update in basic_2

advances on fpb to be continued ...

diff --git a/helm/www/lambdadelta/web/home/documentation_3.tbl b/helm/www/lambdadelta/web/home/documentation_3.tbl
index b8a0eb9d82da2b68615bac85fb77c7c83b79914c..4522bea00a21982de3f425397b0d8d13d6beb3e5 100644 (file)
--- a/helm/www/lambdadelta/web/home/documentation_3.tbl
+++ b/helm/www/lambdadelta/web/home/documentation_3.tbl
@@ -24,7 +24,7 @@ table {
      "F. Guidi:" + 
      @@("download/ld_talk_10s.pdf"
      "Adding Schematic Abstraction to λP") +
      "F. Guidi:" + 
      @@("download/ld_talk_10s.pdf"
      "Adding Schematic Abstraction to λP") +

-     "(revised <span class=\"emph gamma\">2018-02</span>)." +
+     "(<span class=\"emph alpha\">2018-02</span>)." +

      "Presentation at University of Bologna (slides)."
      * }
    ]
      "Presentation at University of Bologna (slides)."
      * }
    ]

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/fpb/fpb_fleq.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/fpb/fpb_fleq.etc
deleted file mode 100644 (file)
index 6463870..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/etc/fpb/fpb_fleq.etc
+++ /dev/null
@@ -1,41 +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                  *)
-(*                                                                        *)
-(**************************************************************************)
-
-include "basic_2/multiple/fleq.ma".
-include "basic_2/reduction/fpb_lleq.ma".
-
-(* "RST" PROPER PARALLEL COMPUTATION FOR CLOSURES ***************************)
-
-(* Properties on lazy equivalence for closures ******************************)
-
-lemma fleq_fpb_trans: ∀h,o,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≡[0] ⦃F2, K2, T2⦄ →
-                      ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, o] ⦃G2, L2, U2⦄ →
-                      ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, o] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≡[0] ⦃G2, L2, U2⦄.
-#h #o #F1 #F2 #K1 #K2 #T1 #T2 * -F2 -K2 -T2
-#K2 #HK12 #G2 #L2 #U2 #H12 elim (lleq_fpb_trans … HK12 … H12) -K2
-/3 width=5 by fleq_intro, ex2_3_intro/
-qed-.
-
-(* Inversion lemmas on lazy equivalence for closures ************************)
-
-lemma fpb_inv_fleq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
-                    ⦃G1, L1, T1⦄ ≡[0] ⦃G2, L2, T2⦄ → ⊥.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
-[ #G2 #L2 #T2 #H12 #H elim (fleq_inv_gen … H) -H
-  /3 width=8 by lleq_fwd_length, fqu_inv_eq/
-| #T2 #_ #HnT #H elim (fleq_inv_gen … H) -H /2 width=1 by/
-| #L2 #_ #HnL #H elim (fleq_inv_gen … H) -H /2 width=1 by/
-]
-qed-.
-

