_conf" ]           class "" [ "lpx_sn_drop_conf" ]           * ]
-  [ class "" [ "lpx_sn_drop_trans" ]          class "" [ "lpx_sn_drop_trans" ]          * ]
+  [ class "" [ "aaa" ]                         class "" [ "aaa" ]                        * ]
+  [ class "" [ "aaa_inv_sort_aux" ]            class "" [ "aaa_inv_sort_aux" ]           * ]
+  [ class "" [ "aaa_inv_sort" ]                class "" [ "aaa_inv_sort" ]               * ]
+  [ class "" [ "aaa_inv_lref_aux" ]            class "" [ "aaa_inv_lref_aux" ]           * ]
+  [ class "" [ "aaa_inv_lref" ]                class "" [ "aaa_inv_lref" ]               * ]
+  [ class "" [ "aaa_inv_gref_aux" ]            class "" [ "aaa_inv_gref_aux" ]           * ]
+  [ class "" [ "aaa_inv_gref" ]                class "" [ "aaa_inv_gref" ]               * ]
+  [ class "" [ "aaa_inv_abbr_aux" ]            class "" [ "aaa_inv_abbr_aux" ]           * ]
+  [ class "" [ "aaa_inv_abbr" ]                class "" [ "aaa_inv_abbr" ]               * ]
+  [ class "" [ "aaa_inv_abst_aux" ]            class "" [ "aaa_inv_abst_aux" ]           * ]
+  [ class "" [ "aaa_inv_abst" ]                class "" [ "aaa_inv_abst" ]               * ]
+  [ class "" [ "aaa_inv_appl_aux" ]            class "" [ "aaa_inv_appl_aux" ]           * ]
+  [ class "" [ "aaa_inv_appl" ]                class "" [ "aaa_inv_appl" ]               * ]
+  [ class "" [ "aaa_inv_cast_aux" ]            class "" [ "aaa_inv_cast_aux" ]           * ]
+  [ class "" [ "aaa_inv_cast" ]                class "" [ "aaa_inv_cast" ]               * ]
+  [ class "" [ "aaa_lift" ]                    class "" [ "aaa_lift" ]                   * ]
+  [ class "" [ "aaa_inv_lift" ]                class "" [ "aaa_inv_lift" ]               * ]
+  [ class "" [ "aaa_mono" ]                    class "" [ "aaa_mono" ]                   * ]
+  [ class "" [ "lsuba" ]                       class "" [ "lsuba" ]                      * ]
+  [ class "" [ "lsuba_inv_atom1_aux" ]         class "" [ "lsuba_inv_atom1_aux" ]        * ]
+  [ class "" [ "lsuba_inv_atom1" ]             class "" [ "lsuba_inv_atom1" ]            * ]
+  [ class "" [ "lsuba_inv_pair1_aux" ]         class "" [ "lsuba_inv_pair1_aux" ]        * ]
+  [ class "" [ "lsuba_inv_pair1" ]             class "" [ "lsuba_inv_pair1" ]            * ]
+  [ class "" [ "lsuba_inv_atom2_aux" ]         class "" [ "lsuba_inv_atom2_aux" ]        * ]
+  [ class "" [ "lsubc_inv_atom2" ]             class "" [ "lsubc_inv_atom2" ]            * ]
+  [ class "" [ "lsuba_inv_pair2_aux" ]         class "" [ "lsuba_inv_pair2_aux" ]        * ]
+  [ class "" [ "lsuba_inv_pair2" ]             class "" [ "lsuba_inv_pair2" ]            * ]
+  [ class "" [ "lsuba_fwd_lsubr" ]             class "" [ "lsuba_fwd_lsubr" ]            * ]
+  [ class "" [ "lsuba_refl" ]                  class "" [ "lsuba_refl" ]                 * ]
+  [ class "" [ "lsuba_drop_O1_conf" ]          class "" [ "lsuba_drop_O1_conf" ]         * ]
+  [ class "" [ "lsuba_drop_O1_trans" ]         class "" [ "lsuba_drop_O1_trans" ]        * ]
+  [ class "" [ "lsuba_aaa_conf" ]              class "" [ "lsuba_aaa_conf" ]             * ]
+  [ class "" [ "lsuba_aaa_trans" ]             class "" [ "lsuba_aaa_trans" ]            * ]
+  [ class "" [ "lreq" ]                        class "" [ "lreq" ]                       * ]
+  [ class "" [ "lreq_pair_lt" ]                class "" [ "lreq_pair_lt" ]               * ]
+  [ class "" [ "lreq_succ_lt" ]                class "" [ "lreq_succ_lt" ]               * ]
+  [ class "" [ "lreq_pair_O_Y" ]               class "" [ "lreq_pair_O_Y" ]              * ]
+  [ class "" [ "lreq_refl" ]                   class "" [ "lreq_refl" ]                  * ]
+  [ class "" [ "lreq_O2" ]                     class "" [ "lreq_O2" ]                    * ]
+  [ class "" [ "lreq_sym" ]                    class "" [ "lreq_sym" ]                   * ]
+  [ class "" [ "lreq_inv_atom1_aux" ]          class "" [ "lreq_inv_atom1_aux" ]         * ]
+  [ class "" [ "lreq_inv_atom1" ]              class "" [ "lreq_inv_atom1" ]             * ]
+  [ class "" [ "lreq_inv_zero1_aux" ]          class "" [ "lreq_inv_zero1_aux" ]         * ]
+  [ class "" [ "lreq_inv_zero1" ]              class "" [ "lreq_inv_zero1" ]             * ]
+  [ class "" [ "lreq_inv_pair1_aux" ]          class "" [ "lreq_inv_pair1_aux" ]         * ]
+  [ class "" [ "lreq_inv_pair1" ]              class "" [ "lreq_inv_pair1" ]             * ]
+  [ class "" [ "lreq_inv_pair" ]               class "" [ "lreq_inv_pair" ]              * ]
+  [ class "" [ "lreq_inv_succ1_aux" ]          class "" [ "lreq_inv_succ1_aux" ]         * ]
+  [ class "" [ "lreq_inv_succ1" ]              class "" [ "lreq_inv_succ1" ]             * ]
+  [ class "" [ "lreq_inv_atom2" ]              class "" [ "lreq_inv_atom2" ]             * ]
+  [ class "" [ "lreq_inv_succ" ]               class "" [ "lreq_inv_succ" ]              * ]
+  [ class "" [ "lreq_inv_zero2" ]              class "" [ "lreq_inv_zero2" ]             * ]
+  [ class "" [ "lreq_inv_pair2" ]              class "" [ "lreq_inv_pair2" ]             * ]
+  [ class "" [ "lreq_inv_succ2" ]              class "" [ "lreq_inv_succ2" ]             * ]
+  [ class "" [ "lreq_fwd_length" ]             class "" [ "lreq_fwd_length" ]            * ]
+  [ class "" [ "lreq_inv_O_Y_aux" ]            class "" [ "lreq_inv_O_Y_aux" ]           * ]
+  [ class "" [ "lreq_inv_O_Y" ]                class "" [ "lreq_inv_O_Y" ]               * ]
+  [ class "" [ "lreq_trans" ]                  class "" [ "lreq_trans" ]                 * ]
+  [ class "" [ "lreq_canc_sn" ]                class "" [ "lreq_canc_sn" ]               * ]
+  [ class "" [ "lreq_canc_dx" ]                class "" [ "lreq_canc_dx" ]               * ]
+  [ class "" [ "lreq_join" ]                   class "" [ "lreq_join" ]                  * ]
+  [ class "" [ "dedropable_sn" ]               class "" [ "dedropable_sn" ]              * ]
+  [ class "" [ "lreq_drop_trans_be" ]          class "" [ "lreq_drop_trans_be" ]         * ]
+  [ class "" [ "lreq_drop_conf_be" ]           class "" [ "lreq_drop_conf_be" ]          * ]
+  [ class "" [ "drop_O1_ex" ]                  class "" [ "drop_O1_ex" ]                 * ]
+  [ class "" [ "dedropable_sn_TC" ]            class "" [ "dedropable_sn_TC" ]           * ]
+  [ class "" [ "drop_O1_inj" ]                 class "" [ "drop_O1_inj" ]                * ]
+  [ class "" [ "lpx_sn" ]                      class "" [ "lpx_sn" ]                     * ]
+  [ class "" [ "lpx_sn_refl" ]                 class "" [ "lpx_sn_refl" ]                * ]
+  [ class "" [ "lpx_sn_inv_atom1_aux" ]        class "" [ "lpx_sn_inv_atom1_aux" ]       * ]
+  [ class "" [ "lpx_sn_inv_atom1" ]            class "" [ "lpx_sn_inv_atom1" ]           * ]
+  [ class "" [ "lpx_sn_inv_pair1_aux" ]        class "" [ "lpx_sn_inv_pair1_aux" ]       * ]
+  [ class "" [ "lpx_sn_inv_pair1" ]            class "" [ "lpx_sn_inv_pair1" ]           * ]
+  [ class "" [ "lpx_sn_inv_atom2_aux" ]        class "" [ "lpx_sn_inv_atom2_aux" ]       * ]
+  [ class "" [ "lpx_sn_inv_atom2" ]            class "" [ "lpx_sn_inv_atom2" ]           * ]
+  [ class "" [ "lpx_sn_inv_pair2_aux" ]        class "" [ "lpx_sn_inv_pair2_aux" ]       * ]
+  [ class "" [ "lpx_sn_inv_pair2" ]            class "" [ "lpx_sn_inv_pair2" ]           * ]
+  [ class "" [ "lpx_sn_inv_pair" ]             class "" [ "lpx_sn_inv_pair" ]            * ]
+  [ class "" [ "lpx_sn_fwd_length" ]           class "" [ "lpx_sn_fwd_length" ]          * ]
+  [ class "" [ "lpx_sn_drop_conf" ]            class "" [ "lpx_sn_drop_conf" ]           * ]
+  [ class "" [ "lpx_sn_drop_trans" ]           class "" [ "lpx_sn_drop_trans" ]          * ]
   [ class "" [ "lpx_sn_deliftable_dropable" ]  class "" [ "lpx_sn_deliftable_dropable" ] * ]
   [ class "" [ "lpx_sn_liftable_dedropable" ]  class "" [ "lpx_sn_liftable_dedropable" ] * ]
-  [ class "" [ "lpx_sn_dropable_aux" ]        class "" [ "lpx_sn_dropable_aux" ]        * ]
-  [ class "" [ "lpx_sn_dropable" ]            class "" [ "lpx_sn_dropable" ]            * ]
-  [ class "" [ "fw" ]                         class "" [ "fw" ]                         * ]
-  [ class "" [ "fw_shift" ]                   class "" [ "fw_shift" ]                   * ]
-  [ class "" [ "fw_tpair_sn" ]                class "" [ "fw_tpair_sn" ]                * ]
-  [ class "" [ "fw_tpair_dx" ]                class "" [ "fw_tpair_dx" ]                * ]
-  [ class "" [ "fw_lpair_sn" ]                class "" [ "fw_lpair_sn" ]                * ]
-  [ class "" [ "fqu" ]                        class "" [ "fqu" ]                        * ]
-  [ class "" [ "fqu_drop_lt" ]                class "" [ "fqu_drop_lt" ]                * ]
-  [ class "" [ "fqu_lref_S_lt" ]              class "" [ "fqu_lref_S_lt" ]              * ]
-  [ class "" [ "fqu_fwd_fw" ]                 class "" [ "fqu_fwd_fw" ]                 * ]
+  [ class "" [ "lpx_sn_dropable_aux" ]         class "" [ "lpx_sn_dropable_aux" ]        * ]
+  [ class "" [ "lpx_sn_dropable" ]             class "" [ "lpx_sn_dropable" ]            * ]
+  [ class "" [ "fw" ]                          class "" [ "fw" ]                         * ]
+  [ class "" [ "fw_shift" ]                    class "" [ "fw_shift" ]                   * ]
+  [ class "" [ "fw_tpair_sn" ]                 class "" [ "fw_tpair_sn" ]                * ]
+  [ class "" [ "fw_tpair_dx" ]                 class "" [ "fw_tpair_dx" ]                * ]
+  [ class "" [ "fw_lpair_sn" ]                 class "" [ "fw_lpair_sn" ]                * ]
+  [ class "" [ "fqu" ]                         class "" [ "fqu" ]                        * ]
+  [ class "" [ "fqu_drop_lt" ]                 class "" [ "fqu_drop_lt" ]                * ]
+  [ class "" [ "fqu_lref_S_lt" ]               class "" [ "fqu_lref_S_lt" ]              * ]
+  [ class "" [ "fqu_fwd_fw" ]                  class "" [ "fqu_fwd_fw" ]                 * ]
   [ class "" [ "fqu_fwd_length_lref1_aux" ]    class "" [ "fqu_fwd_length_lref1_aux" ]   * ]
-  [ class "" [ "fqu_fwd_length_lref1" ]               class "" [ "fqu_fwd_length_lref1" ]       * ]
-  [ class "" [ "fqu_inv_eq_aux" ]             class "" [ "fqu_inv_eq_aux" ]             * ]
-  [ class "" [ "fqu_inv_eq" ]                 class "" [ "fqu_inv_eq" ]                 * ]
-  [ class "" [ "fqu_wf_ind" ]                 class "" [ "fqu_wf_ind" ]                 * ]
-  [ class "" [ "fquq" ]                               class "" [ "fquq" ]                       * ]
-  [ class "" [ "fquq_refl" ]                  class "" [ "fquq_refl" ]                  * ]
-  [ class "" [ "fqu_fquq" ]                   class "" [ "fqu_fquq" ]                   * ]
-  [ class "" [ "fquq_fwd_fw" ]                class "" [ "fquq_fwd_fw" ]                * ]
+  [ class "" [ "fqu_fwd_length_lref1" ]        class "" [ "fqu_fwd_length_lref1" ]       * ]
+  [ class "" [ "fqu_inv_eq_aux" ]              class "" [ "fqu_inv_eq_aux" ]             * ]
+  [ class "" [ "fqu_inv_eq" ]                  class "" [ "fqu_inv_eq" ]                 * ]
+  [ class "" [ "fqu_wf_ind" ]                  class "" [ "fqu_wf_ind" ]                 * ]
+  [ class "" [ "fquq" ]                        class "" [ "fquq" ]                       * ]
+  [ class "" [ "fquq_refl" ]                   class "" [ "fquq_refl" ]                  * ]
+  [ class "" [ "fqu_fquq" ]                    class "" [ "fqu_fquq" ]                   * ]
+  [ class "" [ "fquq_fwd_fw" ]                 class "" [ "fquq_fwd_fw" ]                * ]
   [ class "" [ "fquq_fwd_length_lref1_aux" ]   class "" [ "fquq_fwd_length_lref1_aux" ]  * ]
   [ class "" [ "fquq_fwd_length_lref1" ]       class "" [ "fquq_fwd_length_lref1" ]      * ]
-  [ class "" [ "fquqa" ]                      class "" [ "fquqa" ]                      * ]
-  [ class "" [ "fquqa_refl" ]                 class "" [ "fquqa_refl" ]                 * ]
-  [ class "" [ "fquqa_drop" ]                 class "" [ "fquqa_drop" ]                 * ]
-  [ class "" [ "fquq_fquqa" ]                 class "" [ "fquq_fquqa" ]                 * ]
-  [ class "" [ "fquqa_inv_fquq" ]             class "" [ "fquqa_inv_fquq" ]             * ]
-  [ class "" [ "fquq_inv_gen" ]                       class "" [ "fquq_inv_gen" ]               * ]
-  [ class "" [ "fqup" ]                               class "" [ "fqup" ]                       * ]
-  [ class "" [ "fqu_fqup" ]                   class "" [ "fqu_fqup" ]                   * ]
-  [ class "" [ "fqup_strap1" ]                class "" [ "fqup_strap1" ]                * ]
-  [ class "" [ "fqup_strap2" ]                class "" [ "fqup_strap2" ]                * ]
-  [ class "" [ "fqup_drop" ]                  class "" [ "fqup_drop" ]                  * ]
-  [ class "" [ "fqup_lref" ]                  class "" [ "fqup_lref" ]                  * ]
-  [ class "" [ "fqup_pair_sn" ]                       class "" [ "fqup_pair_sn" ]               * ]
-  [ class "" [ "fqup_bind_dx" ]                       class "" [ "fqup_bind_dx" ]               * ]
-  [ class "" [ "fqup_flat_dx" ]                       class "" [ "fqup_flat_dx" ]               * ]
-  [ class "" [ "fqup_flat_dx_pair_sn" ]               class "" [ "fqup_flat_dx_pair_sn" ]       * ]
-  [ class "" [ "fqup_bind_dx_flat_dx" ]               class "" [ "fqup_bind_dx_flat_dx" ]       * ]
-  [ class "" [ "fqup_flat_dx_bind_dx" ]               class "" [ "fqup_flat_dx_bind_dx" ]       * ]
-  [ class "" [ "fqup_ind" ]                   class "" [ "fqup_ind" ]                   * ]
-  [ class "" [ "fqup_ind_dx" ]                class "" [ "fqup_ind_dx" ]                * ]
-  [ class "" [ "fqup_fwd_fw" ]                class "" [ "fqup_fwd_fw" ]                * ]
-  [ class "" [ "fqup_wf_ind" ]                class "" [ "fqup_wf_ind" ]                * ]
-  [ class "" [ "fqup_wf_ind_eq" ]             class "" [ "fqup_wf_ind_eq" ]             * ]
-  [ class "" [ "fqus" ]                               class "" [ "fqus" ]                       * ]
-  [ class "" [ "fqus_ind" ]                   class "" [ "fqus_ind" ]                   * ]
-  [ class "" [ "fqus_ind_dx" ]                class "" [ "fqus_ind_dx" ]                * ]
-  [ class "" [ "fqus_refl" ]                  class "" [ "fqus_refl" ]                  * ]
-  [ class "" [ "fquq_fqus" ]                  class "" [ "fquq_fqus" ]                  * ]
-  [ class "" [ "fqus_strap1" ]                class "" [ "fqus_strap1" ]                * ]
-  [ class "" [ "fqus_strap2" ]                class "" [ "fqus_strap2" ]                * ]
-  [ class "" [ "fqus_drop" ]                  class "" [ "fqus_drop" ]                  * ]
-  [ class "" [ "fqup_fqus" ]                  class "" [ "fqup_fqus" ]                  * ]
-  [ class "" [ "fqus_fwd_fw" ]                class "" [ "fqus_fwd_fw" ]                * ]
-  [ class "" [ "fqup_inv_step_sn" ]           class "" [ "fqup_inv_step_sn" ]           * ]
-  [ class "" [ "fqus_inv_gen" ]                       class "" [ "fqus_inv_gen" ]               * ]
-  [ class "" [ "fqus_strap1_fqu" ]            class "" [ "fqus_strap1_fqu" ]            * ]
-  [ class "" [ "fqus_strap2_fqu" ]            class "" [ "fqus_strap2_fqu" ]            * ]
-  [ class "" [ "fqus_fqup_trans" ]            class "" [ "fqus_fqup_trans" ]            * ]
-  [ class "" [ "fqup_fqus_trans" ]            class "" [ "fqup_fqus_trans" ]            * ]
-  [ class "" [ "cpx" ]                        class "" [ "cpx" ]                        * ]
-  [ class "" [ "lsubr_cpx_trans" ]            class "" [ "lsubr_cpx_trans" ]            * ]
-  [ class "" [ "cpx_refl" ]                   class "" [ "cpx_refl" ]                   * ]
-  [ class "" [ "cpr_cpx" ]                    class "" [ "cpr_cpx" ]                    * ]
-  [ class "" [ "cpx_pair_sn" ]                class "" [ "cpx_pair_sn" ]                * ]
-  [ class "" [ "cpx_delift" ]                 class "" [ "cpx_delift" ]                 * ]
-  [ class "" [ "cpx_inv_atom1_aux" ]          class "" [ "cpx_inv_atom1_aux" ]          * ]
-  [ class "" [ "cpx_inv_atom1" ]              class "" [ "cpx_inv_atom1" ]              * ]
-  [ class "" [ "cpx_inv_sort1" ]              class "" [ "cpx_inv_sort1" ]              * ]
-  [ class "" [ "cpx_inv_lref1" ]              class "" [ "cpx_inv_lref1" ]              * ]
-  [ class "" [ "cpx_inv_lref1_ge" ]           class "" [ "cpx_inv_lref1_ge" ]           * ]
-  [ class "" [ "cpx_inv_gref1" ]              class "" [ "cpx_inv_gref1" ]              * ]
-  [ class "" [ "cpx_inv_bind1_aux" ]          class "" [ "cpx_inv_bind1_aux" ]          * ]
-  [ class "" [ "cpx_inv_bind1" ]              class "" [ "cpx_inv_bind1" ]              * ]
-  [ class "" [ "cpx_inv_abbr1" ]              class "" [ "cpx_inv_abbr1" ]              * ]
-  [ class "" [ "cpx_inv_abst1" ]              class "" [ "cpx_inv_abst1" ]              * ]
-  [ class "" [ "cpx_inv_flat1_aux" ]          class "" [ "cpx_inv_flat1_aux" ]          * ]
-  [ class "" [ "cpx_inv_flat1" ]              class "" [ "cpx_inv_flat1" ]              * ]
-  [ class "" [ "cpx_inv_appl1" ]              class "" [ "cpx_inv_appl1" ]              * ]
-  [ class "" [ "cpx_inv_appl1_simple" ]               class "" [ "cpx_inv_appl1_simple" ]       * ]
-  [ class "" [ "cpx_inv_cast1" ]              class "" [ "cpx_inv_cast1" ]              * ]
-  [ class "" [ "cpx_fwd_bind1_minus" ]        class "" [ "cpx_fwd_bind1_minus" ]        * ]
-  [ class "" [ "sta_cpx_aux" ]                class "" [ "sta_cpx_aux" ]                * ]
-  [ class "" [ "sta_cpx" ]                    class "" [ "sta_cpx" ]                    * ]
-  [ class "" [ "cpx_lift" ]                   class "" [ "cpx_lift" ]                   * ]
-  [ class "" [ "cpx_inv_lift1" ]              class "" [ "cpx_inv_lift1" ]              * ]
-  [ class "" [ "fqu_cpx_trans" ]              class "" [ "fqu_cpx_trans" ]              * ]
-  [ class "" [ "fqu_sta_trans" ]              class "" [ "fqu_sta_trans" ]              * ]
-  [ class "" [ "fquq_cpx_trans" ]             class "" [ "fquq_cpx_trans" ]             * ]
-  [ class "" [ "fquq_sta_trans" ]             class "" [ "fquq_sta_trans" ]             * ]
-  [ class "" [ "fqup_cpx_trans" ]             class "" [ "fqup_cpx_trans" ]             * ]
-  [ class "" [ "fqus_cpx_trans" ]             class "" [ "fqus_cpx_trans" ]             * ]
-  [ class "" [ "fqu_cpx_trans_neq" ]          class "" [ "fqu_cpx_trans_neq" ]          * ]
-  [ class "" [ "fquq_cpx_trans_neq" ]         class "" [ "fquq_cpx_trans_neq" ]         * ]
-  [ class "" [ "fqup_cpx_trans_neq" ]         class "" [ "fqup_cpx_trans_neq" ]         * ]
-  [ class "" [ "fqus_cpx_trans_neq" ]         class "" [ "fqus_cpx_trans_neq" ]         * ]
-  [ class "" [ "lpr" ]                        class "" [ "lpr" ]                        * ]
-  [ class "" [ "lpr_inv_atom1" ]              class "" [ "lpr_inv_atom1" ]              * ]
-  [ class "" [ "lpr_inv_pair1" ]              class "" [ "lpr_inv_pair1" ]              * ]
-  [ class "" [ "lpr_inv_atom2" ]              class "" [ "lpr_inv_atom2" ]              * ]
-  [ class "" [ "lpr_inv_pair2" ]              class "" [ "lpr_inv_pair2" ]              * ]
-  [ class "" [ "lpr_refl" ]                   class "" [ "lpr_refl" ]                   * ]
-  [ class "" [ "lpr_pair" ]                   class "" [ "lpr_pair" ]                   * ]
-  [ class "" [ "lpr_fwd_length" ]             class "" [ "lpr_fwd_length" ]             * ]
-  [ class "" [ "lpx" ]                        class "" [ "lpx" ]                        * ]
-  [ class "" [ "lpx_inv_atom1" ]              class "" [ "lpx_inv_atom1" ]              * ]
-  [ class "" [ "lpx_inv_pair1" ]              class "" [ "lpx_inv_pair1" ]              * ]
-  [ class "" [ "lpx_inv_atom2" ]              class "" [ "lpx_inv_atom2" ]              * ]
-  [ class "" [ "lpx_inv_pair2" ]              class "" [ "lpx_inv_pair2" ]              * ]
-  [ class "" [ "lpx_inv_pair" ]                       class "" [ "lpx_inv_pair" ]               * ]
-  [ class "" [ "lpx_refl" ]                   class "" [ "lpx_refl" ]                   * ]
-  [ class "" [ "lpx_pair" ]                   class "" [ "lpx_pair" ]                   * ]
-  [ class "" [ "lpr_lpx" ]                    class "" [ "lpr_lpx" ]                    * ]
-  [ class "" [ "lpx_fwd_length" ]             class "" [ "lpx_fwd_length" ]             * ]
-  [ class "" [ "lpx_drop_conf" ]              class "" [ "lpx_drop_conf" ]              * ]
-  [ class "" [ "drop_lpx_trans" ]             class "" [ "drop_lpx_trans" ]             * ]
-  [ class "" [ "lpx_drop_trans_O1" ]          class "" [ "lpx_drop_trans_O1" ]          * ]
-  [ class "" [ "fqu_lpx_trans" ]              class "" [ "fqu_lpx_trans" ]              * ]
-  [ class "" [ "fquq_lpx_trans" ]             class "" [ "fquq_lpx_trans" ]             * ]
-  [ class "" [ "lpx_fqu_trans" ]              class "" [ "lpx_fqu_trans" ]              * ]
-  [ class "" [ "lpx_fquq_trans" ]             class "" [ "lpx_fquq_trans" ]             * ]
-  [ class "" [ "cpx_lpx_aaa_conf" ]           class "" [ "cpx_lpx_aaa_conf" ]           * ]
-  [ class "" [ "cpx_aaa_conf" ]                       class "" [ "cpx_aaa_conf" ]               * ]
-  [ class "" [ "lpx_aaa_conf" ]                       class "" [ "lpx_aaa_conf" ]               * ]
-  [ class "" [ "cpr_aaa_conf" ]                       class "" [ "cpr_aaa_conf" ]               * ]
-  [ class "" [ "lpr_aaa_conf" ]                       class "" [ "lpr_aaa_conf" ]               * ]
-  [ class "" [ "cnx" ]                        class "" [ "cnx" ]                        * ]
-  [ class "" [ "cnx_inv_sort" ]                       class "" [ "cnx_inv_sort" ]               * ]
-  [ class "" [ "cnx_inv_delta" ]              class "" [ "cnx_inv_delta" ]              * ]
-  [ class "" [ "cnx_inv_abst" ]                       class "" [ "cnx_inv_abst" ]               * ]
-  [ class "" [ "cnx_inv_abbr" ]                       class "" [ "cnx_inv_abbr" ]               * ]
-  [ class "" [ "cnx_inv_zeta" ]                       class "" [ "cnx_inv_zeta" ]               * ]
-  [ class "" [ "cnx_inv_appl" ]                       class "" [ "cnx_inv_appl" ]               * ]
-  [ class "" [ "cnx_inv_eps" ]                class "" [ "cnx_inv_eps" ]                * ]
-  [ class "" [ "cnx_fwd_cnr" ]                class "" [ "cnx_fwd_cnr" ]                * ]
-  [ class "" [ "cnx_sort" ]                   class "" [ "cnx_sort" ]                   * ]
-  [ class "" [ "cnx_sort_iter" ]              class "" [ "cnx_sort_iter" ]              * ]
-  [ class "" [ "cnx_lref_free" ]              class "" [ "cnx_lref_free" ]              * ]
-  [ class "" [ "cnx_lref_atom" ]              class "" [ "cnx_lref_atom" ]              * ]
-  [ class "" [ "cnx_abst" ]                   class "" [ "cnx_abst" ]                   * ]
-  [ class "" [ "cnx_appl_simple" ]            class "" [ "cnx_appl_simple" ]            * ]
-  [ class "" [ "cnx_dec" ]                    class "" [ "cnx_dec" ]                    * ]
-  [ class "" [ "cpxs" ]                               class "" [ "cpxs" ]                       * ]
-  [ class "" [ "cpxs_ind" ]                   class "" [ "cpxs_ind" ]                   * ]
-  [ class "" [ "cpxs_ind_dx" ]                class "" [ "cpxs_ind_dx" ]                * ]
-  [ class "" [ "cpxs_refl" ]                  class "" [ "cpxs_refl" ]                  * ]
-  [ class "" [ "cpx_cpxs" ]                   class "" [ "cpx_cpxs" ]                   * ]
-  [ class "" [ "cpxs_strap1" ]                class "" [ "cpxs_strap1" ]                * ]
-  [ class "" [ "cpxs_strap2" ]                class "" [ "cpxs_strap2" ]                * ]
-  [ class "" [ "lsubr_cpxs_trans" ]           class "" [ "lsubr_cpxs_trans" ]           * ]
-  [ class "" [ "cprs_cpxs" ]                  class "" [ "cprs_cpxs" ]                  * ]
-  [ class "" [ "cpxs_sort" ]                  class "" [ "cpxs_sort" ]                  * ]
-  [ class "" [ "cpxs_bind_dx" ]                       class "" [ "cpxs_bind_dx" ]               * ]
-  [ class "" [ "cpxs_flat_dx" ]                       class "" [ "cpxs_flat_dx" ]               * ]
-  [ class "" [ "cpxs_flat_sn" ]                       class "" [ "cpxs_flat_sn" ]               * ]
-  [ class "" [ "cpxs_pair_sn" ]                       class "" [ "cpxs_pair_sn" ]               * ]
-  [ class "" [ "cpxs_zeta" ]                  class "" [ "cpxs_zeta" ]                  * ]
-  [ class "" [ "cpxs_eps" ]                   class "" [ "cpxs_eps" ]                   * ]
-  [ class "" [ "cpxs_ct" ]                    class "" [ "cpxs_ct" ]                    * ]
-  [ class "" [ "cpxs_beta_dx" ]                       class "" [ "cpxs_beta_dx" ]               * ]
-  [ class "" [ "cpxs_theta_dx" ]              class "" [ "cpxs_theta_dx" ]              * ]
-  [ class "" [ "cpxs_inv_sort1" ]             class "" [ "cpxs_inv_sort1" ]             * ]
-  [ class "" [ "cpxs_inv_cast1" ]             class "" [ "cpxs_inv_cast1" ]             * ]
-  [ class "" [ "cpxs_inv_cnx1" ]              class "" [ "cpxs_inv_cnx1" ]              * ]
-  [ class "" [ "cpxs_neq_inv_step_sn" ]               class "" [ "cpxs_neq_inv_step_sn" ]       * ]
-  [ class "" [ "cpxs_aaa_conf" ]              class "" [ "cpxs_aaa_conf" ]              * ]
-  [ class "" [ "cprs_aaa_conf" ]              class "" [ "cprs_aaa_conf" ]              * ]
-  [ class "" [ "lpx_sn_confluent" ]           class "" [ "lpx_sn_confluent" ]           * ]
-  [ class "" [ "lpx_sn_transitive" ]          class "" [ "lpx_sn_transitive" ]          * ]
-  [ class "" [ "lpx_sn_trans" ]                       class "" [ "lpx_sn_trans" ]               * ]
-  [ class "" [ "lpx_sn_conf" ]                class "" [ "lpx_sn_conf" ]                * ]
-  [ class "" [ "cpr_lift" ]                   class "" [ "cpr_lift" ]                   * ]
-  [ class "" [ "cpr_inv_lift1" ]              class "" [ "cpr_inv_lift1" ]              * ]
-  [ class "" [ "lpr_drop_conf" ]              class "" [ "lpr_drop_conf" ]              * ]
-  [ class "" [ "drop_lpr_trans" ]             class "" [ "drop_lpr_trans" ]             * ]
-  [ class "" [ "lpr_drop_trans_O1" ]          class "" [ "lpr_drop_trans_O1" ]          * ]
-  [ class "" [ "fqu_cpr_trans_dx" ]           class "" [ "fqu_cpr_trans_dx" ]           * ]
-  [ class "" [ "fquq_cpr_trans_dx" ]          class "" [ "fquq_cpr_trans_dx" ]          * ]
-  [ class "" [ "fqu_cpr_trans_sn" ]           class "" [ "fqu_cpr_trans_sn" ]           * ]
-  [ class "" [ "fquq_cpr_trans_sn" ]          class "" [ "fquq_cpr_trans_sn" ]          * ]
-  [ class "" [ "fqu_lpr_trans" ]              class "" [ "fqu_lpr_trans" ]              * ]
-  [ class "" [ "fquq_lpr_trans" ]             class "" [ "fquq_lpr_trans" ]             * ]
+  [ class "" [ "fquqa" ]                       class "" [ "fquqa" ]                      * ]
+  [ class "" [ "fquqa_refl" ]                  class "" [ "fquqa_refl" ]                 * ]
+  [ class "" [ "fquqa_drop" ]                  class "" [ "fquqa_drop" ]                 * ]
+  [ class "" [ "fquq_fquqa" ]                  class "" [ "fquq_fquqa" ]                 * ]
+  [ class "" [ "fquqa_inv_fquq" ]              class "" [ "fquqa_inv_fquq" ]             * ]
+  [ class "" [ "fquq_inv_gen" ]                class "" [ "fquq_inv_gen" ]               * ]
+  [ class "" [ "fqup" ]                        class "" [ "fqup" ]                       * ]
+  [ class "" [ "fqu_fqup" ]                    class "" [ "fqu_fqup" ]                   * ]
+  [ class "" [ "fqup_strap1" ]                 class "" [ "fqup_strap1" ]                * ]
+  [ class "" [ "fqup_strap2" ]                 class "" [ "fqup_strap2" ]                * ]
+  [ class "" [ "fqup_drop" ]                   class "" [ "fqup_drop" ]                  * ]
+  [ class "" [ "fqup_lref" ]                   class "" [ "fqup_lref" ]                  * ]
+  [ class "" [ "fqup_pair_sn" ]                class "" [ "fqup_pair_sn" ]               * ]
+  [ class "" [ "fqup_bind_dx" ]                class "" [ "fqup_bind_dx" ]               * ]
+  [ class "" [ "fqup_flat_dx" ]                class "" [ "fqup_flat_dx" ]               * ]
+  [ class "" [ "fqup_flat_dx_pair_sn" ]        class "" [ "fqup_flat_dx_pair_sn" ]       * ]
+  [ class "" [ "fqup_bind_dx_flat_dx" ]        class "" [ "fqup_bind_dx_flat_dx" ]       * ]
+  [ class "" [ "fqup_flat_dx_bind_dx" ]        class "" [ "fqup_flat_dx_bind_dx" ]       * ]
+  [ class "" [ "fqup_ind" ]                    class "" [ "fqup_ind" ]                   * ]
+  [ class "" [ "fqup_ind_dx" ]                 class "" [ "fqup_ind_dx" ]                * ]
+  [ class "" [ "fqup_fwd_fw" ]                 class "" [ "fqup_fwd_fw" ]                * ]
+  [ class "" [ "fqup_wf_ind" ]                 class "" [ "fqup_wf_ind" ]                * ]
+  [ class "" [ "fqup_wf_ind_eq" ]              class "" [ "fqup_wf_ind_eq" ]             * ]
+  [ class "" [ "fqus" ]                        class "" [ "fqus" ]                       * ]
+  [ class "" [ "fqus_ind" ]                    class "" [ "fqus_ind" ]                   * ]
+  [ class "" [ "fqus_ind_dx" ]                 class "" [ "fqus_ind_dx" ]                * ]
+  [ class "" [ "fqus_refl" ]                   class "" [ "fqus_refl" ]                  * ]
+  [ class "" [ "fquq_fqus" ]                   class "" [ "fquq_fqus" ]                  * ]
+  [ class "" [ "fqus_strap1" ]                 class "" [ "fqus_strap1" ]                * ]
+  [ class "" [ "fqus_strap2" ]                 class "" [ "fqus_strap2" ]                * ]
+  [ class "" [ "fqus_drop" ]                   class "" [ "fqus_drop" ]                  * ]
+  [ class "" [ "fqup_fqus" ]                   class "" [ "fqup_fqus" ]                  * ]
+  [ class "" [ "fqus_fwd_fw" ]                 class "" [ "fqus_fwd_fw" ]                * ]
+  [ class "" [ "fqup_inv_step_sn" ]            class "" [ "fqup_inv_step_sn" ]           * ]
+  [ class "" [ "fqus_inv_gen" ]                class "" [ "fqus_inv_gen" ]               * ]
+  [ class "" [ "fqus_strap1_fqu" ]             class "" [ "fqus_strap1_fqu" ]            * ]
+  [ class "" [ "fqus_strap2_fqu" ]             class "" [ "fqus_strap2_fqu" ]            * ]
+  [ class "" [ "fqus_fqup_trans" ]             class "" [ "fqus_fqup_trans" ]            * ]
+  [ class "" [ "fqup_fqus_trans" ]             class "" [ "fqup_fqus_trans" ]            * ]
+  [ class "" [ "cpx" ]                         class "" [ "cpx" ]                        * ]
+  [ class "" [ "lsubr_cpx_trans" ]             class "" [ "lsubr_cpx_trans" ]            * ]
+  [ class "" [ "cpx_refl" ]                    class "" [ "cpx_refl" ]                   * ]
+  [ class "" [ "cpr_cpx" ]                     class "" [ "cpr_cpx" ]                    * ]
+  [ class "" [ "cpx_pair_sn" ]                 class "" [ "cpx_pair_sn" ]                * ]
+  [ class "" [ "cpx_delift" ]                  class "" [ "cpx_delift" ]                 * ]
+  [ class "" [ "cpx_inv_atom1_aux" ]           class "" [ "cpx_inv_atom1_aux" ]          * ]
+  [ class "" [ "cpx_inv_atom1" ]               class "" [ "cpx_inv_atom1" ]              * ]
+  [ class "" [ "cpx_inv_sort1" ]               class "" [ "cpx_inv_sort1" ]              * ]
+  [ class "" [ "cpx_inv_lref1" ]               class "" [ "cpx_inv_lref1" ]              * ]
+  [ class "" [ "cpx_inv_lref1_ge" ]            class "" [ "cpx_inv_lref1_ge" ]           * ]
+  [ class "" [ "cpx_inv_gref1" ]               class "" [ "cpx_inv_gref1" ]              * ]
+  [ class "" [ "cpx_inv_bind1_aux" ]           class "" [ "cpx_inv_bind1_aux" ]          * ]
+  [ class "" [ "cpx_inv_bind1" ]               class "" [ "cpx_inv_bind1" ]              * ]
+  [ class "" [ "cpx_inv_abbr1" ]               class "" [ "cpx_inv_abbr1" ]              * ]
+  [ class "" [ "cpx_inv_abst1" ]               class "" [ "cpx_inv_abst1" ]              * ]
+  [ class "" [ "cpx_inv_flat1_aux" ]           class "" [ "cpx_inv_flat1_aux" ]          * ]
+  [ class "" [ "cpx_inv_flat1" ]               class "" [ "cpx_inv_flat1" ]              * ]
+  [ class "" [ "cpx_inv_appl1" ]               class "" [ "cpx_inv_appl1" ]              * ]
