- cpxs completed

- changed colors in sunnary tables for web site

diff --git a/matita/matita/contribs/lambdadelta/Makefile b/matita/matita/contribs/lambdadelta/Makefile
index 7065d3a1f57f92d268404f4c146af178abe93063..e0817c219f9702a8b1255d65d9e0692254c32f21 100644 (file)
--- a/matita/matita/contribs/lambdadelta/Makefile
+++ b/matita/matita/contribs/lambdadelta/Makefile
@@ -207,12 +207,12 @@ define SUMMARY_TEMPLATE
        @printf '   class "gray"   [ "category"\n'                >> $$@
        @printf '      [ "objects" * ]\n'                         >> $$@
        @printf '   ]\n'                                          >> $$@
-       @printf '   class "cyan"   [ "sizes"\n'                   >> $$@
+       @printf '   class "water"  [ "sizes"\n'                   >> $$@
        @printf '      [ "files"      "$$(S1)" ]\n'               >> $$@
        @printf '      [ "characters" "$$(S2)" ]\n'               >> $$@
        @printf '      [ "nodes"      "$$(S4)" ]\n'               >> $$@
        @printf '   ]\n'                                          >> $$@        
-       @printf '   class "green"  [ "propositions"\n'            >> $$@
+       @printf '   class "grass"  [ "propositions"\n'            >> $$@
        @printf '      [ "theorems" "$$(P1)" ]\n'                 >> $$@
        @printf '      [ "lemmas"   "$$(P2)" ]\n'                 >> $$@
        @printf '      [ "total"    "$$(P3)" ]\n'                 >> $$@

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc/lstas/lstas_cpxs.etc b/matita/matita/contribs/lambdadelta/basic_2/etc/lstas/lstas_cpxs.etc
new file mode 100644 (file)
index 0000000..088b4da
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc/lstas/lstas_cpxs.etc
@@ -0,0 +1,45 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* Advanced properties ******************************************************)
+
+lemma lstas_cpxs: ∀h,o,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 →
+                  ∀d1. ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 → d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ⬈*[h, o] T2.
+#h #o #G #L #T1 #T2 #d2 #H elim H -G -L -T1 -T2 -d2 //
+[ /3 width=3 by cpxs_sort, da_inv_sort/
+| #G #L #K #V1 #V2 #W2 #i #d2 #HLK #_ #HVW2 #IHV12 #d1 #H #Hd21
+  elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0
+  lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct /3 width=7 by cpxs_delta/
+| #G #L #K #V1 #V2 #W2 #i #d2 #HLK #_ #HVW2 #IHV12 #d1 #H #Hd21
+  elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0
+  lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct
+  #HV1 #H destruct lapply (le_plus_to_le_c … Hd21) -Hd21
+  /3 width=7 by cpxs_delta/
+| /4 width=3 by cpxs_bind_dx, da_inv_bind/
+| /4 width=3 by cpxs_flat_dx, da_inv_flat/
+| /4 width=3 by cpxs_eps, da_inv_flat/
+]
+qed.
+
+lemma fquq_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
+                        ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 →
+                        ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 →
+                        ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
+/3 width=5 by fquq_cpxs_trans, lstas_cpxs/ qed-.
+
+lemma fqus_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
+                        ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 →
+                        ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 →
+                        ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
+/3 width=6 by fqus_cpxs_trans, lstas_cpxs/ qed-.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
index 82e21018e18e735dfd149b3a2bc3ec9443ee9a0f..9ecbc31c60794963d26550bc1ca5d4060093709a 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_fqus.ma
@@ -1,132 +1,118 @@
-include "basic_2/computation/cpxs_lift.ma".
-include "basic_2/multiple/fqus_fqus.ma".
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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                  *)
+(*                                                                        *)
+(**************************************************************************)
 
-(* Advanced properties ******************************************************)
+(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
 