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_ffdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_ffdeq.ma
new file mode 100644 (file)
index 0000000..1d0d211
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_ffdeq.ma
@@ -0,0 +1,50 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/static/ffdeq.ma".
+include "basic_2/rt_transition/fpb_lfdeq.ma".
+
+(* PROPER PARALLEL RST-TRANSITION FOR CLOSURES ******************************)
+
+(* Properties with degree-based equivalence for closures ********************)
+
+(* Basic_2A1: uses: fleq_fpb_trans *)
+lemma ffdeq_fpb_trans: ∀h,o,F1,F2,K1,K2,T1,T2. ⦃F1, K1, T1⦄ ≛[h, o] ⦃F2, K2, T2⦄ →
+                       ∀G2,L2,U2. ⦃F2, K2, T2⦄ ≻[h, o] ⦃G2, L2, U2⦄ →
+                       ∃∃G1,L1,U1. ⦃F1, K1, T1⦄ ≻[h, o] ⦃G1, L1, U1⦄ & ⦃G1, L1, U1⦄ ≛[h, o] ⦃G2, L2, U2⦄.
+#h #o #F1 #F2 #K1 #K2 #T1 #T2 * -F2 -K2 -T2
+#K2 #T2 #HK12 #HT12 #G2 #L2 #U2 #H12
+elim (tdeq_fpb_trans … HT12 … H12) -T2 #K0 #T0 #H #HT0 #HK0
+elim (lfdeq_fpb_trans … HK12 … H) -K2 #L0 #U0 #H #HUT0 #HLK0
+@(ex2_3_intro … H) -H (**) (* full auto too slow *)
+/4 width=3 by ffdeq_intro_dx, lfdeq_trans, tdeq_lfdeq_conf, tdeq_trans/
+qed-.
+
+(* Inversion lemmas with degree-based equivalence for closures **************)
+(*
+(* Basic_2A1: uses: fpb_inv_fleq *)
+lemma fpb_inv_ffdeq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ≻[h, o] ⦃G2, L2, T2⦄ →
+                     ⦃G1, L1, T1⦄ ≛[h, o] ⦃G2, L2, T2⦄ → ⊥.
+#h #o #G1 #G2 #L1 #L2 #T1 #T2 * -G2 -L2 -T2
+[ #G2 #L2 #T2 #H12 #H elim (ffdeq_inv_gen_sn … H) -H
+  #_ #H1 #H2
+(*
+
+  /3 width=8 by lfdeq_fwd_length, fqu_inv_eq/
+*)  
+| #T2 #_ #HnT #H elim (ffdeq_inv_gen_sn … H) -H /2 width=1 by/
+| #L2 #_ #HnL #H elim (ffdeq_inv_gen_sn … H) -H /2 width=1 by/
+]
+qed-.
+*)
\ No newline at end of file

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lfdeq.ma
index c4489bccf7332242285f5f8d63dd295409932627..b98034aa30462862b8a2d27e34a3bd5910d98bcb 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lfdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/fpb_lfdeq.ma
@@ -21,6 +21,20 @@ include "basic_2/rt_transition/fpb.ma".
 
 (* Properties with degree-based equivalence for local environments **********)
 
 
 (* Properties with degree-based equivalence for local environments **********)
 

+lemma tdeq_fpb_trans: ∀h,o,U2,U1. U2 ≛[h, o] U1 →
+                      ∀G1,G2,L1,L2,T1. ⦃G1, L1, U1⦄ ≻[h, o] ⦃G2, L2, T1⦄ → 
+                      ∃∃L,T2. ⦃G1, L1, U2⦄ ≻[h, o] ⦃G2, L, T2⦄ & T2 ≛[h, o] T1 & L ≛[h, o, T1] L2.
+#h #o #U2 #U1 #HU21 #G1 #G2 #L1 #L2 #T1 * -G2 -L2 -T1
+[ #G2 #L2 #T1 #H
+  elim (tdeq_fqu_trans … H … HU21) -H
+  /3 width=5 by fpb_fqu, ex3_2_intro/
+| #T1 #HUT1 #HnUT1
+  elim (tdeq_cpx_trans … HU21 … HUT1) -HUT1
+  /6 width=5 by fpb_cpx, tdeq_canc_sn, tdeq_trans, ex3_2_intro/
+| /6 width=5 by fpb_lfpx, lfpx_tdeq_div, tdeq_lfdeq_conf, ex3_2_intro/
+]
+qed-.
+

 (* Basic_2A1: was just: lleq_fpb_trans *)
 lemma lfdeq_fpb_trans: ∀h,o,F,K1,K2,T. K1 ≛[h, o, T] K2 →
                        ∀G,L2,U. ⦃F, K2, T⦄ ≻[h, o] ⦃G, L2, U⦄ →
 (* Basic_2A1: was just: lleq_fpb_trans *)
 lemma lfdeq_fpb_trans: ∀h,o,F,K1,K2,T. K1 ≛[h, o, T] K2 →
                        ∀G,L2,U. ⦃F, K2, T⦄ ≻[h, o] ⦃G, L2, U⦄ →

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lfdeq.ma
index 9dc71abaf68e0bcce0802cb374386eb26fa096e5..856fccf535b10d4e24607d69267a585a5496308e 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lfdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/lfpx_lfdeq.ma
@@ -36,6 +36,13 @@ lemma lfpx_bind_dx_split_void: ∀h,G,K1,L2,T. ⦃G, K1.ⓧ⦄ ⊢ ⬈[h, T] L2
                                ∃∃K2. ⦃G, K1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] K2 & K2.ⓧ ≛[h, o, T] L2.
 /3 width=5 by lfpx_fsge_comp, lfxs_bind_dx_split_void/ qed-.
 