+  [ class "" [ "cpx_inv_appl1_simple" ]        class "" [ "cpx_inv_appl1_simple" ]       * ]
+  [ class "" [ "cpx_inv_cast1" ]               class "" [ "cpx_inv_cast1" ]              * ]
+  [ class "" [ "cpx_fwd_bind1_minus" ]         class "" [ "cpx_fwd_bind1_minus" ]        * ]
+  [ class "" [ "sta_cpx_aux" ]                 class "" [ "sta_cpx_aux" ]                * ]
+  [ class "" [ "sta_cpx" ]                     class "" [ "sta_cpx" ]                    * ]
+  [ class "" [ "cpx_lift" ]                    class "" [ "cpx_lift" ]                   * ]
+  [ class "" [ "cpx_inv_lift1" ]               class "" [ "cpx_inv_lift1" ]              * ]
+  [ class "" [ "fqu_cpx_trans" ]               class "" [ "fqu_cpx_trans" ]              * ]
+  [ class "" [ "fqu_sta_trans" ]               class "" [ "fqu_sta_trans" ]              * ]
+  [ class "" [ "fquq_cpx_trans" ]              class "" [ "fquq_cpx_trans" ]             * ]
+  [ class "" [ "fquq_sta_trans" ]              class "" [ "fquq_sta_trans" ]             * ]
+  [ class "" [ "fqup_cpx_trans" ]              class "" [ "fqup_cpx_trans" ]             * ]
+  [ class "" [ "fqus_cpx_trans" ]              class "" [ "fqus_cpx_trans" ]             * ]
+  [ class "" [ "fqu_cpx_trans_neq" ]           class "" [ "fqu_cpx_trans_neq" ]          * ]
+  [ class "" [ "fquq_cpx_trans_neq" ]          class "" [ "fquq_cpx_trans_neq" ]         * ]
+  [ class "" [ "fqup_cpx_trans_neq" ]          class "" [ "fqup_cpx_trans_neq" ]         * ]
+  [ class "" [ "fqus_cpx_trans_neq" ]          class "" [ "fqus_cpx_trans_neq" ]         * ]
+  [ class "" [ "lpr" ]                         class "" [ "lpr" ]                        * ]
+  [ class "" [ "lpr_inv_atom1" ]               class "" [ "lpr_inv_atom1" ]              * ]
+  [ class "" [ "lpr_inv_pair1" ]               class "" [ "lpr_inv_pair1" ]              * ]
+  [ class "" [ "lpr_inv_atom2" ]               class "" [ "lpr_inv_atom2" ]              * ]
+  [ class "" [ "lpr_inv_pair2" ]               class "" [ "lpr_inv_pair2" ]              * ]
+  [ class "" [ "lpr_refl" ]                    class "" [ "lpr_refl" ]                   * ]
+  [ class "" [ "lpr_pair" ]                    class "" [ "lpr_pair" ]                   * ]
+  [ class "" [ "lpr_fwd_length" ]              class "" [ "lpr_fwd_length" ]             * ]
+  [ class "" [ "lpx" ]                         class "" [ "lpx" ]                        * ]
+  [ class "" [ "lpx_inv_atom1" ]               class "" [ "lpx_inv_atom1" ]              * ]
+  [ class "" [ "lpx_inv_pair1" ]               class "" [ "lpx_inv_pair1" ]              * ]
+  [ class "" [ "lpx_inv_atom2" ]               class "" [ "lpx_inv_atom2" ]              * ]
+  [ class "" [ "lpx_inv_pair2" ]               class "" [ "lpx_inv_pair2" ]              * ]
+  [ class "" [ "lpx_inv_pair" ]                class "" [ "lpx_inv_pair" ]               * ]
+  [ class "" [ "lpx_refl" ]                    class "" [ "lpx_refl" ]                   * ]
+  [ class "" [ "lpx_pair" ]                    class "" [ "lpx_pair" ]                   * ]
+  [ class "" [ "lpr_lpx" ]                     class "" [ "lpr_lpx" ]                    * ]
+  [ class "" [ "lpx_fwd_length" ]              class "" [ "lpx_fwd_length" ]             * ]
+  [ class "" [ "lpx_drop_conf" ]               class "" [ "lpx_drop_conf" ]              * ]
+  [ class "" [ "drop_lpx_trans" ]              class "" [ "drop_lpx_trans" ]             * ]
+  [ class "" [ "lpx_drop_trans_O1" ]           class "" [ "lpx_drop_trans_O1" ]          * ]
+  [ class "" [ "fqu_lpx_trans" ]               class "" [ "fqu_lpx_trans" ]              * ]
+  [ class "" [ "fquq_lpx_trans" ]              class "" [ "fquq_lpx_trans" ]             * ]
+  [ class "" [ "lpx_fqu_trans" ]               class "" [ "lpx_fqu_trans" ]              * ]
+  [ class "" [ "lpx_fquq_trans" ]              class "" [ "lpx_fquq_trans" ]             * ]
+  [ class "" [ "cpx_lpx_aaa_conf" ]            class "" [ "cpx_lpx_aaa_conf" ]           * ]
+  [ class "" [ "cpx_aaa_conf" ]                class "" [ "cpx_aaa_conf" ]               * ]
+  [ class "" [ "lpx_aaa_conf" ]                class "" [ "lpx_aaa_conf" ]               * ]
+  [ class "" [ "cpr_aaa_conf" ]                class "" [ "cpr_aaa_conf" ]               * ]
+  [ class "" [ "lpr_aaa_conf" ]                class "" [ "lpr_aaa_conf" ]               * ]
+  [ class "" [ "cnx" ]                         class "" [ "cnx" ]                        * ]
+  [ class "" [ "cnx_inv_sort" ]                class "" [ "cnx_inv_sort" ]               * ]
+  [ class "" [ "cnx_inv_delta" ]               class "" [ "cnx_inv_delta" ]              * ]
+  [ class "" [ "cnx_inv_abst" ]                class "" [ "cnx_inv_abst" ]               * ]
+  [ class "" [ "cnx_inv_abbr" ]                class "" [ "cnx_inv_abbr" ]               * ]
+  [ class "" [ "cnx_inv_zeta" ]                class "" [ "cnx_inv_zeta" ]               * ]
+  [ class "" [ "cnx_inv_appl" ]                class "" [ "cnx_inv_appl" ]               * ]
+  [ class "" [ "cnx_inv_eps" ]                 class "" [ "cnx_inv_eps" ]                * ]
+  [ class "" [ "cnx_fwd_cnr" ]                 class "" [ "cnx_fwd_cnr" ]                * ]
+  [ class "" [ "cnx_sort" ]                    class "" [ "cnx_sort" ]                   * ]
+  [ class "" [ "cnx_sort_iter" ]               class "" [ "cnx_sort_iter" ]              * ]
+  [ class "" [ "cnx_lref_free" ]               class "" [ "cnx_lref_free" ]              * ]
+  [ class "" [ "cnx_lref_atom" ]               class "" [ "cnx_lref_atom" ]              * ]
+  [ class "" [ "cnx_abst" ]                    class "" [ "cnx_abst" ]                   * ]
+  [ class "" [ "cnx_appl_simple" ]             class "" [ "cnx_appl_simple" ]            * ]
+  [ class "" [ "cnx_dec" ]                     class "" [ "cnx_dec" ]                    * ]
+  [ class "" [ "cpxs" ]                        class "" [ "cpxs" ]                       * ]
+  [ class "" [ "cpxs_ind" ]                    class "" [ "cpxs_ind" ]                   * ]
+  [ class "" [ "cpxs_ind_dx" ]                 class "" [ "cpxs_ind_dx" ]                * ]
+  [ class "" [ "cpxs_refl" ]                   class "" [ "cpxs_refl" ]                  * ]
+  [ class "" [ "cpx_cpxs" ]                    class "" [ "cpx_cpxs" ]                   * ]
+  [ class "" [ "cpxs_strap1" ]                 class "" [ "cpxs_strap1" ]                * ]
+  [ class "" [ "cpxs_strap2" ]                 class "" [ "cpxs_strap2" ]                * ]
+  [ class "" [ "lsubr_cpxs_trans" ]            class "" [ "lsubr_cpxs_trans" ]           * ]
+  [ class "" [ "cprs_cpxs" ]                   class "" [ "cprs_cpxs" ]                  * ]
+  [ class "" [ "cpxs_sort" ]                   class "" [ "cpxs_sort" ]                  * ]
+  [ class "" [ "cpxs_bind_dx" ]                class "" [ "cpxs_bind_dx" ]               * ]
+  [ class "" [ "cpxs_flat_dx" ]                class "" [ "cpxs_flat_dx" ]               * ]
+  [ class "" [ "cpxs_flat_sn" ]                class "" [ "cpxs_flat_sn" ]               * ]
+  [ class "" [ "cpxs_pair_sn" ]                class "" [ "cpxs_pair_sn" ]               * ]
+  [ class "" [ "cpxs_zeta" ]                   class "" [ "cpxs_zeta" ]                  * ]
+  [ class "" [ "cpxs_eps" ]                    class "" [ "cpxs_eps" ]                   * ]
+  [ class "" [ "cpxs_ct" ]                     class "" [ "cpxs_ct" ]                    * ]
+  [ class "" [ "cpxs_beta_dx" ]                class "" [ "cpxs_beta_dx" ]               * ]
+  [ class "" [ "cpxs_theta_dx" ]               class "" [ "cpxs_theta_dx" ]              * ]
+  [ class "" [ "cpxs_inv_sort1" ]              class "" [ "cpxs_inv_sort1" ]             * ]
+  [ class "" [ "cpxs_inv_cast1" ]              class "" [ "cpxs_inv_cast1" ]             * ]
+  [ class "" [ "cpxs_inv_cnx1" ]               class "" [ "cpxs_inv_cnx1" ]              * ]
+  [ class "" [ "cpxs_neq_inv_step_sn" ]        class "" [ "cpxs_neq_inv_step_sn" ]       * ]
+  [ class "" [ "cpxs_aaa_conf" ]               class "" [ "cpxs_aaa_conf" ]              * ]
+  [ class "" [ "cprs_aaa_conf" ]               class "" [ "cprs_aaa_conf" ]              * ]
+  [ class "" [ "lpx_sn_confluent" ]            class "" [ "lpx_sn_confluent" ]           * ]
+  [ class "" [ "lpx_sn_transitive" ]           class "" [ "lpx_sn_transitive" ]          * ]
+  [ class "" [ "lpx_sn_trans" ]                class "" [ "lpx_sn_trans" ]               * ]
+  [ class "" [ "lpx_sn_conf" ]                 class "" [ "lpx_sn_conf" ]                * ]
+  [ class "" [ "cpr_lift" ]                    class "" [ "cpr_lift" ]                   * ]
+  [ class "" [ "cpr_inv_lift1" ]               class "" [ "cpr_inv_lift1" ]              * ]
+  [ class "" [ "lpr_drop_conf" ]               class "" [ "lpr_drop_conf" ]              * ]
+  [ class "" [ "drop_lpr_trans" ]              class "" [ "drop_lpr_trans" ]             * ]
+  [ class "" [ "lpr_drop_trans_O1" ]           class "" [ "lpr_drop_trans_O1" ]          * ]
+  [ class "" [ "fqu_cpr_trans_dx" ]            class "" [ "fqu_cpr_trans_dx" ]           * ]
+  [ class "" [ "fquq_cpr_trans_dx" ]           class "" [ "fquq_cpr_trans_dx" ]          * ]
+  [ class "" [ "fqu_cpr_trans_sn" ]            class "" [ "fqu_cpr_trans_sn" ]           * ]
+  [ class "" [ "fquq_cpr_trans_sn" ]           class "" [ "fquq_cpr_trans_sn" ]          * ]
+  [ class "" [ "fqu_lpr_trans" ]               class "" [ "fqu_lpr_trans" ]              * ]
+  [ class "" [ "fquq_lpr_trans" ]              class "" [ "fquq_lpr_trans" ]             * ]
   [ class "" [ "cpr_conf_lpr_atom_atom" ]      class "" [ "cpr_conf_lpr_atom_atom" ]     * ]
   [ class "" [ "cpr_conf_lpr_atom_delta" ]     class "" [ "cpr_conf_lpr_atom_delta" ]    * ]
   [ class "" [ "cpr_conf_lpr_delta_delta" ]    class "" [ "cpr_conf_lpr_delta_delta" ]   * ]
@@ -592,506 +592,506 @@ table {
   [ class "" [ "cpr_conf_lpr_zeta_zeta" ]      class "" [ "cpr_conf_lpr_zeta_zeta" ]     * ]
   [ class "" [ "cpr_conf_lpr_flat_flat" ]      class "" [ "cpr_conf_lpr_flat_flat" ]     * ]
   [ class "" [ "cpr_conf_lpr_flat_eps" ]       class "" [ "cpr_conf_lpr_flat_eps" ]      * ]
-  [ class "" [ "cpr_conf_lpr_eps_eps" ]               class "" [ "cpr_conf_lpr_eps_eps" ]       * ]
+  [ class "" [ "cpr_conf_lpr_eps_eps" ]        class "" [ "cpr_conf_lpr_eps_eps" ]       * ]
   [ class "" [ "cpr_conf_lpr_flat_beta" ]      class "" [ "cpr_conf_lpr_flat_beta" ]     * ]
   [ class "" [ "cpr_conf_lpr_flat_theta" ]     class "" [ "cpr_conf_lpr_flat_theta" ]    * ]
   [ class "" [ "cpr_conf_lpr_beta_beta" ]      class "" [ "cpr_conf_lpr_beta_beta" ]     * ]
   [ class "" [ "cpr_conf_lpr_theta_theta" ]    class "" [ "cpr_conf_lpr_theta_theta" ]   * ]
-  [ class "" [ "cpr_conf_lpr" ]                       class "" [ "cpr_conf_lpr" ]               * ]
-  [ class "" [ "cpr_conf" ]                   class "" [ "cpr_conf" ]                   * ]
-  [ class "" [ "lpr_cpr_conf_dx" ]            class "" [ "lpr_cpr_conf_dx" ]            * ]
-  [ class "" [ "lpr_cpr_conf_sn" ]            class "" [ "lpr_cpr_conf_sn" ]            * ]
-  [ class "" [ "lpr_conf" ]                   class "" [ "lpr_conf" ]                   * ]
-  [ class "" [ "cprs_delta" ]                 class "" [ "cprs_delta" ]                 * ]
-  [ class "" [ "cprs_inv_lref1" ]             class "" [ "cprs_inv_lref1" ]             * ]
-  [ class "" [ "cprs_lift" ]                  class "" [ "cprs_lift" ]                  * ]
-  [ class "" [ "cprs_inv_lift1" ]             class "" [ "cprs_inv_lift1" ]             * ]
-  [ class "" [ "cprs_trans" ]                 class "" [ "cprs_trans" ]                 * ]
-  [ class "" [ "cprs_conf" ]                  class "" [ "cprs_conf" ]                  * ]
-  [ class "" [ "cprs_bind" ]                  class "" [ "cprs_bind" ]                  * ]
-  [ class "" [ "cprs_flat" ]                  class "" [ "cprs_flat" ]                  * ]
-  [ class "" [ "cprs_beta_rc" ]                       class "" [ "cprs_beta_rc" ]               * ]
-  [ class "" [ "cprs_beta" ]                  class "" [ "cprs_beta" ]                  * ]
-  [ class "" [ "cprs_theta_rc" ]              class "" [ "cprs_theta_rc" ]              * ]
-  [ class "" [ "cprs_theta" ]                 class "" [ "cprs_theta" ]                 * ]
-  [ class "" [ "cprs_inv_appl1" ]             class "" [ "cprs_inv_appl1" ]             * ]
-  [ class "" [ "lpr_cpr_trans" ]              class "" [ "lpr_cpr_trans" ]              * ]
-  [ class "" [ "cpr_bind2" ]                  class "" [ "cpr_bind2" ]                  * ]
-  [ class "" [ "lpr_cprs_trans" ]             class "" [ "lpr_cprs_trans" ]             * ]
-  [ class "" [ "cprs_strip" ]                 class "" [ "cprs_strip" ]                 * ]
-  [ class "" [ "cprs_lpr_conf_dx" ]           class "" [ "cprs_lpr_conf_dx" ]           * ]
-  [ class "" [ "cprs_lpr_conf_sn" ]           class "" [ "cprs_lpr_conf_sn" ]           * ]
-  [ class "" [ "cprs_bind2_dx" ]              class "" [ "cprs_bind2_dx" ]              * ]
-  [ class "" [ "TC_lpx_sn_pair_refl" ]        class "" [ "TC_lpx_sn_pair_refl" ]        * ]
-  [ class "" [ "TC_lpx_sn_pair" ]             class "" [ "TC_lpx_sn_pair" ]             * ]
-  [ class "" [ "lpx_sn_LTC_TC_lpx_sn" ]               class "" [ "lpx_sn_LTC_TC_lpx_sn" ]       * ]
-  [ class "" [ "TC_lpx_sn_inv_atom2" ]        class "" [ "TC_lpx_sn_inv_atom2" ]        * ]
-  [ class "" [ "TC_lpx_sn_inv_pair2" ]        class "" [ "TC_lpx_sn_inv_pair2" ]        * ]
-  [ class "" [ "TC_lpx_sn_ind" ]              class "" [ "TC_lpx_sn_ind" ]              * ]
-  [ class "" [ "TC_lpx_sn_inv_atom1" ]        class "" [ "TC_lpx_sn_inv_atom1" ]        * ]
+  [ class "" [ "cpr_conf_lpr" ]                class "" [ "cpr_conf_lpr" ]               * ]
+  [ class "" [ "cpr_conf" ]                    class "" [ "cpr_conf" ]                   * ]
+  [ class "" [ "lpr_cpr_conf_dx" ]             class "" [ "lpr_cpr_conf_dx" ]            * ]
+  [ class "" [ "lpr_cpr_conf_sn" ]             class "" [ "lpr_cpr_conf_sn" ]            * ]
+  [ class "" [ "lpr_conf" ]                    class "" [ "lpr_conf" ]                   * ]
+  [ class "" [ "cprs_delta" ]                  class "" [ "cprs_delta" ]                 * ]
+  [ class "" [ "cprs_inv_lref1" ]              class "" [ "cprs_inv_lref1" ]             * ]
+  [ class "" [ "cprs_lift" ]                   class "" [ "cprs_lift" ]                  * ]
+  [ class "" [ "cprs_inv_lift1" ]              class "" [ "cprs_inv_lift1" ]             * ]
+  [ class "" [ "cprs_trans" ]                  class "" [ "cprs_trans" ]                 * ]
+  [ class "" [ "cprs_conf" ]                   class "" [ "cprs_conf" ]                  * ]
+  [ class "" [ "cprs_bind" ]                   class "" [ "cprs_bind" ]                  * ]
+  [ class "" [ "cprs_flat" ]                   class "" [ "cprs_flat" ]                  * ]
+  [ class "" [ "cprs_beta_rc" ]                class "" [ "cprs_beta_rc" ]               * ]
+  [ class "" [ "cprs_beta" ]                   class "" [ "cprs_beta" ]                  * ]
+  [ class "" [ "cprs_theta_rc" ]               class "" [ "cprs_theta_rc" ]              * ]
+  [ class "" [ "cprs_theta" ]                  class "" [ "cprs_theta" ]                 * ]
+  [ class "" [ "cprs_inv_appl1" ]              class "" [ "cprs_inv_appl1" ]             * ]
+  [ class "" [ "lpr_cpr_trans" ]               class "" [ "lpr_cpr_trans" ]              * ]
+  [ class "" [ "cpr_bind2" ]                   class "" [ "cpr_bind2" ]                  * ]
+  [ class "" [ "lpr_cprs_trans" ]              class "" [ "lpr_cprs_trans" ]             * ]
+  [ class "" [ "cprs_strip" ]                  class "" [ "cprs_strip" ]                 * ]
+  [ class "" [ "cprs_lpr_conf_dx" ]            class "" [ "cprs_lpr_conf_dx" ]           * ]
+  [ class "" [ "cprs_lpr_conf_sn" ]            class "" [ "cprs_lpr_conf_sn" ]           * ]
+  [ class "" [ "cprs_bind2_dx" ]               class "" [ "cprs_bind2_dx" ]              * ]
+  [ class "" [ "TC_lpx_sn_pair_refl" ]         class "" [ "TC_lpx_sn_pair_refl" ]        * ]
+  [ class "" [ "TC_lpx_sn_pair" ]              class "" [ "TC_lpx_sn_pair" ]             * ]
+  [ class "" [ "lpx_sn_LTC_TC_lpx_sn" ]        class "" [ "lpx_sn_LTC_TC_lpx_sn" ]       * ]
+  [ class "" [ "TC_lpx_sn_inv_atom2" ]         class "" [ "TC_lpx_sn_inv_atom2" ]        * ]
+  [ class "" [ "TC_lpx_sn_inv_pair2" ]         class "" [ "TC_lpx_sn_inv_pair2" ]        * ]
+  [ class "" [ "TC_lpx_sn_ind" ]               class "" [ "TC_lpx_sn_ind" ]              * ]
+  [ class "" [ "TC_lpx_sn_inv_atom1" ]         class "" [ "TC_lpx_sn_inv_atom1" ]        * ]
   [ class "" [ "TC_lpx_sn_inv_pair1_aux" ]     class "" [ "TC_lpx_sn_inv_pair1_aux" ]    * ]
-  [ class "" [ "TC_lpx_sn_inv_pair1" ]        class "" [ "TC_lpx_sn_inv_pair1" ]        * ]
+  [ class "" [ "TC_lpx_sn_inv_pair1" ]         class "" [ "TC_lpx_sn_inv_pair1" ]        * ]
   [ class "" [ "TC_lpx_sn_inv_lpx_sn_LTC" ]    class "" [ "TC_lpx_sn_inv_lpx_sn_LTC" ]   * ]
-  [ class "" [ "TC_lpx_sn_fwd_length" ]               class "" [ "TC_lpx_sn_fwd_length" ]       * ]
-  [ class "" [ "lprs" ]                               class "" [ "lprs" ]                       * ]
-  [ class "" [ "lprs_ind" ]                   class "" [ "lprs_ind" ]                   * ]
-  [ class "" [ "lprs_ind_dx" ]                class "" [ "lprs_ind_dx" ]                * ]
-  [ class "" [ "lpr_lprs" ]                   class "" [ "lpr_lprs" ]                   * ]
-  [ class "" [ "lprs_refl" ]                  class "" [ "lprs_refl" ]                  * ]
-  [ class "" [ "lprs_strap1" ]                class "" [ "lprs_strap1" ]                * ]
-  [ class "" [ "lprs_strap2" ]                class "" [ "lprs_strap2" ]                * ]
-  [ class "" [ "lprs_pair_refl" ]             class "" [ "lprs_pair_refl" ]             * ]
-  [ class "" [ "lprs_inv_atom1" ]             class "" [ "lprs_inv_atom1" ]             * ]
-  [ class "" [ "lprs_inv_atom2" ]             class "" [ "lprs_inv_atom2" ]             * ]
-  [ class "" [ "lprs_fwd_length" ]            class "" [ "lprs_fwd_length" ]            * ]
-  [ class "" [ "lprs_pair" ]                  class "" [ "lprs_pair" ]                  * ]
-  [ class "" [ "lprs_inv_pair1" ]             class "" [ "lprs_inv_pair1" ]             * ]
-  [ class "" [ "lprs_inv_pair2" ]             class "" [ "lprs_inv_pair2" ]             * ]
-  [ class "" [ "lprs_ind_alt" ]                       class "" [ "lprs_ind_alt" ]               * ]
-  [ class "" [ "lprs_cpr_trans" ]             class "" [ "lprs_cpr_trans" ]             * ]
-  [ class "" [ "lprs_cprs_trans" ]            class "" [ "lprs_cprs_trans" ]            * ]
-  [ class "" [ "lprs_cprs_conf_dx" ]          class "" [ "lprs_cprs_conf_dx" ]          * ]
-  [ class "" [ "lprs_cpr_conf_dx" ]           class "" [ "lprs_cpr_conf_dx" ]           * ]
-  [ class "" [ "lprs_cprs_conf_sn" ]          class "" [ "lprs_cprs_conf_sn" ]          * ]
-  [ class "" [ "lprs_cpr_conf_sn" ]           class "" [ "lprs_cpr_conf_sn" ]           * ]
-  [ class "" [ "cprs_bind2" ]                 class "" [ "cprs_bind2" ]                 * ]
-  [ class "" [ "cprs_inv_abst1" ]             class "" [ "cprs_inv_abst1" ]             * ]
-  [ class "" [ "cprs_inv_abst" ]              class "" [ "cprs_inv_abst" ]              * ]
-  [ class "" [ "cprs_inv_abbr1" ]             class "" [ "cprs_inv_abbr1" ]             * ]
-  [ class "" [ "lprs_pair2" ]                 class "" [ "lprs_pair2" ]                 * ]
-  [ class "" [ "cpc" ]                        class "" [ "cpc" ]                        * ]
-  [ class "" [ "cpc_refl" ]                   class "" [ "cpc_refl" ]                   * ]
-  [ class "" [ "cpc_sym" ]                    class "" [ "cpc_sym" ]                    * ]
-  [ class "" [ "cpc_fwd_cpr" ]                class "" [ "cpc_fwd_cpr" ]                * ]
-  [ class "" [ "cpc_conf" ]                   class "" [ "cpc_conf" ]                   * ]
-  [ class "" [ "cpcs" ]                               class "" [ "cpcs" ]                       * ]
-  [ class "" [ "cpcs_ind" ]                   class "" [ "cpcs_ind" ]                   * ]
-  [ class "" [ "cpcs_ind_dx" ]                class "" [ "cpcs_ind_dx" ]                * ]
-  [ class "" [ "cpcs_refl" ]                  class "" [ "cpcs_refl" ]                  * ]
-  [ class "" [ "cpcs_sym" ]                   class "" [ "cpcs_sym" ]                   * ]
-  [ class "" [ "cpc_cpcs" ]                   class "" [ "cpc_cpcs" ]                   * ]
-  [ class "" [ "cpcs_strap1" ]                class "" [ "cpcs_strap1" ]                * ]
-  [ class "" [ "cpcs_strap2" ]                class "" [ "cpcs_strap2" ]                * ]
-  [ class "" [ "cpr_cpcs_dx" ]                class "" [ "cpr_cpcs_dx" ]                * ]
-  [ class "" [ "cpr_cpcs_sn" ]                class "" [ "cpr_cpcs_sn" ]                * ]
-  [ class "" [ "cpcs_cpr_strap1" ]            class "" [ "cpcs_cpr_strap1" ]            * ]
-  [ class "" [ "cpcs_cpr_strap2" ]            class "" [ "cpcs_cpr_strap2" ]            * ]
-  [ class "" [ "cpcs_cpr_div" ]                       class "" [ "cpcs_cpr_div" ]               * ]
-  [ class "" [ "cpr_div" ]                    class "" [ "cpr_div" ]                    * ]
-  [ class "" [ "cpcs_cpr_conf" ]              class "" [ "cpcs_cpr_conf" ]              * ]
-  [ class "" [ "cpcs_cprs_dx" ]                       class "" [ "cpcs_cprs_dx" ]               * ]
-  [ class "" [ "cpcs_cprs_sn" ]                       class "" [ "cpcs_cprs_sn" ]               * ]
-  [ class "" [ "cpcs_cprs_strap1" ]           class "" [ "cpcs_cprs_strap1" ]           * ]
-  [ class "" [ "cpcs_cprs_strap2" ]           class "" [ "cpcs_cprs_strap2" ]           * ]
-  [ class "" [ "cpcs_cprs_div" ]              class "" [ "cpcs_cprs_div" ]              * ]
-  [ class "" [ "cpcs_cprs_conf" ]             class "" [ "cpcs_cprs_conf" ]             * ]
-  [ class "" [ "cprs_div" ]                   class "" [ "cprs_div" ]                   * ]
-  [ class "" [ "cprs_cpr_div" ]                       class "" [ "cprs_cpr_div" ]               * ]
-  [ class "" [ "cpr_cprs_div" ]                       class "" [ "cpr_cprs_div" ]               * ]
-  [ class "" [ "cpcs_inv_cprs" ]              class "" [ "cpcs_inv_cprs" ]              * ]
-  [ class "" [ "cpcs_inv_sort" ]              class "" [ "cpcs_inv_sort" ]              * ]
-  [ class "" [ "cpcs_inv_abst1" ]             class "" [ "cpcs_inv_abst1" ]             * ]
-  [ class "" [ "cpcs_inv_abst2" ]             class "" [ "cpcs_inv_abst2" ]             * ]
-  [ class "" [ "cpcs_inv_sort_abst" ]         class "" [ "cpcs_inv_sort_abst" ]         * ]
-  [ class "" [ "cpcs_inv_lift" ]              class "" [ "cpcs_inv_lift" ]              * ]
-  [ class "" [ "lpr_cpcs_trans" ]             class "" [ "lpr_cpcs_trans" ]             * ]
-  [ class "" [ "lprs_cpcs_trans" ]            class "" [ "lprs_cpcs_trans" ]            * ]
-  [ class "" [ "cpr_cprs_conf_cpcs" ]         class "" [ "cpr_cprs_conf_cpcs" ]         * ]
-  [ class "" [ "cprs_cpr_conf_cpcs" ]         class "" [ "cprs_cpr_conf_cpcs" ]         * ]
-  [ class "" [ "cprs_conf_cpcs" ]             class "" [ "cprs_conf_cpcs" ]             * ]
-  [ class "" [ "lprs_cprs_conf" ]             class "" [ "lprs_cprs_conf" ]             * ]
-  [ class "" [ "lpr_cprs_conf" ]              class "" [ "lpr_cprs_conf" ]              * ]
-  [ class "" [ "lpr_cpr_conf" ]                       class "" [ "lpr_cpr_conf" ]               * ]
-  [ class "" [ "cpcs_flat" ]                  class "" [ "cpcs_flat" ]                  * ]
-  [ class "" [ "cpcs_flat_dx_cpr_rev" ]               class "" [ "cpcs_flat_dx_cpr_rev" ]       * ]
-  [ class "" [ "cpcs_bind_dx" ]                       class "" [ "cpcs_bind_dx" ]               * ]
-  [ class "" [ "cpcs_bind_sn" ]                       class "" [ "cpcs_bind_sn" ]               * ]
-  [ class "" [ "lsubr_cpcs_trans" ]           class "" [ "lsubr_cpcs_trans" ]           * ]
-  [ class "" [ "cpcs_lift" ]                  class "" [ "cpcs_lift" ]                  * ]
-  [ class "" [ "cpcs_strip" ]                 class "" [ "cpcs_strip" ]                 * ]
-  [ class "" [ "cpcs_inv_abst_sn" ]           class "" [ "cpcs_inv_abst_sn" ]           * ]
-  [ class "" [ "cpcs_inv_abst_dx" ]           class "" [ "cpcs_inv_abst_dx" ]           * ]
-  [ class "" [ "cpcs_trans" ]                 class "" [ "cpcs_trans" ]                 * ]
-  [ class "" [ "cpcs_canc_sn" ]                       class "" [ "cpcs_canc_sn" ]               * ]
-  [ class "" [ "cpcs_canc_dx" ]                       class "" [ "cpcs_canc_dx" ]               * ]
-  [ class "" [ "cpcs_bind1" ]                 class "" [ "cpcs_bind1" ]                 * ]
-  [ class "" [ "cpcs_bind2" ]                 class "" [ "cpcs_bind2" ]                 * ]
-  [ class "" [ "lpr_cpcs_conf" ]              class "" [ "lpr_cpcs_conf" ]              * ]
-  [ class "" [ "cpcs_aaa_mono" ]              class "" [ "cpcs_aaa_mono" ]              * ]
-  [ class "" [ "da_lift" ]                    class "" [ "da_lift" ]                    * ]
-  [ class "" [ "da_inv_lift" ]                class "" [ "da_inv_lift" ]                * ]
-  [ class "" [ "da_mono" ]                    class "" [ "da_mono" ]                    * ]
-  [ class "" [ "lstas_lift" ]                 class "" [ "lstas_lift" ]                 * ]
-  [ class "" [ "lstas_inv_lift1" ]            class "" [ "lstas_inv_lift1" ]            * ]
-  [ class "" [ "lstas_split_aux" ]            class "" [ "lstas_split_aux" ]            * ]
-  [ class "" [ "lstas_split" ]                class "" [ "lstas_split" ]                * ]
-  [ class "" [ "lstas_lstas" ]                class "" [ "lstas_lstas" ]                * ]
-  [ class "" [ "lstas_trans" ]                class "" [ "lstas_trans" ]                * ]
-  [ class "" [ "lstas_mono" ]                 class "" [ "lstas_mono" ]                 * ]
-  [ class "" [ "lstas_correct" ]              class "" [ "lstas_correct" ]              * ]
-  [ class "" [ "lstas_conf_le" ]              class "" [ "lstas_conf_le" ]              * ]
-  [ class "" [ "lstas_conf" ]                 class "" [ "lstas_conf" ]                 * ]
-  [ class "" [ "da_lstas" ]                   class "" [ "da_lstas" ]                   * ]
-  [ class "" [ "lstas_da_conf" ]              class "" [ "lstas_da_conf" ]              * ]
-  [ class "" [ "lstas_inv_da" ]                       class "" [ "lstas_inv_da" ]               * ]
-  [ class "" [ "lstas_inv_da_ge" ]            class "" [ "lstas_inv_da_ge" ]            * ]
-  [ class "" [ "lstas_inv_refl_pos" ]         class "" [ "lstas_inv_refl_pos" ]         * ]
-  [ class "" [ "fqus_trans" ]                 class "" [ "fqus_trans" ]                 * ]
-  [ class "" [ "cpxs_delta" ]                 class "" [ "cpxs_delta" ]                 * ]
-  [ class "" [ "lstas_cpxs" ]                 class "" [ "lstas_cpxs" ]                 * ]
-  [ class "" [ "cpxs_inv_lref1" ]             class "" [ "cpxs_inv_lref1" ]             * ]
-  [ class "" [ "cpxs_lift" ]                  class "" [ "cpxs_lift" ]                  * ]
-  [ class "" [ "cpxs_inv_lift1" ]             class "" [ "cpxs_inv_lift1" ]             * ]
-  [ class "" [ "fqu_cpxs_trans" ]             class "" [ "fqu_cpxs_trans" ]             * ]
-  [ class "" [ "fquq_cpxs_trans" ]            class "" [ "fquq_cpxs_trans" ]            * ]
-  [ class "" [ "fquq_lstas_trans" ]           class "" [ "fquq_lstas_trans" ]           * ]
-  [ class "" [ "fqup_cpxs_trans" ]            class "" [ "fqup_cpxs_trans" ]            * ]
-  [ class "" [ "fqus_cpxs_trans" ]            class "" [ "fqus_cpxs_trans" ]            * ]
-  [ class "" [ "fqus_lstas_trans" ]           class "" [ "fqus_lstas_trans" ]           * ]
-  [ class "" [ "cpxs_trans" ]                 class "" [ "cpxs_trans" ]                 * ]
-  [ class "" [ "cpxs_bind" ]                  class "" [ "cpxs_bind" ]                  * ]
-  [ class "" [ "cpxs_flat" ]                  class "" [ "cpxs_flat" ]                  * ]
-  [ class "" [ "cpxs_beta_rc" ]                       class "" [ "cpxs_beta_rc" ]               * ]
-  [ class "" [ "cpxs_beta" ]                  class "" [ "cpxs_beta" ]                  * ]
-  [ class "" [ "cpxs_theta_rc" ]              class "" [ "cpxs_theta_rc" ]              * ]
-  [ class "" [ "cpxs_theta" ]                 class "" [ "cpxs_theta" ]                 * ]
-  [ class "" [ "cpxs_inv_appl1" ]             class "" [ "cpxs_inv_appl1" ]             * ]
-  [ class "" [ "lpx_cpx_trans" ]              class "" [ "lpx_cpx_trans" ]              * ]
-  [ class "" [ "cpx_bind2" ]                  class "" [ "cpx_bind2" ]                  * ]
-  [ class "" [ "lpx_cpxs_trans" ]             class "" [ "lpx_cpxs_trans" ]             * ]
-  [ class "" [ "cpxs_bind2_dx" ]              class "" [ "cpxs_bind2_dx" ]              * ]
-  [ class "" [ "fqu_cpxs_trans_neq" ]         class "" [ "fqu_cpxs_trans_neq" ]         * ]
-  [ class "" [ "fquq_cpxs_trans_neq" ]        class "" [ "fquq_cpxs_trans_neq" ]        * ]
-  [ class "" [ "fqup_cpxs_trans_neq" ]        class "" [ "fqup_cpxs_trans_neq" ]        * ]
-  [ class "" [ "fqus_cpxs_trans_neq" ]        class "" [ "fqus_cpxs_trans_neq" ]        * ]
-  [ class "" [ "scpds_strap2" ]                       class "" [ "scpds_strap2" ]               * ]
-  [ class "" [ "scpds_cprs_trans" ]           class "" [ "scpds_cprs_trans" ]           * ]
-  [ class "" [ "lstas_scpds_trans" ]          class "" [ "lstas_scpds_trans" ]          * ]
-  [ class "" [ "scpds_inv_abst1" ]            class "" [ "scpds_inv_abst1" ]            * ]
-  [ class "" [ "scpds_inv_abbr_abst" ]        class "" [ "scpds_inv_abbr_abst" ]        * ]
-  [ class "" [ "scpds_inv_lstas_eq" ]         class "" [ "scpds_inv_lstas_eq" ]         * ]
-  [ class "" [ "scpds_fwd_cpxs" ]             class "" [ "scpds_fwd_cpxs" ]             * ]
-  [ class "" [ "scpds_conf_eq" ]              class "" [ "scpds_conf_eq" ]              * ]
-  [ class "" [ "scpes_inv_lstas_eq" ]         class "" [ "scpes_inv_lstas_eq" ]         * ]
-  [ class "" [ "cpcs_scpes" ]                 class "" [ "cpcs_scpes" ]                 * ]
-  [ class "" [ "scpes_inv_abst2" ]            class "" [ "scpes_inv_abst2" ]            * ]
-  [ class "" [ "scpes_refl" ]                 class "" [ "scpes_refl" ]                 * ]
-  [ class "" [ "lstas_scpes_trans" ]          class "" [ "lstas_scpes_trans" ]          * ]
-  [ class "" [ "cprs_scpds_div" ]             class "" [ "cprs_scpds_div" ]             * ]
-  [ class "" [ "scpes_trans" ]                class "" [ "scpes_trans" ]                * ]
-  [ class "" [ "scpes_canc_sn" ]              class "" [ "scpes_canc_sn" ]              * ]
-  [ class "" [ "scpes_canc_dx" ]              class "" [ "scpes_canc_dx" ]              * ]
-  [ class "" [ "aaa_lstas" ]                  class "" [ "aaa_lstas" ]                  * ]
-  [ class "" [ "lstas_aaa_conf" ]             class "" [ "lstas_aaa_conf" ]             * ]
-  [ class "" [ "scpds_aaa_conf" ]             class "" [ "scpds_aaa_conf" ]             * ]
-  [ class "" [ "scpes_aaa_mono" ]             class "" [ "scpes_aaa_mono" ]             * ]
-  [ class "" [ "lsubr_inv_pair1_aux" ]        class "" [ "lsubr_inv_pair1_aux" ]        * ]
-  [ class "" [ "lsubr_inv_pair1" ]            class "" [ "lsubr_inv_pair1" ]            * ]
-  [ class "" [ "lsubr_trans" ]                class "" [ "lsubr_trans" ]                * ]
-  [ class "" [ "applv" ]                      class "" [ "applv" ]                      * ]
-  [ class "" [ "applv_simple" ]                       class "" [ "applv_simple" ]               * ]
-  [ class "" [ "at" ]                         class "" [ "at" ]                         * ]
-  [ class "" [ "at_inv_nil_aux" ]             class "" [ "at_inv_nil_aux" ]             * ]
-  [ class "" [ "at_inv_nil" ]                 class "" [ "at_inv_nil" ]                 * ]
-  [ class "" [ "at_inv_cons_aux" ]            class "" [ "at_inv_cons_aux" ]            * ]
-  [ class "" [ "at_inv_cons" ]                class "" [ "at_inv_cons" ]                * ]
