(* CONTEXT-SENSITIVE PARALLEL R-CONVERSION FOR TERMS ************************)
definition cpc: sh → relation4 genv lenv term term ≝
- λh,G,L,T1,T2. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡[h] T2 â\88¨ â¦\83G,Lâ¦\84 ⊢ T2 ➡[h] T1.
+ λh,G,L,T1,T2. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h] T2 â\88¨ â\9dªG,Lâ\9d« ⊢ T2 ➡[h] T1.
interpretation
"context-sensitive parallel r-conversion (term)"
(* Basic forward lemmas *****************************************************)
-lemma cpc_fwd_cpr: â\88\80h,G,L,T1,T2. â¦\83G,Lâ¦\84 ⊢ T1 ⬌[h] T2 →
- â\88\83â\88\83T. â¦\83G,Lâ¦\84 â\8a¢ T1 â\9e¡[h] T & â¦\83G,Lâ¦\84 ⊢ T2 ➡[h] T.
+lemma cpc_fwd_cpr: â\88\80h,G,L,T1,T2. â\9dªG,Lâ\9d« ⊢ T1 ⬌[h] T2 →
+ â\88\83â\88\83T. â\9dªG,Lâ\9d« â\8a¢ T1 â\9e¡[h] T & â\9dªG,Lâ\9d« ⊢ T2 ➡[h] T.
#h #G #L #T1 #T2 * /2 width=3 by ex2_intro/
qed-.