update in ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / dynamic / snv_preserve.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.ma b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.ma
index 5f76fea80a0cbce0d4e3d71e0509c1bc13e5c18f..482b944510621f083e3c95d077b55d2c81e654f6 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/dynamic/snv_preserve.ma
@@ -22,13 +22,13 @@ include "basic_2/dynamic/snv_lpr.ma".
 
 (* Main preservation properties *********************************************)
 
-lemma snv_preserve: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] →
-                    ∧∧ IH_da_cpr_lpr h g G L T
-                     & IH_snv_cpr_lpr h g G L T
-                     & IH_snv_lstas h g G L T
-                     & IH_lstas_cpr_lpr h g G L T.
-#h #g #G #L #T #HT elim (snv_fwd_aaa … HT) -HT
-#A #HT @(aaa_ind_fpbg h g … HT) -G -L -T -A
+lemma snv_preserve: ∀h,o,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, o] →
+                    ∧∧ IH_da_cpr_lpr h o G L T
+                     & IH_snv_cpr_lpr h o G L T
+                     & IH_snv_lstas h o G L T
+                     & IH_lstas_cpr_lpr h o G L T.
+#h #o #G #L #T #HT elim (snv_fwd_aaa … HT) -HT
+#A #HT @(aaa_ind_fpbg h o … HT) -G -L -T -A
 #G #L #T #A #_ #IH -A @and4_intro
 [ letin aux ≝ da_cpr_lpr_aux | letin aux ≝ snv_cpr_lpr_aux
 | letin aux ≝ snv_lstas_aux | letin aux ≝ lstas_cpr_lpr_aux
@@ -36,26 +36,59 @@ lemma snv_preserve: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] →
 @(aux … G L T) // #G0 #L0 #T0 #H elim (IH … H) -IH -H //
 qed-.
 
-theorem da_cpr_lpr: ∀h,g,G,L,T. IH_da_cpr_lpr h g G L T.
-#h #g #G #L #T #HT elim (snv_preserve … HT) /2 width=1 by/
+theorem da_cpr_lpr: ∀h,o,G,L,T. IH_da_cpr_lpr h o G L T.
+#h #o #G #L #T #HT elim (snv_preserve … HT) /2 width=1 by/
 qed-.
 
-theorem snv_cpr_lpr: ∀h,g,G,L,T. IH_snv_cpr_lpr h g G L T.
-#h #g #G #L #T #HT elim (snv_preserve … HT) /2 width=1 by/
+theorem snv_cpr_lpr: ∀h,o,G,L,T. IH_snv_cpr_lpr h o G L T.
+#h #o #G #L #T #HT elim (snv_preserve … HT) /2 width=1 by/
 qed-.
 
-theorem snv_lstas: ∀h,g,G,L,T. IH_snv_lstas h g G L T.
-#h #g #G #L #T #HT elim (snv_preserve … HT) /2 width=5 by/
+theorem snv_lstas: ∀h,o,G,L,T. IH_snv_lstas h o G L T.
+#h #o #G #L #T #HT elim (snv_preserve … HT) /2 width=5 by/
 qed-.
 
-theorem lstas_cpr_lpr: ∀h,g,G,L,T. IH_lstas_cpr_lpr h g G L T.
-#h #g #G #L #T #HT elim (snv_preserve … HT) /2 width=3 by/
+theorem lstas_cpr_lpr: ∀h,o,G,L,T. IH_lstas_cpr_lpr h o G L T.
+#h #o #G #L #T #HT elim (snv_preserve … HT) /2 width=3 by/
 qed-.
 
 (* Advanced preservation properties *****************************************)
 
-lemma snv_cprs_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
-                    ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ¡[h, g].
-#h #g #G #L1 #T1 #HT1 #T2 #H
+lemma snv_cprs_lpr: ∀h,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] →
+                    ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ¡[h, o].
+#h #o #G #L1 #T1 #HT1 #T2 #H
 @(cprs_ind … H) -T2 /3 width=5 by snv_cpr_lpr/
 qed-.
+
+lemma da_cprs_lpr: ∀h,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] →
+                   ∀d. ⦃G, L1⦄ ⊢ T1 ▪[h, o] d →
+                   ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ▪[h, o] d.
+#h #o #G #L1 #T1 #HT1 #d #Hd #T2 #H
+@(cprs_ind … H) -T2 /3 width=6 by snv_cprs_lpr, da_cpr_lpr/
+qed-.
+
+lemma lstas_cprs_lpr: ∀h,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] →
+                      ∀d1,d2. d2 ≤ d1 → ⦃G, L1⦄ ⊢ T1 ▪[h, o] d1 →
+                      ∀U1. ⦃G, L1⦄ ⊢ T1 •*[h, d2] U1 →
+                      ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 →
+                      ∃∃U2. ⦃G, L2⦄ ⊢ T2 •*[h, d2] U2 & ⦃G, L2⦄ ⊢ U1 ⬌* U2.
+#h #o #G #L1 #T1 #HT1 #d1 #d2 #Hd21 #Hd1 #U1 #HTU1 #T2 #H
+@(cprs_ind … H) -T2 [ /2 width=10 by lstas_cpr_lpr/ ]
+#T #T2 #HT1T #HTT2 #IHT1 #L2 #HL12
+elim (IHT1 L1) // -IHT1 #U #HTU #HU1
+elim (lstas_cpr_lpr … o … Hd21 … HTU … HTT2 … HL12) -HTU -HTT2
+[2,3: /2 width=7 by snv_cprs_lpr, da_cprs_lpr/ ] -T1 -T -d1
+/4 width=5 by lpr_cpcs_conf, cpcs_trans, ex2_intro/
+qed-.
+
+lemma lstas_cpcs_lpr: ∀h,o,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, o] →
+                      ∀d,d1. d ≤ d1 → ⦃G, L1⦄ ⊢ T1 ▪[h, o] d1 → ∀U1. ⦃G, L1⦄ ⊢ T1 •*[h, d] U1 →
+                      ∀T2. ⦃G, L1⦄ ⊢ T2 ¡[h, o] →
+                      ∀d2. d ≤ d2 → ⦃G, L1⦄ ⊢ T2 ▪[h, o] d2 → ∀U2. ⦃G, L1⦄ ⊢ T2 •*[h, d] U2 →
+                      ⦃G, L1⦄ ⊢ T1 ⬌* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ U1 ⬌* U2.
+#h #o #G #L1 #T1 #HT1 #d #d1 #Hd1 #HTd1 #U1 #HTU1 #T2 #HT2 #d2 #Hd2 #HTd2 #U2 #HTU2 #H #L2 #HL12
+elim (cpcs_inv_cprs … H) -H #T #H1 #H2
+elim (lstas_cprs_lpr … HT1 … Hd1 HTd1 … HTU1 … H1 … HL12) -T1 #W1 #H1 #HUW1
+elim (lstas_cprs_lpr … HT2 … Hd2 HTd2 … HTU2 … H2 … HL12) -T2 #W2 #H2 #HUW2
+lapply (lstas_mono … H1 … H2) -h -T -d #H destruct /2 width=3 by cpcs_canc_dx/
+qed-.