X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Flambdadelta%2Fbasic_2%2Fequivalence%2Fcpcs_cprs.ma;h=d9db0509f9349fefa27218fbd2945a7570bf923c;hb=e62715437a9c39244c9809c00585a5ef44a39797;hp=30ee9fb9d2730b0a76a0f3af745909a5bd787848;hpb=29973426e0227ee48368d1c24dc0c17bf2baef77;p=helm.git

diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma
index 30ee9fb9d..d9db0509f 100644
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma
@@ -20,40 +20,43 @@ include "basic_2/equivalence/cpcs.ma".
 (* Properties about context sensitive computation on terms ******************)
 
 (* Basic_1: was: pc3_pr3_r *)
-lemma cpcs_cprs_dx: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T2 #H @(cprs_ind … H) -T2 /width=1/ /3 width=3/
+lemma cpcs_cprs_dx: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T2 #H @(cprs_ind … H) -T2
+/3 width=3 by cpcs_cpr_strap1, cpcs_strap1, cpc_cpcs/
 qed.
 
 (* Basic_1: was: pc3_pr3_x *)
-lemma cpcs_cprs_sn: ∀L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡* T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /3 width=3/
+lemma cpcs_cprs_sn: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡* T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T2 #H @(cprs_ind_dx … H) -T2
+/3 width=3 by cpcs_cpr_div, cpcs_strap1, cpcs_cprs_dx/
 qed.
 
-lemma cpcs_cprs_strap1: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T #HT1 #T2 #H @(cprs_ind … H) -T2 /width=1/ /2 width=3/
-qed.
+lemma cpcs_cprs_strap1: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T ➡* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T #HT1 #T2 #H @(cprs_ind … H) -T2 /2 width=3 by cpcs_cpr_strap1/
+qed-.
 
-lemma cpcs_cprs_strap2: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T #H #T2 #HT2 @(cprs_ind_dx … H) -T1 /width=1/ /2 width=3/
-qed.
+lemma cpcs_cprs_strap2: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T #H #T2 #HT2 @(cprs_ind_dx … H) -T1 /2 width=3 by cpcs_cpr_strap2/
+qed-.
 
-lemma cpcs_cprs_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /2 width=3/
-qed.
+lemma cpcs_cprs_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ⬌* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /2 width=3 by cpcs_cpr_div/
+qed-.
 
 (* Basic_1: was: pc3_pr3_conf *)
-lemma cpcs_cprs_conf: ∀L,T1,T. ⦃G, L⦄ ⊢ T ➡* T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T #H #T2 #HT2 @(cprs_ind … H) -T1 /width=1/ /2 width=3/
-qed.
+lemma cpcs_cprs_conf: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T ➡* T1 → ∀T2. ⦃G, L⦄ ⊢ T ⬌* T2 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T #H #T2 #HT2 @(cprs_ind … H) -T1 /2 width=3 by cpcs_cpr_conf/
+qed-.
 
 (* Basic_1: was: pc3_pr3_t *)
 (* Basic_1: note: pc3_pr3_t should be renamed *)
-lemma cprs_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2 /2 width=1/ /2 width=3/
+lemma cprs_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+#G #L #T1 #T #HT1 #T2 #H @(cprs_ind_dx … H) -T2
+/2 width=3 by cpcs_cpr_div, cpcs_cprs_dx/
 qed.
 
-lemma cprs_cpr_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+lemma cprs_cpr_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=5 by cpr_cprs, cprs_div/ qed-.
 
-lemma cpr_cprs_div: ∀L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
+lemma cpr_cprs_div: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡ T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡* T → ⦃G, L⦄ ⊢ T1 ⬌* T2.
 /3 width=3 by cpr_cprs, cprs_div/ qed-.