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

[helm.git] / matita / matita / contribs / lambda-delta / Basic-2 / unfold / ltpss_ltpss.ma

diff --git a/matita/matita/contribs/lambda-delta/Basic-2/unfold/ltpss_ltpss.ma b/matita/matita/contribs/lambda-delta/Basic-2/unfold/ltpss_ltpss.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||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/unfold/ltpss_tpss.ma".
+
+(* PARTIAL UNFOLD ON LOCAL ENVIRONMENTS *************************************)
+
+(* Main properties **********************************************************)
+
+theorem ltpss_trans_eq: ∀L1,L,L2,d,e.
+                        L1 [d, e] ≫* L → L [d, e] ≫* L2 → L1 [d, e] ≫* L2. 
+/2/ qed.
+
+lemma ltpss_tpss2: ∀L1,L2,I,V1,V2,e.
+                   L1 [0, e] ≫* L2 → L2 ⊢ V1 [0, e] ≫* V2 →
+                   L1. 𝕓{I} V1 [0, e + 1] ≫* L2. 𝕓{I} V2.
+#L1 #L2 #I #V1 #V2 #e #HL12 #H @(tpss_ind … H) -V2
+[ /2/
+| #V #V2 #_ #HV2 #IHV @(ltpss_trans_eq … IHV) /2/
+]
+qed.
+
+lemma ltpss_tpss2_lt: ∀L1,L2,I,V1,V2,e.
+                      L1 [0, e - 1] ≫* L2 → L2 ⊢ V1 [0, e - 1] ≫* V2 →
+                      0 < e → L1. 𝕓{I} V1 [0, e] ≫* L2. 𝕓{I} V2.
+#L1 #L2 #I #V1 #V2 #e #HL12 #HV12 #He
+>(plus_minus_m_m e 1) /2/
+qed.
+
+lemma ltpss_tpss1: ∀L1,L2,I,V1,V2,d,e.
+                   L1 [d, e] ≫* L2 → L2 ⊢ V1 [d, e] ≫* V2 →
+                   L1. 𝕓{I} V1 [d + 1, e] ≫* L2. 𝕓{I} V2.
+#L1 #L2 #I #V1 #V2 #d #e #HL12 #H @(tpss_ind … H) -V2
+[ /2/
+| #V #V2 #_ #HV2 #IHV @(ltpss_trans_eq … IHV) /2/
+]
+qed.
+
+lemma ltpss_tpss1_lt: ∀L1,L2,I,V1,V2,d,e.
+                      L1 [d - 1, e] ≫* L2 → L2 ⊢ V1 [d - 1, e] ≫* V2 →
+                      0 < d → L1. 𝕓{I} V1 [d, e] ≫* L2. 𝕓{I} V2.
+#L1 #L2 #I #V1 #V2 #d #e #HL12 #HV12 #Hd
+>(plus_minus_m_m d 1) /2/
+qed.