(* *)
(**************************************************************************)
-include "Basic-2/reduction/tpr_tpr.ma".
-include "Basic-2/reduction/cpr.ma".
+include "Basic_2/reduction/tpr_tpr.ma".
+include "Basic_2/reduction/cpr.ma".
(* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
@ex2_1_intro [2: @(tpr_delta … HV1 HT12) | skip ] /2/ (* /3 width=5/ is too slow *)
qed.
-(* Basic-1: was only: pr2_gen_cbind *)
+(* Basic_1: was only: pr2_gen_cbind *)
lemma cpr_bind_dx: ∀I,L,V1,V2,T1,T2. V1 ⇒ V2 → L. 𝕓{I} V2 ⊢ T1 ⇒ T2 →
L ⊢ 𝕓{I} V1. T1 ⇒ 𝕓{I} V2. T2.
#I #L #V1 #V2 #T1 #T2 #HV12 * #T #HT1 normalize #HT2
elim (tpss_split_up … HT2 1 ? ?) -HT2 // #T0 <minus_n_O #HT0 normalize <minus_plus_m_m #HT02
-lapply (tpss_leq_repl_dx … HT0 (⋆. 𝕓{I} V2) ?) -HT0 /2/ #HT0
+lapply (tpss_lsubs_conf … HT0 (⋆. 𝕓{I} V2) ?) -HT0 /2/ #HT0
lapply (tpss_tps … HT0) -HT0 #HT0
@ex2_1_intro [2: @(tpr_delta … HV12 HT1 HT0) | skip | /2/ ] (**) (* /3 width=5/ is too slow *)
qed.
(* Main properties **********************************************************)
-(* Basic-1: was: pr2_confluence *)
+(* Basic_1: was: pr2_confluence *)
theorem cpr_conf: ∀L,U0,T1,T2. L ⊢ U0 ⇒ T1 → L ⊢ U0 ⇒ T2 →
∃∃T. L ⊢ T1 ⇒ T & L ⊢ T2 ⇒ T.
#L #U0 #T1 #T2 * #U1 #HU01 #HUT1 * #U2 #HU02 #HUT2