-  [ class "" [ "at_inv_cons_lt" ]             class "" [ "at_inv_cons_lt" ]             * ]
-  [ class "" [ "at_inv_cons_ge" ]             class "" [ "at_inv_cons_ge" ]             * ]
-  [ class "" [ "minuss" ]                     class "" [ "minuss" ]                     * ]
-  [ class "" [ "minuss_inv_nil1_aux" ]        class "" [ "minuss_inv_nil1_aux" ]        * ]
-  [ class "" [ "minuss_inv_nil1" ]            class "" [ "minuss_inv_nil1" ]            * ]
-  [ class "" [ "minuss_inv_cons1_aux" ]               class "" [ "minuss_inv_cons1_aux" ]       * ]
-  [ class "" [ "minuss_inv_cons1" ]           class "" [ "minuss_inv_cons1" ]           * ]
-  [ class "" [ "minuss_inv_cons1_ge" ]        class "" [ "minuss_inv_cons1_ge" ]        * ]
-  [ class "" [ "minuss_inv_cons1_lt" ]        class "" [ "minuss_inv_cons1_lt" ]        * ]
-  [ class "" [ "liftv" ]                      class "" [ "liftv" ]                      * ]
-  [ class "" [ "liftv_inv_nil1_aux" ]         class "" [ "liftv_inv_nil1_aux" ]         * ]
-  [ class "" [ "liftv_inv_nil1" ]             class "" [ "liftv_inv_nil1" ]             * ]
-  [ class "" [ "liftv_inv_cons1_aux" ]        class "" [ "liftv_inv_cons1_aux" ]        * ]
-  [ class "" [ "liftv_inv_cons1" ]            class "" [ "liftv_inv_cons1" ]            * ]
-  [ class "" [ "liftv_total" ]                class "" [ "liftv_total" ]                * ]
-  [ class "" [ "pluss" ]                      class "" [ "pluss" ]                      * ]
-  [ class "" [ "pluss_inv_nil2" ]             class "" [ "pluss_inv_nil2" ]             * ]
-  [ class "" [ "pluss_inv_cons2" ]            class "" [ "pluss_inv_cons2" ]            * ]
-  [ class "" [ "lifts" ]                      class "" [ "lifts" ]                      * ]
-  [ class "" [ "lifts_inv_nil_aux" ]          class "" [ "lifts_inv_nil_aux" ]          * ]
-  [ class "" [ "lifts_inv_nil" ]              class "" [ "lifts_inv_nil" ]              * ]
-  [ class "" [ "lifts_inv_cons_aux" ]         class "" [ "lifts_inv_cons_aux" ]         * ]
-  [ class "" [ "lifts_inv_cons" ]             class "" [ "lifts_inv_cons" ]             * ]
-  [ class "" [ "lifts_inv_sort1" ]            class "" [ "lifts_inv_sort1" ]            * ]
-  [ class "" [ "lifts_inv_lref1" ]            class "" [ "lifts_inv_lref1" ]            * ]
-  [ class "" [ "lifts_inv_gref1" ]            class "" [ "lifts_inv_gref1" ]            * ]
-  [ class "" [ "lifts_inv_bind1" ]            class "" [ "lifts_inv_bind1" ]            * ]
-  [ class "" [ "lifts_inv_flat1" ]            class "" [ "lifts_inv_flat1" ]            * ]
-  [ class "" [ "lifts_simple_dx" ]            class "" [ "lifts_simple_dx" ]            * ]
-  [ class "" [ "lifts_simple_sn" ]            class "" [ "lifts_simple_sn" ]            * ]
-  [ class "" [ "lifts_bind" ]                 class "" [ "lifts_bind" ]                 * ]
-  [ class "" [ "lifts_flat" ]                 class "" [ "lifts_flat" ]                 * ]
-  [ class "" [ "lifts_total" ]                class "" [ "lifts_total" ]                * ]
-  [ class "" [ "liftsv" ]                     class "" [ "liftsv" ]                     * ]
-  [ class "" [ "lifts_inv_applv1" ]           class "" [ "lifts_inv_applv1" ]           * ]
-  [ class "" [ "lifts_applv" ]                class "" [ "lifts_applv" ]                * ]
-  [ class "" [ "drops" ]                      class "" [ "drops" ]                      * ]
-  [ class "" [ "d_liftable1" ]                class "" [ "d_liftable1" ]                * ]
-  [ class "" [ "d_liftables1" ]                       class "" [ "d_liftables1" ]               * ]
-  [ class "" [ "d_liftables1_all" ]           class "" [ "d_liftables1_all" ]           * ]
-  [ class "" [ "drops_inv_nil_aux" ]          class "" [ "drops_inv_nil_aux" ]          * ]
-  [ class "" [ "drops_inv_nil" ]              class "" [ "drops_inv_nil" ]              * ]
-  [ class "" [ "drops_inv_cons_aux" ]         class "" [ "drops_inv_cons_aux" ]         * ]
-  [ class "" [ "drops_inv_cons" ]             class "" [ "drops_inv_cons" ]             * ]
-  [ class "" [ "drops_inv_skip2" ]            class "" [ "drops_inv_skip2" ]            * ]
-  [ class "" [ "drops_skip" ]                 class "" [ "drops_skip" ]                 * ]
+  [ class "" [ "TC_lpx_sn_fwd_length" ]        class "" [ "TC_lpx_sn_fwd_length" ]       * ]
+  [ class "" [ "lprs" ]                        class "" [ "lprs" ]                       * ]
+  [ class "" [ "lprs_ind" ]                    class "" [ "lprs_ind" ]                   * ]
+  [ class "" [ "lprs_ind_dx" ]                 class "" [ "lprs_ind_dx" ]                * ]
+  [ class "" [ "lpr_lprs" ]                    class "" [ "lpr_lprs" ]                   * ]
+  [ class "" [ "lprs_refl" ]                   class "" [ "lprs_refl" ]                  * ]
+  [ class "" [ "lprs_strap1" ]                 class "" [ "lprs_strap1" ]                * ]
+  [ class "" [ "lprs_strap2" ]                 class "" [ "lprs_strap2" ]                * ]
+  [ class "" [ "lprs_pair_refl" ]              class "" [ "lprs_pair_refl" ]             * ]
+  [ class "" [ "lprs_inv_atom1" ]              class "" [ "lprs_inv_atom1" ]             * ]
+  [ class "" [ "lprs_inv_atom2" ]              class "" [ "lprs_inv_atom2" ]             * ]
+  [ class "" [ "lprs_fwd_length" ]             class "" [ "lprs_fwd_length" ]            * ]
+  [ class "" [ "lprs_pair" ]                   class "" [ "lprs_pair" ]                  * ]
+  [ class "" [ "lprs_inv_pair1" ]              class "" [ "lprs_inv_pair1" ]             * ]
+  [ class "" [ "lprs_inv_pair2" ]              class "" [ "lprs_inv_pair2" ]             * ]
+  [ class "" [ "lprs_ind_alt" ]                class "" [ "lprs_ind_alt" ]               * ]
+  [ class "" [ "lprs_cpr_trans" ]              class "" [ "lprs_cpr_trans" ]             * ]
+  [ class "" [ "lprs_cprs_trans" ]             class "" [ "lprs_cprs_trans" ]            * ]
+  [ class "" [ "lprs_cprs_conf_dx" ]           class "" [ "lprs_cprs_conf_dx" ]          * ]
+  [ class "" [ "lprs_cpr_conf_dx" ]            class "" [ "lprs_cpr_conf_dx" ]           * ]
+  [ class "" [ "lprs_cprs_conf_sn" ]           class "" [ "lprs_cprs_conf_sn" ]          * ]
+  [ class "" [ "lprs_cpr_conf_sn" ]            class "" [ "lprs_cpr_conf_sn" ]           * ]
+  [ class "" [ "cprs_bind2" ]                  class "" [ "cprs_bind2" ]                 * ]
+  [ class "" [ "cprs_inv_abst1" ]              class "" [ "cprs_inv_abst1" ]             * ]
+  [ class "" [ "cprs_inv_abst" ]               class "" [ "cprs_inv_abst" ]              * ]
+  [ class "" [ "cprs_inv_abbr1" ]              class "" [ "cprs_inv_abbr1" ]             * ]
+  [ class "" [ "lprs_pair2" ]                  class "" [ "lprs_pair2" ]                 * ]
+  [ class "" [ "cpc" ]                         class "" [ "cpc" ]                        * ]
+  [ class "" [ "cpc_refl" ]                    class "" [ "cpc_refl" ]                   * ]
+  [ class "" [ "cpc_sym" ]                     class "" [ "cpc_sym" ]                    * ]
+  [ class "" [ "cpc_fwd_cpr" ]                 class "" [ "cpc_fwd_cpr" ]                * ]
+  [ class "" [ "cpc_conf" ]                    class "" [ "cpc_conf" ]                   * ]
+  [ class "" [ "cpcs" ]                        class "" [ "cpcs" ]                       * ]
+  [ class "" [ "cpcs_ind" ]                    class "" [ "cpcs_ind" ]                   * ]
+  [ class "" [ "cpcs_ind_dx" ]                 class "" [ "cpcs_ind_dx" ]                * ]
+  [ class "" [ "cpcs_refl" ]                   class "" [ "cpcs_refl" ]                  * ]
+  [ class "" [ "cpcs_sym" ]                    class "" [ "cpcs_sym" ]                   * ]
+  [ class "" [ "cpc_cpcs" ]                    class "" [ "cpc_cpcs" ]                   * ]
+  [ class "" [ "cpcs_strap1" ]                 class "" [ "cpcs_strap1" ]                * ]
+  [ class "" [ "cpcs_strap2" ]                 class "" [ "cpcs_strap2" ]                * ]
+  [ class "" [ "cpr_cpcs_dx" ]                 class "" [ "cpr_cpcs_dx" ]                * ]
+  [ class "" [ "cpr_cpcs_sn" ]                 class "" [ "cpr_cpcs_sn" ]                * ]
+  [ class "" [ "cpcs_cpr_strap1" ]             class "" [ "cpcs_cpr_strap1" ]            * ]
+  [ class "" [ "cpcs_cpr_strap2" ]             class "" [ "cpcs_cpr_strap2" ]            * ]
+  [ class "" [ "cpcs_cpr_div" ]                class "" [ "cpcs_cpr_div" ]               * ]
+  [ class "" [ "cpr_div" ]                     class "" [ "cpr_div" ]                    * ]
+  [ class "" [ "cpcs_cpr_conf" ]               class "" [ "cpcs_cpr_conf" ]              * ]
+  [ class "" [ "cpcs_cprs_dx" ]                class "" [ "cpcs_cprs_dx" ]               * ]
+  [ class "" [ "cpcs_cprs_sn" ]                class "" [ "cpcs_cprs_sn" ]               * ]
+  [ class "" [ "cpcs_cprs_strap1" ]            class "" [ "cpcs_cprs_strap1" ]           * ]
+  [ class "" [ "cpcs_cprs_strap2" ]            class "" [ "cpcs_cprs_strap2" ]           * ]
+  [ class "" [ "cpcs_cprs_div" ]               class "" [ "cpcs_cprs_div" ]              * ]
+  [ class "" [ "cpcs_cprs_conf" ]              class "" [ "cpcs_cprs_conf" ]             * ]
+  [ class "" [ "cprs_div" ]                    class "" [ "cprs_div" ]                   * ]
+  [ class "" [ "cprs_cpr_div" ]                class "" [ "cprs_cpr_div" ]               * ]
+  [ class "" [ "cpr_cprs_div" ]                class "" [ "cpr_cprs_div" ]               * ]
+  [ class "" [ "cpcs_inv_cprs" ]               class "" [ "cpcs_inv_cprs" ]              * ]
+  [ class "" [ "cpcs_inv_sort" ]               class "" [ "cpcs_inv_sort" ]              * ]
+  [ class "" [ "cpcs_inv_abst1" ]              class "" [ "cpcs_inv_abst1" ]             * ]
+  [ class "" [ "cpcs_inv_abst2" ]              class "" [ "cpcs_inv_abst2" ]             * ]
+  [ class "" [ "cpcs_inv_sort_abst" ]          class "" [ "cpcs_inv_sort_abst" ]         * ]
+  [ class "" [ "cpcs_inv_lift" ]               class "" [ "cpcs_inv_lift" ]              * ]
+  [ class "" [ "lpr_cpcs_trans" ]              class "" [ "lpr_cpcs_trans" ]             * ]
+  [ class "" [ "lprs_cpcs_trans" ]             class "" [ "lprs_cpcs_trans" ]            * ]
+  [ class "" [ "cpr_cprs_conf_cpcs" ]          class "" [ "cpr_cprs_conf_cpcs" ]         * ]
+  [ class "" [ "cprs_cpr_conf_cpcs" ]          class "" [ "cprs_cpr_conf_cpcs" ]         * ]
+  [ class "" [ "cprs_conf_cpcs" ]              class "" [ "cprs_conf_cpcs" ]             * ]
+  [ class "" [ "lprs_cprs_conf" ]              class "" [ "lprs_cprs_conf" ]             * ]
+  [ class "" [ "lpr_cprs_conf" ]               class "" [ "lpr_cprs_conf" ]              * ]
+  [ class "" [ "lpr_cpr_conf" ]                class "" [ "lpr_cpr_conf" ]               * ]
+  [ class "" [ "cpcs_flat" ]                   class "" [ "cpcs_flat" ]                  * ]
+  [ class "" [ "cpcs_flat_dx_cpr_rev" ]        class "" [ "cpcs_flat_dx_cpr_rev" ]       * ]
+  [ class "" [ "cpcs_bind_dx" ]                class "" [ "cpcs_bind_dx" ]               * ]
+  [ class "" [ "cpcs_bind_sn" ]                class "" [ "cpcs_bind_sn" ]               * ]
+  [ class "" [ "lsubr_cpcs_trans" ]            class "" [ "lsubr_cpcs_trans" ]           * ]
+  [ class "" [ "cpcs_lift" ]                   class "" [ "cpcs_lift" ]                  * ]
+  [ class "" [ "cpcs_strip" ]                  class "" [ "cpcs_strip" ]                 * ]
+  [ class "" [ "cpcs_inv_abst_sn" ]            class "" [ "cpcs_inv_abst_sn" ]           * ]
+  [ class "" [ "cpcs_inv_abst_dx" ]            class "" [ "cpcs_inv_abst_dx" ]           * ]
+  [ class "" [ "cpcs_trans" ]                  class "" [ "cpcs_trans" ]                 * ]
+  [ class "" [ "cpcs_canc_sn" ]                class "" [ "cpcs_canc_sn" ]               * ]
+  [ class "" [ "cpcs_canc_dx" ]                class "" [ "cpcs_canc_dx" ]               * ]
+  [ class "" [ "cpcs_bind1" ]                  class "" [ "cpcs_bind1" ]                 * ]
+  [ class "" [ "cpcs_bind2" ]                  class "" [ "cpcs_bind2" ]                 * ]
+  [ class "" [ "lpr_cpcs_conf" ]               class "" [ "lpr_cpcs_conf" ]              * ]
+  [ class "" [ "cpcs_aaa_mono" ]               class "" [ "cpcs_aaa_mono" ]              * ]
+  [ class "" [ "da_lift" ]                     class "" [ "da_lift" ]                    * ]
+  [ class "" [ "da_inv_lift" ]                 class "" [ "da_inv_lift" ]                * ]
+  [ class "" [ "da_mono" ]                     class "" [ "da_mono" ]                    * ]
+  [ class "" [ "lstas_lift" ]                  class "" [ "lstas_lift" ]                 * ]
+  [ class "" [ "lstas_inv_lift1" ]             class "" [ "lstas_inv_lift1" ]            * ]
+  [ class "" [ "lstas_split_aux" ]             class "" [ "lstas_split_aux" ]            * ]
+  [ class "" [ "lstas_split" ]                 class "" [ "lstas_split" ]                * ]
+  [ class "" [ "lstas_lstas" ]                 class "" [ "lstas_lstas" ]                * ]
+  [ class "" [ "lstas_trans" ]                 class "" [ "lstas_trans" ]                * ]
+  [ class "" [ "lstas_mono" ]                  class "" [ "lstas_mono" ]                 * ]
+  [ class "" [ "lstas_correct" ]               class "" [ "lstas_correct" ]              * ]
+  [ class "" [ "lstas_conf_le" ]               class "" [ "lstas_conf_le" ]              * ]
+  [ class "" [ "lstas_conf" ]                  class "" [ "lstas_conf" ]                 * ]
+  [ class "" [ "da_lstas" ]                    class "" [ "da_lstas" ]                   * ]
+  [ class "" [ "lstas_da_conf" ]               class "" [ "lstas_da_conf" ]              * ]
+  [ class "" [ "lstas_inv_da" ]                class "" [ "lstas_inv_da" ]               * ]
+  [ class "" [ "lstas_inv_da_ge" ]             class "" [ "lstas_inv_da_ge" ]            * ]
+  [ class "" [ "lstas_inv_refl_pos" ]          class "" [ "lstas_inv_refl_pos" ]         * ]
+  [ class "" [ "fqus_trans" ]                  class "" [ "fqus_trans" ]                 * ]
+  [ class "" [ "cpxs_delta" ]                  class "" [ "cpxs_delta" ]                 * ]
+  [ class "" [ "lstas_cpxs" ]                  class "" [ "lstas_cpxs" ]                 * ]
+  [ class "" [ "cpxs_inv_lref1" ]              class "" [ "cpxs_inv_lref1" ]             * ]
+  [ class "" [ "cpxs_lift" ]                   class "" [ "cpxs_lift" ]                  * ]
+  [ class "" [ "cpxs_inv_lift1" ]              class "" [ "cpxs_inv_lift1" ]             * ]
+  [ class "" [ "fqu_cpxs_trans" ]              class "" [ "fqu_cpxs_trans" ]             * ]
+  [ class "" [ "fquq_cpxs_trans" ]             class "" [ "fquq_cpxs_trans" ]            * ]
+  [ class "" [ "fquq_lstas_trans" ]            class "" [ "fquq_lstas_trans" ]           * ]
+  [ class "" [ "fqup_cpxs_trans" ]             class "" [ "fqup_cpxs_trans" ]            * ]
+  [ class "" [ "fqus_cpxs_trans" ]             class "" [ "fqus_cpxs_trans" ]            * ]
+  [ class "" [ "fqus_lstas_trans" ]            class "" [ "fqus_lstas_trans" ]           * ]
+  [ class "" [ "cpxs_trans" ]                  class "" [ "cpxs_trans" ]                 * ]
+  [ class "" [ "cpxs_bind" ]                   class "" [ "cpxs_bind" ]                  * ]
+  [ class "" [ "cpxs_flat" ]                   class "" [ "cpxs_flat" ]                  * ]
+  [ class "" [ "cpxs_beta_rc" ]                class "" [ "cpxs_beta_rc" ]               * ]
+  [ class "" [ "cpxs_beta" ]                   class "" [ "cpxs_beta" ]                  * ]
+  [ class "" [ "cpxs_theta_rc" ]               class "" [ "cpxs_theta_rc" ]              * ]
+  [ class "" [ "cpxs_theta" ]                  class "" [ "cpxs_theta" ]                 * ]
+  [ class "" [ "cpxs_inv_appl1" ]              class "" [ "cpxs_inv_appl1" ]             * ]
+  [ class "" [ "lpx_cpx_trans" ]               class "" [ "lpx_cpx_trans" ]              * ]
+  [ class "" [ "cpx_bind2" ]                   class "" [ "cpx_bind2" ]                  * ]
+  [ class "" [ "lpx_cpxs_trans" ]              class "" [ "lpx_cpxs_trans" ]             * ]
+  [ class "" [ "cpxs_bind2_dx" ]               class "" [ "cpxs_bind2_dx" ]              * ]
+  [ class "" [ "fqu_cpxs_trans_neq" ]          class "" [ "fqu_cpxs_trans_neq" ]         * ]
+  [ class "" [ "fquq_cpxs_trans_neq" ]         class "" [ "fquq_cpxs_trans_neq" ]        * ]
+  [ class "" [ "fqup_cpxs_trans_neq" ]         class "" [ "fqup_cpxs_trans_neq" ]        * ]
+  [ class "" [ "fqus_cpxs_trans_neq" ]         class "" [ "fqus_cpxs_trans_neq" ]        * ]
+  [ class "" [ "scpds_strap2" ]                class "" [ "scpds_strap2" ]               * ]
+  [ class "" [ "scpds_cprs_trans" ]            class "" [ "scpds_cprs_trans" ]           * ]
+  [ class "" [ "lstas_scpds_trans" ]           class "" [ "lstas_scpds_trans" ]          * ]
+  [ class "" [ "scpds_inv_abst1" ]             class "" [ "scpds_inv_abst1" ]            * ]
+  [ class "" [ "scpds_inv_abbr_abst" ]         class "" [ "scpds_inv_abbr_abst" ]        * ]
+  [ class "" [ "scpds_inv_lstas_eq" ]          class "" [ "scpds_inv_lstas_eq" ]         * ]
+  [ class "" [ "scpds_fwd_cpxs" ]              class "" [ "scpds_fwd_cpxs" ]             * ]
+  [ class "" [ "scpds_conf_eq" ]               class "" [ "scpds_conf_eq" ]              * ]
+  [ class "" [ "scpes_inv_lstas_eq" ]          class "" [ "scpes_inv_lstas_eq" ]         * ]
+  [ class "" [ "cpcs_scpes" ]                  class "" [ "cpcs_scpes" ]                 * ]
+  [ class "" [ "scpes_inv_abst2" ]             class "" [ "scpes_inv_abst2" ]            * ]
+  [ class "" [ "scpes_refl" ]                  class "" [ "scpes_refl" ]                 * ]
+  [ class "" [ "lstas_scpes_trans" ]           class "" [ "lstas_scpes_trans" ]          * ]
+  [ class "" [ "cprs_scpds_div" ]              class "" [ "cprs_scpds_div" ]             * ]
+  [ class "" [ "scpes_trans" ]                 class "" [ "scpes_trans" ]                * ]
+  [ class "" [ "scpes_canc_sn" ]               class "" [ "scpes_canc_sn" ]              * ]
+  [ class "" [ "scpes_canc_dx" ]               class "" [ "scpes_canc_dx" ]              * ]
+  [ class "" [ "aaa_lstas" ]                   class "" [ "aaa_lstas" ]                  * ]
+  [ class "" [ "lstas_aaa_conf" ]              class "" [ "lstas_aaa_conf" ]             * ]
+  [ class "" [ "scpds_aaa_conf" ]              class "" [ "scpds_aaa_conf" ]             * ]
+  [ class "" [ "scpes_aaa_mono" ]              class "" [ "scpes_aaa_mono" ]             * ]
+  [ class "" [ "lsubr_inv_pair1_aux" ]         class "" [ "lsubr_inv_pair1_aux" ]        * ]
+  [ class "" [ "lsubr_inv_pair1" ]             class "" [ "lsubr_inv_pair1" ]            * ]
+  [ class "" [ "lsubr_trans" ]                 class "" [ "lsubr_trans" ]                * ]
+  [ class "" [ "applv" ]                       class "" [ "applv" ]                      * ]
+  [ class "" [ "applv_simple" ]                class "" [ "applv_simple" ]               * ]
+  [ class "" [ "at" ]                          class "" [ "at" ]                         * ]
+  [ class "" [ "at_inv_nil_aux" ]              class "" [ "at_inv_nil_aux" ]             * ]
+  [ class "" [ "at_inv_nil" ]                  class "" [ "at_inv_nil" ]                 * ]
+  [ class "" [ "at_inv_cons_aux" ]             class "" [ "at_inv_cons_aux" ]            * ]
+  [ class "" [ "at_inv_cons" ]                 class "" [ "at_inv_cons" ]                * ]
+  [ class "" [ "at_inv_cons_lt" ]              class "" [ "at_inv_cons_lt" ]             * ]
+  [ class "" [ "at_inv_cons_ge" ]              class "" [ "at_inv_cons_ge" ]             * ]
+  [ class "" [ "minuss" ]                      class "" [ "minuss" ]                     * ]
+  [ class "" [ "minuss_inv_nil1_aux" ]         class "" [ "minuss_inv_nil1_aux" ]        * ]
+  [ class "" [ "minuss_inv_nil1" ]             class "" [ "minuss_inv_nil1" ]            * ]
+  [ class "" [ "minuss_inv_cons1_aux" ]        class "" [ "minuss_inv_cons1_aux" ]       * ]
+  [ class "" [ "minuss_inv_cons1" ]            class "" [ "minuss_inv_cons1" ]           * ]
+  [ class "" [ "minuss_inv_cons1_ge" ]         class "" [ "minuss_inv_cons1_ge" ]        * ]
+  [ class "" [ "minuss_inv_cons1_lt" ]         class "" [ "minuss_inv_cons1_lt" ]        * ]
+  [ class "" [ "liftv" ]                       class "" [ "liftv" ]                      * ]
+  [ class "" [ "liftv_inv_nil1_aux" ]          class "" [ "liftv_inv_nil1_aux" ]         * ]
+  [ class "" [ "liftv_inv_nil1" ]              class "" [ "liftv_inv_nil1" ]             * ]
+  [ class "" [ "liftv_inv_cons1_aux" ]         class "" [ "liftv_inv_cons1_aux" ]        * ]
+  [ class "" [ "liftv_inv_cons1" ]             class "" [ "liftv_inv_cons1" ]            * ]
+  [ class "" [ "liftv_total" ]                 class "" [ "liftv_total" ]                * ]
+  [ class "" [ "pluss" ]                       class "" [ "pluss" ]                      * ]
+  [ class "" [ "pluss_inv_nil2" ]              class "" [ "pluss_inv_nil2" ]             * ]
+  [ class "" [ "pluss_inv_cons2" ]             class "" [ "pluss_inv_cons2" ]            * ]
+  [ class "" [ "lifts" ]                       class "" [ "lifts" ]                      * ]
+  [ class "" [ "lifts_inv_nil_aux" ]           class "" [ "lifts_inv_nil_aux" ]          * ]
+  [ class "" [ "lifts_inv_nil" ]               class "" [ "lifts_inv_nil" ]              * ]
+  [ class "" [ "lifts_inv_cons_aux" ]          class "" [ "lifts_inv_cons_aux" ]         * ]
+  [ class "" [ "lifts_inv_cons" ]              class "" [ "lifts_inv_cons" ]             * ]
+  [ class "" [ "lifts_inv_sort1" ]             class "" [ "lifts_inv_sort1" ]            * ]
+  [ class "" [ "lifts_inv_lref1" ]             class "" [ "lifts_inv_lref1" ]            * ]
+  [ class "" [ "lifts_inv_gref1" ]             class "" [ "lifts_inv_gref1" ]            * ]
+  [ class "" [ "lifts_inv_bind1" ]             class "" [ "lifts_inv_bind1" ]            * ]
+  [ class "" [ "lifts_inv_flat1" ]             class "" [ "lifts_inv_flat1" ]            * ]
+  [ class "" [ "lifts_simple_dx" ]             class "" [ "lifts_simple_dx" ]            * ]
+  [ class "" [ "lifts_simple_sn" ]             class "" [ "lifts_simple_sn" ]            * ]
+  [ class "" [ "lifts_bind" ]                  class "" [ "lifts_bind" ]                 * ]
+  [ class "" [ "lifts_flat" ]                  class "" [ "lifts_flat" ]                 * ]
+  [ class "" [ "lifts_total" ]                 class "" [ "lifts_total" ]                * ]
+  [ class "" [ "liftsv" ]                      class "" [ "liftsv" ]                     * ]
+  [ class "" [ "lifts_inv_applv1" ]            class "" [ "lifts_inv_applv1" ]           * ]
+  [ class "" [ "lifts_applv" ]                 class "" [ "lifts_applv" ]                * ]
+  [ class "" [ "drops" ]                       class "" [ "drops" ]                      * ]
+  [ class "" [ "d_liftable1" ]                 class "" [ "d_liftable1" ]                * ]
+  [ class "" [ "d_liftables1" ]                class "" [ "d_liftables1" ]               * ]
+  [ class "" [ "d_liftables1_all" ]            class "" [ "d_liftables1_all" ]           * ]
+  [ class "" [ "drops_inv_nil_aux" ]           class "" [ "drops_inv_nil_aux" ]          * ]
+  [ class "" [ "drops_inv_nil" ]               class "" [ "drops_inv_nil" ]              * ]
+  [ class "" [ "drops_inv_cons_aux" ]          class "" [ "drops_inv_cons_aux" ]         * ]
+  [ class "" [ "drops_inv_cons" ]              class "" [ "drops_inv_cons" ]             * ]
+  [ class "" [ "drops_inv_skip2" ]             class "" [ "drops_inv_skip2" ]            * ]
+  [ class "" [ "drops_skip" ]                  class "" [ "drops_skip" ]                 * ]
   [ class "" [ "d1_liftable_liftables" ]       class "" [ "d1_liftable_liftables" ]      * ]
   [ class "" [ "d1_liftables_liftables_all" ]  class "" [ "d1_liftables_liftables_all" ] * ]
-  [ class "" [ "aaa_lifts" ]                  class "" [ "aaa_lifts" ]                  * ]
-  [ class "" [ "aaa_fqu_conf" ]                       class "" [ "aaa_fqu_conf" ]               * ]
-  [ class "" [ "aaa_fquq_conf" ]              class "" [ "aaa_fquq_conf" ]              * ]
-  [ class "" [ "aaa_fqup_conf" ]              class "" [ "aaa_fqup_conf" ]              * ]
-  [ class "" [ "aaa_fqus_conf" ]              class "" [ "aaa_fqus_conf" ]              * ]
-  [ class "" [ "lsubd" ]                      class "" [ "lsubd" ]                      * ]
-  [ class "" [ "lsubd_fwd_lsubr" ]            class "" [ "lsubd_fwd_lsubr" ]            * ]
-  [ class "" [ "lsubd_inv_atom1_aux" ]        class "" [ "lsubd_inv_atom1_aux" ]        * ]
-  [ class "" [ "lsubd_inv_atom1" ]            class "" [ "lsubd_inv_atom1" ]            * ]
-  [ class "" [ "lsubd_inv_pair1_aux" ]        class "" [ "lsubd_inv_pair1_aux" ]        * ]
-  [ class "" [ "lsubd_inv_pair1" ]            class "" [ "lsubd_inv_pair1" ]            * ]
-  [ class "" [ "lsubd_inv_atom2_aux" ]        class "" [ "lsubd_inv_atom2_aux" ]        * ]
-  [ class "" [ "lsubd_inv_atom2" ]            class "" [ "lsubd_inv_atom2" ]            * ]
-  [ class "" [ "lsubd_inv_pair2_aux" ]        class "" [ "lsubd_inv_pair2_aux" ]        * ]
-  [ class "" [ "lsubd_inv_pair2" ]            class "" [ "lsubd_inv_pair2" ]            * ]
-  [ class "" [ "lsubd_refl" ]                 class "" [ "lsubd_refl" ]                 * ]
-  [ class "" [ "lsubd_drop_O1_conf" ]         class "" [ "lsubd_drop_O1_conf" ]         * ]
-  [ class "" [ "lsubd_drop_O1_trans" ]        class "" [ "lsubd_drop_O1_trans" ]        * ]
-  [ class "" [ "lsubd_da_trans" ]             class "" [ "lsubd_da_trans" ]             * ]
-  [ class "" [ "lsubd_da_conf" ]              class "" [ "lsubd_da_conf" ]              * ]
-  [ class "" [ "lsubd_trans" ]                class "" [ "lsubd_trans" ]                * ]
-  [ class "" [ "aaa_da" ]                     class "" [ "aaa_da" ]                     * ]
-  [ class "" [ "llpx_sn" ]                    class "" [ "llpx_sn" ]                    * ]
-  [ class "" [ "llpx_sn_inv_bind_aux" ]               class "" [ "llpx_sn_inv_bind_aux" ]       * ]
-  [ class "" [ "llpx_sn_inv_bind" ]           class "" [ "llpx_sn_inv_bind" ]           * ]
-  [ class "" [ "llpx_sn_inv_flat_aux" ]               class "" [ "llpx_sn_inv_flat_aux" ]       * ]
-  [ class "" [ "llpx_sn_inv_flat" ]           class "" [ "llpx_sn_inv_flat" ]           * ]
-  [ class "" [ "llpx_sn_fwd_length" ]         class "" [ "llpx_sn_fwd_length" ]         * ]
-  [ class "" [ "llpx_sn_fwd_drop_sn" ]        class "" [ "llpx_sn_fwd_drop_sn" ]        * ]
-  [ class "" [ "llpx_sn_fwd_drop_dx" ]        class "" [ "llpx_sn_fwd_drop_dx" ]        * ]
-  [ class "" [ "llpx_sn_fwd_lref_aux" ]               class "" [ "llpx_sn_fwd_lref_aux" ]       * ]
-  [ class "" [ "llpx_sn_fwd_lref" ]           class "" [ "llpx_sn_fwd_lref" ]           * ]
-  [ class "" [ "llpx_sn_fwd_bind_sn" ]        class "" [ "llpx_sn_fwd_bind_sn" ]        * ]
-  [ class "" [ "llpx_sn_fwd_bind_dx" ]        class "" [ "llpx_sn_fwd_bind_dx" ]        * ]
-  [ class "" [ "llpx_sn_fwd_flat_sn" ]        class "" [ "llpx_sn_fwd_flat_sn" ]        * ]
-  [ class "" [ "llpx_sn_fwd_flat_dx" ]        class "" [ "llpx_sn_fwd_flat_dx" ]        * ]
-  [ class "" [ "llpx_sn_fwd_pair_sn" ]        class "" [ "llpx_sn_fwd_pair_sn" ]        * ]
-  [ class "" [ "llpx_sn_refl" ]                       class "" [ "llpx_sn_refl" ]               * ]
-  [ class "" [ "llpx_sn_Y" ]                  class "" [ "llpx_sn_Y" ]                  * ]
-  [ class "" [ "llpx_sn_ge_up" ]              class "" [ "llpx_sn_ge_up" ]              * ]
-  [ class "" [ "llpx_sn_ge" ]                 class "" [ "llpx_sn_ge" ]                 * ]
-  [ class "" [ "llpx_sn_bind_O" ]             class "" [ "llpx_sn_bind_O" ]             * ]
-  [ class "" [ "llpx_sn_co" ]                 class "" [ "llpx_sn_co" ]                 * ]
-  [ class "" [ "lreq_llpx_sn_trans" ]         class "" [ "lreq_llpx_sn_trans" ]         * ]
-  [ class "" [ "llpx_sn_lreq_trans" ]         class "" [ "llpx_sn_lreq_trans" ]         * ]
-  [ class "" [ "llpx_sn_lreq_repl" ]          class "" [ "llpx_sn_lreq_repl" ]          * ]
-  [ class "" [ "llpx_sn_bind_repl_SO" ]               class "" [ "llpx_sn_bind_repl_SO" ]       * ]
-  [ class "" [ "llpx_sn_fwd_lref_dx" ]        class "" [ "llpx_sn_fwd_lref_dx" ]        * ]
-  [ class "" [ "llpx_sn_fwd_lref_sn" ]        class "" [ "llpx_sn_fwd_lref_sn" ]        * ]
+  [ class "" [ "aaa_lifts" ]                   class "" [ "aaa_lifts" ]                  * ]
+  [ class "" [ "aaa_fqu_conf" ]                class "" [ "aaa_fqu_conf" ]               * ]
+  [ class "" [ "aaa_fquq_conf" ]               class "" [ "aaa_fquq_conf" ]              * ]
+  [ class "" [ "aaa_fqup_conf" ]               class "" [ "aaa_fqup_conf" ]              * ]
+  [ class "" [ "aaa_fqus_conf" ]               class "" [ "aaa_fqus_conf" ]              * ]
+  [ class "" [ "lsubd" ]                       class "" [ "lsubd" ]                      * ]
+  [ class "" [ "lsubd_fwd_lsubr" ]             class "" [ "lsubd_fwd_lsubr" ]            * ]
+  [ class "" [ "lsubd_inv_atom1_aux" ]         class "" [ "lsubd_inv_atom1_aux" ]        * ]
+  [ class "" [ "lsubd_inv_atom1" ]             class "" [ "lsubd_inv_atom1" ]            * ]
+  [ class "" [ "lsubd_inv_pair1_aux" ]         class "" [ "lsubd_inv_pair1_aux" ]        * ]
+  [ class "" [ "lsubd_inv_pair1" ]             class "" [ "lsubd_inv_pair1" ]            * ]
+  [ class "" [ "lsubd_inv_atom2_aux" ]         class "" [ "lsubd_inv_atom2_aux" ]        * ]
+  [ class "" [ "lsubd_inv_atom2" ]             class "" [ "lsubd_inv_atom2" ]            * ]
+  [ class "" [ "lsubd_inv_pair2_aux" ]         class "" [ "lsubd_inv_pair2_aux" ]        * ]
+  [ class "" [ "lsubd_inv_pair2" ]             class "" [ "lsubd_inv_pair2" ]            * ]
+  [ class "" [ "lsubd_refl" ]                  class "" [ "lsubd_refl" ]                 * ]
+  [ class "" [ "lsubd_drop_O1_conf" ]          class "" [ "lsubd_drop_O1_conf" ]         * ]
+  [ class "" [ "lsubd_drop_O1_trans" ]         class "" [ "lsubd_drop_O1_trans" ]        * ]
+  [ class "" [ "lsubd_da_trans" ]              class "" [ "lsubd_da_trans" ]             * ]
+  [ class "" [ "lsubd_da_conf" ]               class "" [ "lsubd_da_conf" ]              * ]
+  [ class "" [ "lsubd_trans" ]                 class "" [ "lsubd_trans" ]                * ]
+  [ class "" [ "aaa_da" ]                      class "" [ "aaa_da" ]                     * ]
+  [ class "" [ "llpx_sn" ]                     class "" [ "llpx_sn" ]                    * ]
+  [ class "" [ "llpx_sn_inv_bind_aux" ]        class "" [ "llpx_sn_inv_bind_aux" ]       * ]
+  [ class "" [ "llpx_sn_inv_bind" ]            class "" [ "llpx_sn_inv_bind" ]           * ]
+  [ class "" [ "llpx_sn_inv_flat_aux" ]        class "" [ "llpx_sn_inv_flat_aux" ]       * ]
+  [ class "" [ "llpx_sn_inv_flat" ]            class "" [ "llpx_sn_inv_flat" ]           * ]
+  [ class "" [ "llpx_sn_fwd_length" ]          class "" [ "llpx_sn_fwd_length" ]         * ]
+  [ class "" [ "llpx_sn_fwd_drop_sn" ]         class "" [ "llpx_sn_fwd_drop_sn" ]        * ]
+  [ class "" [ "llpx_sn_fwd_drop_dx" ]         class "" [ "llpx_sn_fwd_drop_dx" ]        * ]
+  [ class "" [ "llpx_sn_fwd_lref_aux" ]        class "" [ "llpx_sn_fwd_lref_aux" ]       * ]
+  [ class "" [ "llpx_sn_fwd_lref" ]            class "" [ "llpx_sn_fwd_lref" ]           * ]
+  [ class "" [ "llpx_sn_fwd_bind_sn" ]         class "" [ "llpx_sn_fwd_bind_sn" ]        * ]
+  [ class "" [ "llpx_sn_fwd_bind_dx" ]         class "" [ "llpx_sn_fwd_bind_dx" ]        * ]
+  [ class "" [ "llpx_sn_fwd_flat_sn" ]         class "" [ "llpx_sn_fwd_flat_sn" ]        * ]
+  [ class "" [ "llpx_sn_fwd_flat_dx" ]         class "" [ "llpx_sn_fwd_flat_dx" ]        * ]
+  [ class "" [ "llpx_sn_fwd_pair_sn" ]         class "" [ "llpx_sn_fwd_pair_sn" ]        * ]
+  [ class "" [ "llpx_sn_refl" ]                class "" [ "llpx_sn_refl" ]               * ]
+  [ class "" [ "llpx_sn_Y" ]                   class "" [ "llpx_sn_Y" ]                  * ]
