- degree-based equivalene for terms

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / etc_2A1 / cpr / cpr_cpr.etc

diff --git a/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/cpr_cpr.etc b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/cpr_cpr.etc
new file mode 100644 (file)
index 0000000..d231c84
--- /dev/null
+++ b/matita/matita/contribs/lambdadelta/basic_2/etc_2A1/cpr/cpr_cpr.etc
@@ -0,0 +1,63 @@
+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+include "basic_2/reducibility/tpr_tpr.ma".
+include "basic_2/reducibility/cpr.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL REDUCTION ON TERMS ****************************)
+
+(* Advanced properties ******************************************************)
+
+lemma cpr_bind_sn: ∀a,I,L,V1,V2,T1,T2. L ⊢ V1 ➡ V2 → T1 ➡ T2 →
+                   L ⊢ ⓑ{a,I} V1. T1 ➡ ⓑ{a,I} V2. T2.
+#a #I #L #V1 #V2 #T1 #T2 * #V #HV1 #HV2 #HT12
+@ex2_intro [2: @(tpr_delta … HV1 HT12) | skip ] /2 width=3/ (* /3 width=5/ is too slow *)
+qed.
+
+(* Basic_1: was only: pr2_gen_cbind *)
+lemma cpr_bind_dx: ∀a,I,L,V1,V2,T1,T2. V1 ➡ V2 → L. ⓑ{I} V2 ⊢ T1 ➡ T2 →
+                   L ⊢ ⓑ{a,I} V1. T1 ➡ ⓑ{a,I} V2. T2.
+#a #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_lsubr_trans … HT0 (⋆. ⓑ{I} V2) ?) -HT0 /2 width=1/ #HT0
+lapply (tpss_inv_SO2 … HT0) -HT0 #HT0
+@ex2_intro [2: @(tpr_delta … HV12 HT1 HT0) | skip | /2 width=1/ ] (**) (* /3 width=5/ is too slow *)
+qed.
+
+(* Basic_1: was only: pr2_head_1 *)
+lemma cpr_pair_sn: ∀I,L,V1,V2,T1,T2. L ⊢ V1 ➡ V2 → T1 ➡ T2 →
+                   L ⊢ ②{I} V1. T1 ➡ ②{I} V2. T2.
+* /2 width=1/ /3 width=1/
+qed.
+
+(* Advanced forward lemmas **************************************************)
+
+lemma cpr_shift_fwd: ∀L,T1,T2. L ⊢ T1 ➡ T2 → L @@ T1 ➡ L @@ T2.
+#L elim L -L
+[ #T1 #T2 #HT12 @(cpr_inv_atom … HT12)
+| normalize /3 width=1/
+].
+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 (ltpr_tpr_tpss_conf ? L … HU1 … HUT1) -U1 // #U1 #HTU1 #HU1
+elim (ltpr_tpr_tpss_conf ? L … HU2 … HUT2) -U2 // #U2 #HTU2 #HU2
+elim (tpss_conf_eq … HU1 … HU2) -U /3 width=5/
+qed.