- lambda_delta: subject reduction for nativa type assignment begins ...

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

diff --git a/matita/matita/contribs/lambda_delta/basic_2/equivalence/cpcs.ma b/matita/matita/contribs/lambda_delta/basic_2/equivalence/cpcs.ma
index 58e53ed781b856f5336e89aed10517742ed2b657..346189f92a0bdc01ea57c563ed85bc22addb96ab 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/equivalence/cpcs.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/equivalence/cpcs.ma
@@ -30,18 +30,60 @@ lemma cpcs_ind: ∀L,T1. ∀R:predicate term. R T1 →
 #L #T1 #R #HT1 #IHT1 #T2 #HT12 @(TC_star_ind … HT1 IHT1 … HT12) //
 qed-.
 
+lemma cpcs_ind_dx: ∀L,T2. ∀R:predicate term. R T2 →
+                   (∀T1,T. L ⊢ T1 ⬌ T → L ⊢ T ⬌* T2 → R T → R T1) →
+                   ∀T1. L ⊢ T1 ⬌* T2 → R T1.
+#L #T2 #R #HT2 #IHT2 #T1 #HT12
+@(TC_star_ind_dx … HT2 IHT2 … HT12) //
+qed-.
+
 (* Basic properties *********************************************************)
 
 (* Basic_1: was: pc3_refl *)
 lemma cpcs_refl: ∀L,T. L ⊢ T ⬌* T.
 /2 width=1/ qed.
 
-lemma cpcs_strap1: ∀L,T1,T,T2.
-                   L ⊢ T1 ⬌* T → L ⊢ T ⬌ T2 → L ⊢ T1 ⬌* T2.
+lemma cpcs_sym: ∀L,T1,T2. L ⊢ T1 ⬌* T2 → L ⊢ T2 ⬌* T1.
+/3 width=1/ qed.
+
+lemma cpcs_strap1: ∀L,T1,T,T2. L ⊢ T1 ⬌* T → L ⊢ T ⬌ T2 → L ⊢ T1 ⬌* T2.
 /2 width=3/ qed.
 
-lemma cpcs_strap2: ∀L,T1,T,T2.
-                   L ⊢ T1 ⬌ T → L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
+lemma cpcs_strap2: ∀L,T1,T,T2. L ⊢ T1 ⬌ T → L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
 /2 width=3/ qed.
 
-(* Basic_1: removed theorems 1: clear_pc3_trans *)
+(* Basic_1: was: pc3_pr2_r *)
+lemma cpcs_cpr_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_cpr_strap1: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T ➡ T2 → L ⊢ T1 ⬌* T2.
+/3 width=3/ qed.
+
+(* Basic_1: was: pc3_pr2_u *)
+lemma cpcs_cpr_strap2: ∀L,T1,T. L ⊢ T1 ➡ T → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
+/3 width=3/ qed.
+
+lemma cpcs_cpr_div: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T2 ➡ T → L ⊢ T1 ⬌* T2.
+/3 width=3/ qed.
+
+(* Basic_1: was: pc3_pr2_u2 *)
+lemma cpcs_cpr_conf: ∀L,T1,T. L ⊢ T ➡ T1 → ∀T2. L ⊢ T ⬌* T2 → L ⊢ T1 ⬌* T2.
+/3 width=3/ qed.
+
+(* Basic_1: was: pc3_s *)
+lemma cprs_comm: ∀L,T1,T2. L ⊢ T1 ⬌* T2 → L ⊢ T2 ⬌* T1.
+#L #T1 #T2 #H @(cpcs_ind … H) -T2 // /3 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:
+            pc3_left_pr3 pc3_left_trans pc3_left_sym pc3_left_pc3 pc3_pc3_left
+            pc3_wcpr0_t_aux
+*)