-lemma lstas_cpxs: ∀h,o,G,L,T1,T2,d2. ⦃G, L⦄ ⊢ T1 •*[h, d2] T2 →
-                  ∀d1. ⦃G, L⦄ ⊢ T1 ▪[h, o] d1 → d2 ≤ d1 → ⦃G, L⦄ ⊢ T1 ⬈*[h, o] T2.
-#h #o #G #L #T1 #T2 #d2 #H elim H -G -L -T1 -T2 -d2 //
-[ /3 width=3 by cpxs_sort, da_inv_sort/
-| #G #L #K #V1 #V2 #W2 #i #d2 #HLK #_ #HVW2 #IHV12 #d1 #H #Hd21
-  elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0
-  lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct /3 width=7 by cpxs_delta/
-| #G #L #K #V1 #V2 #W2 #i #d2 #HLK #_ #HVW2 #IHV12 #d1 #H #Hd21
-  elim (da_inv_lref … H) -H * #K0 #V0 [| #d0 ] #HLK0
-  lapply (drop_mono … HLK0 … HLK) -HLK0 #H destruct
-  #HV1 #H destruct lapply (le_plus_to_le_c … Hd21) -Hd21
-  /3 width=7 by cpxs_delta/
-| /4 width=3 by cpxs_bind_dx, da_inv_bind/
-| /4 width=3 by cpxs_flat_dx, da_inv_flat/
-| /4 width=3 by cpxs_eps, da_inv_flat/
-]
-qed.
+include "basic_2/rt_transition/cpx_fqus.ma".
+include "basic_2/rt_computation/cpxs_drops.ma".
+include "basic_2/rt_computation/cpxs_lsubr.ma".
+include "basic_2/rt_computation/cpxs_cpxs.ma".
 
 (* Properties on supclosure *************************************************)
 
-lemma fqu_cpxs_trans: ∀h,o,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 →
-                      ∀T1. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
-                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
+lemma fqu_cpxs_trans: ∀h,b,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 →
+                      ∀T1. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
+                      ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & ⦃G1, L1, U1⦄ ⊐[b] ⦃G2, L2, U2⦄.
+#h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqu_cpx_trans … HT1 … HT2) -T
 #T #HT1 #HT2 elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
-lemma fquq_cpxs_trans: ∀h,o,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 →
-                       ∀T1. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
-                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T2 #U2 #HTU2 #T1 #H elim (fquq_inv_gen … H) -H
-[ #HT12 elim (fqu_cpxs_trans … HTU2 … HT12) /3 width=3 by fqu_fquq, ex2_intro/
-| * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
-]
+lemma fquq_cpxs_trans: ∀h,b,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 →
+                       ∀T1. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
+                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & ⦃G1, L1, U1⦄ ⊐⸮[b] ⦃G2, L2, U2⦄.
+#h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
+#T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fquq_cpx_trans … HT1 … HT2) -T
+#T #HT1 #HT2 elim (IHTU2 … HT2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
-lemma fquq_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
-                        ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 →
-                        ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 →
-                        ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
-/3 width=5 by fquq_cpxs_trans, lstas_cpxs/ qed-.
-
-lemma fqup_cpxs_trans: ∀h,o,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 →
-                       ∀T1. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
-                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
+lemma fqup_cpxs_trans: ∀h,b,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 →
+                       ∀T1. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
+                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & ⦃G1, L1, U1⦄ ⊐+[b] ⦃G2, L2, U2⦄.
+#h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
 #T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqup_cpx_trans … HT1 … HT2) -T
 #U1 #HTU1 #H2 elim (IHTU2 … H2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
-lemma fqus_cpxs_trans: ∀h,o,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 →
-                       ∀T1. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
-                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T2 #U2 #HTU2 #T1 #H elim (fqus_inv_gen … H) -H
-[ #HT12 elim (fqup_cpxs_trans … HTU2 … HT12) /3 width=3 by fqup_fqus, ex2_intro/
-| * #H1 #H2 #H3 destruct /2 width=3 by ex2_intro/
-]
+lemma fqus_cpxs_trans: ∀h,b,G1,G2,L1,L2,T2,U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 →
+                       ∀T1. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
+                       ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & ⦃G1, L1, U1⦄ ⊐*[b] ⦃G2, L2, U2⦄.
+#h #b #G1 #G2 #L1 #L2 #T2 #U2 #H @(cpxs_ind_dx … H) -T2 /2 width=3 by ex2_intro/
+#T #T2 #HT2 #_ #IHTU2 #T1 #HT1 elim (fqus_cpx_trans … HT1 … HT2) -T
+#U1 #HTU1 #H2 elim (IHTU2 … H2) -T2 /3 width=3 by cpxs_strap2, ex2_intro/
 qed-.
 
