update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / equivalence / cpcs_cprs.ma

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 69641dbf72ceb3b3fd3134dcdad92fc18bebc8be..d9db0509f9349fefa27218fbd2945a7570bf923c 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs_cprs.ma
@@ -21,35 +21,38 @@ include "basic_2/equivalence/cpcs.ma".
 
 (* Basic_1: was: pc3_pr3_r *)
 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 /width=1/ /3 width=3/
+#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: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T2 ➡* T1 → ⦃G, L⦄ ⊢ T1 ⬌* T2.
-#G #L #T1 #T2 #H @(cprs_ind_dx … H) -T2 /width=1/ /3 width=3/
+#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: ∀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 /width=1/ /2 width=3/
-qed.
+#G #L #T1 #T #HT1 #T2 #H @(cprs_ind … H) -T2 /2 width=3 by cpcs_cpr_strap1/
+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 /width=1/ /2 width=3/
-qed.
+#G #L #T1 #T #H #T2 #HT2 @(cprs_ind_dx … H) -T1 /2 width=3 by cpcs_cpr_strap2/
+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 /width=1/ /2 width=3/
-qed.
+#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: ∀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 /width=1/ /2 width=3/
-qed.
+#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: ∀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=1/ /2 width=3/
+#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: ∀G,L,T1,T. ⦃G, L⦄ ⊢ T1 ➡* T → ∀T2. ⦃G, L⦄ ⊢ T2 ➡ T → ⦃G, L⦄ ⊢ T1 ⬌* T2.