                                ∃∃K2. ⦃G, K1⦄ ⊢ ⬈[h, ⓑ{p,I}V.T] K2 & K2.ⓧ ≛[h, o, T] L2.
 /3 width=5 by lfpx_fsge_comp, lfxs_bind_dx_split_void/ qed-.
 

+lemma lfpx_tdeq_conf: ∀h,o,G. s_r_confluent1 … (cdeq h o) (lfpx h G).
+/2 width=5 by tdeq_lfxs_conf/ qed-.
+
+lemma lfpx_tdeq_div: ∀h,o,T1,T2. T1 ≛[h, o] T2 →
+                     ∀G,L1,L2. ⦃G, L1⦄ ⊢ ⬈[h, T2] L2 → ⦃G, L1⦄ ⊢ ⬈[h, T1] L2.
+/2 width=5 by tdeq_lfxs_div/ qed-.
+

 lemma cpx_tdeq_conf_lexs: ∀h,o,G. R_confluent2_lfxs … (cpx h G) (cdeq h o) (cpx h G) (cdeq h o).
 #h #o #G #L0 #T0 #T1 #H @(cpx_ind … H) -G -L0 -T0 -T1 /2 width=3 by ex2_intro/
 [ #G #L0 #s0 #X0 #H0 #L1 #HL01 #L2 #HL02
 lemma cpx_tdeq_conf_lexs: ∀h,o,G. R_confluent2_lfxs … (cpx h G) (cdeq h o) (cpx h G) (cdeq h o).
 #h #o #G #L0 #T0 #T1 #H @(cpx_ind … H) -G -L0 -T0 -T1 /2 width=3 by ex2_intro/
 [ #G #L0 #s0 #X0 #H0 #L1 #HL01 #L2 #HL02

diff --git a/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq.ma
index 14994967ab00d3d2d8c522a458a6dfc88562a498..9784f34904ddc209745c628de2a3d92dee9894be 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/static/lfdeq.ma
@@ -73,14 +73,21 @@ lemma frees_lfdeq_conf: ∀h,o,f,L1,T. L1 ⊢ 𝐅*⦃T⦄ ≡ f →
                         ∀L2. L1 ≛[h, o, f] L2 → L2 ⊢ 𝐅*⦃T⦄ ≡ f.
 /2 width=7 by frees_tdeq_conf_lfdeq, tdeq_refl/ qed-.
 
                         ∀L2. L1 ≛[h, o, f] L2 → L2 ⊢ 𝐅*⦃T⦄ ≡ f.
 /2 width=7 by frees_tdeq_conf_lfdeq, tdeq_refl/ qed-.
 

-lemma tdeq_lfdeq_conf: ∀h,o. s_r_confluent1 … (cdeq h o) (lfdeq h o).
-#h #o #L1 #T1 #T2 #HT12 #L2 *
+lemma tdeq_lfxs_conf: ∀R,h,o. s_r_confluent1 … (cdeq h o) (lfxs R).
+#R #h #o #L1 #T1 #T2 #HT12 #L2 *

 /3 width=5 by frees_tdeq_conf, ex2_intro/
 qed-.
 
 /3 width=5 by frees_tdeq_conf, ex2_intro/
 qed-.
 

