X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fdynamic%2Fsnv_preserve.ma;h=482b944510621f083e3c95d077b55d2c81e654f6;hb=1083ac3b1acac5f1ac1fa40a9a417dd9d268dced;hp=c3e0444d24fdff95f6763147c8bb244125d769d5;hpb=5d669f492522b055f76c627eb89da97d0be05c2a;p=helm.git

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 c3e0444d2..482b94451 100644
--- 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
@@ -36,111 +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,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
-                   ∀l. ⦃G, L1⦄ ⊢ T1 ▪[h, g] l →
-                   ∀T2. ⦃G, L1⦄ ⊢ T1 ➡* T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 → ⦃G, L2⦄ ⊢ T2 ▪[h, g] l.
-#h #g #G #L1 #T1 #HT1 #l #Hl #T2 #H
+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 da_cpcs: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ T1 ¡[h, g] →
-               ∀T2. ⦃G, L⦄ ⊢ T2 ¡[h, g] →
-               ∀l1. ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 → ∀l2. ⦃G, L⦄ ⊢ T2 ▪[h, g] l2 →
-               ⦃G, L⦄ ⊢ T1 ⬌* T2 → l1 = l2.
-#h #g #G #L #T1 #HT1 #T2 #HT2 #l1 #Hl1 #l2 #Hl2 #H
-elim (cpcs_inv_cprs … H) -H /3 width=12 by da_cprs_lpr, da_mono/
-qed-.
-
-lemma sta_cpr_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
-                   ∀l. ⦃G, L1⦄ ⊢ T1 ▪[h, g] l+1 →
-                   ∀U1. ⦃G, L1⦄ ⊢ T1 •[h] U1 →
-                   ∀T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 →
-                   ∃∃U2. ⦃G, L2⦄ ⊢ T2 •[h] U2 & ⦃G, L2⦄ ⊢ U1 ⬌* U2.
-#h #g #G #L1 #T1 #HT1 #l #Hl #U1 #HTU1 #T2 #HT12 #L2 #HL12
-elim (lstas_cpr_lpr  … 1 … Hl U1 … HT12 … HL12) -Hl -HT12 -HL12
-/3 width=3 by lstas_inv_SO, sta_lstas, ex2_intro/
-qed-.
-
-lemma lstas_cprs_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
-                      ∀l1,l2. l2 ≤ l1 → ⦃G, L1⦄ ⊢ T1 ▪[h, g] l1 →
-                      ∀U1. ⦃G, L1⦄ ⊢ T1 •*[h, l2] U1 →
+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, l2] U2 & ⦃G, L2⦄ ⊢ U1 ⬌* U2.
-#h #g #G #L1 #T1 #HT1 #l1 #l2 #Hl21 #Hl1 #U1 #HTU1 #T2 #H
+                      ∃∃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 … g … Hl21 … HTU … HTT2 … HL12) -HTU -HTT2
-[2,3: /2 width=7 by snv_cprs_lpr, da_cprs_lpr/ ] -T1 -T -l1
+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,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
-                      ∀l,l1. l ≤ l1 → ⦃G, L1⦄ ⊢ T1 ▪[h, g] l1 → ∀U1. ⦃G, L1⦄ ⊢ T1 •*[h, l] U1 →
-                      ∀T2. ⦃G, L1⦄ ⊢ T2 ¡[h, g] →
-                      ∀l2. l ≤ l2 → ⦃G, L1⦄ ⊢ T2 ▪[h, g] l2 → ∀U2. ⦃G, L1⦄ ⊢ T2 •*[h, l] U2 →
+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 #g #G #L1 #T1 #HT1 #l #l1 #Hl1 #HTl1 #U1 #HTU1 #T2 #HT2 #l2 #Hl2 #HTl2 #U2 #HTU2 #H #L2 #HL12
+#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 … Hl1 HTl1 … HTU1 … H1 … HL12) -T1 #W1 #H1 #HUW1
-elim (lstas_cprs_lpr … HT2 … Hl2 HTl2 … HTU2 … H2 … HL12) -T2 #W2 #H2 #HUW2
-lapply (lstas_mono … H1 … H2) -h -T -l #H destruct /2 width=3 by cpcs_canc_dx/
-qed-.