-lemma fqus_lstas_trans: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
-                        ∀U2,d1. ⦃G2, L2⦄ ⊢ T2 •*[h, d1] U2 →
-                        ∀d2. ⦃G2, L2⦄ ⊢ T2 ▪[h, o] d2 → d1 ≤ d2 →
-                        ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
-/3 width=6 by fqus_cpxs_trans, lstas_cpxs/ qed-.
-
-(* Properties on supclosure *************************************************)
-
-lemma fqu_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐ ⦃G2, L2, T2⦄ →
-                          ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → (T2 = U2 → ⊥) →
-                          ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐ ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
-[ #I #G #L #V1 #V2 #HV12 #_ elim (lift_total V2 0 1)
+(* Note: a proof based on fqu_cpx_trans_ntdeq might exist *)
+lemma fqu_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐[b] ⦃G2, L2, T2⦄ →
+                            ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≡[h, o] U2 → ⊥) →
+                            ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐[b] ⦃G2, L2, U2⦄.
+#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H elim H -G1 -G2 -L1 -L2 -T1 -T2
+[ #I #G #L #V1 #V2 #HV12 #_ elim (lifts_total V2 𝐔❴1❵)
   #U2 #HVU2 @(ex3_intro … U2)
-  [1,3: /3 width=7 by fqu_drop, cpxs_delta, drop_pair, drop_drop/
-  | #H destruct 
-    lapply (lift_inv_lref2_be … HVU2 ? ?) -HVU2 //
+  [1,3: /3 width=7 by cpxs_delta, fqu_drop/
+  | #H lapply (tdeq_inv_lref1 … H) -H
+    #H destruct /2 width=5 by lifts_inv_lref2_uni_lt/
   ]
-| #I #G #L #V1 #T #V2 #HV12 #H @(ex3_intro … (②{I}V2.T))
+| #I #G #L #V1 #T #V2 #HV12 #H0 @(ex3_intro … (②{I}V2.T))
   [1,3: /2 width=4 by fqu_pair_sn, cpxs_pair_sn/
-  | #H0 destruct /2 width=1 by/
+  | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/
   ]
-| #a #I #G #L #V #T1 #T2 #HT12 #H @(ex3_intro … (ⓑ{a,I}V.T2))
+| #p #I #G #L #V #T1 #T2 #HT12 #H0 @(ex3_intro … (ⓑ{p,I}V.T2))
   [1,3: /2 width=4 by fqu_bind_dx, cpxs_bind/
-  | #H0 destruct /2 width=1 by/
+  | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/
+  ]
+| #p #I #G #L #V #T1 #Hb #T2 #HT12 #H0 @(ex3_intro … (ⓑ{p,I}V.T2))
+  [1,3: /4 width=4 by lsubr_cpxs_trans, cpxs_bind, lsubr_unit, fqu_clear/
+  | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/
   ]
-| #I #G #L #V #T1 #T2 #HT12 #H @(ex3_intro … (ⓕ{I}V.T2))
+| #I #G #L #V #T1 #T2 #HT12 #H0 @(ex3_intro … (ⓕ{I}V.T2))
   [1,3: /2 width=4 by fqu_flat_dx, cpxs_flat/
-  | #H0 destruct /2 width=1 by/
+  | #H elim (tdeq_inv_pair … H) -H /2 width=1 by/
   ]
-| #G #L #K #T1 #U1 #k #HLK #HTU1 #T2 #HT12 #H elim (lift_total T2 0 (k+1))
-  #U2 #HTU2 @(ex3_intro … U2)
-  [1,3: /2 width=10 by cpxs_lift, fqu_drop/
-  | #H0 destruct /3 width=5 by lift_inj/
+| #I #G #L #T1 #U1 #HTU1 #T2 #HT12 #H0
+  elim (cpxs_lifts_sn … HT12 (Ⓣ) … (L.ⓘ{I}) … HTU1) -HT12
+  /4 width=6 by fqu_drop, drops_refl, drops_drop, tdeq_inv_lifts_bi, ex3_intro/
 ]
 qed-.
 
-lemma fquq_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮ ⦃G2, L2, T2⦄ →
-                           ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → (T2 = U2 → ⊥) →
-                           ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐⸮ ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fquq_inv_gen … H12) -H12
-[ #H12 elim (fqu_cpxs_trans_neq … H12 … HTU2 H) -T2
+lemma fquq_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐⸮[b] ⦃G2, L2, T2⦄ →
+                             ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≡[h, o] U2 → ⊥) →
+                             ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐⸮[b] ⦃G2, L2, U2⦄.
+#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 elim H12 -H12
+[ #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_ntdeq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fquq, ex3_intro/
 | * #HG #HL #HT destruct /3 width=4 by ex3_intro/
 ]
 qed-.
 
