include "basic_2/computation/cprs_cprs.ma".
include "basic_2/computation/cpre.ma".
-(* CONTEXT-SENSITIVE PARALLEL EVALUATION ON TERMS **************************)
+(* EVALUATION FOR CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS *************)
(* Main properties *********************************************************)
(* Basic_1: was: nf2_pr3_confluence *)
-theorem cpre_mono: ∀L,T,T1. ⦃G, L⦄ ⊢ T ➡* 𝐍⦃T1⦄ → ∀T2. ⦃G, L⦄ ⊢ T ➡* 𝐍⦃T2⦄ → T1 = T2.
-#L #T #T1 * #H1T1 #H2T1 #T2 * #H1T2 #H2T2
+theorem cpre_mono: ∀G,L,T,T1. ⦃G, L⦄ ⊢ T ➡* 𝐍⦃T1⦄ → ∀T2. ⦃G, L⦄ ⊢ T ➡* 𝐍⦃T2⦄ → T1 = T2.
+#G #L #T #T1 * #H1T1 #H2T1 #T2 * #H1T2 #H2T2
elim (cprs_conf … H1T1 … H1T2) -T #T #HT1
>(cprs_inv_cnr1 … HT1 H2T1) -T1 #HT2
>(cprs_inv_cnr1 … HT2 H2T2) -T2 //