+  [ class "" [ "llpx_sn_ge_up" ]               class "" [ "llpx_sn_ge_up" ]              * ]
+  [ class "" [ "llpx_sn_ge" ]                  class "" [ "llpx_sn_ge" ]                 * ]
+  [ class "" [ "llpx_sn_bind_O" ]              class "" [ "llpx_sn_bind_O" ]             * ]
+  [ class "" [ "llpx_sn_co" ]                  class "" [ "llpx_sn_co" ]                 * ]
+  [ class "" [ "lreq_llpx_sn_trans" ]          class "" [ "lreq_llpx_sn_trans" ]         * ]
+  [ class "" [ "llpx_sn_lreq_trans" ]          class "" [ "llpx_sn_lreq_trans" ]         * ]
+  [ class "" [ "llpx_sn_lreq_repl" ]           class "" [ "llpx_sn_lreq_repl" ]          * ]
+  [ class "" [ "llpx_sn_bind_repl_SO" ]        class "" [ "llpx_sn_bind_repl_SO" ]       * ]
+  [ class "" [ "llpx_sn_fwd_lref_dx" ]         class "" [ "llpx_sn_fwd_lref_dx" ]        * ]
+  [ class "" [ "llpx_sn_fwd_lref_sn" ]         class "" [ "llpx_sn_fwd_lref_sn" ]        * ]
   [ class "" [ "llpx_sn_inv_lref_ge_dx" ]      class "" [ "llpx_sn_inv_lref_ge_dx" ]     * ]
   [ class "" [ "llpx_sn_inv_lref_ge_sn" ]      class "" [ "llpx_sn_inv_lref_ge_sn" ]     * ]
   [ class "" [ "llpx_sn_inv_lref_ge_bi" ]      class "" [ "llpx_sn_inv_lref_ge_bi" ]     * ]
-  [ class "" [ "llpx_sn_inv_S_aux" ]          class "" [ "llpx_sn_inv_S_aux" ]          * ]
-  [ class "" [ "llpx_sn_inv_S" ]              class "" [ "llpx_sn_inv_S" ]              * ]
-  [ class "" [ "llpx_sn_inv_bind_O" ]         class "" [ "llpx_sn_inv_bind_O" ]         * ]
+  [ class "" [ "llpx_sn_inv_S_aux" ]           class "" [ "llpx_sn_inv_S_aux" ]          * ]
+  [ class "" [ "llpx_sn_inv_S" ]               class "" [ "llpx_sn_inv_S" ]              * ]
+  [ class "" [ "llpx_sn_inv_bind_O" ]          class "" [ "llpx_sn_inv_bind_O" ]         * ]
   [ class "" [ "llpx_sn_fwd_bind_O_dx" ]       class "" [ "llpx_sn_fwd_bind_O_dx" ]      * ]
-  [ class "" [ "llpx_sn_bind_repl_O" ]        class "" [ "llpx_sn_bind_repl_O" ]        * ]
-  [ class "" [ "llpx_sn_dec" ]                class "" [ "llpx_sn_dec" ]                * ]
-  [ class "" [ "llpx_sn_lift_le" ]            class "" [ "llpx_sn_lift_le" ]            * ]
-  [ class "" [ "llpx_sn_lift_ge" ]            class "" [ "llpx_sn_lift_ge" ]            * ]
-  [ class "" [ "llpx_sn_inv_lift_le" ]        class "" [ "llpx_sn_inv_lift_le" ]        * ]
-  [ class "" [ "llpx_sn_inv_lift_be" ]        class "" [ "llpx_sn_inv_lift_be" ]        * ]
-  [ class "" [ "llpx_sn_inv_lift_ge" ]        class "" [ "llpx_sn_inv_lift_ge" ]        * ]
-  [ class "" [ "llpx_sn_inv_lift_O" ]         class "" [ "llpx_sn_inv_lift_O" ]         * ]
-  [ class "" [ "llpx_sn_drop_conf_O" ]        class "" [ "llpx_sn_drop_conf_O" ]        * ]
-  [ class "" [ "llpx_sn_drop_trans_O" ]               class "" [ "llpx_sn_drop_trans_O" ]       * ]
-  [ class "" [ "nllpx_sn_inv_bind" ]          class "" [ "nllpx_sn_inv_bind" ]          * ]
-  [ class "" [ "nllpx_sn_inv_flat" ]          class "" [ "nllpx_sn_inv_flat" ]          * ]
-  [ class "" [ "nllpx_sn_inv_bind_O" ]        class "" [ "nllpx_sn_inv_bind_O" ]        * ]
-  [ class "" [ "ceq" ]                        class "" [ "ceq" ]                        * ]
-  [ class "" [ "lleq" ]                               class "" [ "lleq" ]                       * ]
-  [ class "" [ "lleq_transitive" ]            class "" [ "lleq_transitive" ]            * ]
-  [ class "" [ "lleq_ind" ]                   class "" [ "lleq_ind" ]                   * ]
-  [ class "" [ "lleq_inv_bind" ]              class "" [ "lleq_inv_bind" ]              * ]
-  [ class "" [ "lleq_inv_flat" ]              class "" [ "lleq_inv_flat" ]              * ]
-  [ class "" [ "lleq_fwd_length" ]            class "" [ "lleq_fwd_length" ]            * ]
-  [ class "" [ "lleq_fwd_lref" ]              class "" [ "lleq_fwd_lref" ]              * ]
-  [ class "" [ "lleq_fwd_drop_sn" ]           class "" [ "lleq_fwd_drop_sn" ]           * ]
-  [ class "" [ "lleq_fwd_drop_dx" ]           class "" [ "lleq_fwd_drop_dx" ]           * ]
-  [ class "" [ "lleq_fwd_bind_sn" ]           class "" [ "lleq_fwd_bind_sn" ]           * ]
-  [ class "" [ "lleq_fwd_bind_dx" ]           class "" [ "lleq_fwd_bind_dx" ]           * ]
-  [ class "" [ "lleq_fwd_flat_sn" ]           class "" [ "lleq_fwd_flat_sn" ]           * ]
-  [ class "" [ "lleq_fwd_flat_dx" ]           class "" [ "lleq_fwd_flat_dx" ]           * ]
-  [ class "" [ "lleq_sort" ]                  class "" [ "lleq_sort" ]                  * ]
-  [ class "" [ "lleq_skip" ]                  class "" [ "lleq_skip" ]                  * ]
-  [ class "" [ "lleq_lref" ]                  class "" [ "lleq_lref" ]                  * ]
-  [ class "" [ "lleq_free" ]                  class "" [ "lleq_free" ]                  * ]
-  [ class "" [ "lleq_gref" ]                  class "" [ "lleq_gref" ]                  * ]
-  [ class "" [ "lleq_bind" ]                  class "" [ "lleq_bind" ]                  * ]
-  [ class "" [ "lleq_flat" ]                  class "" [ "lleq_flat" ]                  * ]
-  [ class "" [ "lleq_refl" ]                  class "" [ "lleq_refl" ]                  * ]
-  [ class "" [ "lleq_Y" ]                     class "" [ "lleq_Y" ]                     * ]
-  [ class "" [ "lleq_sym" ]                   class "" [ "lleq_sym" ]                   * ]
-  [ class "" [ "lleq_ge_up" ]                 class "" [ "lleq_ge_up" ]                 * ]
-  [ class "" [ "lleq_ge" ]                    class "" [ "lleq_ge" ]                    * ]
-  [ class "" [ "lleq_bind_O" ]                class "" [ "lleq_bind_O" ]                * ]
-  [ class "" [ "llpx_sn_lrefl" ]              class "" [ "llpx_sn_lrefl" ]              * ]
-  [ class "" [ "lleq_bind_repl_O" ]           class "" [ "lleq_bind_repl_O" ]           * ]
-  [ class "" [ "lleq_dec" ]                   class "" [ "lleq_dec" ]                   * ]
-  [ class "" [ "lleq_llpx_sn_trans" ]         class "" [ "lleq_llpx_sn_trans" ]         * ]
-  [ class "" [ "lleq_llpx_sn_conf" ]          class "" [ "lleq_llpx_sn_conf" ]          * ]
-  [ class "" [ "lleq_inv_lref_ge_dx" ]        class "" [ "lleq_inv_lref_ge_dx" ]        * ]
-  [ class "" [ "lleq_inv_lref_ge_sn" ]        class "" [ "lleq_inv_lref_ge_sn" ]        * ]
-  [ class "" [ "lleq_inv_lref_ge_bi" ]        class "" [ "lleq_inv_lref_ge_bi" ]        * ]
-  [ class "" [ "lleq_inv_lref_ge" ]           class "" [ "lleq_inv_lref_ge" ]           * ]
-  [ class "" [ "lleq_inv_S" ]                 class "" [ "lleq_inv_S" ]                 * ]
-  [ class "" [ "lleq_inv_bind_O" ]            class "" [ "lleq_inv_bind_O" ]            * ]
-  [ class "" [ "lleq_fwd_lref_dx" ]           class "" [ "lleq_fwd_lref_dx" ]           * ]
-  [ class "" [ "lleq_fwd_lref_sn" ]           class "" [ "lleq_fwd_lref_sn" ]           * ]
-  [ class "" [ "lleq_fwd_bind_O_dx" ]         class "" [ "lleq_fwd_bind_O_dx" ]         * ]
-  [ class "" [ "lleq_lift_le" ]                       class "" [ "lleq_lift_le" ]               * ]
-  [ class "" [ "lleq_lift_ge" ]                       class "" [ "lleq_lift_ge" ]               * ]
-  [ class "" [ "lleq_inv_lift_le" ]           class "" [ "lleq_inv_lift_le" ]           * ]
-  [ class "" [ "lleq_inv_lift_be" ]           class "" [ "lleq_inv_lift_be" ]           * ]
-  [ class "" [ "lleq_inv_lift_ge" ]           class "" [ "lleq_inv_lift_ge" ]           * ]
-  [ class "" [ "nlleq_inv_bind" ]             class "" [ "nlleq_inv_bind" ]             * ]
-  [ class "" [ "nlleq_inv_flat" ]             class "" [ "nlleq_inv_flat" ]             * ]
-  [ class "" [ "nlleq_inv_bind_O" ]           class "" [ "nlleq_inv_bind_O" ]           * ]
-  [ class "" [ "lleq_aaa_trans" ]             class "" [ "lleq_aaa_trans" ]             * ]
-  [ class "" [ "aaa_lleq_conf" ]              class "" [ "aaa_lleq_conf" ]              * ]
-  [ class "" [ "lsuba_trans" ]                class "" [ "lsuba_trans" ]                * ]
-  [ class "" [ "ri2" ]                        class "" [ "ri2" ]                        * ]
-  [ class "" [ "ib2" ]                        class "" [ "ib2" ]                        * ]
-  [ class "" [ "crr" ]                        class "" [ "crr" ]                        * ]
-  [ class "" [ "crr_inv_sort_aux" ]           class "" [ "crr_inv_sort_aux" ]           * ]
-  [ class "" [ "crr_inv_sort" ]                       class "" [ "crr_inv_sort" ]               * ]
-  [ class "" [ "crr_inv_lref_aux" ]           class "" [ "crr_inv_lref_aux" ]           * ]
-  [ class "" [ "crr_inv_lref" ]                       class "" [ "crr_inv_lref" ]               * ]
-  [ class "" [ "crr_inv_gref_aux" ]           class "" [ "crr_inv_gref_aux" ]           * ]
-  [ class "" [ "crr_inv_gref" ]                       class "" [ "crr_inv_gref" ]               * ]
-  [ class "" [ "trr_inv_atom" ]                       class "" [ "trr_inv_atom" ]               * ]
-  [ class "" [ "crr_inv_ib2_aux" ]            class "" [ "crr_inv_ib2_aux" ]            * ]
-  [ class "" [ "crr_inv_ib2" ]                class "" [ "crr_inv_ib2" ]                * ]
-  [ class "" [ "crr_inv_appl_aux" ]           class "" [ "crr_inv_appl_aux" ]           * ]
-  [ class "" [ "crr_inv_appl" ]                       class "" [ "crr_inv_appl" ]               * ]
-  [ class "" [ "cir" ]                        class "" [ "cir" ]                        * ]
-  [ class "" [ "cir_inv_delta" ]              class "" [ "cir_inv_delta" ]              * ]
-  [ class "" [ "cir_inv_ri2" ]                class "" [ "cir_inv_ri2" ]                * ]
-  [ class "" [ "cir_inv_ib2" ]                class "" [ "cir_inv_ib2" ]                * ]
-  [ class "" [ "cir_inv_bind" ]                       class "" [ "cir_inv_bind" ]               * ]
-  [ class "" [ "cir_inv_appl" ]                       class "" [ "cir_inv_appl" ]               * ]
-  [ class "" [ "cir_inv_flat" ]                       class "" [ "cir_inv_flat" ]               * ]
-  [ class "" [ "cir_sort" ]                   class "" [ "cir_sort" ]                   * ]
-  [ class "" [ "cir_gref" ]                   class "" [ "cir_gref" ]                   * ]
-  [ class "" [ "tir_atom" ]                   class "" [ "tir_atom" ]                   * ]
-  [ class "" [ "cir_ib2" ]                    class "" [ "cir_ib2" ]                    * ]
-  [ class "" [ "cir_appl" ]                   class "" [ "cir_appl" ]                   * ]
-  [ class "" [ "crx" ]                        class "" [ "crx" ]                        * ]
-  [ class "" [ "crr_crx" ]                    class "" [ "crr_crx" ]                    * ]
-  [ class "" [ "crx_inv_sort_aux" ]           class "" [ "crx_inv_sort_aux" ]           * ]
-  [ class "" [ "crx_inv_sort" ]                       class "" [ "crx_inv_sort" ]               * ]
-  [ class "" [ "crx_inv_lref_aux" ]           class "" [ "crx_inv_lref_aux" ]           * ]
-  [ class "" [ "crx_inv_lref" ]                       class "" [ "crx_inv_lref" ]               * ]
-  [ class "" [ "crx_inv_gref_aux" ]           class "" [ "crx_inv_gref_aux" ]           * ]
-  [ class "" [ "crx_inv_gref" ]                       class "" [ "crx_inv_gref" ]               * ]
-  [ class "" [ "trx_inv_atom" ]                       class "" [ "trx_inv_atom" ]               * ]
-  [ class "" [ "crx_inv_ib2_aux" ]            class "" [ "crx_inv_ib2_aux" ]            * ]
-  [ class "" [ "crx_inv_ib2" ]                class "" [ "crx_inv_ib2" ]                * ]
-  [ class "" [ "crx_inv_appl_aux" ]           class "" [ "crx_inv_appl_aux" ]           * ]
-  [ class "" [ "crx_inv_appl" ]                       class "" [ "crx_inv_appl" ]               * ]
-  [ class "" [ "cix" ]                        class "" [ "cix" ]                        * ]
-  [ class "" [ "cix_inv_sort" ]                       class "" [ "cix_inv_sort" ]               * ]
-  [ class "" [ "cix_inv_delta" ]              class "" [ "cix_inv_delta" ]              * ]
-  [ class "" [ "cix_inv_ri2" ]                class "" [ "cix_inv_ri2" ]                * ]
-  [ class "" [ "cix_inv_ib2" ]                class "" [ "cix_inv_ib2" ]                * ]
-  [ class "" [ "cix_inv_bind" ]                       class "" [ "cix_inv_bind" ]               * ]
-  [ class "" [ "cix_inv_appl" ]                       class "" [ "cix_inv_appl" ]               * ]
-  [ class "" [ "cix_inv_flat" ]                       class "" [ "cix_inv_flat" ]               * ]
-  [ class "" [ "cix_inv_cir" ]                class "" [ "cix_inv_cir" ]                * ]
-  [ class "" [ "cix_sort" ]                   class "" [ "cix_sort" ]                   * ]
-  [ class "" [ "tix_lref" ]                   class "" [ "tix_lref" ]                   * ]
-  [ class "" [ "cix_gref" ]                   class "" [ "cix_gref" ]                   * ]
-  [ class "" [ "cix_ib2" ]                    class "" [ "cix_ib2" ]                    * ]
-  [ class "" [ "cix_appl" ]                   class "" [ "cix_appl" ]                   * ]
-  [ class "" [ "cpx_fwd_cix" ]                class "" [ "cpx_fwd_cix" ]                * ]
-  [ class "" [ "nlift_lref_be_SO" ]           class "" [ "nlift_lref_be_SO" ]           * ]
-  [ class "" [ "nlift_bind_sn" ]              class "" [ "nlift_bind_sn" ]              * ]
-  [ class "" [ "nlift_bind_dx" ]              class "" [ "nlift_bind_dx" ]              * ]
-  [ class "" [ "nlift_flat_sn" ]              class "" [ "nlift_flat_sn" ]              * ]
-  [ class "" [ "nlift_flat_dx" ]              class "" [ "nlift_flat_dx" ]              * ]
-  [ class "" [ "nlift_inv_lref_be_SO" ]               class "" [ "nlift_inv_lref_be_SO" ]       * ]
-  [ class "" [ "nlift_inv_bind" ]             class "" [ "nlift_inv_bind" ]             * ]
-  [ class "" [ "nlift_inv_flat" ]             class "" [ "nlift_inv_flat" ]             * ]
-  [ class "" [ "frees" ]                      class "" [ "frees" ]                      * ]
-  [ class "" [ "frees_trans" ]                class "" [ "frees_trans" ]                * ]
-  [ class "" [ "frees_inv" ]                  class "" [ "frees_inv" ]                  * ]
-  [ class "" [ "frees_inv_sort" ]             class "" [ "frees_inv_sort" ]             * ]
-  [ class "" [ "frees_inv_gref" ]             class "" [ "frees_inv_gref" ]             * ]
-  [ class "" [ "frees_inv_lref" ]             class "" [ "frees_inv_lref" ]             * ]
-  [ class "" [ "frees_inv_lref_free" ]        class "" [ "frees_inv_lref_free" ]        * ]
-  [ class "" [ "frees_inv_lref_skip" ]        class "" [ "frees_inv_lref_skip" ]        * ]
-  [ class "" [ "frees_inv_lref_ge" ]          class "" [ "frees_inv_lref_ge" ]          * ]
-  [ class "" [ "frees_inv_lref_lt" ]          class "" [ "frees_inv_lref_lt" ]          * ]
-  [ class "" [ "frees_inv_bind" ]             class "" [ "frees_inv_bind" ]             * ]
-  [ class "" [ "frees_inv_flat" ]             class "" [ "frees_inv_flat" ]             * ]
-  [ class "" [ "frees_lref_eq" ]              class "" [ "frees_lref_eq" ]              * ]
-  [ class "" [ "frees_lref_be" ]              class "" [ "frees_lref_be" ]              * ]
-  [ class "" [ "frees_bind_sn" ]              class "" [ "frees_bind_sn" ]              * ]
-  [ class "" [ "frees_bind_dx" ]              class "" [ "frees_bind_dx" ]              * ]
-  [ class "" [ "frees_flat_sn" ]              class "" [ "frees_flat_sn" ]              * ]
-  [ class "" [ "frees_flat_dx" ]              class "" [ "frees_flat_dx" ]              * ]
-  [ class "" [ "frees_weak" ]                 class "" [ "frees_weak" ]                 * ]
-  [ class "" [ "frees_inv_bind_O" ]           class "" [ "frees_inv_bind_O" ]           * ]
-  [ class "" [ "frees_dec" ]                  class "" [ "frees_dec" ]                  * ]
-  [ class "" [ "frees_S" ]                    class "" [ "frees_S" ]                    * ]
-  [ class "" [ "frees_bind_dx_O" ]            class "" [ "frees_bind_dx_O" ]            * ]
-  [ class "" [ "frees_lift_ge" ]              class "" [ "frees_lift_ge" ]              * ]
-  [ class "" [ "frees_inv_lift_be" ]          class "" [ "frees_inv_lift_be" ]          * ]
-  [ class "" [ "frees_inv_lift_ge" ]          class "" [ "frees_inv_lift_ge" ]          * ]
-  [ class "" [ "append" ]                     class "" [ "append" ]                     * ]
-  [ class "" [ "d_appendable_sn" ]            class "" [ "d_appendable_sn" ]            * ]
-  [ class "" [ "append_atom_sn" ]             class "" [ "append_atom_sn" ]             * ]
-  [ class "" [ "append_assoc" ]                       class "" [ "append_assoc" ]               * ]
-  [ class "" [ "append_length" ]              class "" [ "append_length" ]              * ]
-  [ class "" [ "ltail_length" ]                       class "" [ "ltail_length" ]               * ]
-  [ class "" [ "lpair_ltail" ]                class "" [ "lpair_ltail" ]                * ]
-  [ class "" [ "append_inj_sn" ]              class "" [ "append_inj_sn" ]              * ]
-  [ class "" [ "append_inj_dx" ]              class "" [ "append_inj_dx" ]              * ]
-  [ class "" [ "append_inv_refl_dx" ]         class "" [ "append_inv_refl_dx" ]         * ]
-  [ class "" [ "append_inv_pair_dx" ]         class "" [ "append_inv_pair_dx" ]         * ]
+  [ class "" [ "llpx_sn_bind_repl_O" ]         class "" [ "llpx_sn_bind_repl_O" ]        * ]
+  [ class "" [ "llpx_sn_dec" ]                 class "" [ "llpx_sn_dec" ]                * ]
+  [ class "" [ "llpx_sn_lift_le" ]             class "" [ "llpx_sn_lift_le" ]            * ]
+  [ class "" [ "llpx_sn_lift_ge" ]             class "" [ "llpx_sn_lift_ge" ]            * ]
+  [ class "" [ "llpx_sn_inv_lift_le" ]         class "" [ "llpx_sn_inv_lift_le" ]        * ]
+  [ class "" [ "llpx_sn_inv_lift_be" ]         class "" [ "llpx_sn_inv_lift_be" ]        * ]
+  [ class "" [ "llpx_sn_inv_lift_ge" ]         class "" [ "llpx_sn_inv_lift_ge" ]        * ]
+  [ class "" [ "llpx_sn_inv_lift_O" ]          class "" [ "llpx_sn_inv_lift_O" ]         * ]
+  [ class "" [ "llpx_sn_drop_conf_O" ]         class "" [ "llpx_sn_drop_conf_O" ]        * ]
+  [ class "" [ "llpx_sn_drop_trans_O" ]        class "" [ "llpx_sn_drop_trans_O" ]       * ]
+  [ class "" [ "nllpx_sn_inv_bind" ]           class "" [ "nllpx_sn_inv_bind" ]          * ]
+  [ class "" [ "nllpx_sn_inv_flat" ]           class "" [ "nllpx_sn_inv_flat" ]          * ]
+  [ class "" [ "nllpx_sn_inv_bind_O" ]         class "" [ "nllpx_sn_inv_bind_O" ]        * ]
+  [ class "" [ "ceq" ]                         class "" [ "ceq" ]                        * ]
+  [ class "" [ "lleq" ]                        class "" [ "lleq" ]                       * ]
+  [ class "" [ "lleq_transitive" ]             class "" [ "lleq_transitive" ]            * ]
+  [ class "" [ "lleq_ind" ]                    class "" [ "lleq_ind" ]                   * ]
+  [ class "" [ "lleq_inv_bind" ]               class "" [ "lleq_inv_bind" ]              * ]
+  [ class "" [ "lleq_inv_flat" ]               class "" [ "lleq_inv_flat" ]              * ]
+  [ class "" [ "lleq_fwd_length" ]             class "" [ "lleq_fwd_length" ]            * ]
+  [ class "" [ "lleq_fwd_lref" ]               class "" [ "lleq_fwd_lref" ]              * ]
+  [ class "" [ "lleq_fwd_drop_sn" ]            class "" [ "lleq_fwd_drop_sn" ]           * ]
+  [ class "" [ "lleq_fwd_drop_dx" ]            class "" [ "lleq_fwd_drop_dx" ]           * ]
+  [ class "" [ "lleq_fwd_bind_sn" ]            class "" [ "lleq_fwd_bind_sn" ]           * ]
+  [ class "" [ "lleq_fwd_bind_dx" ]            class "" [ "lleq_fwd_bind_dx" ]           * ]
+  [ class "" [ "lleq_fwd_flat_sn" ]            class "" [ "lleq_fwd_flat_sn" ]           * ]
+  [ class "" [ "lleq_fwd_flat_dx" ]            class "" [ "lleq_fwd_flat_dx" ]           * ]
+  [ class "" [ "lleq_sort" ]                   class "" [ "lleq_sort" ]                  * ]
+  [ class "" [ "lleq_skip" ]                   class "" [ "lleq_skip" ]                  * ]
+  [ class "" [ "lleq_lref" ]                   class "" [ "lleq_lref" ]                  * ]
+  [ class "" [ "lleq_free" ]                   class "" [ "lleq_free" ]                  * ]
+  [ class "" [ "lleq_gref" ]                   class "" [ "lleq_gref" ]                  * ]
+  [ class "" [ "lleq_bind" ]                   class "" [ "lleq_bind" ]                  * ]
+  [ class "" [ "lleq_flat" ]                   class "" [ "lleq_flat" ]                  * ]
+  [ class "" [ "lleq_refl" ]                   class "" [ "lleq_refl" ]                  * ]
+  [ class "" [ "lleq_Y" ]                      class "" [ "lleq_Y" ]                     * ]
+  [ class "" [ "lleq_sym" ]                    class "" [ "lleq_sym" ]                   * ]
+  [ class "" [ "lleq_ge_up" ]                  class "" [ "lleq_ge_up" ]                 * ]
+  [ class "" [ "lleq_ge" ]                     class "" [ "lleq_ge" ]                    * ]
+  [ class "" [ "lleq_bind_O" ]                 class "" [ "lleq_bind_O" ]                * ]
+  [ class "" [ "llpx_sn_lrefl" ]               class "" [ "llpx_sn_lrefl" ]              * ]
+  [ class "" [ "lleq_bind_repl_O" ]            class "" [ "lleq_bind_repl_O" ]           * ]
+  [ class "" [ "lleq_dec" ]                    class "" [ "lleq_dec" ]                   * ]
+  [ class "" [ "lleq_llpx_sn_trans" ]          class "" [ "lleq_llpx_sn_trans" ]         * ]
+  [ class "" [ "lleq_llpx_sn_conf" ]           class "" [ "lleq_llpx_sn_conf" ]          * ]
+  [ class "" [ "lleq_inv_lref_ge_dx" ]         class "" [ "lleq_inv_lref_ge_dx" ]        * ]
+  [ class "" [ "lleq_inv_lref_ge_sn" ]         class "" [ "lleq_inv_lref_ge_sn" ]        * ]
+  [ class "" [ "lleq_inv_lref_ge_bi" ]         class "" [ "lleq_inv_lref_ge_bi" ]        * ]
+  [ class "" [ "lleq_inv_lref_ge" ]            class "" [ "lleq_inv_lref_ge" ]           * ]
+  [ class "" [ "lleq_inv_S" ]                  class "" [ "lleq_inv_S" ]                 * ]
+  [ class "" [ "lleq_inv_bind_O" ]             class "" [ "lleq_inv_bind_O" ]            * ]
+  [ class "" [ "lleq_fwd_lref_dx" ]            class "" [ "lleq_fwd_lref_dx" ]           * ]
+  [ class "" [ "lleq_fwd_lref_sn" ]            class "" [ "lleq_fwd_lref_sn" ]           * ]
+  [ class "" [ "lleq_fwd_bind_O_dx" ]          class "" [ "lleq_fwd_bind_O_dx" ]         * ]
+  [ class "" [ "lleq_lift_le" ]                class "" [ "lleq_lift_le" ]               * ]
+  [ class "" [ "lleq_lift_ge" ]                class "" [ "lleq_lift_ge" ]               * ]
+  [ class "" [ "lleq_inv_lift_le" ]            class "" [ "lleq_inv_lift_le" ]           * ]
+  [ class "" [ "lleq_inv_lift_be" ]            class "" [ "lleq_inv_lift_be" ]           * ]
+  [ class "" [ "lleq_inv_lift_ge" ]            class "" [ "lleq_inv_lift_ge" ]           * ]
+  [ class "" [ "nlleq_inv_bind" ]              class "" [ "nlleq_inv_bind" ]             * ]
+  [ class "" [ "nlleq_inv_flat" ]              class "" [ "nlleq_inv_flat" ]             * ]
+  [ class "" [ "nlleq_inv_bind_O" ]            class "" [ "nlleq_inv_bind_O" ]           * ]
+  [ class "" [ "lleq_aaa_trans" ]              class "" [ "lleq_aaa_trans" ]             * ]
+  [ class "" [ "aaa_lleq_conf" ]               class "" [ "aaa_lleq_conf" ]              * ]
+  [ class "" [ "lsuba_trans" ]                 class "" [ "lsuba_trans" ]                * ]
+  [ class "" [ "ri2" ]                         class "" [ "ri2" ]                        * ]
+  [ class "" [ "ib2" ]                         class "" [ "ib2" ]                        * ]
+  [ class "" [ "crr" ]                         class "" [ "crr" ]                        * ]
+  [ class "" [ "crr_inv_sort_aux" ]            class "" [ "crr_inv_sort_aux" ]           * ]
+  [ class "" [ "crr_inv_sort" ]                class "" [ "crr_inv_sort" ]               * ]
+  [ class "" [ "crr_inv_lref_aux" ]            class "" [ "crr_inv_lref_aux" ]           * ]
+  [ class "" [ "crr_inv_lref" ]                class "" [ "crr_inv_lref" ]               * ]
+  [ class "" [ "crr_inv_gref_aux" ]            class "" [ "crr_inv_gref_aux" ]           * ]
+  [ class "" [ "crr_inv_gref" ]                class "" [ "crr_inv_gref" ]               * ]
+  [ class "" [ "trr_inv_atom" ]                class "" [ "trr_inv_atom" ]               * ]
+  [ class "" [ "crr_inv_ib2_aux" ]             class "" [ "crr_inv_ib2_aux" ]            * ]
+  [ class "" [ "crr_inv_ib2" ]                 class "" [ "crr_inv_ib2" ]                * ]
+  [ class "" [ "crr_inv_appl_aux" ]            class "" [ "crr_inv_appl_aux" ]           * ]
+  [ class "" [ "crr_inv_appl" ]                class "" [ "crr_inv_appl" ]               * ]
+  [ class "" [ "cir" ]                         class "" [ "cir" ]                        * ]
+  [ class "" [ "cir_inv_delta" ]               class "" [ "cir_inv_delta" ]              * ]
+  [ class "" [ "cir_inv_ri2" ]                 class "" [ "cir_inv_ri2" ]                * ]
+  [ class "" [ "cir_inv_ib2" ]                 class "" [ "cir_inv_ib2" ]                * ]
+  [ class "" [ "cir_inv_bind" ]                class "" [ "cir_inv_bind" ]               * ]
+  [ class "" [ "cir_inv_appl" ]                class "" [ "cir_inv_appl" ]               * ]
+  [ class "" [ "cir_inv_flat" ]                class "" [ "cir_inv_flat" ]               * ]
+  [ class "" [ "cir_sort" ]                    class "" [ "cir_sort" ]                   * ]
+  [ class "" [ "cir_gref" ]                    class "" [ "cir_gref" ]                   * ]
+  [ class "" [ "tir_atom" ]                    class "" [ "tir_atom" ]                   * ]
+  [ class "" [ "cir_ib2" ]                     class "" [ "cir_ib2" ]                    * ]
+  [ class "" [ "cir_appl" ]                    class "" [ "cir_appl" ]                   * ]
+  [ class "" [ "crx" ]                         class "" [ "crx" ]                        * ]
+  [ class "" [ "crr_crx" ]                     class "" [ "crr_crx" ]                    * ]
+  [ class "" [ "crx_inv_sort_aux" ]            class "" [ "crx_inv_sort_aux" ]           * ]
+  [ class "" [ "crx_inv_sort" ]                class "" [ "crx_inv_sort" ]               * ]
+  [ class "" [ "crx_inv_lref_aux" ]            class "" [ "crx_inv_lref_aux" ]           * ]
+  [ class "" [ "crx_inv_lref" ]                class "" [ "crx_inv_lref" ]               * ]
+  [ class "" [ "crx_inv_gref_aux" ]            class "" [ "crx_inv_gref_aux" ]           * ]
+  [ class "" [ "crx_inv_gref" ]                class "" [ "crx_inv_gref" ]               * ]
+  [ class "" [ "trx_inv_atom" ]                class "" [ "trx_inv_atom" ]               * ]
+  [ class "" [ "crx_inv_ib2_aux" ]             class "" [ "crx_inv_ib2_aux" ]            * ]
+  [ class "" [ "crx_inv_ib2" ]                 class "" [ "crx_inv_ib2" ]                * ]
+  [ class "" [ "crx_inv_appl_aux" ]            class "" [ "crx_inv_appl_aux" ]           * ]
+  [ class "" [ "crx_inv_appl" ]                class "" [ "crx_inv_appl" ]               * ]
+  [ class "" [ "cix" ]                         class "" [ "cix" ]                        * ]
+  [ class "" [ "cix_inv_sort" ]                class "" [ "cix_inv_sort" ]               * ]
+  [ class "" [ "cix_inv_delta" ]               class "" [ "cix_inv_delta" ]              * ]
+  [ class "" [ "cix_inv_ri2" ]                 class "" [ "cix_inv_ri2" ]                * ]
+  [ class "" [ "cix_inv_ib2" ]                 class "" [ "cix_inv_ib2" ]                * ]
+  [ class "" [ "cix_inv_bind" ]                class "" [ "cix_inv_bind" ]               * ]
+  [ class "" [ "cix_inv_appl" ]                class "" [ "cix_inv_appl" ]               * ]
+  [ class "" [ "cix_inv_flat" ]                class "" [ "cix_inv_flat" ]               * ]
+  [ class "" [ "cix_inv_cir" ]                 class "" [ "cix_inv_cir" ]                * ]
+  [ class "" [ "cix_sort" ]                    class "" [ "cix_sort" ]                   * ]
+  [ class "" [ "tix_lref" ]                    class "" [ "tix_lref" ]                   * ]
+  [ class "" [ "cix_gref" ]                    class "" [ "cix_gref" ]                   * ]
+  [ class "" [ "cix_ib2" ]                     class "" [ "cix_ib2" ]                    * ]
+  [ class "" [ "cix_appl" ]                    class "" [ "cix_appl" ]                   * ]
+  [ class "" [ "cpx_fwd_cix" ]                 class "" [ "cpx_fwd_cix" ]                * ]
+  [ class "" [ "nlift_lref_be_SO" ]            class "" [ "nlift_lref_be_SO" ]           * ]
+  [ class "" [ "nlift_bind_sn" ]               class "" [ "nlift_bind_sn" ]              * ]
+  [ class "" [ "nlift_bind_dx" ]               class "" [ "nlift_bind_dx" ]              * ]
+  [ class "" [ "nlift_flat_sn" ]               class "" [ "nlift_flat_sn" ]              * ]
+  [ class "" [ "nlift_flat_dx" ]               class "" [ "nlift_flat_dx" ]              * ]
+  [ class "" [ "nlift_inv_lref_be_SO" ]        class "" [ "nlift_inv_lref_be_SO" ]       * ]
+  [ class "" [ "nlift_inv_bind" ]              class "" [ "nlift_inv_bind" ]             * ]
+  [ class "" [ "nlift_inv_flat" ]              class "" [ "nlift_inv_flat" ]             * ]
+  [ class "" [ "frees" ]                       class "" [ "frees" ]                      * ]
+  [ class "" [ "frees_trans" ]                 class "" [ "frees_trans" ]                * ]
+  [ class "" [ "frees_inv" ]                   class "" [ "frees_inv" ]                  * ]
+  [ class "" [ "frees_inv_sort" ]              class "" [ "frees_inv_sort" ]             * ]
+  [ class "" [ "frees_inv_gref" ]              class "" [ "frees_inv_gref" ]             * ]
+  [ class "" [ "frees_inv_lref" ]              class "" [ "frees_inv_lref" ]             * ]
+  [ class "" [ "frees_inv_lref_free" ]         class "" [ "frees_inv_lref_free" ]        * ]
+  [ class "" [ "frees_inv_lref_skip" ]         class "" [ "frees_inv_lref_skip" ]        * ]
+  [ class "" [ "frees_inv_lref_ge" ]           class "" [ "frees_inv_lref_ge" ]          * ]
+  [ class "" [ "frees_inv_lref_lt" ]           class "" [ "frees_inv_lref_lt" ]          * ]
+  [ class "" [ "frees_inv_bind" ]              class "" [ "frees_inv_bind" ]             * ]
+  [ class "" [ "frees_inv_flat" ]              class "" [ "frees_inv_flat" ]             * ]
+  [ class "" [ "frees_lref_eq" ]               class "" [ "frees_lref_eq" ]              * ]
+  [ class "" [ "frees_lref_be" ]               class "" [ "frees_lref_be" ]              * ]
+  [ class "" [ "frees_bind_sn" ]               class "" [ "frees_bind_sn" ]              * ]
+  [ class "" [ "frees_bind_dx" ]               class "" [ "frees_bind_dx" ]              * ]
+  [ class "" [ "frees_flat_sn" ]               class "" [ "frees_flat_sn" ]              * ]
+  [ class "" [ "frees_flat_dx" ]               class "" [ "frees_flat_dx" ]              * ]
+  [ class "" [ "frees_weak" ]                  class "" [ "frees_weak" ]                 * ]
+  [ class "" [ "frees_inv_bind_O" ]            class "" [ "frees_inv_bind_O" ]           * ]
+  [ class "" [ "frees_dec" ]                   class "" [ "frees_dec" ]                  * ]
+  [ class "" [ "frees_S" ]                     class "" [ "frees_S" ]                    * ]
+  [ class "" [ "frees_bind_dx_O" ]             class "" [ "frees_bind_dx_O" ]            * ]
+  [ class "" [ "frees_lift_ge" ]               class "" [ "frees_lift_ge" ]              * ]
+  [ class "" [ "frees_inv_lift_be" ]           class "" [ "frees_inv_lift_be" ]          * ]
+  [ class "" [ "frees_inv_lift_ge" ]           class "" [ "frees_inv_lift_ge" ]          * ]
+  [ class "" [ "append" ]                      class "" [ "append" ]                     * ]
+  [ class "" [ "d_appendable_sn" ]             class "" [ "d_appendable_sn" ]            * ]
+  [ class "" [ "append_atom_sn" ]              class "" [ "append_atom_sn" ]             * ]
+  [ class "" [ "append_assoc" ]                class "" [ "append_assoc" ]               * ]
+  [ class "" [ "append_length" ]               class "" [ "append_length" ]              * ]
+  [ class "" [ "ltail_length" ]                class "" [ "ltail_length" ]               * ]
+  [ class "" [ "lpair_ltail" ]                 class "" [ "lpair_ltail" ]                * ]
+  [ class "" [ "append_inj_sn" ]               class "" [ "append_inj_sn" ]              * ]
+  [ class "" [ "append_inj_dx" ]               class "" [ "append_inj_dx" ]              * ]