-lemma fqup_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+ ⦃G2, L2, T2⦄ →
-                           ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → (T2 = U2 → ⊥) →
-                           ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐+ ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1
-[ #G1 #L1 #T1 #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_neq … H12 … HTU2 H) -T2
+lemma fqup_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐+[b] ⦃G2, L2, T2⦄ →
+                             ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≡[h, o] U2 → ⊥) →
+                             ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐+[b] ⦃G2, L2, U2⦄.
+#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H @(fqup_ind_dx … H) -G1 -L1 -T1
+[ #G1 #L1 #T1 #H12 #U2 #HTU2 #H elim (fqu_cpxs_trans_ntdeq … H12 … HTU2 H) -T2
   /3 width=4 by fqu_fqup, ex3_intro/
 | #G #G1 #L #L1 #T #T1 #H1 #_ #IH12 #U2 #HTU2 #H elim (IH12 … HTU2 H) -T2
-  #U1 #HTU1 #H #H12 elim (fqu_cpxs_trans_neq … H1 … HTU1 H) -T1
+  #U1 #HTU1 #H #H12 elim (fqu_cpxs_trans_ntdeq … H1 … HTU1 H) -T1
   /3 width=8 by fqup_strap2, ex3_intro/
 ]
 qed-.
 
-lemma fqus_cpxs_trans_neq: ∀h,o,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐* ⦃G2, L2, T2⦄ →
-                           ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h, o] U2 → (T2 = U2 → ⊥) →
-                           ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h, o] U1 & T1 = U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐* ⦃G2, L2, U2⦄.
-#h #o #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_gen … H12) -H12
-[ #H12 elim (fqup_cpxs_trans_neq … H12 … HTU2 H) -T2
+lemma fqus_cpxs_trans_ntdeq: ∀h,o,b,G1,G2,L1,L2,T1,T2. ⦃G1, L1, T1⦄ ⊐*[b] ⦃G2, L2, T2⦄ →
+                             ∀U2. ⦃G2, L2⦄ ⊢ T2 ⬈*[h] U2 → (T2 ≡[h, o] U2 → ⊥) →
+                             ∃∃U1. ⦃G1, L1⦄ ⊢ T1 ⬈*[h] U1 & T1 ≡[h, o] U1 → ⊥ & ⦃G1, L1, U1⦄ ⊐*[b] ⦃G2, L2, U2⦄.
+#h #o #b #G1 #G2 #L1 #L2 #T1 #T2 #H12 #U2 #HTU2 #H elim (fqus_inv_fqup … H12) -H12
+[ #H12 elim (fqup_cpxs_trans_ntdeq … H12 … HTU2 H) -T2
   /3 width=4 by fqup_fqus, ex3_intro/
 | * #HG #HL #HT destruct /3 width=4 by ex3_intro/
 ]

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfdeq.ma
new file mode 100644 (file)
index 0000000..73119ad
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lfdeq.ma
@@ -0,0 +1,49 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/rt_transition/cpx_lfdeq.ma".
+include "basic_2/rt_computation/cpxs_tdeq.ma".
+
+(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
+
+(* Properties with degree-based equivalence for local environments **********)
+
+(* Basic_2A1: was just: lleq_cpxs_trans *) 
+lemma lfdeq_cpxs_trans: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈*[h] T1 →
+                        ∀L2. L2 ≡[h, o, T0] L0 →
+                        ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≡[h, o] T1.
+#h #o #G #L0 #T0 #T1 #H @(cpxs_ind_dx … H) -T0 /2 width=3 by ex2_intro/
+#T0 #T #HT0 #_ #IH #L2 #HL2
+elim (lfdeq_cpx_trans … HL2 … HT0) #U1 #H1 #H2
+elim (IH L2) -IH /2 width=4 by cpx_lfdeq_conf_dx/ -L0 #U2 #H3 #H4
+elim (tdeq_cpxs_trans … H2 … H3) -T #U0 #H2 #H3
+/3 width=5 by cpxs_strap2, tdeq_trans, ex2_intro/
+qed-.
+
+(* Basic_2A1: was just: cpxs_lleq_conf *) 
+lemma cpxs_lfdeq_trans: ∀h,o,G,L0,T0,T1. ⦃G, L0⦄ ⊢ T0 ⬈*[h] T1 →
+                        ∀L2. L0 ≡[h, o, T0] L2 →
+                        ∃∃T. ⦃G, L2⦄ ⊢ T0 ⬈*[h] T & T ≡[h, o] T1.
+/3 width=3 by lfdeq_cpxs_trans, lfdeq_sym/ qed-.
+
+(* Basic_2A1: was just: cpxs_lleq_conf_dx *) 
+lemma cpxs_lfdeq_conf_dx: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈*[h] T2 →
+                          ∀L1. L1 ≡[h, o, T1] L2 → L1 ≡[h, o, T2] L2.
+#h #o #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_lfdeq_conf_dx/
+qed-.
+
+(* Basic_2A1: was just: lleq_conf_sn *) 
+lemma cpxs_lfdeq_conf_sn: ∀h,o,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬈*[h] T2 →
+                          ∀L2. L1 ≡[h, o, T1] L2 → L1 ≡[h, o, T2] L2.
+/4 width=6 by cpxs_lfdeq_conf_dx, lfdeq_sym/ qed-.