-
-lemma snv_sta: ∀h,g,G,L,T. ⦃G, L⦄ ⊢ T ¡[h, g] →
-               ∀l. ⦃G, L⦄ ⊢ T ▪[h, g] l+1 →
-               ∀U. ⦃G, L⦄ ⊢ T •[h] U → ⦃G, L⦄ ⊢ U ¡[h, g].
-/3 width=7 by lstas_inv_SO, sta_lstas, snv_lstas/ qed-.
-
-lemma lstas_cpds: ∀h,g,G,L,T1. ⦃G, L⦄ ⊢ T1 ¡[h, g] →
-                  ∀l1,l2. l2 ≤ l1 → ⦃G, L⦄ ⊢ T1 ▪[h, g] l1 →
-                  ∀U1. ⦃G, L⦄ ⊢ T1 •*[h, l2] U1 → ∀T2. ⦃G, L⦄ ⊢ T1 •*➡*[h, g] T2 →
-                  ∃∃U2,l. l ≤ l2 & ⦃G, L⦄ ⊢ T2 •*[h, l] U2 & ⦃G, L⦄ ⊢ U1 •*⬌*[h, g] U2.
-#h #g #G #L #T1 #HT1 #l1 #l2 #Hl21 #Hl1 #U1 #HTU1 #T2 * #T #l0 #l #Hl0 #H #HT1T #HTT2
-lapply (da_mono … H … Hl1) -H #H destruct
-lapply (lstas_da_conf … HTU1 … Hl1) #Hl12
-elim (le_or_ge l2 l) #Hl2
-[ lapply (lstas_conf_le … HTU1 … HT1T) -HT1T //
-  /5 width=11 by cpds_cpes_dx, monotonic_le_minus_l, ex3_2_intro, ex4_3_intro/
-| lapply (lstas_da_conf … HT1T … Hl1) #Hl1l
-  lapply (lstas_conf_le … HT1T … HTU1) -HTU1 // #HTU1
-  elim (lstas_cprs_lpr … Hl1l … HTU1 … HTT2 L) -Hl1l -HTU1 -HTT2
-  /3 width=7 by snv_lstas, cpcs_cpes, monotonic_le_minus_l, ex3_2_intro/
-]
-qed-.
-
-lemma cpds_cpr_lpr: ∀h,g,G,L1,T1. ⦃G, L1⦄ ⊢ T1 ¡[h, g] →
-                    ∀U1. ⦃G, L1⦄ ⊢ T1 •*➡*[h, g] U1 →
-                    ∀T2. ⦃G, L1⦄ ⊢ T1 ➡ T2 → ∀L2. ⦃G, L1⦄ ⊢ ➡ L2 →
-                    ∃∃U2. ⦃G, L2⦄ ⊢ T2 •*➡*[h, g] U2 & ⦃G, L2⦄ ⊢ U1 ➡* U2.
-#h #g #G #L1 #T1 #HT1 #U1 * #W1 #l1 #l2 #Hl21 #Hl1 #HTW1 #HWU1 #T2 #HT12 #L2 #HL12
-elim (lstas_cpr_lpr … Hl1 … HTW1 … HT12 … HL12) // #W2 #HTW2 #HW12
-lapply (da_cpr_lpr … Hl1 … HT12 … HL12) // -T1
-lapply (lpr_cprs_conf … HL12 … HWU1) -L1 #HWU1
-lapply (cpcs_canc_sn … HW12 HWU1) -W1 #H
-elim (cpcs_inv_cprs … H) -H /3 width=7 by ex4_3_intro, ex2_intro/
+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-.