+  [ class "" [ "append_inv_refl_dx" ]          class "" [ "append_inv_refl_dx" ]         * ]
+  [ class "" [ "append_inv_pair_dx" ]          class "" [ "append_inv_pair_dx" ]         * ]
   [ class "" [ "length_inv_pos_dx_ltail" ]     class "" [ "length_inv_pos_dx_ltail" ]    * ]
   [ class "" [ "length_inv_pos_sn_ltail" ]     class "" [ "length_inv_pos_sn_ltail" ]    * ]
-  [ class "" [ "lenv_ind_alt" ]                       class "" [ "lenv_ind_alt" ]               * ]
+  [ class "" [ "lenv_ind_alt" ]                class "" [ "lenv_ind_alt" ]               * ]
   [ class "" [ "drop_O1_append_sn_le_aux" ]    class "" [ "drop_O1_append_sn_le_aux" ]   * ]
-  [ class "" [ "drop_O1_append_sn_le" ]               class "" [ "drop_O1_append_sn_le" ]       * ]
+  [ class "" [ "drop_O1_append_sn_le" ]        class "" [ "drop_O1_append_sn_le" ]       * ]
   [ class "" [ "drop_O1_inv_append1_ge" ]      class "" [ "drop_O1_inv_append1_ge" ]     * ]
   [ class "" [ "drop_O1_inv_append1_le" ]      class "" [ "drop_O1_inv_append1_le" ]     * ]
-  [ class "" [ "frees_append" ]                       class "" [ "frees_append" ]               * ]
-  [ class "" [ "frees_inv_append_aux" ]               class "" [ "frees_inv_append_aux" ]       * ]
-  [ class "" [ "frees_inv_append" ]           class "" [ "frees_inv_append" ]           * ]
-  [ class "" [ "llor" ]                               class "" [ "llor" ]                       * ]
-  [ class "" [ "llor_atom" ]                  class "" [ "llor_atom" ]                  * ]
-  [ class "" [ "llor_tail_frees" ]            class "" [ "llor_tail_frees" ]            * ]
-  [ class "" [ "llor_tail_cofrees" ]          class "" [ "llor_tail_cofrees" ]          * ]
-  [ class "" [ "llor_skip" ]                  class "" [ "llor_skip" ]                  * ]
-  [ class "" [ "llor_total" ]                 class "" [ "llor_total" ]                 * ]
-  [ class "" [ "lpx_sn_alt" ]                 class "" [ "lpx_sn_alt" ]                 * ]
+  [ class "" [ "frees_append" ]                class "" [ "frees_append" ]               * ]
+  [ class "" [ "frees_inv_append_aux" ]        class "" [ "frees_inv_append_aux" ]       * ]
+  [ class "" [ "frees_inv_append" ]            class "" [ "frees_inv_append" ]           * ]
+  [ class "" [ "llor" ]                        class "" [ "llor" ]                       * ]
+  [ class "" [ "llor_atom" ]                   class "" [ "llor_atom" ]                  * ]
+  [ class "" [ "llor_tail_frees" ]             class "" [ "llor_tail_frees" ]            * ]
+  [ class "" [ "llor_tail_cofrees" ]           class "" [ "llor_tail_cofrees" ]          * ]
+  [ class "" [ "llor_skip" ]                   class "" [ "llor_skip" ]                  * ]
+  [ class "" [ "llor_total" ]                  class "" [ "llor_total" ]                 * ]
+  [ class "" [ "lpx_sn_alt" ]                  class "" [ "lpx_sn_alt" ]                 * ]
   [ class "" [ "lpx_sn_alt_fwd_length" ]       class "" [ "lpx_sn_alt_fwd_length" ]      * ]
-  [ class "" [ "lpx_sn_alt_inv_atom1" ]               class "" [ "lpx_sn_alt_inv_atom1" ]       * ]
-  [ class "" [ "lpx_sn_alt_inv_pair1" ]               class "" [ "lpx_sn_alt_inv_pair1" ]       * ]
-  [ class "" [ "lpx_sn_alt_inv_atom2" ]               class "" [ "lpx_sn_alt_inv_atom2" ]       * ]
-  [ class "" [ "lpx_sn_alt_inv_pair2" ]               class "" [ "lpx_sn_alt_inv_pair2" ]       * ]
-  [ class "" [ "lpx_sn_alt_atom" ]            class "" [ "lpx_sn_alt_atom" ]            * ]
-  [ class "" [ "lpx_sn_alt_pair" ]            class "" [ "lpx_sn_alt_pair" ]            * ]
-  [ class "" [ "lpx_sn_lpx_sn_alt" ]          class "" [ "lpx_sn_lpx_sn_alt" ]          * ]
+  [ class "" [ "lpx_sn_alt_inv_atom1" ]        class "" [ "lpx_sn_alt_inv_atom1" ]       * ]
+  [ class "" [ "lpx_sn_alt_inv_pair1" ]        class "" [ "lpx_sn_alt_inv_pair1" ]       * ]
+  [ class "" [ "lpx_sn_alt_inv_atom2" ]        class "" [ "lpx_sn_alt_inv_atom2" ]       * ]
+  [ class "" [ "lpx_sn_alt_inv_pair2" ]        class "" [ "lpx_sn_alt_inv_pair2" ]       * ]
+  [ class "" [ "lpx_sn_alt_atom" ]             class "" [ "lpx_sn_alt_atom" ]            * ]
+  [ class "" [ "lpx_sn_alt_pair" ]             class "" [ "lpx_sn_alt_pair" ]            * ]
+  [ class "" [ "lpx_sn_lpx_sn_alt" ]           class "" [ "lpx_sn_lpx_sn_alt" ]          * ]
   [ class "" [ "lpx_sn_alt_inv_lpx_sn" ]       class "" [ "lpx_sn_alt_inv_lpx_sn" ]      * ]
-  [ class "" [ "lpx_sn_intro_alt" ]           class "" [ "lpx_sn_intro_alt" ]           * ]
-  [ class "" [ "lpx_sn_inv_alt" ]             class "" [ "lpx_sn_inv_alt" ]             * ]
-  [ class "" [ "llpx_sn_alt_r" ]              class "" [ "llpx_sn_alt_r" ]              * ]
+  [ class "" [ "lpx_sn_intro_alt" ]            class "" [ "lpx_sn_intro_alt" ]           * ]
+  [ class "" [ "lpx_sn_inv_alt" ]              class "" [ "lpx_sn_inv_alt" ]             * ]
+  [ class "" [ "llpx_sn_alt_r" ]               class "" [ "llpx_sn_alt_r" ]              * ]
   [ class "" [ "llpx_sn_alt_r_intro_alt" ]     class "" [ "llpx_sn_alt_r_intro_alt" ]    * ]
   [ class "" [ "llpx_sn_alt_r_ind_alt" ]       class "" [ "llpx_sn_alt_r_ind_alt" ]      * ]
   [ class "" [ "llpx_sn_alt_r_inv_alt" ]       class "" [ "llpx_sn_alt_r_inv_alt" ]      * ]
@@ -1099,670 +1099,670 @@ table {
   [ class "" [ "llpx_sn_alt_r_inv_bind" ]      class "" [ "llpx_sn_alt_r_inv_bind" ]     * ]
   [ class "" [ "llpx_sn_alt_r_fwd_length" ]    class "" [ "llpx_sn_alt_r_fwd_length" ]   * ]
   [ class "" [ "llpx_sn_alt_r_fwd_lref" ]      class "" [ "llpx_sn_alt_r_fwd_lref" ]     * ]
-  [ class "" [ "llpx_sn_alt_r_sort" ]         class "" [ "llpx_sn_alt_r_sort" ]         * ]
-  [ class "" [ "llpx_sn_alt_r_gref" ]         class "" [ "llpx_sn_alt_r_gref" ]         * ]
-  [ class "" [ "llpx_sn_alt_r_skip" ]         class "" [ "llpx_sn_alt_r_skip" ]         * ]
-  [ class "" [ "llpx_sn_alt_r_free" ]         class "" [ "llpx_sn_alt_r_free" ]         * ]
-  [ class "" [ "llpx_sn_alt_r_lref" ]         class "" [ "llpx_sn_alt_r_lref" ]         * ]
-  [ class "" [ "llpx_sn_alt_r_flat" ]         class "" [ "llpx_sn_alt_r_flat" ]         * ]
-  [ class "" [ "llpx_sn_alt_r_bind" ]         class "" [ "llpx_sn_alt_r_bind" ]         * ]
-  [ class "" [ "llpx_sn_lpx_sn_alt_r" ]               class "" [ "llpx_sn_lpx_sn_alt_r" ]       * ]
+  [ class "" [ "llpx_sn_alt_r_sort" ]          class "" [ "llpx_sn_alt_r_sort" ]         * ]
+  [ class "" [ "llpx_sn_alt_r_gref" ]          class "" [ "llpx_sn_alt_r_gref" ]         * ]
+  [ class "" [ "llpx_sn_alt_r_skip" ]          class "" [ "llpx_sn_alt_r_skip" ]         * ]
+  [ class "" [ "llpx_sn_alt_r_free" ]          class "" [ "llpx_sn_alt_r_free" ]         * ]
+  [ class "" [ "llpx_sn_alt_r_lref" ]          class "" [ "llpx_sn_alt_r_lref" ]         * ]
+  [ class "" [ "llpx_sn_alt_r_flat" ]          class "" [ "llpx_sn_alt_r_flat" ]         * ]
+  [ class "" [ "llpx_sn_alt_r_bind" ]          class "" [ "llpx_sn_alt_r_bind" ]         * ]
+  [ class "" [ "llpx_sn_lpx_sn_alt_r" ]        class "" [ "llpx_sn_lpx_sn_alt_r" ]       * ]
   [ class "" [ "llpx_sn_alt_r_inv_lpx_sn" ]    class "" [ "llpx_sn_alt_r_inv_lpx_sn" ]   * ]
-  [ class "" [ "llpx_sn_intro_alt_r" ]        class "" [ "llpx_sn_intro_alt_r" ]        * ]
-  [ class "" [ "llpx_sn_ind_alt_r" ]          class "" [ "llpx_sn_ind_alt_r" ]          * ]
-  [ class "" [ "llpx_sn_inv_alt_r" ]          class "" [ "llpx_sn_inv_alt_r" ]          * ]
-  [ class "" [ "llpx_sn_alt" ]                class "" [ "llpx_sn_alt" ]                * ]
-  [ class "" [ "llpx_sn_llpx_sn_alt" ]        class "" [ "llpx_sn_llpx_sn_alt" ]        * ]
+  [ class "" [ "llpx_sn_intro_alt_r" ]         class "" [ "llpx_sn_intro_alt_r" ]        * ]
+  [ class "" [ "llpx_sn_ind_alt_r" ]           class "" [ "llpx_sn_ind_alt_r" ]          * ]
+  [ class "" [ "llpx_sn_inv_alt_r" ]           class "" [ "llpx_sn_inv_alt_r" ]          * ]
+  [ class "" [ "llpx_sn_alt" ]                 class "" [ "llpx_sn_alt" ]                * ]
+  [ class "" [ "llpx_sn_llpx_sn_alt" ]         class "" [ "llpx_sn_llpx_sn_alt" ]        * ]
   [ class "" [ "llpx_sn_alt_inv_llpx_sn" ]     class "" [ "llpx_sn_alt_inv_llpx_sn" ]    * ]
-  [ class "" [ "lleq_intro_alt" ]             class "" [ "lleq_intro_alt" ]             * ]
-  [ class "" [ "lleq_inv_alt" ]                       class "" [ "lleq_inv_alt" ]               * ]
-  [ class "" [ "llpx_sn_llor_fwd_sn" ]        class "" [ "llpx_sn_llor_fwd_sn" ]        * ]
-  [ class "" [ "lpx_sn_llpx_sn" ]             class "" [ "lpx_sn_llpx_sn" ]             * ]
-  [ class "" [ "lreq_lleq_trans" ]            class "" [ "lreq_lleq_trans" ]            * ]
-  [ class "" [ "lleq_lreq_trans" ]            class "" [ "lleq_lreq_trans" ]            * ]
-  [ class "" [ "lleq_lreq_repl" ]             class "" [ "lleq_lreq_repl" ]             * ]
-  [ class "" [ "lleq_bind_repl_SO" ]          class "" [ "lleq_bind_repl_SO" ]          * ]
+  [ class "" [ "lleq_intro_alt" ]              class "" [ "lleq_intro_alt" ]             * ]
+  [ class "" [ "lleq_inv_alt" ]                class "" [ "lleq_inv_alt" ]               * ]
+  [ class "" [ "llpx_sn_llor_fwd_sn" ]         class "" [ "llpx_sn_llor_fwd_sn" ]        * ]
+  [ class "" [ "lpx_sn_llpx_sn" ]              class "" [ "lpx_sn_llpx_sn" ]             * ]
+  [ class "" [ "lreq_lleq_trans" ]             class "" [ "lreq_lleq_trans" ]            * ]
+  [ class "" [ "lleq_lreq_trans" ]             class "" [ "lleq_lreq_trans" ]            * ]
+  [ class "" [ "lleq_lreq_repl" ]              class "" [ "lleq_lreq_repl" ]             * ]
+  [ class "" [ "lleq_bind_repl_SO" ]           class "" [ "lleq_bind_repl_SO" ]          * ]
   [ class "" [ "llpx_sn_frees_trans_aux" ]     class "" [ "llpx_sn_frees_trans_aux" ]    * ]
-  [ class "" [ "llpx_sn_frees_trans" ]        class "" [ "llpx_sn_frees_trans" ]        * ]
-  [ class "" [ "llpx_sn_llor_dx" ]            class "" [ "llpx_sn_llor_dx" ]            * ]
-  [ class "" [ "llpx_sn_llor_dx_sym" ]        class "" [ "llpx_sn_llor_dx_sym" ]        * ]
-  [ class "" [ "lreq_cpx_trans" ]             class "" [ "lreq_cpx_trans" ]             * ]
-  [ class "" [ "cpx_llpx_sn_conf" ]           class "" [ "cpx_llpx_sn_conf" ]           * ]
-  [ class "" [ "lleq_cpx_trans" ]             class "" [ "lleq_cpx_trans" ]             * ]
-  [ class "" [ "cpx_lleq_conf" ]              class "" [ "cpx_lleq_conf" ]              * ]
-  [ class "" [ "cpx_lleq_conf_sn" ]           class "" [ "cpx_lleq_conf_sn" ]           * ]
-  [ class "" [ "cpx_lleq_conf_dx" ]           class "" [ "cpx_lleq_conf_dx" ]           * ]
-  [ class "" [ "lreq_frees_trans" ]           class "" [ "lreq_frees_trans" ]           * ]
-  [ class "" [ "frees_lreq_conf" ]            class "" [ "frees_lreq_conf" ]            * ]
-  [ class "" [ "lpx_cpx_frees_trans" ]        class "" [ "lpx_cpx_frees_trans" ]        * ]
-  [ class "" [ "cpx_frees_trans" ]            class "" [ "cpx_frees_trans" ]            * ]
-  [ class "" [ "lpx_frees_trans" ]            class "" [ "lpx_frees_trans" ]            * ]
-  [ class "" [ "lleq_lpx_trans" ]             class "" [ "lleq_lpx_trans" ]             * ]
-  [ class "" [ "lpx_lleq_fqu_trans" ]         class "" [ "lpx_lleq_fqu_trans" ]         * ]
-  [ class "" [ "lpx_lleq_fquq_trans" ]        class "" [ "lpx_lleq_fquq_trans" ]        * ]
-  [ class "" [ "lpx_lleq_fqup_trans" ]        class "" [ "lpx_lleq_fqup_trans" ]        * ]
-  [ class "" [ "lpx_lleq_fqus_trans" ]        class "" [ "lpx_lleq_fqus_trans" ]        * ]
+  [ class "" [ "llpx_sn_frees_trans" ]         class "" [ "llpx_sn_frees_trans" ]        * ]
+  [ class "" [ "llpx_sn_llor_dx" ]             class "" [ "llpx_sn_llor_dx" ]            * ]
+  [ class "" [ "llpx_sn_llor_dx_sym" ]         class "" [ "llpx_sn_llor_dx_sym" ]        * ]
+  [ class "" [ "lreq_cpx_trans" ]              class "" [ "lreq_cpx_trans" ]             * ]
+  [ class "" [ "cpx_llpx_sn_conf" ]            class "" [ "cpx_llpx_sn_conf" ]           * ]
+  [ class "" [ "lleq_cpx_trans" ]              class "" [ "lleq_cpx_trans" ]             * ]
+  [ class "" [ "cpx_lleq_conf" ]               class "" [ "cpx_lleq_conf" ]              * ]
+  [ class "" [ "cpx_lleq_conf_sn" ]            class "" [ "cpx_lleq_conf_sn" ]           * ]
+  [ class "" [ "cpx_lleq_conf_dx" ]            class "" [ "cpx_lleq_conf_dx" ]           * ]
+  [ class "" [ "lreq_frees_trans" ]            class "" [ "lreq_frees_trans" ]           * ]
+  [ class "" [ "frees_lreq_conf" ]             class "" [ "frees_lreq_conf" ]            * ]
+  [ class "" [ "lpx_cpx_frees_trans" ]         class "" [ "lpx_cpx_frees_trans" ]        * ]
+  [ class "" [ "cpx_frees_trans" ]             class "" [ "cpx_frees_trans" ]            * ]
+  [ class "" [ "lpx_frees_trans" ]             class "" [ "lpx_frees_trans" ]            * ]
+  [ class "" [ "lleq_lpx_trans" ]              class "" [ "lleq_lpx_trans" ]             * ]
+  [ class "" [ "lpx_lleq_fqu_trans" ]          class "" [ "lpx_lleq_fqu_trans" ]         * ]
+  [ class "" [ "lpx_lleq_fquq_trans" ]         class "" [ "lpx_lleq_fquq_trans" ]        * ]
+  [ class "" [ "lpx_lleq_fqup_trans" ]         class "" [ "lpx_lleq_fqup_trans" ]        * ]
+  [ class "" [ "lpx_lleq_fqus_trans" ]         class "" [ "lpx_lleq_fqus_trans" ]        * ]
   [ class "" [ "lreq_lpx_trans_lleq_aux" ]     class "" [ "lreq_lpx_trans_lleq_aux" ]    * ]
-  [ class "" [ "lreq_lpx_trans_lleq" ]        class "" [ "lreq_lpx_trans_lleq" ]        * ]
-  [ class "" [ "cnx_inv_crx" ]                class "" [ "cnx_inv_crx" ]                * ]
-  [ class "" [ "fleq" ]                               class "" [ "fleq" ]                       * ]
-  [ class "" [ "fleq_refl" ]                  class "" [ "fleq_refl" ]                  * ]
-  [ class "" [ "fleq_sym" ]                   class "" [ "fleq_sym" ]                   * ]
-  [ class "" [ "fleq_inv_gen" ]                       class "" [ "fleq_inv_gen" ]               * ]
-  [ class "" [ "lleq_fqu_trans" ]             class "" [ "lleq_fqu_trans" ]             * ]
-  [ class "" [ "lleq_fquq_trans" ]            class "" [ "lleq_fquq_trans" ]            * ]
-  [ class "" [ "lleq_fqup_trans" ]            class "" [ "lleq_fqup_trans" ]            * ]
-  [ class "" [ "lleq_fqus_trans" ]            class "" [ "lleq_fqus_trans" ]            * ]
-  [ class "" [ "lleq_trans" ]                 class "" [ "lleq_trans" ]                 * ]
-  [ class "" [ "lleq_canc_sn" ]                       class "" [ "lleq_canc_sn" ]               * ]
-  [ class "" [ "lleq_canc_dx" ]                       class "" [ "lleq_canc_dx" ]               * ]
-  [ class "" [ "lleq_nlleq_trans" ]           class "" [ "lleq_nlleq_trans" ]           * ]
-  [ class "" [ "nlleq_lleq_div" ]             class "" [ "nlleq_lleq_div" ]             * ]
-  [ class "" [ "fpb" ]                        class "" [ "fpb" ]                        * ]
-  [ class "" [ "cpr_fpb" ]                    class "" [ "cpr_fpb" ]                    * ]
-  [ class "" [ "lpr_fpb" ]                    class "" [ "lpr_fpb" ]                    * ]
-  [ class "" [ "lleq_fpb_trans" ]             class "" [ "lleq_fpb_trans" ]             * ]
-  [ class "" [ "fleq_fpb_trans" ]             class "" [ "fleq_fpb_trans" ]             * ]
-  [ class "" [ "fpb_inv_fleq" ]                       class "" [ "fpb_inv_fleq" ]               * ]
-  [ class "" [ "fpbq" ]                               class "" [ "fpbq" ]                       * ]
-  [ class "" [ "fpbq_refl" ]                  class "" [ "fpbq_refl" ]                  * ]
-  [ class "" [ "cpr_fpbq" ]                   class "" [ "cpr_fpbq" ]                   * ]
-  [ class "" [ "lpr_fpbq" ]                   class "" [ "lpr_fpbq" ]                   * ]
-  [ class "" [ "fpbqa" ]                      class "" [ "fpbqa" ]                      * ]
-  [ class "" [ "fleq_fpbq" ]                  class "" [ "fleq_fpbq" ]                  * ]
-  [ class "" [ "fpb_fpbq" ]                   class "" [ "fpb_fpbq" ]                   * ]
-  [ class "" [ "fpbq_fpbqa" ]                 class "" [ "fpbq_fpbqa" ]                 * ]
-  [ class "" [ "fpbqa_inv_fpbq" ]             class "" [ "fpbqa_inv_fpbq" ]             * ]
-  [ class "" [ "fpbq_ind_alt" ]                       class "" [ "fpbq_ind_alt" ]               * ]
-  [ class "" [ "fpb_fpbq_alt" ]                       class "" [ "fpb_fpbq_alt" ]               * ]
-  [ class "" [ "fpbq_inv_fpb_alt" ]           class "" [ "fpbq_inv_fpb_alt" ]           * ]
-  [ class "" [ "fpbq_aaa_conf" ]              class "" [ "fpbq_aaa_conf" ]              * ]
-  [ class "" [ "cpr_fwd_cir" ]                class "" [ "cpr_fwd_cir" ]                * ]
-  [ class "" [ "sta_fpb" ]                    class "" [ "sta_fpb" ]                    * ]
-  [ class "" [ "crr_lift" ]                   class "" [ "crr_lift" ]                   * ]
-  [ class "" [ "crr_inv_lift" ]                       class "" [ "crr_inv_lift" ]               * ]
-  [ class "" [ "cir_lift" ]                   class "" [ "cir_lift" ]                   * ]
-  [ class "" [ "cir_inv_lift" ]                       class "" [ "cir_inv_lift" ]               * ]
-  [ class "" [ "cpr_llpx_sn_conf" ]           class "" [ "cpr_llpx_sn_conf" ]           * ]
-  [ class "" [ "crx_lift" ]                   class "" [ "crx_lift" ]                   * ]
-  [ class "" [ "crx_inv_lift" ]                       class "" [ "crx_inv_lift" ]               * ]
-  [ class "" [ "cnx_lift" ]                   class "" [ "cnx_lift" ]                   * ]
-  [ class "" [ "cnx_inv_lift" ]                       class "" [ "cnx_inv_lift" ]               * ]
-  [ class "" [ "cnr_inv_crr" ]                class "" [ "cnr_inv_crr" ]                * ]
-  [ class "" [ "cnr_lref_abst" ]              class "" [ "cnr_lref_abst" ]              * ]
-  [ class "" [ "cnr_lift" ]                   class "" [ "cnr_lift" ]                   * ]
-  [ class "" [ "cnr_inv_lift" ]                       class "" [ "cnr_inv_lift" ]               * ]
-  [ class "" [ "cir_cnr" ]                    class "" [ "cir_cnr" ]                    * ]
-  [ class "" [ "cnr_inv_cir" ]                class "" [ "cnr_inv_cir" ]                * ]
-  [ class "" [ "cix_lref" ]                   class "" [ "cix_lref" ]                   * ]
-  [ class "" [ "cix_lift" ]                   class "" [ "cix_lift" ]                   * ]
-  [ class "" [ "cix_inv_lift" ]                       class "" [ "cix_inv_lift" ]               * ]
-  [ class "" [ "sta_fpbq" ]                   class "" [ "sta_fpbq" ]                   * ]
-  [ class "" [ "cix_cnx" ]                    class "" [ "cix_cnx" ]                    * ]
-  [ class "" [ "cnx_inv_cix" ]                class "" [ "cnx_inv_cix" ]                * ]
-  [ class "" [ "lstas_llpx_sn_conf" ]         class "" [ "lstas_llpx_sn_conf" ]         * ]
-  [ class "" [ "unfold" ]                     class "" [ "unfold" ]                     * ]
-  [ class "" [ "lsuby" ]                      class "" [ "lsuby" ]                      * ]
-  [ class "" [ "lsuby_pair_lt" ]              class "" [ "lsuby_pair_lt" ]              * ]
-  [ class "" [ "lsuby_succ_lt" ]              class "" [ "lsuby_succ_lt" ]              * ]
-  [ class "" [ "lsuby_pair_O_Y" ]             class "" [ "lsuby_pair_O_Y" ]             * ]
-  [ class "" [ "lsuby_refl" ]                 class "" [ "lsuby_refl" ]                 * ]
-  [ class "" [ "lsuby_O2" ]                   class "" [ "lsuby_O2" ]                   * ]
-  [ class "" [ "lsuby_sym" ]                  class "" [ "lsuby_sym" ]                  * ]
-  [ class "" [ "lsuby_inv_atom1_aux" ]        class "" [ "lsuby_inv_atom1_aux" ]        * ]
-  [ class "" [ "lsuby_inv_atom1" ]            class "" [ "lsuby_inv_atom1" ]            * ]
-  [ class "" [ "lsuby_inv_zero1_aux" ]        class "" [ "lsuby_inv_zero1_aux" ]        * ]
-  [ class "" [ "lsuby_inv_zero1" ]            class "" [ "lsuby_inv_zero1" ]            * ]
-  [ class "" [ "lsuby_inv_pair1_aux" ]        class "" [ "lsuby_inv_pair1_aux" ]        * ]
-  [ class "" [ "lsuby_inv_pair1" ]            class "" [ "lsuby_inv_pair1" ]            * ]
-  [ class "" [ "lsuby_inv_succ1_aux" ]        class "" [ "lsuby_inv_succ1_aux" ]        * ]
-  [ class "" [ "lsuby_inv_succ1" ]            class "" [ "lsuby_inv_succ1" ]            * ]
-  [ class "" [ "lsuby_inv_zero2_aux" ]        class "" [ "lsuby_inv_zero2_aux" ]        * ]
-  [ class "" [ "lsuby_inv_zero2" ]            class "" [ "lsuby_inv_zero2" ]            * ]
-  [ class "" [ "lsuby_inv_pair2_aux" ]        class "" [ "lsuby_inv_pair2_aux" ]        * ]
-  [ class "" [ "lsuby_inv_pair2" ]            class "" [ "lsuby_inv_pair2" ]            * ]
-  [ class "" [ "lsuby_inv_succ2_aux" ]        class "" [ "lsuby_inv_succ2_aux" ]        * ]
-  [ class "" [ "lsuby_inv_succ2" ]            class "" [ "lsuby_inv_succ2" ]            * ]
-  [ class "" [ "lsuby_fwd_length" ]           class "" [ "lsuby_fwd_length" ]           * ]
-  [ class "" [ "lsuby_drop_trans_be" ]        class "" [ "lsuby_drop_trans_be" ]        * ]
-  [ class "" [ "cpy" ]                        class "" [ "cpy" ]                        * ]
-  [ class "" [ "lsuby_cpy_trans" ]            class "" [ "lsuby_cpy_trans" ]            * ]
-  [ class "" [ "cpy_refl" ]                   class "" [ "cpy_refl" ]                   * ]
-  [ class "" [ "cpy_full" ]                   class "" [ "cpy_full" ]                   * ]
-  [ class "" [ "cpy_weak" ]                   class "" [ "cpy_weak" ]                   * ]
-  [ class "" [ "cpy_weak_top" ]                       class "" [ "cpy_weak_top" ]               * ]
-  [ class "" [ "cpy_weak_full" ]              class "" [ "cpy_weak_full" ]              * ]
-  [ class "" [ "cpy_split_up" ]                       class "" [ "cpy_split_up" ]               * ]
-  [ class "" [ "cpy_split_down" ]             class "" [ "cpy_split_down" ]             * ]
-  [ class "" [ "cpy_fwd_up" ]                 class "" [ "cpy_fwd_up" ]                 * ]
-  [ class "" [ "cpy_fwd_tw" ]                 class "" [ "cpy_fwd_tw" ]                 * ]
-  [ class "" [ "cpy_inv_atom1_aux" ]          class "" [ "cpy_inv_atom1_aux" ]          * ]
-  [ class "" [ "cpy_inv_atom1" ]              class "" [ "cpy_inv_atom1" ]              * ]
-  [ class "" [ "cpy_inv_sort1" ]              class "" [ "cpy_inv_sort1" ]              * ]
-  [ class "" [ "cpy_inv_lref1" ]              class "" [ "cpy_inv_lref1" ]              * ]
-  [ class "" [ "cpy_inv_gref1" ]              class "" [ "cpy_inv_gref1" ]              * ]
-  [ class "" [ "cpy_inv_bind1_aux" ]          class "" [ "cpy_inv_bind1_aux" ]          * ]
-  [ class "" [ "cpy_inv_bind1" ]              class "" [ "cpy_inv_bind1" ]              * ]
-  [ class "" [ "cpy_inv_flat1_aux" ]          class "" [ "cpy_inv_flat1_aux" ]          * ]
-  [ class "" [ "cpy_inv_flat1" ]              class "" [ "cpy_inv_flat1" ]              * ]
-  [ class "" [ "cpy_inv_refl_O2_aux" ]        class "" [ "cpy_inv_refl_O2_aux" ]        * ]
-  [ class "" [ "cpy_inv_refl_O2" ]            class "" [ "cpy_inv_refl_O2" ]            * ]
-  [ class "" [ "cpy_inv_lift1_eq" ]           class "" [ "cpy_inv_lift1_eq" ]           * ]
-  [ class "" [ "cpy_lift_le" ]                class "" [ "cpy_lift_le" ]                * ]
-  [ class "" [ "cpy_lift_be" ]                class "" [ "cpy_lift_be" ]                * ]
-  [ class "" [ "cpy_lift_ge" ]                class "" [ "cpy_lift_ge" ]                * ]
-  [ class "" [ "cpy_inv_lift1_le" ]           class "" [ "cpy_inv_lift1_le" ]           * ]
-  [ class "" [ "cpy_inv_lift1_be" ]           class "" [ "cpy_inv_lift1_be" ]           * ]
-  [ class "" [ "cpy_inv_lift1_ge" ]           class "" [ "cpy_inv_lift1_ge" ]           * ]
-  [ class "" [ "cpy_inv_lift1_ge_up" ]        class "" [ "cpy_inv_lift1_ge_up" ]        * ]
-  [ class "" [ "cpy_inv_lift1_be_up" ]        class "" [ "cpy_inv_lift1_be_up" ]        * ]
-  [ class "" [ "cpy_inv_lift1_le_up" ]        class "" [ "cpy_inv_lift1_le_up" ]        * ]
-  [ class "" [ "cpy_conf_eq" ]                class "" [ "cpy_conf_eq" ]                * ]
-  [ class "" [ "cpy_conf_neq" ]                       class "" [ "cpy_conf_neq" ]               * ]
-  [ class "" [ "cpy_trans_ge" ]                       class "" [ "cpy_trans_ge" ]               * ]
-  [ class "" [ "cpy_trans_down" ]             class "" [ "cpy_trans_down" ]             * ]
-  [ class "" [ "cpy_fwd_nlift2_ge" ]          class "" [ "cpy_fwd_nlift2_ge" ]          * ]
-  [ class "" [ "gget" ]                               class "" [ "gget" ]                       * ]
-  [ class "" [ "gget_inv_gt" ]                class "" [ "gget_inv_gt" ]                * ]
-  [ class "" [ "gget_inv_eq" ]                class "" [ "gget_inv_eq" ]                * ]
-  [ class "" [ "gget_inv_lt_aux" ]            class "" [ "gget_inv_lt_aux" ]            * ]
-  [ class "" [ "gget_inv_lt" ]                class "" [ "gget_inv_lt" ]                * ]
-  [ class "" [ "gget_total" ]                 class "" [ "gget_total" ]                 * ]
-  [ class "" [ "gget_mono" ]                  class "" [ "gget_mono" ]                  * ]
-  [ class "" [ "gget_dec" ]                   class "" [ "gget_dec" ]                   * ]
-  [ class "" [ "lsuby_trans" ]                class "" [ "lsuby_trans" ]                * ]
-  [ class "" [ "liftv_mono" ]                 class "" [ "liftv_mono" ]                 * ]
-  [ class "" [ "csx" ]                        class "" [ "csx" ]                        * ]
-  [ class "" [ "csx_ind" ]                    class "" [ "csx_ind" ]                    * ]
-  [ class "" [ "csx_intro" ]                  class "" [ "csx_intro" ]                  * ]
-  [ class "" [ "csx_cpx_trans" ]              class "" [ "csx_cpx_trans" ]              * ]
-  [ class "" [ "cnx_csx" ]                    class "" [ "cnx_csx" ]                    * ]
-  [ class "" [ "csx_sort" ]                   class "" [ "csx_sort" ]                   * ]
-  [ class "" [ "csx_cast" ]                   class "" [ "csx_cast" ]                   * ]
-  [ class "" [ "csx_fwd_pair_sn_aux" ]        class "" [ "csx_fwd_pair_sn_aux" ]        * ]
-  [ class "" [ "csx_fwd_pair_sn" ]            class "" [ "csx_fwd_pair_sn" ]            * ]
-  [ class "" [ "csx_fwd_bind_dx_aux" ]        class "" [ "csx_fwd_bind_dx_aux" ]        * ]
-  [ class "" [ "csx_fwd_bind_dx" ]            class "" [ "csx_fwd_bind_dx" ]            * ]
-  [ class "" [ "csx_fwd_flat_dx_aux" ]        class "" [ "csx_fwd_flat_dx_aux" ]        * ]
-  [ class "" [ "csx_fwd_flat_dx" ]            class "" [ "csx_fwd_flat_dx" ]            * ]
-  [ class "" [ "csx_fwd_bind" ]                       class "" [ "csx_fwd_bind" ]               * ]
-  [ class "" [ "csx_fwd_flat" ]                       class "" [ "csx_fwd_flat" ]               * ]
-  [ class "" [ "cpre" ]                               class "" [ "cpre" ]                       * ]
-  [ class "" [ "csx_cpre" ]                   class "" [ "csx_cpre" ]                   * ]
-  [ class "" [ "cpre_mono" ]                  class "" [ "cpre_mono" ]                  * ]
-  [ class "" [ "lpxs" ]                               class "" [ "lpxs" ]                       * ]
-  [ class "" [ "lpxs_ind" ]                   class "" [ "lpxs_ind" ]                   * ]
-  [ class "" [ "lpxs_ind_dx" ]                class "" [ "lpxs_ind_dx" ]                * ]
-  [ class "" [ "lprs_lpxs" ]                  class "" [ "lprs_lpxs" ]                  * ]
-  [ class "" [ "lpx_lpxs" ]                   class "" [ "lpx_lpxs" ]                   * ]
-  [ class "" [ "lpxs_refl" ]                  class "" [ "lpxs_refl" ]                  * ]
-  [ class "" [ "lpxs_strap1" ]                class "" [ "lpxs_strap1" ]                * ]
-  [ class "" [ "lpxs_strap2" ]                class "" [ "lpxs_strap2" ]                * ]
-  [ class "" [ "lpxs_pair_refl" ]             class "" [ "lpxs_pair_refl" ]             * ]
-  [ class "" [ "lpxs_inv_atom1" ]             class "" [ "lpxs_inv_atom1" ]             * ]
-  [ class "" [ "lpxs_inv_atom2" ]             class "" [ "lpxs_inv_atom2" ]             * ]
-  [ class "" [ "lpxs_fwd_length" ]            class "" [ "lpxs_fwd_length" ]            * ]
-  [ class "" [ "fpbs" ]                               class "" [ "fpbs" ]                       * ]
-  [ class "" [ "fpbs_ind" ]                   class "" [ "fpbs_ind" ]                   * ]
-  [ class "" [ "fpbs_ind_dx" ]                class "" [ "fpbs_ind_dx" ]                * ]
-  [ class "" [ "fpbs_refl" ]                  class "" [ "fpbs_refl" ]                  * ]
-  [ class "" [ "fpbq_fpbs" ]                  class "" [ "fpbq_fpbs" ]                  * ]
-  [ class "" [ "fpbs_strap1" ]                class "" [ "fpbs_strap1" ]                * ]
-  [ class "" [ "fpbs_strap2" ]                class "" [ "fpbs_strap2" ]                * ]
-  [ class "" [ "fqup_fpbs" ]                  class "" [ "fqup_fpbs" ]                  * ]
-  [ class "" [ "fqus_fpbs" ]                  class "" [ "fqus_fpbs" ]                  * ]
-  [ class "" [ "cpxs_fpbs" ]                  class "" [ "cpxs_fpbs" ]                  * ]
-  [ class "" [ "lpxs_fpbs" ]                  class "" [ "lpxs_fpbs" ]                  * ]
-  [ class "" [ "lleq_fpbs" ]                  class "" [ "lleq_fpbs" ]                  * ]
-  [ class "" [ "cprs_fpbs" ]                  class "" [ "cprs_fpbs" ]                  * ]
-  [ class "" [ "lprs_fpbs" ]                  class "" [ "lprs_fpbs" ]                  * ]
-  [ class "" [ "fpbs_fqus_trans" ]            class "" [ "fpbs_fqus_trans" ]            * ]
-  [ class "" [ "fpbs_fqup_trans" ]            class "" [ "fpbs_fqup_trans" ]            * ]
-  [ class "" [ "fpbs_cpxs_trans" ]            class "" [ "fpbs_cpxs_trans" ]            * ]
-  [ class "" [ "fpbs_lpxs_trans" ]            class "" [ "fpbs_lpxs_trans" ]            * ]
-  [ class "" [ "fpbs_lleq_trans" ]            class "" [ "fpbs_lleq_trans" ]            * ]
-  [ class "" [ "fqus_fpbs_trans" ]            class "" [ "fqus_fpbs_trans" ]            * ]
-  [ class "" [ "cpxs_fpbs_trans" ]            class "" [ "cpxs_fpbs_trans" ]            * ]
-  [ class "" [ "lpxs_fpbs_trans" ]            class "" [ "lpxs_fpbs_trans" ]            * ]
-  [ class "" [ "lleq_fpbs_trans" ]            class "" [ "lleq_fpbs_trans" ]            * ]
-  [ class "" [ "cpxs_fqus_fpbs" ]             class "" [ "cpxs_fqus_fpbs" ]             * ]
-  [ class "" [ "cpxs_fqup_fpbs" ]             class "" [ "cpxs_fqup_fpbs" ]             * ]
-  [ class "" [ "fqus_lpxs_fpbs" ]             class "" [ "fqus_lpxs_fpbs" ]             * ]
-  [ class "" [ "cpxs_fqus_lpxs_fpbs" ]        class "" [ "cpxs_fqus_lpxs_fpbs" ]        * ]
-  [ class "" [ "lpxs_lleq_fpbs" ]             class "" [ "lpxs_lleq_fpbs" ]             * ]
-  [ class "" [ "cpr_lpr_fpbs" ]                       class "" [ "cpr_lpr_fpbs" ]               * ]
-  [ class "" [ "fpbg" ]                               class "" [ "fpbg" ]                       * ]
-  [ class "" [ "fpb_fpbg" ]                   class "" [ "fpb_fpbg" ]                   * ]
-  [ class "" [ "fpbg_fpbq_trans" ]            class "" [ "fpbg_fpbq_trans" ]            * ]
-  [ class "" [ "sta_fpbg" ]                   class "" [ "sta_fpbg" ]                   * ]
-  [ class "" [ "csx_lleq_conf" ]              class "" [ "csx_lleq_conf" ]              * ]
-  [ class "" [ "csx_lleq_trans" ]             class "" [ "csx_lleq_trans" ]             * ]
-  [ class "" [ "fpbs_trans" ]                 class "" [ "fpbs_trans" ]                 * ]
-  [ class "" [ "lreq_cpxs_trans" ]            class "" [ "lreq_cpxs_trans" ]            * ]
-  [ class "" [ "lpxs_drop_conf" ]             class "" [ "lpxs_drop_conf" ]             * ]
-  [ class "" [ "drop_lpxs_trans" ]            class "" [ "drop_lpxs_trans" ]            * ]
-  [ class "" [ "lpxs_drop_trans_O1" ]         class "" [ "lpxs_drop_trans_O1" ]         * ]
-  [ class "" [ "lpxs_pair" ]                  class "" [ "lpxs_pair" ]                  * ]
-  [ class "" [ "lpxs_inv_pair1" ]             class "" [ "lpxs_inv_pair1" ]             * ]
-  [ class "" [ "lpxs_inv_pair2" ]             class "" [ "lpxs_inv_pair2" ]             * ]