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lleq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lleq.ma
deleted file mode 100644 (file)
index 2765cf1..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_lleq.ma
+++ /dev/null
@@ -1,39 +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/reduction/cpx_lleq.ma".
-include "basic_2/computation/cpxs.ma".
-
-(* CONTEXT-SENSITIVE EXTENDED PARALLEL COMPUTATION ON TERMS *****************)
-
-(* Properties on lazy equivalence for local environments ********************)
-
-lemma lleq_cpxs_trans: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈*[h, o] T2 →
-                       ∀L1. L1 ≡[T1, 0] L2 → ⦃G, L1⦄ ⊢ T1 ⬈*[h, o] T2.
-#h #o #G #L2 #T1 #T2 #H @(cpxs_ind_dx … H) -T1
-/4 width=6 by cpx_lleq_conf_dx, lleq_cpx_trans, cpxs_strap2/
-qed-.
-
-lemma cpxs_lleq_conf: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈*[h, o] T2 →
-                      ∀L1. L2 ≡[T1, 0] L1 → ⦃G, L1⦄ ⊢ T1 ⬈*[h, o] T2.
-/3 width=3 by lleq_cpxs_trans, lleq_sym/ qed-.
-
-lemma cpxs_lleq_conf_dx: ∀h,o,G,L2,T1,T2. ⦃G, L2⦄ ⊢ T1 ⬈*[h, o] T2 →
-                         ∀L1. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
-#h #o #G #L2 #T1 #T2 #H @(cpxs_ind … H) -T2 /3 width=6 by cpx_lleq_conf_dx/
-qed-.
-
-lemma cpxs_lleq_conf_sn: ∀h,o,G,L1,T1,T2. ⦃G, L1⦄ ⊢ T1 ⬈*[h, o] T2 →
-                         ∀L2. L1 ≡[T1, 0] L2 → L1 ≡[T2, 0] L2.
-/4 width=6 by cpxs_lleq_conf_dx, lleq_sym/ qed-.

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 561a9980b0d3982858e8104205cabbb3efb1ad85..2123e5fd9bb545d57de47e8cc107f757fa504d17 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
@@ -119,7 +119,7 @@ table {
              [ "csx ( ⦃?,?⦄ ⊢ ⬈*[?,?] 𝐒⦃?⦄ )" "csx_simple" + "csx_simple_theq" + "csx_drops" + "csx_lsubr" + "csx_aaa" + "csx_gcp" + "csx_gcr" + "csx_lfpx" + "csx_cnx" + "csx_cpxs" + "csx_csx" * ]
 *)             
              [ "lfpxs ( ⦃?,?⦄ ⊢ ⬈*[?,?] ? )" "lfpxs_length" + "lfpxs_drops" + "lfpxs_fqup" + "lfpxs_lfdeq" + "lfpxs_aaa" + "lfpxs_cpxs" + "lfpxs_lfpxs" * ]
-             [ "cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" "cpxs_tdeq" + "cpxs_theq" + "cpxs_theq_vector" + "cpxs_drops" + "cpxs_lsubr" + "cpxs_aaa" + "cpxs_lfpx" + "cpxs_cnx" + "cpxs_cpxs" * ] 
+             [ "cpxs ( ⦃?,?⦄ ⊢ ? ⬈*[?] ? )" "cpxs_tdeq" + "cpxs_theq" + "cpxs_theq_vector" + "cpxs_drops" + "cpxs_fqus" + "cpxs_lsubr" + "cpxs_lfdeq" + "cpxs_aaa" + "cpxs_lfpx" + "cpxs_cnx" + "cpxs_cpxs" * ] 
           }
         ]
      }