- basic_2: induction for preservation results now uses supclosure

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma
index 9d9ceb942c0386bd3b87832307769acdc0114dec..e4388e3b29ae873bc7dd83336605bfb496ca14f9 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/equivalence/cpcs.ma
@@ -16,8 +16,7 @@ include "basic_2/conversion/cpc.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL EQUIVALENCE ON TERMS **************************)
 
-definition cpcs: lenv → relation term ≝
-                 λL. TC … (cpc L).
+definition cpcs: lenv → relation term ≝ LTC … cpc.
 
 interpretation "context-sensitive parallel equivalence (term)"
    'PConvStar L T1 T2 = (cpcs L T1 T2).
@@ -45,26 +44,23 @@ lemma cpcs_refl: ∀L. reflexive … (cpcs L).
 
 (* Basic_1: was: pc3_s *)
 lemma cpcs_sym: ∀L. symmetric … (cpcs L).
-/3 width=1/ qed.
+#L @TC_symmetric // qed.
+
+lemma cpc_cpcs: ∀L,T1,T2. L ⊢ T1 ⬌ T2 → L ⊢ T2 ⬌* T2.
+/2 width=1/ qed.
 
 lemma cpcs_strap1: ∀L,T1,T,T2. L ⊢ T1 ⬌* T → L ⊢ T ⬌ T2 → L ⊢ T1 ⬌* T2.
-/2 width=3/ qed.
+#L @step qed.
 
 lemma cpcs_strap2: ∀L,T1,T,T2. L ⊢ T1 ⬌ T → L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
-/2 width=3/ qed.
+#L @TC_strap qed.
 
 (* Basic_1: was: pc3_pr2_r *)
-lemma cpcs_cpr_dx: ∀L,T1,T2. L ⊢ T1 ➡ T2 → L ⊢ T1 ⬌* T2.
-/3 width=1/ qed.
-
-lemma cpcs_tpr_dx: ∀L,T1,T2. T1 ➡ T2 → L ⊢ T1 ⬌* T2.
+lemma cpr_cpcs_dx: ∀L,T1,T2. L ⊢ T1 ➡ T2 → L ⊢ T1 ⬌* T2.
 /3 width=1/ qed.
 
 (* Basic_1: was: pc3_pr2_x *)
-lemma cpcs_cpr_sn: ∀L,T1,T2. L ⊢ T2 ➡ T1 → L ⊢ T1 ⬌* T2.
-/3 width=1/ qed.
-
-lemma cpcs_tpr_sn: ∀L,T1,T2. T2 ➡ T1 → L ⊢ T1 ⬌* T2.
+lemma cpr_cpcs_sn: ∀L,T1,T2. L ⊢ T2 ➡ T1 → L ⊢ T1 ⬌* T2.
 /3 width=1/ qed.
 
 lemma cpcs_cpr_strap1: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T ➡ T2 → L ⊢ T1 ⬌* T2.
@@ -84,11 +80,32 @@ lemma cpr_div: ∀L,T1,T. L ⊢ T1 ➡ T → ∀T2. L ⊢ T2 ➡ T → L ⊢ T1
 lemma cpcs_cpr_conf: ∀L,T1,T. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
 /3 width=3/ qed.
 
+lemma cpcs_cpss_strap1: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T ▶* T2 → L ⊢ T1 ⬌* T2.
+#L #T1 #T #HT1 #T2 #HT2
+@(cpcs_cpr_strap1 … HT1) -T1 /2 width=3/
+qed-.
+
+lemma cpcs_cpss_strap2: ∀L,T1,T. L ⊢ T1 ▶* T → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
+#L #T1 #T #HT1 #T2 #HT2
+@(cpcs_cpr_strap2 … HT2) -T2 /2 width=3/
+qed-.
+
+lemma cpcs_cpss_conf: ∀L,T,T1. L ⊢ T ▶* T1 → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
+#L #T #T1 #HT1 #T2 #HT2
+@(cpcs_cpr_conf … HT2) -T2 /2 width=3/
+qed-.
+
+lemma cpcs_cpss_div: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T2 ▶* T → L ⊢ T1 ⬌* T2.
+#L #T1 #T #HT1 #T2 #HT2
+@(cpcs_cpr_div … HT1) -T1 /2 width=3/
+qed-.
+
 (* Basic_1: removed theorems 9:
             clear_pc3_trans pc3_ind_left
             pc3_head_1 pc3_head_2 pc3_head_12 pc3_head_21
             pc3_pr2_fsubst0 pc3_pr2_fsubst0_back pc3_fsubst0
-   Basic_1: removed local theorems 6:
+*)
+(* Basic_1: removed local theorems 6:
             pc3_left_pr3 pc3_left_trans pc3_left_sym pc3_left_pc3 pc3_pc3_left
             pc3_wcpr0_t_aux
 *)