-  [ class "" [ "lpxs_ind_alt" ]                       class "" [ "lpxs_ind_alt" ]               * ]
-  [ class "" [ "lpxs_cpx_trans" ]             class "" [ "lpxs_cpx_trans" ]             * ]
-  [ class "" [ "lpxs_cpxs_trans" ]            class "" [ "lpxs_cpxs_trans" ]            * ]
-  [ class "" [ "cpxs_bind2" ]                 class "" [ "cpxs_bind2" ]                 * ]
-  [ class "" [ "cpxs_inv_abst1" ]             class "" [ "cpxs_inv_abst1" ]             * ]
-  [ class "" [ "cpxs_inv_abbr1" ]             class "" [ "cpxs_inv_abbr1" ]             * ]
-  [ class "" [ "lpxs_pair2" ]                 class "" [ "lpxs_pair2" ]                 * ]
-  [ class "" [ "lpx_fqup_trans" ]             class "" [ "lpx_fqup_trans" ]             * ]
-  [ class "" [ "lpx_fqus_trans" ]             class "" [ "lpx_fqus_trans" ]             * ]
-  [ class "" [ "lpxs_fquq_trans" ]            class "" [ "lpxs_fquq_trans" ]            * ]
-  [ class "" [ "lpxs_fqup_trans" ]            class "" [ "lpxs_fqup_trans" ]            * ]
-  [ class "" [ "lpxs_fqus_trans" ]            class "" [ "lpxs_fqus_trans" ]            * ]
-  [ class "" [ "lleq_lpxs_trans" ]            class "" [ "lleq_lpxs_trans" ]            * ]
+  [ class "" [ "lreq_lpx_trans_lleq" ]         class "" [ "lreq_lpx_trans_lleq" ]        * ]
+  [ class "" [ "cnx_inv_crx" ]                 class "" [ "cnx_inv_crx" ]                * ]
+  [ class "" [ "fleq" ]                        class "" [ "fleq" ]                       * ]
+  [ class "" [ "fleq_refl" ]                   class "" [ "fleq_refl" ]                  * ]
+  [ class "" [ "fleq_sym" ]                    class "" [ "fleq_sym" ]                   * ]
+  [ class "" [ "fleq_inv_gen" ]                class "" [ "fleq_inv_gen" ]               * ]
+  [ class "" [ "lleq_fqu_trans" ]              class "" [ "lleq_fqu_trans" ]             * ]
+  [ class "" [ "lleq_fquq_trans" ]             class "" [ "lleq_fquq_trans" ]            * ]
+  [ class "" [ "lleq_fqup_trans" ]             class "" [ "lleq_fqup_trans" ]            * ]
+  [ class "" [ "lleq_fqus_trans" ]             class "" [ "lleq_fqus_trans" ]            * ]
+  [ class "" [ "lleq_trans" ]                  class "" [ "lleq_trans" ]                 * ]
+  [ class "" [ "lleq_canc_sn" ]                class "" [ "lleq_canc_sn" ]               * ]
+  [ class "" [ "lleq_canc_dx" ]                class "" [ "lleq_canc_dx" ]               * ]
+  [ class "" [ "lleq_nlleq_trans" ]            class "" [ "lleq_nlleq_trans" ]           * ]
+  [ class "" [ "nlleq_lleq_div" ]              class "" [ "nlleq_lleq_div" ]             * ]
+  [ class "" [ "fpb" ]                         class "" [ "fpb" ]                        * ]
+  [ class "" [ "cpr_fpb" ]                     class "" [ "cpr_fpb" ]                    * ]
+  [ class "" [ "lpr_fpb" ]                     class "" [ "lpr_fpb" ]                    * ]
+  [ class "" [ "lleq_fpb_trans" ]              class "" [ "lleq_fpb_trans" ]             * ]
+  [ class "" [ "fleq_fpb_trans" ]              class "" [ "fleq_fpb_trans" ]             * ]
+  [ class "" [ "fpb_inv_fleq" ]                class "" [ "fpb_inv_fleq" ]               * ]
+  [ class "" [ "fpbq" ]                        class "" [ "fpbq" ]                       * ]
+  [ class "" [ "fpbq_refl" ]                   class "" [ "fpbq_refl" ]                  * ]
+  [ class "" [ "cpr_fpbq" ]                    class "" [ "cpr_fpbq" ]                   * ]
+  [ class "" [ "lpr_fpbq" ]                    class "" [ "lpr_fpbq" ]                   * ]
+  [ class "" [ "fpbqa" ]                       class "" [ "fpbqa" ]                      * ]
+  [ class "" [ "fleq_fpbq" ]                   class "" [ "fleq_fpbq" ]                  * ]
+  [ class "" [ "fpb_fpbq" ]                    class "" [ "fpb_fpbq" ]                   * ]
+  [ class "" [ "fpbq_fpbqa" ]                  class "" [ "fpbq_fpbqa" ]                 * ]
+  [ class "" [ "fpbqa_inv_fpbq" ]              class "" [ "fpbqa_inv_fpbq" ]             * ]
+  [ class "" [ "fpbq_ind_alt" ]                class "" [ "fpbq_ind_alt" ]               * ]
+  [ class "" [ "fpb_fpbq_alt" ]                class "" [ "fpb_fpbq_alt" ]               * ]
+  [ class "" [ "fpbq_inv_fpb_alt" ]            class "" [ "fpbq_inv_fpb_alt" ]           * ]
+  [ class "" [ "fpbq_aaa_conf" ]               class "" [ "fpbq_aaa_conf" ]              * ]
+  [ class "" [ "cpr_fwd_cir" ]                 class "" [ "cpr_fwd_cir" ]                * ]
+  [ class "" [ "sta_fpb" ]                     class "" [ "sta_fpb" ]                    * ]
+  [ class "" [ "crr_lift" ]                    class "" [ "crr_lift" ]                   * ]
+  [ class "" [ "crr_inv_lift" ]                class "" [ "crr_inv_lift" ]               * ]
+  [ class "" [ "cir_lift" ]                    class "" [ "cir_lift" ]                   * ]
+  [ class "" [ "cir_inv_lift" ]                class "" [ "cir_inv_lift" ]               * ]
+  [ class "" [ "cpr_llpx_sn_conf" ]            class "" [ "cpr_llpx_sn_conf" ]           * ]
+  [ class "" [ "crx_lift" ]                    class "" [ "crx_lift" ]                   * ]
+  [ class "" [ "crx_inv_lift" ]                class "" [ "crx_inv_lift" ]               * ]
+  [ class "" [ "cnx_lift" ]                    class "" [ "cnx_lift" ]                   * ]
+  [ class "" [ "cnx_inv_lift" ]                class "" [ "cnx_inv_lift" ]               * ]
+  [ class "" [ "cnr_inv_crr" ]                 class "" [ "cnr_inv_crr" ]                * ]
+  [ class "" [ "cnr_lref_abst" ]               class "" [ "cnr_lref_abst" ]              * ]
+  [ class "" [ "cnr_lift" ]                    class "" [ "cnr_lift" ]                   * ]
+  [ class "" [ "cnr_inv_lift" ]                class "" [ "cnr_inv_lift" ]               * ]
+  [ class "" [ "cir_cnr" ]                     class "" [ "cir_cnr" ]                    * ]
+  [ class "" [ "cnr_inv_cir" ]                 class "" [ "cnr_inv_cir" ]                * ]
+  [ class "" [ "cix_lref" ]                    class "" [ "cix_lref" ]                   * ]
+  [ class "" [ "cix_lift" ]                    class "" [ "cix_lift" ]                   * ]
+  [ class "" [ "cix_inv_lift" ]                class "" [ "cix_inv_lift" ]               * ]
+  [ class "" [ "sta_fpbq" ]                    class "" [ "sta_fpbq" ]                   * ]
+  [ class "" [ "cix_cnx" ]                     class "" [ "cix_cnx" ]                    * ]
+  [ class "" [ "cnx_inv_cix" ]                 class "" [ "cnx_inv_cix" ]                * ]
+  [ class "" [ "lstas_llpx_sn_conf" ]          class "" [ "lstas_llpx_sn_conf" ]         * ]
+  [ class "" [ "unfold" ]                      class "" [ "unfold" ]                     * ]
+  [ class "" [ "lsuby" ]                       class "" [ "lsuby" ]                      * ]
+  [ class "" [ "lsuby_pair_lt" ]               class "" [ "lsuby_pair_lt" ]              * ]
+  [ class "" [ "lsuby_succ_lt" ]               class "" [ "lsuby_succ_lt" ]              * ]
+  [ class "" [ "lsuby_pair_O_Y" ]              class "" [ "lsuby_pair_O_Y" ]             * ]
+  [ class "" [ "lsuby_refl" ]                  class "" [ "lsuby_refl" ]                 * ]
+  [ class "" [ "lsuby_O2" ]                    class "" [ "lsuby_O2" ]                   * ]
+  [ class "" [ "lsuby_sym" ]                   class "" [ "lsuby_sym" ]                  * ]
+  [ class "" [ "lsuby_inv_atom1_aux" ]         class "" [ "lsuby_inv_atom1_aux" ]        * ]
+  [ class "" [ "lsuby_inv_atom1" ]             class "" [ "lsuby_inv_atom1" ]            * ]
+  [ class "" [ "lsuby_inv_zero1_aux" ]         class "" [ "lsuby_inv_zero1_aux" ]        * ]
+  [ class "" [ "lsuby_inv_zero1" ]             class "" [ "lsuby_inv_zero1" ]            * ]
+  [ class "" [ "lsuby_inv_pair1_aux" ]         class "" [ "lsuby_inv_pair1_aux" ]        * ]
+  [ class "" [ "lsuby_inv_pair1" ]             class "" [ "lsuby_inv_pair1" ]            * ]
+  [ class "" [ "lsuby_inv_succ1_aux" ]         class "" [ "lsuby_inv_succ1_aux" ]        * ]
+  [ class "" [ "lsuby_inv_succ1" ]             class "" [ "lsuby_inv_succ1" ]            * ]
+  [ class "" [ "lsuby_inv_zero2_aux" ]         class "" [ "lsuby_inv_zero2_aux" ]        * ]
+  [ class "" [ "lsuby_inv_zero2" ]             class "" [ "lsuby_inv_zero2" ]            * ]
+  [ class "" [ "lsuby_inv_pair2_aux" ]         class "" [ "lsuby_inv_pair2_aux" ]        * ]
+  [ class "" [ "lsuby_inv_pair2" ]             class "" [ "lsuby_inv_pair2" ]            * ]
+  [ class "" [ "lsuby_inv_succ2_aux" ]         class "" [ "lsuby_inv_succ2_aux" ]        * ]
+  [ class "" [ "lsuby_inv_succ2" ]             class "" [ "lsuby_inv_succ2" ]            * ]
+  [ class "" [ "lsuby_fwd_length" ]            class "" [ "lsuby_fwd_length" ]           * ]
+  [ class "" [ "lsuby_drop_trans_be" ]         class "" [ "lsuby_drop_trans_be" ]        * ]
+  [ class "" [ "cpy" ]                         class "" [ "cpy" ]                        * ]
+  [ class "" [ "lsuby_cpy_trans" ]             class "" [ "lsuby_cpy_trans" ]            * ]
+  [ class "" [ "cpy_refl" ]                    class "" [ "cpy_refl" ]                   * ]
+  [ class "" [ "cpy_full" ]                    class "" [ "cpy_full" ]                   * ]
+  [ class "" [ "cpy_weak" ]                    class "" [ "cpy_weak" ]                   * ]
+  [ class "" [ "cpy_weak_top" ]                class "" [ "cpy_weak_top" ]               * ]
+  [ class "" [ "cpy_weak_full" ]               class "" [ "cpy_weak_full" ]              * ]
+  [ class "" [ "cpy_split_up" ]                class "" [ "cpy_split_up" ]               * ]
+  [ class "" [ "cpy_split_down" ]              class "" [ "cpy_split_down" ]             * ]
+  [ class "" [ "cpy_fwd_up" ]                  class "" [ "cpy_fwd_up" ]                 * ]
+  [ class "" [ "cpy_fwd_tw" ]                  class "" [ "cpy_fwd_tw" ]                 * ]
+  [ class "" [ "cpy_inv_atom1_aux" ]           class "" [ "cpy_inv_atom1_aux" ]          * ]
+  [ class "" [ "cpy_inv_atom1" ]               class "" [ "cpy_inv_atom1" ]              * ]
+  [ class "" [ "cpy_inv_sort1" ]               class "" [ "cpy_inv_sort1" ]              * ]
+  [ class "" [ "cpy_inv_lref1" ]               class "" [ "cpy_inv_lref1" ]              * ]
+  [ class "" [ "cpy_inv_gref1" ]               class "" [ "cpy_inv_gref1" ]              * ]
+  [ class "" [ "cpy_inv_bind1_aux" ]           class "" [ "cpy_inv_bind1_aux" ]          * ]
+  [ class "" [ "cpy_inv_bind1" ]               class "" [ "cpy_inv_bind1" ]              * ]
+  [ class "" [ "cpy_inv_flat1_aux" ]           class "" [ "cpy_inv_flat1_aux" ]          * ]
+  [ class "" [ "cpy_inv_flat1" ]               class "" [ "cpy_inv_flat1" ]              * ]
+  [ class "" [ "cpy_inv_refl_O2_aux" ]         class "" [ "cpy_inv_refl_O2_aux" ]        * ]
+  [ class "" [ "cpy_inv_refl_O2" ]             class "" [ "cpy_inv_refl_O2" ]            * ]
+  [ class "" [ "cpy_inv_lift1_eq" ]            class "" [ "cpy_inv_lift1_eq" ]           * ]
+  [ class "" [ "cpy_lift_le" ]                 class "" [ "cpy_lift_le" ]                * ]
+  [ class "" [ "cpy_lift_be" ]                 class "" [ "cpy_lift_be" ]                * ]
+  [ class "" [ "cpy_lift_ge" ]                 class "" [ "cpy_lift_ge" ]                * ]
+  [ class "" [ "cpy_inv_lift1_le" ]            class "" [ "cpy_inv_lift1_le" ]           * ]
+  [ class "" [ "cpy_inv_lift1_be" ]            class "" [ "cpy_inv_lift1_be" ]           * ]
+  [ class "" [ "cpy_inv_lift1_ge" ]            class "" [ "cpy_inv_lift1_ge" ]           * ]
+  [ class "" [ "cpy_inv_lift1_ge_up" ]         class "" [ "cpy_inv_lift1_ge_up" ]        * ]
+  [ class "" [ "cpy_inv_lift1_be_up" ]         class "" [ "cpy_inv_lift1_be_up" ]        * ]
+  [ class "" [ "cpy_inv_lift1_le_up" ]         class "" [ "cpy_inv_lift1_le_up" ]        * ]
+  [ class "" [ "cpy_conf_eq" ]                 class "" [ "cpy_conf_eq" ]                * ]
+  [ class "" [ "cpy_conf_neq" ]                class "" [ "cpy_conf_neq" ]               * ]
+  [ class "" [ "cpy_trans_ge" ]                class "" [ "cpy_trans_ge" ]               * ]
+  [ class "" [ "cpy_trans_down" ]              class "" [ "cpy_trans_down" ]             * ]
+  [ class "" [ "cpy_fwd_nlift2_ge" ]           class "" [ "cpy_fwd_nlift2_ge" ]          * ]
+  [ class "" [ "gget" ]                        class "" [ "gget" ]                       * ]
+  [ class "" [ "gget_inv_gt" ]                 class "" [ "gget_inv_gt" ]                * ]
+  [ class "" [ "gget_inv_eq" ]                 class "" [ "gget_inv_eq" ]                * ]
+  [ class "" [ "gget_inv_lt_aux" ]             class "" [ "gget_inv_lt_aux" ]            * ]
+  [ class "" [ "gget_inv_lt" ]                 class "" [ "gget_inv_lt" ]                * ]
+  [ class "" [ "gget_total" ]                  class "" [ "gget_total" ]                 * ]
+  [ class "" [ "gget_mono" ]                   class "" [ "gget_mono" ]                  * ]
+  [ class "" [ "gget_dec" ]                    class "" [ "gget_dec" ]                   * ]
+  [ class "" [ "lsuby_trans" ]                 class "" [ "lsuby_trans" ]                * ]
+  [ class "" [ "liftv_mono" ]                  class "" [ "liftv_mono" ]                 * ]
+  [ class "" [ "csx" ]                         class "" [ "csx" ]                        * ]
+  [ class "" [ "csx_ind" ]                     class "" [ "csx_ind" ]                    * ]
+  [ class "" [ "csx_intro" ]                   class "" [ "csx_intro" ]                  * ]
+  [ class "" [ "csx_cpx_trans" ]               class "" [ "csx_cpx_trans" ]              * ]
+  [ class "" [ "cnx_csx" ]                     class "" [ "cnx_csx" ]                    * ]
+  [ class "" [ "csx_sort" ]                    class "" [ "csx_sort" ]                   * ]
+  [ class "" [ "csx_cast" ]                    class "" [ "csx_cast" ]                   * ]
+  [ class "" [ "csx_fwd_pair_sn_aux" ]         class "" [ "csx_fwd_pair_sn_aux" ]        * ]
+  [ class "" [ "csx_fwd_pair_sn" ]             class "" [ "csx_fwd_pair_sn" ]            * ]
+  [ class "" [ "csx_fwd_bind_dx_aux" ]         class "" [ "csx_fwd_bind_dx_aux" ]        * ]
+  [ class "" [ "csx_fwd_bind_dx" ]             class "" [ "csx_fwd_bind_dx" ]            * ]
+  [ class "" [ "csx_fwd_flat_dx_aux" ]         class "" [ "csx_fwd_flat_dx_aux" ]        * ]
+  [ class "" [ "csx_fwd_flat_dx" ]             class "" [ "csx_fwd_flat_dx" ]            * ]
+  [ class "" [ "csx_fwd_bind" ]                class "" [ "csx_fwd_bind" ]               * ]
+  [ class "" [ "csx_fwd_flat" ]                class "" [ "csx_fwd_flat" ]               * ]
+  [ class "" [ "cpre" ]                        class "" [ "cpre" ]                       * ]
+  [ class "" [ "csx_cpre" ]                    class "" [ "csx_cpre" ]                   * ]
+  [ class "" [ "cpre_mono" ]                   class "" [ "cpre_mono" ]                  * ]
+  [ class "" [ "lpxs" ]                        class "" [ "lpxs" ]                       * ]
+  [ class "" [ "lpxs_ind" ]                    class "" [ "lpxs_ind" ]                   * ]
+  [ class "" [ "lpxs_ind_dx" ]                 class "" [ "lpxs_ind_dx" ]                * ]
+  [ class "" [ "lprs_lpxs" ]                   class "" [ "lprs_lpxs" ]                  * ]
+  [ class "" [ "lpx_lpxs" ]                    class "" [ "lpx_lpxs" ]                   * ]
+  [ class "" [ "lpxs_refl" ]                   class "" [ "lpxs_refl" ]                  * ]
+  [ class "" [ "lpxs_strap1" ]                 class "" [ "lpxs_strap1" ]                * ]
+  [ class "" [ "lpxs_strap2" ]                 class "" [ "lpxs_strap2" ]                * ]
+  [ class "" [ "lpxs_pair_refl" ]              class "" [ "lpxs_pair_refl" ]             * ]
+  [ class "" [ "lpxs_inv_atom1" ]              class "" [ "lpxs_inv_atom1" ]             * ]
+  [ class "" [ "lpxs_inv_atom2" ]              class "" [ "lpxs_inv_atom2" ]             * ]
+  [ class "" [ "lpxs_fwd_length" ]             class "" [ "lpxs_fwd_length" ]            * ]
+  [ class "" [ "fpbs" ]                        class "" [ "fpbs" ]                       * ]
+  [ class "" [ "fpbs_ind" ]                    class "" [ "fpbs_ind" ]                   * ]
+  [ class "" [ "fpbs_ind_dx" ]                 class "" [ "fpbs_ind_dx" ]                * ]
+  [ class "" [ "fpbs_refl" ]                   class "" [ "fpbs_refl" ]                  * ]
+  [ class "" [ "fpbq_fpbs" ]                   class "" [ "fpbq_fpbs" ]                  * ]
+  [ class "" [ "fpbs_strap1" ]                 class "" [ "fpbs_strap1" ]                * ]
+  [ class "" [ "fpbs_strap2" ]                 class "" [ "fpbs_strap2" ]                * ]
+  [ class "" [ "fqup_fpbs" ]                   class "" [ "fqup_fpbs" ]                  * ]
+  [ class "" [ "fqus_fpbs" ]                   class "" [ "fqus_fpbs" ]                  * ]
+  [ class "" [ "cpxs_fpbs" ]                   class "" [ "cpxs_fpbs" ]                  * ]
+  [ class "" [ "lpxs_fpbs" ]                   class "" [ "lpxs_fpbs" ]                  * ]
+  [ class "" [ "lleq_fpbs" ]                   class "" [ "lleq_fpbs" ]                  * ]
+  [ class "" [ "cprs_fpbs" ]                   class "" [ "cprs_fpbs" ]                  * ]
+  [ class "" [ "lprs_fpbs" ]                   class "" [ "lprs_fpbs" ]                  * ]
+  [ class "" [ "fpbs_fqus_trans" ]             class "" [ "fpbs_fqus_trans" ]            * ]
+  [ class "" [ "fpbs_fqup_trans" ]             class "" [ "fpbs_fqup_trans" ]            * ]
+  [ class "" [ "fpbs_cpxs_trans" ]             class "" [ "fpbs_cpxs_trans" ]            * ]
+  [ class "" [ "fpbs_lpxs_trans" ]             class "" [ "fpbs_lpxs_trans" ]            * ]
+  [ class "" [ "fpbs_lleq_trans" ]             class "" [ "fpbs_lleq_trans" ]            * ]
+  [ class "" [ "fqus_fpbs_trans" ]             class "" [ "fqus_fpbs_trans" ]            * ]
+  [ class "" [ "cpxs_fpbs_trans" ]             class "" [ "cpxs_fpbs_trans" ]            * ]
+  [ class "" [ "lpxs_fpbs_trans" ]             class "" [ "lpxs_fpbs_trans" ]            * ]
+  [ class "" [ "lleq_fpbs_trans" ]             class "" [ "lleq_fpbs_trans" ]            * ]
+  [ class "" [ "cpxs_fqus_fpbs" ]              class "" [ "cpxs_fqus_fpbs" ]             * ]
+  [ class "" [ "cpxs_fqup_fpbs" ]              class "" [ "cpxs_fqup_fpbs" ]             * ]
+  [ class "" [ "fqus_lpxs_fpbs" ]              class "" [ "fqus_lpxs_fpbs" ]             * ]
+  [ class "" [ "cpxs_fqus_lpxs_fpbs" ]         class "" [ "cpxs_fqus_lpxs_fpbs" ]        * ]
+  [ class "" [ "lpxs_lleq_fpbs" ]              class "" [ "lpxs_lleq_fpbs" ]             * ]
+  [ class "" [ "cpr_lpr_fpbs" ]                class "" [ "cpr_lpr_fpbs" ]               * ]
+  [ class "" [ "fpbg" ]                        class "" [ "fpbg" ]                       * ]
+  [ class "" [ "fpb_fpbg" ]                    class "" [ "fpb_fpbg" ]                   * ]
+  [ class "" [ "fpbg_fpbq_trans" ]             class "" [ "fpbg_fpbq_trans" ]            * ]
+  [ class "" [ "sta_fpbg" ]                    class "" [ "sta_fpbg" ]                   * ]
+  [ class "" [ "csx_lleq_conf" ]               class "" [ "csx_lleq_conf" ]              * ]
+  [ class "" [ "csx_lleq_trans" ]              class "" [ "csx_lleq_trans" ]             * ]
+  [ class "" [ "fpbs_trans" ]                  class "" [ "fpbs_trans" ]                 * ]
+  [ class "" [ "lreq_cpxs_trans" ]             class "" [ "lreq_cpxs_trans" ]            * ]
+  [ class "" [ "lpxs_drop_conf" ]              class "" [ "lpxs_drop_conf" ]             * ]
+  [ class "" [ "drop_lpxs_trans" ]             class "" [ "drop_lpxs_trans" ]            * ]
+  [ class "" [ "lpxs_drop_trans_O1" ]          class "" [ "lpxs_drop_trans_O1" ]         * ]
+  [ class "" [ "lpxs_pair" ]                   class "" [ "lpxs_pair" ]                  * ]
+  [ class "" [ "lpxs_inv_pair1" ]              class "" [ "lpxs_inv_pair1" ]             * ]
+  [ class "" [ "lpxs_inv_pair2" ]              class "" [ "lpxs_inv_pair2" ]             * ]
+  [ class "" [ "lpxs_ind_alt" ]                class "" [ "lpxs_ind_alt" ]               * ]
+  [ class "" [ "lpxs_cpx_trans" ]              class "" [ "lpxs_cpx_trans" ]             * ]
+  [ class "" [ "lpxs_cpxs_trans" ]             class "" [ "lpxs_cpxs_trans" ]            * ]
+  [ class "" [ "cpxs_bind2" ]                  class "" [ "cpxs_bind2" ]                 * ]
+  [ class "" [ "cpxs_inv_abst1" ]              class "" [ "cpxs_inv_abst1" ]             * ]
+  [ class "" [ "cpxs_inv_abbr1" ]              class "" [ "cpxs_inv_abbr1" ]             * ]
+  [ class "" [ "lpxs_pair2" ]                  class "" [ "lpxs_pair2" ]                 * ]
+  [ class "" [ "lpx_fqup_trans" ]              class "" [ "lpx_fqup_trans" ]             * ]
+  [ class "" [ "lpx_fqus_trans" ]              class "" [ "lpx_fqus_trans" ]             * ]
+  [ class "" [ "lpxs_fquq_trans" ]             class "" [ "lpxs_fquq_trans" ]            * ]
+  [ class "" [ "lpxs_fqup_trans" ]             class "" [ "lpxs_fqup_trans" ]            * ]
+  [ class "" [ "lpxs_fqus_trans" ]             class "" [ "lpxs_fqus_trans" ]            * ]
+  [ class "" [ "lleq_lpxs_trans" ]             class "" [ "lleq_lpxs_trans" ]            * ]
   [ class "" [ "lpxs_nlleq_inv_step_sn" ]      class "" [ "lpxs_nlleq_inv_step_sn" ]     * ]
-  [ class "" [ "lpxs_lleq_fqu_trans" ]        class "" [ "lpxs_lleq_fqu_trans" ]        * ]
-  [ class "" [ "lpxs_lleq_fquq_trans" ]               class "" [ "lpxs_lleq_fquq_trans" ]       * ]
-  [ class "" [ "lpxs_lleq_fqup_trans" ]               class "" [ "lpxs_lleq_fqup_trans" ]       * ]
-  [ class "" [ "lpxs_lleq_fqus_trans" ]               class "" [ "lpxs_lleq_fqus_trans" ]       * ]
+  [ class "" [ "lpxs_lleq_fqu_trans" ]         class "" [ "lpxs_lleq_fqu_trans" ]        * ]
+  [ class "" [ "lpxs_lleq_fquq_trans" ]        class "" [ "lpxs_lleq_fquq_trans" ]       * ]
+  [ class "" [ "lpxs_lleq_fqup_trans" ]        class "" [ "lpxs_lleq_fqup_trans" ]       * ]
+  [ class "" [ "lpxs_lleq_fqus_trans" ]        class "" [ "lpxs_lleq_fqus_trans" ]       * ]
   [ class "" [ "lreq_lpxs_trans_lleq_aux" ]    class "" [ "lreq_lpxs_trans_lleq_aux" ]   * ]
-  [ class "" [ "lreq_lpxs_trans_lleq" ]               class "" [ "lreq_lpxs_trans_lleq" ]       * ]
-  [ class "" [ "lstas_fpbs" ]                 class "" [ "lstas_fpbs" ]                 * ]
-  [ class "" [ "sta_fpbs" ]                   class "" [ "sta_fpbs" ]                   * ]
-  [ class "" [ "cpr_lpr_sta_fpbs" ]           class "" [ "cpr_lpr_sta_fpbs" ]           * ]
-  [ class "" [ "fleq_trans" ]                 class "" [ "fleq_trans" ]                 * ]
-  [ class "" [ "fleq_canc_sn" ]                       class "" [ "fleq_canc_sn" ]               * ]
-  [ class "" [ "fleq_canc_dx" ]                       class "" [ "fleq_canc_dx" ]               * ]
-  [ class "" [ "fpbg_fleq_trans" ]            class "" [ "fpbg_fleq_trans" ]            * ]
-  [ class "" [ "fleq_fpbg_trans" ]            class "" [ "fleq_fpbg_trans" ]            * ]
-  [ class "" [ "fleq_fpbs" ]                  class "" [ "fleq_fpbs" ]                  * ]
-  [ class "" [ "fpbg_fwd_fpbs" ]              class "" [ "fpbg_fwd_fpbs" ]              * ]
-  [ class "" [ "fpbs_fpbg" ]                  class "" [ "fpbs_fpbg" ]                  * ]
-  [ class "" [ "fpbs_fpb_trans" ]             class "" [ "fpbs_fpb_trans" ]             * ]
-  [ class "" [ "fpb_fpbg_trans" ]             class "" [ "fpb_fpbg_trans" ]             * ]
-  [ class "" [ "fpbq_fpbg_trans" ]            class "" [ "fpbq_fpbg_trans" ]            * ]
-  [ class "" [ "fpbs_fpbg_trans" ]            class "" [ "fpbs_fpbg_trans" ]            * ]
-  [ class "" [ "fpbg_fpbs_trans" ]            class "" [ "fpbg_fpbs_trans" ]            * ]
-  [ class "" [ "fqup_fpbg" ]                  class "" [ "fqup_fpbg" ]                  * ]
-  [ class "" [ "cpxs_fpbg" ]                  class "" [ "cpxs_fpbg" ]                  * ]
-  [ class "" [ "lstas_fpbg" ]                 class "" [ "lstas_fpbg" ]                 * ]
-  [ class "" [ "lpxs_fpbg" ]                  class "" [ "lpxs_fpbg" ]                  * ]
-  [ class "" [ "fsb" ]                        class "" [ "fsb" ]                        * ]
-  [ class "" [ "fsb_ind_alt" ]                class "" [ "fsb_ind_alt" ]                * ]
-  [ class "" [ "fsb_inv_csx" ]                class "" [ "fsb_inv_csx" ]                * ]
-  [ class "" [ "fsba" ]                               class "" [ "fsba" ]                       * ]
-  [ class "" [ "fsba_ind_alt" ]                       class "" [ "fsba_ind_alt" ]               * ]
-  [ class "" [ "fsba_fpbs_trans" ]            class "" [ "fsba_fpbs_trans" ]            * ]
-  [ class "" [ "fsb_fsba" ]                   class "" [ "fsb_fsba" ]                   * ]
-  [ class "" [ "fsba_inv_fsb" ]                       class "" [ "fsba_inv_fsb" ]               * ]
-  [ class "" [ "fsb_fpbs_trans" ]             class "" [ "fsb_fpbs_trans" ]             * ]
-  [ class "" [ "fsb_ind_fpbg" ]                       class "" [ "fsb_ind_fpbg" ]               * ]
-  [ class "" [ "lpxs_trans" ]                 class "" [ "lpxs_trans" ]                 * ]
-  [ class "" [ "lsx" ]                        class "" [ "lsx" ]                        * ]
-  [ class "" [ "lsx_ind" ]                    class "" [ "lsx_ind" ]                    * ]
-  [ class "" [ "lsx_intro" ]                  class "" [ "lsx_intro" ]                  * ]
-  [ class "" [ "lsx_atom" ]                   class "" [ "lsx_atom" ]                   * ]
-  [ class "" [ "lsx_sort" ]                   class "" [ "lsx_sort" ]                   * ]
-  [ class "" [ "lsx_gref" ]                   class "" [ "lsx_gref" ]                   * ]
-  [ class "" [ "lsx_ge_up" ]                  class "" [ "lsx_ge_up" ]                  * ]
-  [ class "" [ "lsx_ge" ]                     class "" [ "lsx_ge" ]                     * ]
-  [ class "" [ "lsx_fwd_bind_sn" ]            class "" [ "lsx_fwd_bind_sn" ]            * ]
-  [ class "" [ "lsx_fwd_flat_sn" ]            class "" [ "lsx_fwd_flat_sn" ]            * ]
-  [ class "" [ "lsx_fwd_flat_dx" ]            class "" [ "lsx_fwd_flat_dx" ]            * ]
-  [ class "" [ "lsx_fwd_pair_sn" ]            class "" [ "lsx_fwd_pair_sn" ]            * ]
-  [ class "" [ "lsx_inv_flat" ]                       class "" [ "lsx_inv_flat" ]               * ]
-  [ class "" [ "lsxa" ]                               class "" [ "lsxa" ]                       * ]
-  [ class "" [ "lsxa_ind" ]                   class "" [ "lsxa_ind" ]                   * ]
-  [ class "" [ "lsxa_intro" ]                 class "" [ "lsxa_intro" ]                 * ]
-  [ class "" [ "lsxa_intro_aux" ]             class "" [ "lsxa_intro_aux" ]             * ]
-  [ class "" [ "lsxa_lleq_trans" ]            class "" [ "lsxa_lleq_trans" ]            * ]
-  [ class "" [ "lsxa_lpxs_trans" ]            class "" [ "lsxa_lpxs_trans" ]            * ]
-  [ class "" [ "lsxa_intro_lpx" ]             class "" [ "lsxa_intro_lpx" ]             * ]
-  [ class "" [ "lsx_lsxa" ]                   class "" [ "lsx_lsxa" ]                   * ]
-  [ class "" [ "lsxa_inv_lsx" ]                       class "" [ "lsxa_inv_lsx" ]               * ]
-  [ class "" [ "lsx_intro_alt" ]              class "" [ "lsx_intro_alt" ]              * ]
-  [ class "" [ "lsx_lpxs_trans" ]             class "" [ "lsx_lpxs_trans" ]             * ]
-  [ class "" [ "lsx_ind_alt" ]                class "" [ "lsx_ind_alt" ]                * ]
-  [ class "" [ "lsx_bind_lpxs_aux" ]          class "" [ "lsx_bind_lpxs_aux" ]          * ]
-  [ class "" [ "lsx_bind" ]                   class "" [ "lsx_bind" ]                   * ]
-  [ class "" [ "lsx_flat_lpxs" ]              class "" [ "lsx_flat_lpxs" ]              * ]
-  [ class "" [ "lsx_flat" ]                   class "" [ "lsx_flat" ]                   * ]
-  [ class "" [ "tsts" ]                               class "" [ "tsts" ]                       * ]
-  [ class "" [ "tsts_inv_atom1_aux" ]         class "" [ "tsts_inv_atom1_aux" ]         * ]
-  [ class "" [ "tsts_inv_atom1" ]             class "" [ "tsts_inv_atom1" ]             * ]
-  [ class "" [ "tsts_inv_pair1_aux" ]         class "" [ "tsts_inv_pair1_aux" ]         * ]
-  [ class "" [ "tsts_inv_pair1" ]             class "" [ "tsts_inv_pair1" ]             * ]
-  [ class "" [ "tsts_inv_atom2_aux" ]         class "" [ "tsts_inv_atom2_aux" ]         * ]
-  [ class "" [ "tsts_inv_atom2" ]             class "" [ "tsts_inv_atom2" ]             * ]
-  [ class "" [ "tsts_inv_pair2_aux" ]         class "" [ "tsts_inv_pair2_aux" ]         * ]
-  [ class "" [ "tsts_inv_pair2" ]             class "" [ "tsts_inv_pair2" ]             * ]
-  [ class "" [ "tsts_refl" ]                  class "" [ "tsts_refl" ]                  * ]
-  [ class "" [ "tsts_sym" ]                   class "" [ "tsts_sym" ]                   * ]
-  [ class "" [ "tsts_dec" ]                   class "" [ "tsts_dec" ]                   * ]
-  [ class "" [ "simple_tsts_repl_dx" ]        class "" [ "simple_tsts_repl_dx" ]        * ]
-  [ class "" [ "simple_tsts_repl_sn" ]        class "" [ "simple_tsts_repl_sn" ]        * ]
-  [ class "" [ "tsts_trans" ]                 class "" [ "tsts_trans" ]                 * ]
-  [ class "" [ "tsts_canc_sn" ]                       class "" [ "tsts_canc_sn" ]               * ]
-  [ class "" [ "tsts_canc_dx" ]                       class "" [ "tsts_canc_dx" ]               * ]
-  [ class "" [ "csxa" ]                               class "" [ "csxa" ]                       * ]
-  [ class "" [ "csxa_ind" ]                   class "" [ "csxa_ind" ]                   * ]
-  [ class "" [ "csx_intro_cpxs" ]             class "" [ "csx_intro_cpxs" ]             * ]
-  [ class "" [ "csxa_intro" ]                 class "" [ "csxa_intro" ]                 * ]
-  [ class "" [ "csxa_intro_aux" ]             class "" [ "csxa_intro_aux" ]             * ]
-  [ class "" [ "csxa_cpxs_trans" ]            class "" [ "csxa_cpxs_trans" ]            * ]
-  [ class "" [ "csxa_intro_cpx" ]             class "" [ "csxa_intro_cpx" ]             * ]
-  [ class "" [ "csx_csxa" ]                   class "" [ "csx_csxa" ]                   * ]
-  [ class "" [ "csxa_csx" ]                   class "" [ "csxa_csx" ]                   * ]
-  [ class "" [ "csx_cpxs_trans" ]             class "" [ "csx_cpxs_trans" ]             * ]
-  [ class "" [ "csx_ind_alt" ]                class "" [ "csx_ind_alt" ]                * ]
-  [ class "" [ "nf" ]                         class "" [ "nf" ]                         * ]
-  [ class "" [ "candidate" ]                  class "" [ "candidate" ]                  * ]
-  [ class "" [ "CP0" ]                        class "" [ "CP0" ]                        * ]
-  [ class "" [ "CP1" ]                        class "" [ "CP1" ]                        * ]
-  [ class "" [ "CP2" ]                        class "" [ "CP2" ]                        * ]
-  [ class "" [ "CP3" ]                        class "" [ "CP3" ]                        * ]
-  [ class "" [ "gcp" ]                        class "" [ "gcp" ]                        * ]
-  [ class "" [ "gcp0_lifts" ]                 class "" [ "gcp0_lifts" ]                 * ]
-  [ class "" [ "gcp2_lifts" ]                 class "" [ "gcp2_lifts" ]                 * ]
-  [ class "" [ "gcp2_lifts_all" ]             class "" [ "gcp2_lifts_all" ]             * ]
-  [ class "" [ "csx_lift" ]                   class "" [ "csx_lift" ]                   * ]
-  [ class "" [ "csx_inv_lift" ]                       class "" [ "csx_inv_lift" ]               * ]
-  [ class "" [ "csx_inv_lref_bind" ]          class "" [ "csx_inv_lref_bind" ]          * ]
-  [ class "" [ "csx_lref_bind" ]              class "" [ "csx_lref_bind" ]              * ]
-  [ class "" [ "csx_appl_simple" ]            class "" [ "csx_appl_simple" ]            * ]
-  [ class "" [ "csx_fqu_conf" ]                       class "" [ "csx_fqu_conf" ]               * ]
-  [ class "" [ "csx_fquq_conf" ]              class "" [ "csx_fquq_conf" ]              * ]
-  [ class "" [ "csx_fqup_conf" ]              class "" [ "csx_fqup_conf" ]              * ]
