(* CONTEXT-SENSITIVE PARALLEL R-CONVERSION FOR TERMS ************************)
definition cpc: sh → relation4 genv lenv term term ≝
- λh,G,L,T1,T2. ❪G,L❫ ⊢ T1 ➡[h] T2 ∨ ❪G,L❫ ⊢ T2 ➡[h] T1.
+ λh,G,L,T1,T2. ❪G,L❫ ⊢ T1 ➡[h,0] T2 ∨ ❪G,L❫ ⊢ T2 ➡[h,0] T1.
interpretation
"context-sensitive parallel r-conversion (term)"
(* Basic forward lemmas *****************************************************)
lemma cpc_fwd_cpr: ∀h,G,L,T1,T2. ❪G,L❫ ⊢ T1 ⬌[h] T2 →
- ∃∃T. ❪G,L❫ ⊢ T1 ➡[h] T & ❪G,L❫ ⊢ T2 ➡[h] T.
+ ∃∃T. ❪G,L❫ ⊢ T1 ➡[h,0] T & ❪G,L❫ ⊢ T2 ➡[h,0] T.
#h #G #L #T1 #T2 * /2 width=3 by ex2_intro/
qed-.