- lambda: first half of the standardization theorem is proved!

[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 e38825fe1a2bbf1ad0a83143b4c2b0c7cfd1cc2a..9d9ceb942c0386bd3b87832307769acdc0114dec 100644 (file)
--- a/matita/matita/contribs/lambda_delta/basic_2/equivalence/cpcs.ma
+++ b/matita/matita/contribs/lambda_delta/basic_2/equivalence/cpcs.ma
@@ -40,9 +40,13 @@ qed-.
 (* Basic properties *********************************************************)
 
 (* Basic_1: was: pc3_refl *)
-lemma cpcs_refl: ∀L,T. L ⊢ T ⬌* T.
+lemma cpcs_refl: ∀L. reflexive … (cpcs L).
 /2 width=1/ qed.
 
+(* Basic_1: was: pc3_s *)
+lemma cpcs_sym: ∀L. symmetric … (cpcs L).
+/3 width=1/ qed.
+
 lemma cpcs_strap1: ∀L,T1,T,T2. L ⊢ T1 ⬌* T → L ⊢ T ⬌ T2 → L ⊢ T1 ⬌* T2.
 /2 width=3/ qed.
 
@@ -53,10 +57,16 @@ lemma cpcs_strap2: ∀L,T1,T,T2. L ⊢ T1 ⬌ T → L ⊢ T ⬌* T2 → L ⊢ T1
 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.
+/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.
+/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.
 
@@ -67,18 +77,18 @@ lemma cpcs_cpr_strap2: ∀L,T1,T. L ⊢ T1 ➡ T → ∀T2. L ⊢ T ⬌* T2 →
 lemma cpcs_cpr_div: ∀L,T1,T. L ⊢ T1 ⬌* T → ∀T2. L ⊢ T2 ➡ T → L ⊢ T1 ⬌* T2.
 /3 width=3/ qed.
 
+lemma 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 6:
+(* Basic_1: removed theorems 9:
             clear_pc3_trans pc3_ind_left
             pc3_head_1 pc3_head_2 pc3_head_12 pc3_head_21
-   Basic_1: removed local theorems 5:
+            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
 *)