-  [ class "" [ "csx_fqus_conf" ]              class "" [ "csx_fqus_conf" ]              * ]
-  [ class "" [ "csx_gcp" ]                    class "" [ "csx_gcp" ]                    * ]
-  [ class "" [ "csx_lpx_conf" ]                       class "" [ "csx_lpx_conf" ]               * ]
-  [ class "" [ "csx_abst" ]                   class "" [ "csx_abst" ]                   * ]
-  [ class "" [ "csx_abbr" ]                   class "" [ "csx_abbr" ]                   * ]
-  [ class "" [ "csx_appl_beta_aux" ]          class "" [ "csx_appl_beta_aux" ]          * ]
-  [ class "" [ "csx_appl_beta" ]              class "" [ "csx_appl_beta" ]              * ]
-  [ class "" [ "csx_appl_theta_aux" ]         class "" [ "csx_appl_theta_aux" ]         * ]
-  [ class "" [ "csx_appl_theta" ]             class "" [ "csx_appl_theta" ]             * ]
-  [ class "" [ "csx_appl_simple_tsts" ]               class "" [ "csx_appl_simple_tsts" ]       * ]
-  [ class "" [ "csx_lpxs_conf" ]              class "" [ "csx_lpxs_conf" ]              * ]
-  [ class "" [ "lsx_lref_free" ]              class "" [ "lsx_lref_free" ]              * ]
-  [ class "" [ "lsx_lref_skip" ]              class "" [ "lsx_lref_skip" ]              * ]
-  [ class "" [ "lsx_fwd_lref_be" ]            class "" [ "lsx_fwd_lref_be" ]            * ]
-  [ class "" [ "lsx_lift_le" ]                class "" [ "lsx_lift_le" ]                * ]
-  [ class "" [ "lsx_lift_ge" ]                class "" [ "lsx_lift_ge" ]                * ]
-  [ class "" [ "lsx_inv_lift_le" ]            class "" [ "lsx_inv_lift_le" ]            * ]
-  [ class "" [ "lsx_inv_lift_be" ]            class "" [ "lsx_inv_lift_be" ]            * ]
-  [ class "" [ "lsx_inv_lift_ge" ]            class "" [ "lsx_inv_lift_ge" ]            * ]
-  [ class "" [ "lsx_lleq_trans" ]             class "" [ "lsx_lleq_trans" ]             * ]
-  [ class "" [ "lsx_lpx_trans" ]              class "" [ "lsx_lpx_trans" ]              * ]
-  [ class "" [ "lsx_lreq_conf" ]              class "" [ "lsx_lreq_conf" ]              * ]
-  [ class "" [ "lsx_fwd_bind_dx" ]            class "" [ "lsx_fwd_bind_dx" ]            * ]
-  [ class "" [ "lsx_inv_bind" ]                       class "" [ "lsx_inv_bind" ]               * ]
-  [ class "" [ "lcosx" ]                      class "" [ "lcosx" ]                      * ]
-  [ class "" [ "lcosx_O" ]                    class "" [ "lcosx_O" ]                    * ]
-  [ class "" [ "lcosx_drop_trans_lt" ]        class "" [ "lcosx_drop_trans_lt" ]        * ]
-  [ class "" [ "lcosx_inv_succ_aux" ]         class "" [ "lcosx_inv_succ_aux" ]         * ]
-  [ class "" [ "lcosx_inv_succ" ]             class "" [ "lcosx_inv_succ" ]             * ]
-  [ class "" [ "lcosx_inv_pair" ]             class "" [ "lcosx_inv_pair" ]             * ]
-  [ class "" [ "lsx_cpx_trans_lcosx" ]        class "" [ "lsx_cpx_trans_lcosx" ]        * ]
-  [ class "" [ "lsx_cpx_trans_O" ]            class "" [ "lsx_cpx_trans_O" ]            * ]
-  [ class "" [ "lsx_lref_be_lpxs" ]           class "" [ "lsx_lref_be_lpxs" ]           * ]
-  [ class "" [ "lsx_lref_be" ]                class "" [ "lsx_lref_be" ]                * ]
-  [ class "" [ "csx_lsx" ]                    class "" [ "csx_lsx" ]                    * ]
-  [ class "" [ "fpbs_aaa_conf" ]              class "" [ "fpbs_aaa_conf" ]              * ]
-  [ class "" [ "at_mono" ]                    class "" [ "at_mono" ]                    * ]
-  [ class "" [ "lifts_lift_trans_le" ]        class "" [ "lifts_lift_trans_le" ]        * ]
-  [ class "" [ "lifts_lift_trans" ]           class "" [ "lifts_lift_trans" ]           * ]
+  [ class "" [ "lreq_lpxs_trans_lleq" ]        class "" [ "lreq_lpxs_trans_lleq" ]       * ]
+  [ class "" [ "lstas_fpbs" ]                  class "" [ "lstas_fpbs" ]                 * ]
+  [ class "" [ "sta_fpbs" ]                    class "" [ "sta_fpbs" ]                   * ]
+  [ class "" [ "cpr_lpr_sta_fpbs" ]            class "" [ "cpr_lpr_sta_fpbs" ]           * ]
+  [ class "" [ "fleq_trans" ]                  class "" [ "fleq_trans" ]                 * ]
+  [ class "" [ "fleq_canc_sn" ]                class "" [ "fleq_canc_sn" ]               * ]
+  [ class "" [ "fleq_canc_dx" ]                class "" [ "fleq_canc_dx" ]               * ]
+  [ class "" [ "fpbg_fleq_trans" ]             class "" [ "fpbg_fleq_trans" ]            * ]
+  [ class "" [ "fleq_fpbg_trans" ]             class "" [ "fleq_fpbg_trans" ]            * ]
+  [ class "" [ "fleq_fpbs" ]                   class "" [ "fleq_fpbs" ]                  * ]
+  [ class "" [ "fpbg_fwd_fpbs" ]               class "" [ "fpbg_fwd_fpbs" ]              * ]
+  [ class "" [ "fpbs_fpbg" ]                   class "" [ "fpbs_fpbg" ]                  * ]
+  [ class "" [ "fpbs_fpb_trans" ]              class "" [ "fpbs_fpb_trans" ]             * ]
+  [ class "" [ "fpb_fpbg_trans" ]              class "" [ "fpb_fpbg_trans" ]             * ]
+  [ class "" [ "fpbq_fpbg_trans" ]             class "" [ "fpbq_fpbg_trans" ]            * ]
+  [ class "" [ "fpbs_fpbg_trans" ]             class "" [ "fpbs_fpbg_trans" ]            * ]
+  [ class "" [ "fpbg_fpbs_trans" ]             class "" [ "fpbg_fpbs_trans" ]            * ]
+  [ class "" [ "fqup_fpbg" ]                   class "" [ "fqup_fpbg" ]                  * ]
+  [ class "" [ "cpxs_fpbg" ]                   class "" [ "cpxs_fpbg" ]                  * ]
+  [ class "" [ "lstas_fpbg" ]                  class "" [ "lstas_fpbg" ]                 * ]
+  [ class "" [ "lpxs_fpbg" ]                   class "" [ "lpxs_fpbg" ]                  * ]
+  [ class "" [ "fsb" ]                         class "" [ "fsb" ]                        * ]
+  [ class "" [ "fsb_ind_alt" ]                 class "" [ "fsb_ind_alt" ]                * ]
+  [ class "" [ "fsb_inv_csx" ]                 class "" [ "fsb_inv_csx" ]                * ]
+  [ class "" [ "fsba" ]                        class "" [ "fsba" ]                       * ]
+  [ class "" [ "fsba_ind_alt" ]                class "" [ "fsba_ind_alt" ]               * ]
+  [ class "" [ "fsba_fpbs_trans" ]             class "" [ "fsba_fpbs_trans" ]            * ]
+  [ class "" [ "fsb_fsba" ]                    class "" [ "fsb_fsba" ]                   * ]
+  [ class "" [ "fsba_inv_fsb" ]                class "" [ "fsba_inv_fsb" ]               * ]
+  [ class "" [ "fsb_fpbs_trans" ]              class "" [ "fsb_fpbs_trans" ]             * ]
+  [ class "" [ "fsb_ind_fpbg" ]                class "" [ "fsb_ind_fpbg" ]               * ]
+  [ class "" [ "lpxs_trans" ]                  class "" [ "lpxs_trans" ]                 * ]
+  [ class "" [ "lsx" ]                         class "" [ "lsx" ]                        * ]
+  [ class "" [ "lsx_ind" ]                     class "" [ "lsx_ind" ]                    * ]
+  [ class "" [ "lsx_intro" ]                   class "" [ "lsx_intro" ]                  * ]
+  [ class "" [ "lsx_atom" ]                    class "" [ "lsx_atom" ]                   * ]
+  [ class "" [ "lsx_sort" ]                    class "" [ "lsx_sort" ]                   * ]
+  [ class "" [ "lsx_gref" ]                    class "" [ "lsx_gref" ]                   * ]
+  [ class "" [ "lsx_ge_up" ]                   class "" [ "lsx_ge_up" ]                  * ]
+  [ class "" [ "lsx_ge" ]                      class "" [ "lsx_ge" ]                     * ]
+  [ class "" [ "lsx_fwd_bind_sn" ]             class "" [ "lsx_fwd_bind_sn" ]            * ]
+  [ class "" [ "lsx_fwd_flat_sn" ]             class "" [ "lsx_fwd_flat_sn" ]            * ]
+  [ class "" [ "lsx_fwd_flat_dx" ]             class "" [ "lsx_fwd_flat_dx" ]            * ]
+  [ class "" [ "lsx_fwd_pair_sn" ]             class "" [ "lsx_fwd_pair_sn" ]            * ]
+  [ class "" [ "lsx_inv_flat" ]                class "" [ "lsx_inv_flat" ]               * ]
+  [ class "" [ "lsxa" ]                        class "" [ "lsxa" ]                       * ]
+  [ class "" [ "lsxa_ind" ]                    class "" [ "lsxa_ind" ]                   * ]
+  [ class "" [ "lsxa_intro" ]                  class "" [ "lsxa_intro" ]                 * ]
+  [ class "" [ "lsxa_intro_aux" ]              class "" [ "lsxa_intro_aux" ]             * ]
+  [ class "" [ "lsxa_lleq_trans" ]             class "" [ "lsxa_lleq_trans" ]            * ]
+  [ class "" [ "lsxa_lpxs_trans" ]             class "" [ "lsxa_lpxs_trans" ]            * ]
+  [ class "" [ "lsxa_intro_lpx" ]              class "" [ "lsxa_intro_lpx" ]             * ]
+  [ class "" [ "lsx_lsxa" ]                    class "" [ "lsx_lsxa" ]                   * ]
+  [ class "" [ "lsxa_inv_lsx" ]                class "" [ "lsxa_inv_lsx" ]               * ]
+  [ class "" [ "lsx_intro_alt" ]               class "" [ "lsx_intro_alt" ]              * ]
+  [ class "" [ "lsx_lpxs_trans" ]              class "" [ "lsx_lpxs_trans" ]             * ]
+  [ class "" [ "lsx_ind_alt" ]                 class "" [ "lsx_ind_alt" ]                * ]
+  [ class "" [ "lsx_bind_lpxs_aux" ]           class "" [ "lsx_bind_lpxs_aux" ]          * ]
+  [ class "" [ "lsx_bind" ]                    class "" [ "lsx_bind" ]                   * ]
+  [ class "" [ "lsx_flat_lpxs" ]               class "" [ "lsx_flat_lpxs" ]              * ]
+  [ class "" [ "lsx_flat" ]                    class "" [ "lsx_flat" ]                   * ]
+  [ class "" [ "tsts" ]                        class "" [ "tsts" ]                       * ]
+  [ class "" [ "tsts_inv_atom1_aux" ]          class "" [ "tsts_inv_atom1_aux" ]         * ]
+  [ class "" [ "tsts_inv_atom1" ]              class "" [ "tsts_inv_atom1" ]             * ]
+  [ class "" [ "tsts_inv_pair1_aux" ]          class "" [ "tsts_inv_pair1_aux" ]         * ]
+  [ class "" [ "tsts_inv_pair1" ]              class "" [ "tsts_inv_pair1" ]             * ]
+  [ class "" [ "tsts_inv_atom2_aux" ]          class "" [ "tsts_inv_atom2_aux" ]         * ]
+  [ class "" [ "tsts_inv_atom2" ]              class "" [ "tsts_inv_atom2" ]             * ]
+  [ class "" [ "tsts_inv_pair2_aux" ]          class "" [ "tsts_inv_pair2_aux" ]         * ]
+  [ class "" [ "tsts_inv_pair2" ]              class "" [ "tsts_inv_pair2" ]             * ]
+  [ class "" [ "tsts_refl" ]                   class "" [ "tsts_refl" ]                  * ]
+  [ class "" [ "tsts_sym" ]                    class "" [ "tsts_sym" ]                   * ]
+  [ class "" [ "tsts_dec" ]                    class "" [ "tsts_dec" ]                   * ]
+  [ class "" [ "simple_tsts_repl_dx" ]         class "" [ "simple_tsts_repl_dx" ]        * ]
+  [ class "" [ "simple_tsts_repl_sn" ]         class "" [ "simple_tsts_repl_sn" ]        * ]
+  [ class "" [ "tsts_trans" ]                  class "" [ "tsts_trans" ]                 * ]
+  [ class "" [ "tsts_canc_sn" ]                class "" [ "tsts_canc_sn" ]               * ]
+  [ class "" [ "tsts_canc_dx" ]                class "" [ "tsts_canc_dx" ]               * ]
+  [ class "" [ "csxa" ]                        class "" [ "csxa" ]                       * ]
+  [ class "" [ "csxa_ind" ]                    class "" [ "csxa_ind" ]                   * ]
+  [ class "" [ "csx_intro_cpxs" ]              class "" [ "csx_intro_cpxs" ]             * ]
+  [ class "" [ "csxa_intro" ]                  class "" [ "csxa_intro" ]                 * ]
+  [ class "" [ "csxa_intro_aux" ]              class "" [ "csxa_intro_aux" ]             * ]
+  [ class "" [ "csxa_cpxs_trans" ]             class "" [ "csxa_cpxs_trans" ]            * ]
+  [ class "" [ "csxa_intro_cpx" ]              class "" [ "csxa_intro_cpx" ]             * ]
+  [ class "" [ "csx_csxa" ]                    class "" [ "csx_csxa" ]                   * ]
+  [ class "" [ "csxa_csx" ]                    class "" [ "csxa_csx" ]                   * ]
+  [ class "" [ "csx_cpxs_trans" ]              class "" [ "csx_cpxs_trans" ]             * ]
+  [ class "" [ "csx_ind_alt" ]                 class "" [ "csx_ind_alt" ]                * ]
+  [ class "" [ "nf" ]                          class "" [ "nf" ]                         * ]
+  [ class "" [ "candidate" ]                   class "" [ "candidate" ]                  * ]
+  [ class "" [ "CP0" ]                         class "" [ "CP0" ]                        * ]
+  [ class "" [ "CP1" ]                         class "" [ "CP1" ]                        * ]
+  [ class "" [ "CP2" ]                         class "" [ "CP2" ]                        * ]
+  [ class "" [ "CP3" ]                         class "" [ "CP3" ]                        * ]
+  [ class "" [ "gcp" ]                         class "" [ "gcp" ]                        * ]
+  [ class "" [ "gcp0_lifts" ]                  class "" [ "gcp0_lifts" ]                 * ]
+  [ class "" [ "gcp2_lifts" ]                  class "" [ "gcp2_lifts" ]                 * ]
+  [ class "" [ "gcp2_lifts_all" ]              class "" [ "gcp2_lifts_all" ]             * ]
+  [ class "" [ "csx_lift" ]                    class "" [ "csx_lift" ]                   * ]
+  [ class "" [ "csx_inv_lift" ]                class "" [ "csx_inv_lift" ]               * ]
+  [ class "" [ "csx_inv_lref_bind" ]           class "" [ "csx_inv_lref_bind" ]          * ]
+  [ class "" [ "csx_lref_bind" ]               class "" [ "csx_lref_bind" ]              * ]
+  [ class "" [ "csx_appl_simple" ]             class "" [ "csx_appl_simple" ]            * ]
+  [ class "" [ "csx_fqu_conf" ]                class "" [ "csx_fqu_conf" ]               * ]
+  [ class "" [ "csx_fquq_conf" ]               class "" [ "csx_fquq_conf" ]              * ]
+  [ class "" [ "csx_fqup_conf" ]               class "" [ "csx_fqup_conf" ]              * ]
+  [ class "" [ "csx_fqus_conf" ]               class "" [ "csx_fqus_conf" ]              * ]
+  [ class "" [ "csx_gcp" ]                     class "" [ "csx_gcp" ]                    * ]
+  [ class "" [ "csx_lpx_conf" ]                class "" [ "csx_lpx_conf" ]               * ]
+  [ class "" [ "csx_abst" ]                    class "" [ "csx_abst" ]                   * ]
+  [ class "" [ "csx_abbr" ]                    class "" [ "csx_abbr" ]                   * ]
+  [ class "" [ "csx_appl_beta_aux" ]           class "" [ "csx_appl_beta_aux" ]          * ]
+  [ class "" [ "csx_appl_beta" ]               class "" [ "csx_appl_beta" ]              * ]
+  [ class "" [ "csx_appl_theta_aux" ]          class "" [ "csx_appl_theta_aux" ]         * ]
+  [ class "" [ "csx_appl_theta" ]              class "" [ "csx_appl_theta" ]             * ]
+  [ class "" [ "csx_appl_simple_tsts" ]        class "" [ "csx_appl_simple_tsts" ]       * ]
+  [ class "" [ "csx_lpxs_conf" ]               class "" [ "csx_lpxs_conf" ]              * ]
+  [ class "" [ "lsx_lref_free" ]               class "" [ "lsx_lref_free" ]              * ]
+  [ class "" [ "lsx_lref_skip" ]               class "" [ "lsx_lref_skip" ]              * ]
+  [ class "" [ "lsx_fwd_lref_be" ]             class "" [ "lsx_fwd_lref_be" ]            * ]
+  [ class "" [ "lsx_lift_le" ]                 class "" [ "lsx_lift_le" ]                * ]
+  [ class "" [ "lsx_lift_ge" ]                 class "" [ "lsx_lift_ge" ]                * ]
+  [ class "" [ "lsx_inv_lift_le" ]             class "" [ "lsx_inv_lift_le" ]            * ]
+  [ class "" [ "lsx_inv_lift_be" ]             class "" [ "lsx_inv_lift_be" ]            * ]
+  [ class "" [ "lsx_inv_lift_ge" ]             class "" [ "lsx_inv_lift_ge" ]            * ]
+  [ class "" [ "lsx_lleq_trans" ]              class "" [ "lsx_lleq_trans" ]             * ]
+  [ class "" [ "lsx_lpx_trans" ]               class "" [ "lsx_lpx_trans" ]              * ]
+  [ class "" [ "lsx_lreq_conf" ]               class "" [ "lsx_lreq_conf" ]              * ]
+  [ class "" [ "lsx_fwd_bind_dx" ]             class "" [ "lsx_fwd_bind_dx" ]            * ]
+  [ class "" [ "lsx_inv_bind" ]                class "" [ "lsx_inv_bind" ]               * ]
+  [ class "" [ "lcosx" ]                       class "" [ "lcosx" ]                      * ]
+  [ class "" [ "lcosx_O" ]                     class "" [ "lcosx_O" ]                    * ]
+  [ class "" [ "lcosx_drop_trans_lt" ]         class "" [ "lcosx_drop_trans_lt" ]        * ]
+  [ class "" [ "lcosx_inv_succ_aux" ]          class "" [ "lcosx_inv_succ_aux" ]         * ]
+  [ class "" [ "lcosx_inv_succ" ]              class "" [ "lcosx_inv_succ" ]             * ]
+  [ class "" [ "lcosx_inv_pair" ]              class "" [ "lcosx_inv_pair" ]             * ]
+  [ class "" [ "lsx_cpx_trans_lcosx" ]         class "" [ "lsx_cpx_trans_lcosx" ]        * ]
+  [ class "" [ "lsx_cpx_trans_O" ]             class "" [ "lsx_cpx_trans_O" ]            * ]
+  [ class "" [ "lsx_lref_be_lpxs" ]            class "" [ "lsx_lref_be_lpxs" ]           * ]
+  [ class "" [ "lsx_lref_be" ]                 class "" [ "lsx_lref_be" ]                * ]
+  [ class "" [ "csx_lsx" ]                     class "" [ "csx_lsx" ]                    * ]
+  [ class "" [ "fpbs_aaa_conf" ]               class "" [ "fpbs_aaa_conf" ]              * ]
+  [ class "" [ "at_mono" ]                     class "" [ "at_mono" ]                    * ]
+  [ class "" [ "lifts_lift_trans_le" ]         class "" [ "lifts_lift_trans_le" ]        * ]
+  [ class "" [ "lifts_lift_trans" ]            class "" [ "lifts_lift_trans" ]           * ]
   [ class "" [ "liftsv_liftv_trans_le" ]       class "" [ "liftsv_liftv_trans_le" ]      * ]
-  [ class "" [ "drops_drop_trans" ]           class "" [ "drops_drop_trans" ]           * ]
-  [ class "" [ "S1" ]                         class "" [ "S1" ]                         * ]
-  [ class "" [ "S2" ]                         class "" [ "S2" ]                         * ]
-  [ class "" [ "S3" ]                         class "" [ "S3" ]                         * ]
-  [ class "" [ "S4" ]                         class "" [ "S4" ]                         * ]
-  [ class "" [ "S5" ]                         class "" [ "S5" ]                         * ]
-  [ class "" [ "S6" ]                         class "" [ "S6" ]                         * ]
-  [ class "" [ "S7" ]                         class "" [ "S7" ]                         * ]
-  [ class "" [ "gcr" ]                        class "" [ "gcr" ]                        * ]
-  [ class "" [ "cfun" ]                               class "" [ "cfun" ]                       * ]
-  [ class "" [ "acr" ]                        class "" [ "acr" ]                        * ]
-  [ class "" [ "gcr_lift" ]                   class "" [ "gcr_lift" ]                   * ]
-  [ class "" [ "gcr_lifts" ]                  class "" [ "gcr_lifts" ]                  * ]
-  [ class "" [ "acr_gcr" ]                    class "" [ "acr_gcr" ]                    * ]
-  [ class "" [ "acr_abst" ]                   class "" [ "acr_abst" ]                   * ]
-  [ class "" [ "cpxs_fwd_cnx" ]                       class "" [ "cpxs_fwd_cnx" ]               * ]
-  [ class "" [ "cpxs_fwd_sort" ]              class "" [ "cpxs_fwd_sort" ]              * ]
-  [ class "" [ "cpxs_fwd_beta" ]              class "" [ "cpxs_fwd_beta" ]              * ]
-  [ class "" [ "cpxs_fwd_delta" ]             class "" [ "cpxs_fwd_delta" ]             * ]
-  [ class "" [ "cpxs_fwd_theta" ]             class "" [ "cpxs_fwd_theta" ]             * ]
-  [ class "" [ "cpxs_fwd_cast" ]              class "" [ "cpxs_fwd_cast" ]              * ]
-  [ class "" [ "lleq_cpxs_trans" ]            class "" [ "lleq_cpxs_trans" ]            * ]
-  [ class "" [ "cpxs_lleq_conf" ]             class "" [ "cpxs_lleq_conf" ]             * ]
-  [ class "" [ "cpxs_lleq_conf_dx" ]          class "" [ "cpxs_lleq_conf_dx" ]          * ]
-  [ class "" [ "cpxs_lleq_conf_sn" ]          class "" [ "cpxs_lleq_conf_sn" ]          * ]
-  [ class "" [ "lprs_drop_conf" ]             class "" [ "lprs_drop_conf" ]             * ]
-  [ class "" [ "drop_lprs_trans" ]            class "" [ "drop_lprs_trans" ]            * ]
-  [ class "" [ "lprs_drop_trans_O1" ]         class "" [ "lprs_drop_trans_O1" ]         * ]
-  [ class "" [ "fpbg_trans" ]                 class "" [ "fpbg_trans" ]                 * ]
-  [ class "" [ "scpds_lift" ]                 class "" [ "scpds_lift" ]                 * ]
-  [ class "" [ "scpds_inv_lift1" ]            class "" [ "scpds_inv_lift1" ]            * ]
-  [ class "" [ "lifts_trans" ]                class "" [ "lifts_trans" ]                * ]
-  [ class "" [ "drops_trans" ]                class "" [ "drops_trans" ]                * ]
-  [ class "" [ "lsubc" ]                      class "" [ "lsubc" ]                      * ]
-  [ class "" [ "lsubc_inv_atom1_aux" ]        class "" [ "lsubc_inv_atom1_aux" ]        * ]
-  [ class "" [ "lsubc_inv_atom1" ]            class "" [ "lsubc_inv_atom1" ]            * ]
-  [ class "" [ "lsubc_inv_pair1_aux" ]        class "" [ "lsubc_inv_pair1_aux" ]        * ]
-  [ class "" [ "lsubc_inv_pair1" ]            class "" [ "lsubc_inv_pair1" ]            * ]
-  [ class "" [ "lsubc_inv_atom2_aux" ]        class "" [ "lsubc_inv_atom2_aux" ]        * ]
-  [ class "" [ "lsubc_inv_atom2" ]            class "" [ "lsubc_inv_atom2" ]            * ]
-  [ class "" [ "lsubc_inv_pair2_aux" ]        class "" [ "lsubc_inv_pair2_aux" ]        * ]
-  [ class "" [ "lsubc_inv_pair2" ]            class "" [ "lsubc_inv_pair2" ]            * ]
-  [ class "" [ "lsubc_fwd_lsubr" ]            class "" [ "lsubc_fwd_lsubr" ]            * ]
-  [ class "" [ "lsubc_refl" ]                 class "" [ "lsubc_refl" ]                 * ]
-  [ class "" [ "lsubc_drop_O1_trans" ]        class "" [ "lsubc_drop_O1_trans" ]        * ]
-  [ class "" [ "drop_lsubc_trans" ]           class "" [ "drop_lsubc_trans" ]           * ]
-  [ class "" [ "drops_lsubc_trans" ]          class "" [ "drops_lsubc_trans" ]          * ]
-  [ class "" [ "acr_aaa_csubc_lifts" ]        class "" [ "acr_aaa_csubc_lifts" ]        * ]
-  [ class "" [ "acr_aaa" ]                    class "" [ "acr_aaa" ]                    * ]
-  [ class "" [ "gcr_aaa" ]                    class "" [ "gcr_aaa" ]                    * ]
+  [ class "" [ "drops_drop_trans" ]            class "" [ "drops_drop_trans" ]           * ]
+  [ class "" [ "S1" ]                          class "" [ "S1" ]                         * ]
+  [ class "" [ "S2" ]                          class "" [ "S2" ]                         * ]
+  [ class "" [ "S3" ]                          class "" [ "S3" ]                         * ]
+  [ class "" [ "S4" ]                          class "" [ "S4" ]                         * ]
+  [ class "" [ "S5" ]                          class "" [ "S5" ]                         * ]
+  [ class "" [ "S6" ]                          class "" [ "S6" ]                         * ]
+  [ class "" [ "S7" ]                          class "" [ "S7" ]                         * ]
+  [ class "" [ "gcr" ]                         class "" [ "gcr" ]                        * ]
+  [ class "" [ "cfun" ]                        class "" [ "cfun" ]                       * ]
+  [ class "" [ "acr" ]                         class "" [ "acr" ]                        * ]
+  [ class "" [ "gcr_lift" ]                    class "" [ "gcr_lift" ]                   * ]
+  [ class "" [ "gcr_lifts" ]                   class "" [ "gcr_lifts" ]                  * ]
+  [ class "" [ "acr_gcr" ]                     class "" [ "acr_gcr" ]                    * ]
+  [ class "" [ "acr_abst" ]                    class "" [ "acr_abst" ]                   * ]
+  [ class "" [ "cpxs_fwd_cnx" ]                class "" [ "cpxs_fwd_cnx" ]               * ]
+  [ class "" [ "cpxs_fwd_sort" ]               class "" [ "cpxs_fwd_sort" ]              * ]
+  [ class "" [ "cpxs_fwd_beta" ]               class "" [ "cpxs_fwd_beta" ]              * ]
+  [ class "" [ "cpxs_fwd_delta" ]              class "" [ "cpxs_fwd_delta" ]             * ]
+  [ class "" [ "cpxs_fwd_theta" ]              class "" [ "cpxs_fwd_theta" ]             * ]
+  [ class "" [ "cpxs_fwd_cast" ]               class "" [ "cpxs_fwd_cast" ]              * ]
+  [ class "" [ "lleq_cpxs_trans" ]             class "" [ "lleq_cpxs_trans" ]            * ]
+  [ class "" [ "cpxs_lleq_conf" ]              class "" [ "cpxs_lleq_conf" ]             * ]
+  [ class "" [ "cpxs_lleq_conf_dx" ]           class "" [ "cpxs_lleq_conf_dx" ]          * ]
+  [ class "" [ "cpxs_lleq_conf_sn" ]           class "" [ "cpxs_lleq_conf_sn" ]          * ]
+  [ class "" [ "lprs_drop_conf" ]              class "" [ "lprs_drop_conf" ]             * ]
+  [ class "" [ "drop_lprs_trans" ]             class "" [ "drop_lprs_trans" ]            * ]
+  [ class "" [ "lprs_drop_trans_O1" ]          class "" [ "lprs_drop_trans_O1" ]         * ]
+  [ class "" [ "fpbg_trans" ]                  class "" [ "fpbg_trans" ]                 * ]
+  [ class "" [ "scpds_lift" ]                  class "" [ "scpds_lift" ]                 * ]
+  [ class "" [ "scpds_inv_lift1" ]             class "" [ "scpds_inv_lift1" ]            * ]
+  [ class "" [ "lifts_trans" ]                 class "" [ "lifts_trans" ]                * ]
+  [ class "" [ "drops_trans" ]                 class "" [ "drops_trans" ]                * ]
+  [ class "" [ "lsubc" ]                       class "" [ "lsubc" ]                      * ]
+  [ class "" [ "lsubc_inv_atom1_aux" ]         class "" [ "lsubc_inv_atom1_aux" ]        * ]
+  [ class "" [ "lsubc_inv_atom1" ]             class "" [ "lsubc_inv_atom1" ]            * ]
+  [ class "" [ "lsubc_inv_pair1_aux" ]         class "" [ "lsubc_inv_pair1_aux" ]        * ]
+  [ class "" [ "lsubc_inv_pair1" ]             class "" [ "lsubc_inv_pair1" ]            * ]
+  [ class "" [ "lsubc_inv_atom2_aux" ]         class "" [ "lsubc_inv_atom2_aux" ]        * ]
+  [ class "" [ "lsubc_inv_atom2" ]             class "" [ "lsubc_inv_atom2" ]            * ]
+  [ class "" [ "lsubc_inv_pair2_aux" ]         class "" [ "lsubc_inv_pair2_aux" ]        * ]
+  [ class "" [ "lsubc_inv_pair2" ]             class "" [ "lsubc_inv_pair2" ]            * ]
+  [ class "" [ "lsubc_fwd_lsubr" ]             class "" [ "lsubc_fwd_lsubr" ]            * ]
+  [ class "" [ "lsubc_refl" ]                  class "" [ "lsubc_refl" ]                 * ]
+  [ class "" [ "lsubc_drop_O1_trans" ]         class "" [ "lsubc_drop_O1_trans" ]        * ]
+  [ class "" [ "drop_lsubc_trans" ]            class "" [ "drop_lsubc_trans" ]           * ]
+  [ class "" [ "drops_lsubc_trans" ]           class "" [ "drops_lsubc_trans" ]          * ]
+  [ class "" [ "acr_aaa_csubc_lifts" ]         class "" [ "acr_aaa_csubc_lifts" ]        * ]
+  [ class "" [ "acr_aaa" ]                     class "" [ "acr_aaa" ]                    * ]
+  [ class "" [ "gcr_aaa" ]                     class "" [ "gcr_aaa" ]                    * ]
   [ class "" [ "tsts_inv_bind_applv_simple" ]  class "" [ "tsts_inv_bind_applv_simple" ] * ]
-  [ class "" [ "cpxs_fwd_cnx_vector" ]        class "" [ "cpxs_fwd_cnx_vector" ]        * ]
-  [ class "" [ "cpxs_fwd_sort_vector" ]               class "" [ "cpxs_fwd_sort_vector" ]       * ]
-  [ class "" [ "cpxs_fwd_beta_vector" ]               class "" [ "cpxs_fwd_beta_vector" ]       * ]
+  [ class "" [ "cpxs_fwd_cnx_vector" ]         class "" [ "cpxs_fwd_cnx_vector" ]        * ]
+  [ class "" [ "cpxs_fwd_sort_vector" ]        class "" [ "cpxs_fwd_sort_vector" ]       * ]
+  [ class "" [ "cpxs_fwd_beta_vector" ]        class "" [ "cpxs_fwd_beta_vector" ]       * ]
   [ class "" [ "cpxs_fwd_delta_vector" ]       class "" [ "cpxs_fwd_delta_vector" ]      * ]
   [ class "" [ "cpxs_fwd_theta_vector" ]       class "" [ "cpxs_fwd_theta_vector" ]      * ]
-  [ class "" [ "cpxs_fwd_cast_vector" ]               class "" [ "cpxs_fwd_cast_vector" ]       * ]
-  [ class "" [ "csxv" ]                               class "" [ "csxv" ]                       * ]
-  [ class "" [ "csxv_inv_cons" ]              class "" [ "csxv_inv_cons" ]              * ]
-  [ class "" [ "csx_fwd_applv" ]              class "" [ "csx_fwd_applv" ]              * ]
-  [ class "" [ "csx_applv_cnx" ]              class "" [ "csx_applv_cnx" ]              * ]
-  [ class "" [ "csx_applv_sort" ]             class "" [ "csx_applv_sort" ]             * ]
-  [ class "" [ "csx_applv_beta" ]             class "" [ "csx_applv_beta" ]             * ]
-  [ class "" [ "csx_applv_delta" ]            class "" [ "csx_applv_delta" ]            * ]
-  [ class "" [ "csx_applv_theta" ]            class "" [ "csx_applv_theta" ]            * ]
-  [ class "" [ "csx_applv_cast" ]             class "" [ "csx_applv_cast" ]             * ]
-  [ class "" [ "csx_gcr" ]                    class "" [ "csx_gcr" ]                    * ]
-  [ class "" [ "aaa_csx" ]                    class "" [ "aaa_csx" ]                    * ]
-  [ class "" [ "aaa_ind_csx_aux" ]            class "" [ "aaa_ind_csx_aux" ]            * ]
-  [ class "" [ "aaa_ind_csx" ]                class "" [ "aaa_ind_csx" ]                * ]
-  [ class "" [ "aaa_ind_csx_alt_aux" ]        class "" [ "aaa_ind_csx_alt_aux" ]        * ]
-  [ class "" [ "aaa_ind_csx_alt" ]            class "" [ "aaa_ind_csx_alt" ]            * ]
-  [ class "" [ "lprs_strip" ]                 class "" [ "lprs_strip" ]                 * ]
-  [ class "" [ "lprs_conf" ]                  class "" [ "lprs_conf" ]                  * ]
-  [ class "" [ "lprs_trans" ]                 class "" [ "lprs_trans" ]                 * ]
-  [ class "" [ "fpbsa" ]                      class "" [ "fpbsa" ]                      * ]
-  [ class "" [ "fpb_fpbsa_trans" ]            class "" [ "fpb_fpbsa_trans" ]            * ]
-  [ class "" [ "fpbs_fpbsa" ]                 class "" [ "fpbs_fpbsa" ]                 * ]
-  [ class "" [ "fpbsa_inv_fpbs" ]             class "" [ "fpbsa_inv_fpbs" ]             * ]
-  [ class "" [ "fpbs_intro_alt" ]             class "" [ "fpbs_intro_alt" ]             * ]
-  [ class "" [ "fpbs_inv_alt" ]                       class "" [ "fpbs_inv_alt" ]               * ]
-  [ class "" [ "fpbs_cpx_trans_neq" ]         class "" [ "fpbs_cpx_trans_neq" ]         * ]
-  [ class "" [ "fpb_fpbs" ]                   class "" [ "fpb_fpbs" ]                   * ]
-  [ class "" [ "csx_fpb_conf" ]                       class "" [ "csx_fpb_conf" ]               * ]
-  [ class "" [ "csx_fpbs_conf" ]              class "" [ "csx_fpbs_conf" ]              * ]
-  [ class "" [ "csx_fsb_fpbs" ]                       class "" [ "csx_fsb_fpbs" ]               * ]
-  [ class "" [ "csx_fsb" ]                    class "" [ "csx_fsb" ]                    * ]
-  [ class "" [ "csx_ind_fpb" ]                class "" [ "csx_ind_fpb" ]                * ]
-  [ class "" [ "csx_ind_fpbg" ]                       class "" [ "csx_ind_fpbg" ]               * ]
-  [ class "" [ "aaa_fsb" ]                    class "" [ "aaa_fsb" ]                    * ]
-  [ class "" [ "aaa_fsba" ]                   class "" [ "aaa_fsba" ]                   * ]
-  [ class "" [ "aaa_ind_fpb_aux" ]            class "" [ "aaa_ind_fpb_aux" ]            * ]
-  [ class "" [ "aaa_ind_fpb" ]                class "" [ "aaa_ind_fpb" ]                * ]
-  [ class "" [ "aaa_ind_fpbg_aux" ]           class "" [ "aaa_ind_fpbg_aux" ]           * ]
-  [ class "" [ "aaa_ind_fpbg" ]                       class "" [ "aaa_ind_fpbg" ]               * ]
-  [ class "" [ "cpxe" ]                               class "" [ "cpxe" ]                       * ]
-  [ class "" [ "csx_cpxe" ]                   class "" [ "csx_cpxe" ]                   * ]
-  [ class "" [ "lpxs_aaa_conf" ]              class "" [ "lpxs_aaa_conf" ]              * ]
-  [ class "" [ "lprs_aaa_conf" ]              class "" [ "lprs_aaa_conf" ]              * ]
-  [ class "" [ "lsuba_lsubc" ]                class "" [ "lsuba_lsubc" ]                * ]
-  [ class "" [ "ApplDelta" ]                  class "" [ "ApplDelta" ]                  * ]
-  [ class "" [ "ApplOmega1" ]                 class "" [ "ApplOmega1" ]                 * ]
-  [ class "" [ "ApplOmega2" ]                 class "" [ "ApplOmega2" ]                 * ]
-  [ class "" [ "ApplOmega3" ]                 class "" [ "ApplOmega3" ]                 * ]
-  [ class "" [ "ApplDelta_lift" ]             class "" [ "ApplDelta_lift" ]             * ]
-  [ class "" [ "cpr_ApplOmega_12" ]           class "" [ "cpr_ApplOmega_12" ]           * ]
-  [ class "" [ "cpr_ApplOmega_23" ]           class "" [ "cpr_ApplOmega_23" ]           * ]
