(* 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.
-lemma cpcs_sym: ∀L,T1,T2. L ⊢ T1 ⬌* T2 → L ⊢ T2 ⬌* T1.
+(* 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.
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.
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 9:
clear_pc3_trans pc3_ind_left
pc3_head_1 pc3_head_2 pc3_head_12 pc3_head_21