update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / reduction / cpr_cir.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/reduction/cpr_cir.ma b/matita/matita/contribs/lambdadelta/basic_2A/reduction/cpr_cir.ma
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/reduction/cpr_cir.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_2A/reduction/cir.ma".
+include "basic_2A/reduction/cpr.ma".
+
+(* CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS ***************************)
+
+(* Advanced forward lemmas on irreducibility ********************************)
+
+lemma cpr_fwd_cir: ∀G,L,T1,T2. ⦃G, L⦄ ⊢ T1 ➡ T2 → ⦃G, L⦄ ⊢ ➡ 𝐈⦃T1⦄ → T2 = T1.
+#G #L #T1 #T2 #H elim H -G -L -T1 -T2
+[ //
+| #G #L #K #V1 #V2 #W2 #i #HLK #_ #HVW2 #IHV12 #H
+  elim (cir_inv_delta … HLK) //
+| #a * #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV1 #IHT1 #H
+  [ elim (cir_inv_bind … H) -H #HV1 #HT1 * #H destruct
+    lapply (IHV1 … HV1) -IHV1 -HV1 #H destruct
+    lapply (IHT1 … HT1) -IHT1 #H destruct //
+  | elim (cir_inv_ib2 … H) -H /3 width=2 by or_introl, eq_f2/
+  ]
+| * #G #L #V1 #V2 #T1 #T2 #_ #_ #IHV1 #IHT1 #H
+  [ elim (cir_inv_appl … H) -H #HV1 #HT1 #_
+    >IHV1 -IHV1 // -HV1 >IHT1 -IHT1 //
+  | elim (cir_inv_ri2 … H) /2 width=1 by/
+  ]
+| #G #L #V1 #T1 #T #T2 #_ #_ #_ #H
+  elim (cir_inv_ri2 … H) /2 width=1 by or_introl/
+| #G #L #V1 #T1 #T2 #_ #_ #H
+  elim (cir_inv_ri2 … H) /2 width=1 by/
+| #a #G #L #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #H
+  elim (cir_inv_appl … H) -H #_ #_ #H
+  elim (simple_inv_bind … H)
+| #a #G #L #V #V1 #V2 #W1 #W2 #T1 #T2 #_ #_ #_ #_ #_ #_ #_ #H
+  elim (cir_inv_appl … H) -H #_ #_ #H
+  elim (simple_inv_bind … H)
+]
+qed-.