-  [ class "" [ "cpxs_ApplOmega_13" ]          class "" [ "cpxs_ApplOmega_13" ]          * ]
-  [ class "" [ "fqup_ApplOmega_13" ]          class "" [ "fqup_ApplOmega_13" ]          * ]
-  [ class "" [ "fpbg_refl" ]                  class "" [ "fpbg_refl" ]                  * ]
-  [ class "" [ "Delta" ]                      class "" [ "Delta" ]                      * ]
-  [ class "" [ "Omega1" ]                     class "" [ "Omega1" ]                     * ]
-  [ class "" [ "Omega2" ]                     class "" [ "Omega2" ]                     * ]
-  [ class "" [ "Delta_lift" ]                 class "" [ "Delta_lift" ]                 * ]
-  [ class "" [ "cpr_Omega_12" ]                       class "" [ "cpr_Omega_12" ]               * ]
-  [ class "" [ "cpr_Omega_21" ]                       class "" [ "cpr_Omega_21" ]               * ]
-  [ class "" [ "sta_ldec" ]                   class "" [ "sta_ldec" ]                   * ]
-  [ class "" [ "snv" ]                        class "" [ "snv" ]                        * ]
-  [ class "" [ "snv_inv_lref_aux" ]           class "" [ "snv_inv_lref_aux" ]           * ]
-  [ class "" [ "snv_inv_lref" ]                       class "" [ "snv_inv_lref" ]               * ]
-  [ class "" [ "snv_inv_gref_aux" ]           class "" [ "snv_inv_gref_aux" ]           * ]
-  [ class "" [ "snv_inv_gref" ]                       class "" [ "snv_inv_gref" ]               * ]
-  [ class "" [ "snv_inv_bind_aux" ]           class "" [ "snv_inv_bind_aux" ]           * ]
-  [ class "" [ "snv_inv_bind" ]                       class "" [ "snv_inv_bind" ]               * ]
-  [ class "" [ "snv_inv_appl_aux" ]           class "" [ "snv_inv_appl_aux" ]           * ]
-  [ class "" [ "snv_inv_appl" ]                       class "" [ "snv_inv_appl" ]               * ]
-  [ class "" [ "snv_inv_cast_aux" ]           class "" [ "snv_inv_cast_aux" ]           * ]
-  [ class "" [ "snv_inv_cast" ]                       class "" [ "snv_inv_cast" ]               * ]
-  [ class "" [ "snv_extended" ]                       class "" [ "snv_extended" ]               * ]
-  [ class "" [ "snv_restricted" ]             class "" [ "snv_restricted" ]             * ]
-  [ class "" [ "snv_fwd_aaa" ]                class "" [ "snv_fwd_aaa" ]                * ]
-  [ class "" [ "snv_fwd_da" ]                 class "" [ "snv_fwd_da" ]                 * ]
-  [ class "" [ "snv_fwd_lstas" ]              class "" [ "snv_fwd_lstas" ]              * ]
-  [ class "" [ "snv_fwd_fsb" ]                class "" [ "snv_fwd_fsb" ]                * ]
-  [ class "" [ "snv_lift" ]                   class "" [ "snv_lift" ]                   * ]
-  [ class "" [ "snv_inv_lift" ]                       class "" [ "snv_inv_lift" ]               * ]
-  [ class "" [ "snv_fqu_conf" ]                       class "" [ "snv_fqu_conf" ]               * ]
-  [ class "" [ "snv_fquq_conf" ]              class "" [ "snv_fquq_conf" ]              * ]
-  [ class "" [ "snv_fqup_conf" ]              class "" [ "snv_fqup_conf" ]              * ]
-  [ class "" [ "snv_fqus_conf" ]              class "" [ "snv_fqus_conf" ]              * ]
-  [ class "" [ "IH_snv_cpr_lpr" ]             class "" [ "IH_snv_cpr_lpr" ]             * ]
-  [ class "" [ "IH_da_cpr_lpr" ]              class "" [ "IH_da_cpr_lpr" ]              * ]
-  [ class "" [ "IH_lstas_cpr_lpr" ]           class "" [ "IH_lstas_cpr_lpr" ]           * ]
-  [ class "" [ "IH_snv_lstas" ]                       class "" [ "IH_snv_lstas" ]               * ]
-  [ class "" [ "snv_cprs_lpr_aux" ]           class "" [ "snv_cprs_lpr_aux" ]           * ]
-  [ class "" [ "da_cprs_lpr_aux" ]            class "" [ "da_cprs_lpr_aux" ]            * ]
-  [ class "" [ "da_scpds_lpr_aux" ]           class "" [ "da_scpds_lpr_aux" ]           * ]
-  [ class "" [ "da_scpes_aux" ]                       class "" [ "da_scpes_aux" ]               * ]
-  [ class "" [ "lstas_cprs_lpr_aux" ]         class "" [ "lstas_cprs_lpr_aux" ]         * ]
-  [ class "" [ "scpds_cpr_lpr_aux" ]          class "" [ "scpds_cpr_lpr_aux" ]          * ]
-  [ class "" [ "scpes_cpr_lpr_aux" ]          class "" [ "scpes_cpr_lpr_aux" ]          * ]
-  [ class "" [ "lstas_scpds_aux" ]            class "" [ "lstas_scpds_aux" ]            * ]
-  [ class "" [ "scpes_le_aux" ]                       class "" [ "scpes_le_aux" ]               * ]
-  [ class "" [ "snv_cast_scpes" ]             class "" [ "snv_cast_scpes" ]             * ]
-  [ class "" [ "shnv" ]                               class "" [ "shnv" ]                       * ]
-  [ class "" [ "shnv_inv_cast_aux" ]          class "" [ "shnv_inv_cast_aux" ]          * ]
-  [ class "" [ "shnv_inv_cast" ]              class "" [ "shnv_inv_cast" ]              * ]
-  [ class "" [ "shnv_inv_snv" ]                       class "" [ "shnv_inv_snv" ]               * ]
-  [ class "" [ "snv_shnv_cast" ]              class "" [ "snv_shnv_cast" ]              * ]
-  [ class "" [ "lsubsv" ]                     class "" [ "lsubsv" ]                     * ]
-  [ class "" [ "lsubsv_inv_atom1_aux" ]               class "" [ "lsubsv_inv_atom1_aux" ]       * ]
-  [ class "" [ "lsubsv_inv_atom1" ]           class "" [ "lsubsv_inv_atom1" ]           * ]
-  [ class "" [ "lsubsv_inv_pair1_aux" ]               class "" [ "lsubsv_inv_pair1_aux" ]       * ]
-  [ class "" [ "lsubsv_inv_pair1" ]           class "" [ "lsubsv_inv_pair1" ]           * ]
-  [ class "" [ "lsubsv_inv_atom2_aux" ]               class "" [ "lsubsv_inv_atom2_aux" ]       * ]
-  [ class "" [ "lsubsv_inv_atom2" ]           class "" [ "lsubsv_inv_atom2" ]           * ]
-  [ class "" [ "lsubsv_inv_pair2_aux" ]               class "" [ "lsubsv_inv_pair2_aux" ]       * ]
-  [ class "" [ "lsubsv_inv_pair2" ]           class "" [ "lsubsv_inv_pair2" ]           * ]
-  [ class "" [ "lsubsv_fwd_lsubr" ]           class "" [ "lsubsv_fwd_lsubr" ]           * ]
-  [ class "" [ "lsubsv_refl" ]                class "" [ "lsubsv_refl" ]                * ]
-  [ class "" [ "lsubsv_cprs_trans" ]          class "" [ "lsubsv_cprs_trans" ]          * ]
-  [ class "" [ "lsubsv_drop_O1_conf" ]        class "" [ "lsubsv_drop_O1_conf" ]        * ]
-  [ class "" [ "lsubsv_drop_O1_trans" ]               class "" [ "lsubsv_drop_O1_trans" ]       * ]
-  [ class "" [ "lsubsv_fwd_lsubd" ]           class "" [ "lsubsv_fwd_lsubd" ]           * ]
-  [ class "" [ "lsubsv_lstas_trans" ]         class "" [ "lsubsv_lstas_trans" ]         * ]
-  [ class "" [ "lsubsv_sta_trans" ]           class "" [ "lsubsv_sta_trans" ]           * ]
-  [ class "" [ "lsubsv_scpds_trans" ]         class "" [ "lsubsv_scpds_trans" ]         * ]
-  [ class "" [ "lsubsv_snv_trans" ]           class "" [ "lsubsv_snv_trans" ]           * ]
-  [ class "" [ "snv_cpr_lpr_aux" ]            class "" [ "snv_cpr_lpr_aux" ]            * ]
-  [ class "" [ "lstas_cpr_lpr_aux" ]          class "" [ "lstas_cpr_lpr_aux" ]          * ]
-  [ class "" [ "snv_lstas_aux" ]              class "" [ "snv_lstas_aux" ]              * ]
-  [ class "" [ "lsubsv_fwd_lsuba" ]           class "" [ "lsubsv_fwd_lsuba" ]           * ]
-  [ class "" [ "da_cpr_lpr_aux" ]             class "" [ "da_cpr_lpr_aux" ]             * ]
-  [ class "" [ "lsubsv_cpcs_trans" ]          class "" [ "lsubsv_cpcs_trans" ]          * ]
-  [ class "" [ "snv_preserve" ]                       class "" [ "snv_preserve" ]               * ]
-  [ class "" [ "da_cpr_lpr" ]                 class "" [ "da_cpr_lpr" ]                 * ]
-  [ class "" [ "snv_cpr_lpr" ]                class "" [ "snv_cpr_lpr" ]                * ]
-  [ class "" [ "snv_lstas" ]                  class "" [ "snv_lstas" ]                  * ]
-  [ class "" [ "lstas_cpr_lpr" ]              class "" [ "lstas_cpr_lpr" ]              * ]
-  [ class "" [ "snv_cprs_lpr" ]                       class "" [ "snv_cprs_lpr" ]               * ]
-  [ class "" [ "da_cprs_lpr" ]                class "" [ "da_cprs_lpr" ]                * ]
-  [ class "" [ "lstas_cprs_lpr" ]             class "" [ "lstas_cprs_lpr" ]             * ]
-  [ class "" [ "lstas_cpcs_lpr" ]             class "" [ "lstas_cpcs_lpr" ]             * ]
-  [ class "" [ "cpys" ]                               class "" [ "cpys" ]                       * ]
-  [ class "" [ "cpys_ind" ]                   class "" [ "cpys_ind" ]                   * ]
-  [ class "" [ "cpys_ind_dx" ]                class "" [ "cpys_ind_dx" ]                * ]
-  [ class "" [ "cpy_cpys" ]                   class "" [ "cpy_cpys" ]                   * ]
-  [ class "" [ "cpys_strap1" ]                class "" [ "cpys_strap1" ]                * ]
-  [ class "" [ "cpys_strap2" ]                class "" [ "cpys_strap2" ]                * ]
-  [ class "" [ "lsuby_cpys_trans" ]           class "" [ "lsuby_cpys_trans" ]           * ]
-  [ class "" [ "cpys_refl" ]                  class "" [ "cpys_refl" ]                  * ]
-  [ class "" [ "cpys_bind" ]                  class "" [ "cpys_bind" ]                  * ]
-  [ class "" [ "cpys_flat" ]                  class "" [ "cpys_flat" ]                  * ]
-  [ class "" [ "cpys_weak" ]                  class "" [ "cpys_weak" ]                  * ]
-  [ class "" [ "cpys_weak_top" ]              class "" [ "cpys_weak_top" ]              * ]
-  [ class "" [ "cpys_weak_full" ]             class "" [ "cpys_weak_full" ]             * ]
-  [ class "" [ "cpys_fwd_up" ]                class "" [ "cpys_fwd_up" ]                * ]
-  [ class "" [ "cpys_fwd_tw" ]                class "" [ "cpys_fwd_tw" ]                * ]
-  [ class "" [ "cpys_inv_sort1" ]             class "" [ "cpys_inv_sort1" ]             * ]
-  [ class "" [ "cpys_inv_gref1" ]             class "" [ "cpys_inv_gref1" ]             * ]
-  [ class "" [ "cpys_inv_bind1" ]             class "" [ "cpys_inv_bind1" ]             * ]
-  [ class "" [ "cpys_inv_flat1" ]             class "" [ "cpys_inv_flat1" ]             * ]
-  [ class "" [ "cpys_inv_refl_O2" ]           class "" [ "cpys_inv_refl_O2" ]           * ]
-  [ class "" [ "cpys_inv_lift1_eq" ]          class "" [ "cpys_inv_lift1_eq" ]          * ]
-  [ class "" [ "cpys_subst" ]                 class "" [ "cpys_subst" ]                 * ]
-  [ class "" [ "cpys_subst_Y2" ]              class "" [ "cpys_subst_Y2" ]              * ]
-  [ class "" [ "cpys_inv_atom1" ]             class "" [ "cpys_inv_atom1" ]             * ]
-  [ class "" [ "cpys_inv_lref1" ]             class "" [ "cpys_inv_lref1" ]             * ]
-  [ class "" [ "cpys_inv_lref1_Y2" ]          class "" [ "cpys_inv_lref1_Y2" ]          * ]
-  [ class "" [ "cpys_inv_lref1_drop" ]        class "" [ "cpys_inv_lref1_drop" ]        * ]
-  [ class "" [ "cpys_lift_le" ]                       class "" [ "cpys_lift_le" ]               * ]
-  [ class "" [ "cpys_lift_be" ]                       class "" [ "cpys_lift_be" ]               * ]
-  [ class "" [ "cpys_lift_ge" ]                       class "" [ "cpys_lift_ge" ]               * ]
-  [ class "" [ "cpys_inv_lift1_le" ]          class "" [ "cpys_inv_lift1_le" ]          * ]
-  [ class "" [ "cpys_inv_lift1_be" ]          class "" [ "cpys_inv_lift1_be" ]          * ]
-  [ class "" [ "cpys_inv_lift1_ge" ]          class "" [ "cpys_inv_lift1_ge" ]          * ]
-  [ class "" [ "cpys_inv_lift1_ge_up" ]               class "" [ "cpys_inv_lift1_ge_up" ]       * ]
-  [ class "" [ "cpys_inv_lift1_be_up" ]               class "" [ "cpys_inv_lift1_be_up" ]       * ]
-  [ class "" [ "cpys_inv_lift1_le_up" ]               class "" [ "cpys_inv_lift1_le_up" ]       * ]
-  [ class "" [ "cpys_inv_lift1_subst" ]               class "" [ "cpys_inv_lift1_subst" ]       * ]
-  [ class "" [ "cpysa" ]                      class "" [ "cpysa" ]                      * ]
-  [ class "" [ "lsuby_cpysa_trans" ]          class "" [ "lsuby_cpysa_trans" ]          * ]
-  [ class "" [ "cpysa_refl" ]                 class "" [ "cpysa_refl" ]                 * ]
-  [ class "" [ "cpysa_cpy_trans" ]            class "" [ "cpysa_cpy_trans" ]            * ]
-  [ class "" [ "cpys_cpysa" ]                 class "" [ "cpys_cpysa" ]                 * ]
-  [ class "" [ "cpysa_inv_cpys" ]             class "" [ "cpysa_inv_cpys" ]             * ]
-  [ class "" [ "cpys_ind_alt" ]                       class "" [ "cpys_ind_alt" ]               * ]
-  [ class "" [ "cpys_inv_SO2" ]                       class "" [ "cpys_inv_SO2" ]               * ]
-  [ class "" [ "cpys_strip_eq" ]              class "" [ "cpys_strip_eq" ]              * ]
-  [ class "" [ "cpys_strip_neq" ]             class "" [ "cpys_strip_neq" ]             * ]
-  [ class "" [ "cpys_strap1_down" ]           class "" [ "cpys_strap1_down" ]           * ]
-  [ class "" [ "cpys_strap2_down" ]           class "" [ "cpys_strap2_down" ]           * ]
-  [ class "" [ "cpys_split_up" ]              class "" [ "cpys_split_up" ]              * ]
-  [ class "" [ "cpys_inv_lift1_up" ]          class "" [ "cpys_inv_lift1_up" ]          * ]
-  [ class "" [ "cpys_conf_eq" ]                       class "" [ "cpys_conf_eq" ]               * ]
-  [ class "" [ "cpys_conf_neq" ]              class "" [ "cpys_conf_neq" ]              * ]
-  [ class "" [ "cpys_trans_eq" ]              class "" [ "cpys_trans_eq" ]              * ]
-  [ class "" [ "cpys_trans_down" ]            class "" [ "cpys_trans_down" ]            * ]
-  [ class "" [ "cpys_antisym_eq" ]            class "" [ "cpys_antisym_eq" ]            * ]
-  [ class "" [ "llpx_sn_TC_pair_dx" ]         class "" [ "llpx_sn_TC_pair_dx" ]         * ]
-  [ class "" [ "fqup_trans" ]                 class "" [ "fqup_trans" ]                 * ]
-  [ class "" [ "lleq_intro_alt_r" ]           class "" [ "lleq_intro_alt_r" ]           * ]
-  [ class "" [ "lleq_ind_alt_r" ]             class "" [ "lleq_ind_alt_r" ]             * ]
+  [ class "" [ "cpxs_fwd_cast_vector" ]        class "" [ "cpxs_fwd_cast_vector" ]       * ]
+  [ class "" [ "csxv" ]                        class "" [ "csxv" ]                       * ]
+  [ class "" [ "csxv_inv_cons" ]               class "" [ "csxv_inv_cons" ]              * ]
+  [ class "" [ "csx_fwd_applv" ]               class "" [ "csx_fwd_applv" ]              * ]
+  [ class "" [ "csx_applv_cnx" ]               class "" [ "csx_applv_cnx" ]              * ]
+  [ class "" [ "csx_applv_sort" ]              class "" [ "csx_applv_sort" ]             * ]
+  [ class "" [ "csx_applv_beta" ]              class "" [ "csx_applv_beta" ]             * ]
+  [ class "" [ "csx_applv_delta" ]             class "" [ "csx_applv_delta" ]            * ]
+  [ class "" [ "csx_applv_theta" ]             class "" [ "csx_applv_theta" ]            * ]
+  [ class "" [ "csx_applv_cast" ]              class "" [ "csx_applv_cast" ]             * ]
+  [ class "" [ "csx_gcr" ]                     class "" [ "csx_gcr" ]                    * ]
+  [ class "" [ "aaa_csx" ]                     class "" [ "aaa_csx" ]                    * ]
+  [ class "" [ "aaa_ind_csx_aux" ]             class "" [ "aaa_ind_csx_aux" ]            * ]
+  [ class "" [ "aaa_ind_csx" ]                 class "" [ "aaa_ind_csx" ]                * ]
+  [ class "" [ "aaa_ind_csx_alt_aux" ]         class "" [ "aaa_ind_csx_alt_aux" ]        * ]
+  [ class "" [ "aaa_ind_csx_alt" ]             class "" [ "aaa_ind_csx_alt" ]            * ]
+  [ class "" [ "lprs_strip" ]                  class "" [ "lprs_strip" ]                 * ]
+  [ class "" [ "lprs_conf" ]                   class "" [ "lprs_conf" ]                  * ]
+  [ class "" [ "lprs_trans" ]                  class "" [ "lprs_trans" ]                 * ]
+  [ class "" [ "fpbsa" ]                       class "" [ "fpbsa" ]                      * ]
+  [ class "" [ "fpb_fpbsa_trans" ]             class "" [ "fpb_fpbsa_trans" ]            * ]
+  [ class "" [ "fpbs_fpbsa" ]                  class "" [ "fpbs_fpbsa" ]                 * ]
+  [ class "" [ "fpbsa_inv_fpbs" ]              class "" [ "fpbsa_inv_fpbs" ]             * ]
+  [ class "" [ "fpbs_intro_alt" ]              class "" [ "fpbs_intro_alt" ]             * ]
+  [ class "" [ "fpbs_inv_alt" ]                class "" [ "fpbs_inv_alt" ]               * ]
+  [ class "" [ "fpbs_cpx_trans_neq" ]          class "" [ "fpbs_cpx_trans_neq" ]         * ]
+  [ class "" [ "fpb_fpbs" ]                    class "" [ "fpb_fpbs" ]                   * ]
+  [ class "" [ "csx_fpb_conf" ]                class "" [ "csx_fpb_conf" ]               * ]
+  [ class "" [ "csx_fpbs_conf" ]               class "" [ "csx_fpbs_conf" ]              * ]
+  [ class "" [ "csx_fsb_fpbs" ]                class "" [ "csx_fsb_fpbs" ]               * ]
+  [ class "" [ "csx_fsb" ]                     class "" [ "csx_fsb" ]                    * ]
+  [ class "" [ "csx_ind_fpb" ]                 class "" [ "csx_ind_fpb" ]                * ]
+  [ class "" [ "csx_ind_fpbg" ]                class "" [ "csx_ind_fpbg" ]               * ]
+  [ class "" [ "aaa_fsb" ]                     class "" [ "aaa_fsb" ]                    * ]
+  [ class "" [ "aaa_fsba" ]                    class "" [ "aaa_fsba" ]                   * ]
+  [ class "" [ "aaa_ind_fpb_aux" ]             class "" [ "aaa_ind_fpb_aux" ]            * ]
+  [ class "" [ "aaa_ind_fpb" ]                 class "" [ "aaa_ind_fpb" ]                * ]
+  [ class "" [ "aaa_ind_fpbg_aux" ]            class "" [ "aaa_ind_fpbg_aux" ]           * ]
+  [ class "" [ "aaa_ind_fpbg" ]                class "" [ "aaa_ind_fpbg" ]               * ]
+  [ class "" [ "cpxe" ]                        class "" [ "cpxe" ]                       * ]
+  [ class "" [ "csx_cpxe" ]                    class "" [ "csx_cpxe" ]                   * ]
+  [ class "" [ "lpxs_aaa_conf" ]               class "" [ "lpxs_aaa_conf" ]              * ]
+  [ class "" [ "lprs_aaa_conf" ]               class "" [ "lprs_aaa_conf" ]              * ]
+  [ class "" [ "lsuba_lsubc" ]                 class "" [ "lsuba_lsubc" ]                * ]
+  [ class "" [ "ApplDelta" ]                   class "" [ "ApplDelta" ]                  * ]
+  [ class "" [ "ApplOmega1" ]                  class "" [ "ApplOmega1" ]                 * ]
+  [ class "" [ "ApplOmega2" ]                  class "" [ "ApplOmega2" ]                 * ]
+  [ class "" [ "ApplOmega3" ]                  class "" [ "ApplOmega3" ]                 * ]
+  [ class "" [ "ApplDelta_lift" ]              class "" [ "ApplDelta_lift" ]             * ]
+  [ class "" [ "cpr_ApplOmega_12" ]            class "" [ "cpr_ApplOmega_12" ]           * ]
+  [ class "" [ "cpr_ApplOmega_23" ]            class "" [ "cpr_ApplOmega_23" ]           * ]
+  [ class "" [ "cpxs_ApplOmega_13" ]           class "" [ "cpxs_ApplOmega_13" ]          * ]
+  [ class "" [ "fqup_ApplOmega_13" ]           class "" [ "fqup_ApplOmega_13" ]          * ]
+  [ class "" [ "fpbg_refl" ]                   class "" [ "fpbg_refl" ]                  * ]
+  [ class "" [ "Delta" ]                       class "" [ "Delta" ]                      * ]
+  [ class "" [ "Omega1" ]                      class "" [ "Omega1" ]                     * ]
+  [ class "" [ "Omega2" ]                      class "" [ "Omega2" ]                     * ]
+  [ class "" [ "Delta_lift" ]                  class "" [ "Delta_lift" ]                 * ]
+  [ class "" [ "cpr_Omega_12" ]                class "" [ "cpr_Omega_12" ]               * ]
+  [ class "" [ "cpr_Omega_21" ]                class "" [ "cpr_Omega_21" ]               * ]
+  [ class "" [ "sta_ldec" ]                    class "" [ "sta_ldec" ]                   * ]
+  [ class "" [ "snv" ]                         class "" [ "snv" ]                        * ]
+  [ class "" [ "snv_inv_lref_aux" ]            class "" [ "snv_inv_lref_aux" ]           * ]
+  [ class "" [ "snv_inv_lref" ]                class "" [ "snv_inv_lref" ]               * ]
+  [ class "" [ "snv_inv_gref_aux" ]            class "" [ "snv_inv_gref_aux" ]           * ]
+  [ class "" [ "snv_inv_gref" ]                class "" [ "snv_inv_gref" ]               * ]
+  [ class "" [ "snv_inv_bind_aux" ]            class "" [ "snv_inv_bind_aux" ]           * ]
+  [ class "" [ "snv_inv_bind" ]                class "" [ "snv_inv_bind" ]               * ]
+  [ class "" [ "snv_inv_appl_aux" ]            class "" [ "snv_inv_appl_aux" ]           * ]
+  [ class "" [ "snv_inv_appl" ]                class "" [ "snv_inv_appl" ]               * ]
+  [ class "" [ "snv_inv_cast_aux" ]            class "" [ "snv_inv_cast_aux" ]           * ]
+  [ class "" [ "snv_inv_cast" ]                class "" [ "snv_inv_cast" ]               * ]
+  [ class "" [ "snv_extended" ]                class "" [ "snv_extended" ]               * ]
+  [ class "" [ "snv_restricted" ]              class "" [ "snv_restricted" ]             * ]
+  [ class "" [ "snv_fwd_aaa" ]                 class "" [ "snv_fwd_aaa" ]                * ]
+  [ class "" [ "snv_fwd_da" ]                  class "" [ "snv_fwd_da" ]                 * ]
+  [ class "" [ "snv_fwd_lstas" ]               class "" [ "snv_fwd_lstas" ]              * ]
+  [ class "" [ "snv_fwd_fsb" ]                 class "" [ "snv_fwd_fsb" ]                * ]
+  [ class "" [ "snv_lift" ]                    class "" [ "snv_lift" ]                   * ]
+  [ class "" [ "snv_inv_lift" ]                class "" [ "snv_inv_lift" ]               * ]
+  [ class "" [ "snv_fqu_conf" ]                class "" [ "snv_fqu_conf" ]               * ]
+  [ class "" [ "snv_fquq_conf" ]               class "" [ "snv_fquq_conf" ]              * ]
+  [ class "" [ "snv_fqup_conf" ]               class "" [ "snv_fqup_conf" ]              * ]
+  [ class "" [ "snv_fqus_conf" ]               class "" [ "snv_fqus_conf" ]              * ]
+  [ class "" [ "IH_snv_cpr_lpr" ]              class "" [ "IH_snv_cpr_lpr" ]             * ]
+  [ class "" [ "IH_da_cpr_lpr" ]               class "" [ "IH_da_cpr_lpr" ]              * ]
+  [ class "" [ "IH_lstas_cpr_lpr" ]            class "" [ "IH_lstas_cpr_lpr" ]           * ]
+  [ class "" [ "IH_snv_lstas" ]                class "" [ "IH_snv_lstas" ]               * ]
+  [ class "" [ "snv_cprs_lpr_aux" ]            class "" [ "snv_cprs_lpr_aux" ]           * ]
+  [ class "" [ "da_cprs_lpr_aux" ]             class "" [ "da_cprs_lpr_aux" ]            * ]
+  [ class "" [ "da_scpds_lpr_aux" ]            class "" [ "da_scpds_lpr_aux" ]           * ]
+  [ class "" [ "da_scpes_aux" ]                class "" [ "da_scpes_aux" ]               * ]
+  [ class "" [ "lstas_cprs_lpr_aux" ]          class "" [ "lstas_cprs_lpr_aux" ]         * ]
+  [ class "" [ "scpds_cpr_lpr_aux" ]           class "" [ "scpds_cpr_lpr_aux" ]          * ]
+  [ class "" [ "scpes_cpr_lpr_aux" ]           class "" [ "scpes_cpr_lpr_aux" ]          * ]
+  [ class "" [ "lstas_scpds_aux" ]             class "" [ "lstas_scpds_aux" ]            * ]
+  [ class "" [ "scpes_le_aux" ]                class "" [ "scpes_le_aux" ]               * ]
+  [ class "" [ "snv_cast_scpes" ]              class "" [ "snv_cast_scpes" ]             * ]
+  [ class "" [ "shnv" ]                        class "" [ "shnv" ]                       * ]
+  [ class "" [ "shnv_inv_cast_aux" ]           class "" [ "shnv_inv_cast_aux" ]          * ]
+  [ class "" [ "shnv_inv_cast" ]               class "" [ "shnv_inv_cast" ]              * ]
+  [ class "" [ "shnv_inv_snv" ]                class "" [ "shnv_inv_snv" ]               * ]
+  [ class "" [ "snv_shnv_cast" ]               class "" [ "snv_shnv_cast" ]              * ]
+  [ class "" [ "lsubsv" ]                      class "" [ "lsubsv" ]                     * ]
+  [ class "" [ "lsubsv_inv_atom1_aux" ]        class "" [ "lsubsv_inv_atom1_aux" ]       * ]
+  [ class "" [ "lsubsv_inv_atom1" ]            class "" [ "lsubsv_inv_atom1" ]           * ]
+  [ class "" [ "lsubsv_inv_pair1_aux" ]        class "" [ "lsubsv_inv_pair1_aux" ]       * ]
+  [ class "" [ "lsubsv_inv_pair1" ]            class "" [ "lsubsv_inv_pair1" ]           * ]
+  [ class "" [ "lsubsv_inv_atom2_aux" ]        class "" [ "lsubsv_inv_atom2_aux" ]       * ]
+  [ class "" [ "lsubsv_inv_atom2" ]            class "" [ "lsubsv_inv_atom2" ]           * ]
+  [ class "" [ "lsubsv_inv_pair2_aux" ]        class "" [ "lsubsv_inv_pair2_aux" ]       * ]
+  [ class "" [ "lsubsv_inv_pair2" ]            class "" [ "lsubsv_inv_pair2" ]           * ]
+  [ class "" [ "lsubsv_fwd_lsubr" ]            class "" [ "lsubsv_fwd_lsubr" ]           * ]
+  [ class "" [ "lsubsv_refl" ]                 class "" [ "lsubsv_refl" ]                * ]
+  [ class "" [ "lsubsv_cprs_trans" ]           class "" [ "lsubsv_cprs_trans" ]          * ]
+  [ class "" [ "lsubsv_drop_O1_conf" ]         class "" [ "lsubsv_drop_O1_conf" ]        * ]
+  [ class "" [ "lsubsv_drop_O1_trans" ]        class "" [ "lsubsv_drop_O1_trans" ]       * ]
+  [ class "" [ "lsubsv_fwd_lsubd" ]            class "" [ "lsubsv_fwd_lsubd" ]           * ]
+  [ class "" [ "lsubsv_lstas_trans" ]          class "" [ "lsubsv_lstas_trans" ]         * ]
+  [ class "" [ "lsubsv_sta_trans" ]            class "" [ "lsubsv_sta_trans" ]           * ]
+  [ class "" [ "lsubsv_scpds_trans" ]          class "" [ "lsubsv_scpds_trans" ]         * ]
+  [ class "" [ "lsubsv_snv_trans" ]            class "" [ "lsubsv_snv_trans" ]           * ]
+  [ class "" [ "snv_cpr_lpr_aux" ]             class "" [ "snv_cpr_lpr_aux" ]            * ]
+  [ class "" [ "lstas_cpr_lpr_aux" ]           class "" [ "lstas_cpr_lpr_aux" ]          * ]
+  [ class "" [ "snv_lstas_aux" ]               class "" [ "snv_lstas_aux" ]              * ]
+  [ class "" [ "lsubsv_fwd_lsuba" ]            class "" [ "lsubsv_fwd_lsuba" ]           * ]
+  [ class "" [ "da_cpr_lpr_aux" ]              class "" [ "da_cpr_lpr_aux" ]             * ]
+  [ class "" [ "lsubsv_cpcs_trans" ]           class "" [ "lsubsv_cpcs_trans" ]          * ]
+  [ class "" [ "snv_preserve" ]                class "" [ "snv_preserve" ]               * ]
+  [ class "" [ "da_cpr_lpr" ]                  class "" [ "da_cpr_lpr" ]                 * ]
+  [ class "" [ "snv_cpr_lpr" ]                 class "" [ "snv_cpr_lpr" ]                * ]
+  [ class "" [ "snv_lstas" ]                   class "" [ "snv_lstas" ]                  * ]
+  [ class "" [ "lstas_cpr_lpr" ]               class "" [ "lstas_cpr_lpr" ]              * ]
+  [ class "" [ "snv_cprs_lpr" ]                class "" [ "snv_cprs_lpr" ]               * ]
+  [ class "" [ "da_cprs_lpr" ]                 class "" [ "da_cprs_lpr" ]                * ]
+  [ class "" [ "lstas_cprs_lpr" ]              class "" [ "lstas_cprs_lpr" ]             * ]
+  [ class "" [ "lstas_cpcs_lpr" ]              class "" [ "lstas_cpcs_lpr" ]             * ]
+  [ class "" [ "cpys" ]                        class "" [ "cpys" ]                       * ]
+  [ class "" [ "cpys_ind" ]                    class "" [ "cpys_ind" ]                   * ]
+  [ class "" [ "cpys_ind_dx" ]                 class "" [ "cpys_ind_dx" ]                * ]
+  [ class "" [ "cpy_cpys" ]                    class "" [ "cpy_cpys" ]                   * ]
+  [ class "" [ "cpys_strap1" ]                 class "" [ "cpys_strap1" ]                * ]
+  [ class "" [ "cpys_strap2" ]                 class "" [ "cpys_strap2" ]                * ]
+  [ class "" [ "lsuby_cpys_trans" ]            class "" [ "lsuby_cpys_trans" ]           * ]
+  [ class "" [ "cpys_refl" ]                   class "" [ "cpys_refl" ]                  * ]
+  [ class "" [ "cpys_bind" ]                   class "" [ "cpys_bind" ]                  * ]
+  [ class "" [ "cpys_flat" ]                   class "" [ "cpys_flat" ]                  * ]
+  [ class "" [ "cpys_weak" ]                   class "" [ "cpys_weak" ]                  * ]
+  [ class "" [ "cpys_weak_top" ]               class "" [ "cpys_weak_top" ]              * ]
+  [ class "" [ "cpys_weak_full" ]              class "" [ "cpys_weak_full" ]             * ]
+  [ class "" [ "cpys_fwd_up" ]                 class "" [ "cpys_fwd_up" ]                * ]
+  [ class "" [ "cpys_fwd_tw" ]                 class "" [ "cpys_fwd_tw" ]                * ]
+  [ class "" [ "cpys_inv_sort1" ]              class "" [ "cpys_inv_sort1" ]             * ]
+  [ class "" [ "cpys_inv_gref1" ]              class "" [ "cpys_inv_gref1" ]             * ]
+  [ class "" [ "cpys_inv_bind1" ]              class "" [ "cpys_inv_bind1" ]             * ]
+  [ class "" [ "cpys_inv_flat1" ]              class "" [ "cpys_inv_flat1" ]             * ]
+  [ class "" [ "cpys_inv_refl_O2" ]            class "" [ "cpys_inv_refl_O2" ]           * ]
+  [ class "" [ "cpys_inv_lift1_eq" ]           class "" [ "cpys_inv_lift1_eq" ]          * ]
+  [ class "" [ "cpys_subst" ]                  class "" [ "cpys_subst" ]                 * ]
+  [ class "" [ "cpys_subst_Y2" ]               class "" [ "cpys_subst_Y2" ]              * ]
+  [ class "" [ "cpys_inv_atom1" ]              class "" [ "cpys_inv_atom1" ]             * ]
+  [ class "" [ "cpys_inv_lref1" ]              class "" [ "cpys_inv_lref1" ]             * ]
+  [ class "" [ "cpys_inv_lref1_Y2" ]           class "" [ "cpys_inv_lref1_Y2" ]          * ]
+  [ class "" [ "cpys_inv_lref1_drop" ]         class "" [ "cpys_inv_lref1_drop" ]        * ]
+  [ class "" [ "cpys_lift_le" ]                class "" [ "cpys_lift_le" ]               * ]
+  [ class "" [ "cpys_lift_be" ]                class "" [ "cpys_lift_be" ]               * ]
+  [ class "" [ "cpys_lift_ge" ]                class "" [ "cpys_lift_ge" ]               * ]
+  [ class "" [ "cpys_inv_lift1_le" ]           class "" [ "cpys_inv_lift1_le" ]          * ]
+  [ class "" [ "cpys_inv_lift1_be" ]           class "" [ "cpys_inv_lift1_be" ]          * ]
+  [ class "" [ "cpys_inv_lift1_ge" ]           class "" [ "cpys_inv_lift1_ge" ]          * ]
+  [ class "" [ "cpys_inv_lift1_ge_up" ]        class "" [ "cpys_inv_lift1_ge_up" ]       * ]
+  [ class "" [ "cpys_inv_lift1_be_up" ]        class "" [ "cpys_inv_lift1_be_up" ]       * ]
+  [ class "" [ "cpys_inv_lift1_le_up" ]        class "" [ "cpys_inv_lift1_le_up" ]       * ]
+  [ class "" [ "cpys_inv_lift1_subst" ]        class "" [ "cpys_inv_lift1_subst" ]       * ]
+  [ class "" [ "cpysa" ]                       class "" [ "cpysa" ]                      * ]
+  [ class "" [ "lsuby_cpysa_trans" ]           class "" [ "lsuby_cpysa_trans" ]          * ]
+  [ class "" [ "cpysa_refl" ]                  class "" [ "cpysa_refl" ]                 * ]
+  [ class "" [ "cpysa_cpy_trans" ]             class "" [ "cpysa_cpy_trans" ]            * ]
+  [ class "" [ "cpys_cpysa" ]                  class "" [ "cpys_cpysa" ]                 * ]
+  [ class "" [ "cpysa_inv_cpys" ]              class "" [ "cpysa_inv_cpys" ]             * ]
+  [ class "" [ "cpys_ind_alt" ]                class "" [ "cpys_ind_alt" ]               * ]
+  [ class "" [ "cpys_inv_SO2" ]                class "" [ "cpys_inv_SO2" ]               * ]
+  [ class "" [ "cpys_strip_eq" ]               class "" [ "cpys_strip_eq" ]              * ]
+  [ class "" [ "cpys_strip_neq" ]              class "" [ "cpys_strip_neq" ]             * ]
+  [ class "" [ "cpys_strap1_down" ]            class "" [ "cpys_strap1_down" ]           * ]
+  [ class "" [ "cpys_strap2_down" ]            class "" [ "cpys_strap2_down" ]           * ]
+  [ class "" [ "cpys_split_up" ]               class "" [ "cpys_split_up" ]              * ]
+  [ class "" [ "cpys_inv_lift1_up" ]           class "" [ "cpys_inv_lift1_up" ]          * ]
+  [ class "" [ "cpys_conf_eq" ]                class "" [ "cpys_conf_eq" ]               * ]
+  [ class "" [ "cpys_conf_neq" ]               class "" [ "cpys_conf_neq" ]              * ]
+  [ class "" [ "cpys_trans_eq" ]               class "" [ "cpys_trans_eq" ]              * ]
+  [ class "" [ "cpys_trans_down" ]             class "" [ "cpys_trans_down" ]            * ]
+  [ class "" [ "cpys_antisym_eq" ]             class "" [ "cpys_antisym_eq" ]            * ]
+  [ class "" [ "llpx_sn_TC_pair_dx" ]          class "" [ "llpx_sn_TC_pair_dx" ]         * ]
+  [ class "" [ "fqup_trans" ]                  class "" [ "fqup_trans" ]                 * ]
+  [ class "" [ "lleq_intro_alt_r" ]            class "" [ "lleq_intro_alt_r" ]           * ]
+  [ class "" [ "lleq_ind_alt_r" ]              class "" [ "lleq_ind_alt_r" ]             * ]
   [ class "" [ "lleq_inv_alt_r" ]              class "" [ "lleq_inv_alt_r" ]             * ]
 }