(* *)
(**************************************************************************)
+include "basic_2/notation/relations/pconvstar_3.ma".
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).
(* 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.
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_gen_abst pc3_gen_abst_shift
+*)
+(* 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
*)