+lemma tdeq_lfxs_div: ∀R,h,o,T1,T2. T1 ≛[h, o] T2 →
+                     ∀L1,L2. L1 ⪤*[R, T2] L2 → L1 ⪤*[R, T1] L2.
+/3 width=5 by tdeq_lfxs_conf, tdeq_sym/ qed-.
+
+lemma tdeq_lfdeq_conf: ∀h,o. s_r_confluent1 … (cdeq h o) (lfdeq h o).
+/2 width=5 by tdeq_lfxs_conf/ qed-.
+

 lemma tdeq_lfdeq_div: ∀h,o,T1,T2. T1 ≛[h, o] T2 →
                       ∀L1,L2. L1 ≛[h, o, T2] L2 → L1 ≛[h, o, T1] L2.
 lemma tdeq_lfdeq_div: ∀h,o,T1,T2. T1 ≛[h, o] T2 →
                       ∀L1,L2. L1 ≛[h, o, T2] L2 → L1 ≛[h, o, T1] L2.

-/3 width=3 by tdeq_lfdeq_conf, tdeq_sym/ qed-.
+/2 width=5 by tdeq_lfxs_div/ qed-.

 
 lemma lfdeq_atom: ∀h,o,I. ⋆ ≛[h, o, ⓪{I}] ⋆.
 /2 width=1 by lfxs_atom/ qed.
 
 lemma lfdeq_atom: ∀h,o,I. ⋆ ≛[h, o, ⓪{I}] ⋆.
 /2 width=1 by lfxs_atom/ qed.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml
index dcf2f4693e22a87943ff656690ca49a829944f44..f1f4b8415f630b74c3763474a46a65c3ef0cec43 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2.ldw.xml
@@ -34,6 +34,9 @@
 
    <subsection name="A2">Stage "A2": "Extending the Applicability Condition"</subsection>
 
 
    <subsection name="A2">Stage "A2": "Extending the Applicability Condition"</subsection>
 

+   <news class="alpha" date="2018 March 9.">
+         Support for rt-computation completed.
+   </news>

    <news class="alpha" date="2017 October 17.">
          Exclusion binder in local environments.
          Syntactic component updated:
    <news class="alpha" date="2017 October 17.">
          Exclusion binder in local environments.
          Syntactic component updated:


@@ -45,7 +48,7 @@
          (anniversary milestone).
    </news>
    <news class="alpha" date="2017 March 16.">
          (anniversary milestone).
    </news>
    <news class="alpha" date="2017 March 16.">

-         First behavioral component reconstructed:
+         First behavioral component completed:

          rt_transition.
    </news>
    <news class="alpha" date="2017 February 19.">
          rt_transition.
    </news>
    <news class="alpha" date="2017 February 19.">


@@ -58,7 +61,7 @@
          Confluence for context-sensitive parallel r-transition on terms.
    </news>
    <news class="alpha" date="2016 April 16.">
          Confluence for context-sensitive parallel r-transition on terms.
    </news>
    <news class="alpha" date="2016 April 16.">

-         Syntactic component reconstructed:
+         Syntactic component completed:

          syntax, relocation, s_transition, s_computation, static
          (anniversary milestone).
    </news>
          syntax, relocation, s_transition, s_computation, static
          (anniversary milestone).
    </news>

diff --git a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
index 4da8d232f58b54bd8b344b3419311dd606680866..e8cb493089dd86e5808d19d23909256d6681c3a6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
+++ b/matita/matita/contribs/lambdadelta/basic_2/web/basic_2_src.tbl
@@ -123,7 +123,7 @@ table {
    [ { "rt-transition" * } {
         [ { "uncounted parallel rst-transition" * } {
              [ [ "for closures" ] "fpbq" + "( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpbq_aaa" * ]
    [ { "rt-transition" * } {
         [ { "uncounted parallel rst-transition" * } {
              [ [ "for closures" ] "fpbq" + "( ⦃?,?,?⦄ ≽[?,?] ⦃?,?,?⦄ )" "fpbq_aaa" * ]

-             [ [ "proper for closures" ] "fpb" + "( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpb_lfdeq" * ]
+             [ [ "proper for closures" ] "fpb" + "( ⦃?,?,?⦄ ≻[?,?] ⦃?,?,?⦄ )" "fpb_lfdeq" + "fpb_ffdeq" * ]

           }
         ]
         [ { "context-sensitive parallel r-transition" * } {
           }
         ]
         [ { "context-sensitive parallel r-transition" * } {