- the confluence of context-senstitive parallel reduction (cpr) is closed!

[helm.git] / matita / matita / contribs / lambda-delta / Basic-2 / reduction / cpr_cpr.ma

diff --git a/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr_cpr.ma b/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr_cpr.ma
index d544918acc0e6dc2267619da5a948581b3a4c9fd..08620900765d54f2097db20b105bd7d17ae9a78f 100644 (file)
--- a/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr_cpr.ma
+++ b/matita/matita/contribs/lambda-delta/Basic-2/reduction/cpr_cpr.ma
@@ -17,12 +17,42 @@ include "Basic-2/reduction/cpr.ma".
 
 (* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
 
+(* Advanced properties ******************************************************)
+
+lemma cpr_bind_sn: ∀I,L,V1,V2,T1,T2. L ⊢ V1 ⇒ V2 → T1 ⇒ T2 →
+                   L ⊢ 𝕓{I} V1. T1 ⇒ 𝕓{I} V2. T2.
+#I #L #V1 #V2 #T1 #T2 * #V #HV1 #HV2 #HT12 
+@ex2_1_intro [2: @(tpr_delta … HV1 HT12) | skip ] /2/ (* /3 width=5/ is too slow *)
+qed.
+
+(* 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_tps … HT0) -HT0 #HT0
+@ex2_1_intro [2: @(tpr_delta … HV12 HT1 HT0) | skip | /2/ ] (**) (* /3 width=5/ is too slow *)
+qed.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma cpr_shift_fwd: ∀L,T1,T2. L ⊢ T1 ⇒ T2 → L @ T1 ⇒ L @ T2.
+#L elim L -L
+[ /2/
+| normalize /3/
+].
+qed.
+
 (* Main properties **********************************************************)
-(*
+
 (* 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
 elim (tpr_conf … HU01 HU02) -U0 #U #HU1 #HU2 
+elim (tpr_tpss_ltpr ? L … HU1 … HUT1) -U1 // #U1 #HTU1 #HU1
+elim (tpr_tpss_ltpr ? L … HU2 … HUT2) -U2 // #U2 #HTU2 #HU2
+elim (tpss_conf_eq … HU1 … HU2) -U /3 width=5/
 qed.
-*)
+