+(* 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 6:
+ 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_left_pr3 pc3_left_trans pc3_left_sym pc3_left_pc3 pc3_pc3_left
+*)