(* CONTEXT-SENSITIVE PARALLEL CONVERSION ON TERMS ***************************)
definition cpc: lenv → relation term ≝
- λL,T1,T2. L ⊢ T1 ➡ T2 ∨ L ⊢ T2 ➡ T1.
+ λL,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 ∨ ⦃G, L⦄ ⊢ T2 ➡ T1.
interpretation
"context-sensitive parallel conversion (term)"
(* Basic forward lemmas *****************************************************)
-lemma cpc_fwd_cpr: ∀L,T1,T2. L ⊢ T1 ⬌ T2 → ∃∃T. L ⊢ T1 ➡ T & L ⊢ T2 ➡ T.
+lemma cpc_fwd_cpr: ∀L,T1,T2. ⦃G, L⦄ ⊢ T1 ⬌ T2 → ∃∃T. ⦃G, L⦄ ⊢ T1 ➡ T & ⦃G, L⦄ ⊢ T2 ➡ T.
#L #T1 #T2 * /2 width=3/
qed.