X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fequivalence%2Fcpcs_lpss.ma;h=3da649bc5a18c7bb46f07f1c4729d158d1dee749;hb=90ee1e85245752414b93826aabe388409571187a;hp=c9bcdc83d56f77c6aee431068acc1160aa67aecf;hpb=7d2817401273978654ca725fb3794a4a465a93bb;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_lpss.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_lpss.ma
index c9bcdc83d..3da649bc5 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_lpss.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_lpss.ma
@@ -20,8 +20,9 @@ include "basic_2/equivalence/cpcs_cpcs.ma".
 
 (* Properties on sn parallel substitution for local environments ************)
 
-lemma cpcs_lpss_conf: ∀L1,L2. L1 ⊢ ▶* L2 → ∀T1,T2. L1 ⊢ T1 ⬌* T2 → L2 ⊢ T1 ⬌* T2.
-#L1 #L2 #HL12 #T1 #T2 #H
+lemma cpcs_lpss_conf: ∀L1,T1,T2. L1 ⊢ T1 ⬌* T2 →
+                      ∀L2. L1 ⊢ ▶* L2 → L2 ⊢ T1 ⬌* T2.
+#L1 #T1 #T2 #H #L2 #HL12
 elim (cpcs_inv_cprs … H) -H #T #HT1 #HT2
 elim (cprs_lpss_conf_dx … HT1 … HL12) -HT1 #U1 #H1 #HTU1
 elim (cprs_lpss_conf_dx … HT2 … HL12) -L1 #U2 #H2 #HTU2
@@ -30,19 +31,21 @@ lapply (cprs_cpss_trans … HTU1 … HU1) -U1
 lapply (cprs_cpss_trans … HTU2 … HU2) -U2 /2 width=3/
 qed-.
 
-lemma cpcs_lpss_cpss_conf: ∀L1,L2. L1 ⊢ ▶* L2 →
-                           ∀T,T2. L1 ⊢ T ⬌* T2 →
-                           ∀T1. L2 ⊢ T ▶* T1 →
-                           L2 ⊢ T1 ⬌* T2.
-#L1 #L2 #HL12 #T #T2 #HT2 #T1 #HT1
-lapply (cpcs_lpss_conf … HL12 … HT2) -L1 #HT2
-lapply (cpcs_cpss_conf … HT1 … HT2) -T //
+lemma cpcs_cpss_lpss_conf: ∀L1,T,T2. L1 ⊢ T ⬌* T2 → ∀T1. L1 ⊢ T ▶* T1 →
+                           ∀L2. L1 ⊢ ▶* L2 → L2 ⊢ T1 ⬌* T2.
+#L1 #T #T2 #HT2 #T1 #HT1 #L2 #HL12
+lapply (cpcs_lpss_conf … HT2 … HL12) -HT2 #HT2
+elim (lpss_cpss_conf_dx … HT1 … HL12) -L1 #T0 #HT0 #HT10
+lapply (cpcs_cpss_conf … HT0 … HT2) -T #HT02
+lapply (cpcs_cpss_strap2 … HT10 … HT02) -T0 //
 qed-.
 
-lemma cpcs_lpss_cpss2_conf: ∀L1,L2. L1 ⊢ ▶* L2 → ∀T1,T2. L1 ⊢ T1 ⬌* T2 →
-                            ∀T3. L2 ⊢ T1 ▶* T3 → ∀T4. L2 ⊢ T2 ▶* T4 →
-                            L2 ⊢ T3 ⬌* T4.
-#L1 #L2 #HL12 #T1 #T2 #HT12 #T3 #HT13 #T4 #HT24
-lapply (cpcs_lpss_cpss_conf … HL12 … HT12 … HT13) -L1 -T1 #HT32
-lapply (cpcs_cpss_strap1 … HT32 … HT24) -T2 //
+lemma cpcs_cpss2_lpss_conf: ∀L1,T1,T2. L1 ⊢ T1 ⬌* T2 →
+                            ∀T3. L1 ⊢ T1 ▶* T3 → ∀T4. L1 ⊢ T2 ▶* T4 →
+                            ∀L2. L1 ⊢ ▶* L2 → L2 ⊢ T3 ⬌* T4.
+#L1 #T1 #T2 #HT12 #T3 #HT13 #T4 #HT24 #L2 #HL12
+lapply (cpcs_cpss_lpss_conf … HT12 … HT13 … HL12) -T1 #HT32
+elim (lpss_cpss_conf_dx … HT24 … HL12) -L1 #T #HT2 #HT4
+lapply (cpcs_cpss_strap1 … HT32 … HT2) -T2 #HT3
+lapply (cpcs_cpss_div … HT3 … HT4) -T //
 qed-.