- advances towards strong normalization

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / csx_lsubr.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lsubr.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_lsubr.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/rt_transition/cpx_lsubr.ma".
+include "basic_2/rt_computation/csx_csx.ma".
+
+(* STRONGLY NORMALIZING TERMS FOR UNCOUNTED PARALLEL RT-TRANSITION **********)
+
+(* Advanced properties ******************************************************)
+
+fact csx_appl_beta_aux: ∀h,o,p,G,L,U1. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃U1⦄ →
+                        ∀V,W,T1. U1 = ⓓ{p}ⓝW.V.T1 → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.ⓛ{p}W.T1⦄.
+#h #o #p #G #L #X #H @(csx_ind … H) -X
+#X #HT1 #IHT1 #V #W #T1 #H1 destruct
+@csx_intro #X #H1 #H2
+elim (cpx_inv_appl1 … H1) -H1 *
+[ -HT1 #V0 #Y #HLV0 #H #H0 destruct
+  elim (cpx_inv_abst1 … H) -H #W0 #T0 #HLW0 #HLT0 #H destruct
+  @IHT1 -IHT1 [4: // | skip ]
+  [ lapply (lsubr_cpx_trans … HLT0 (L.ⓓⓝW.V) ?) -HLT0 -H2
+    /3 width=1 by cpx_bind, cpx_flat, lsubr_beta/
+  | #H elim (tdeq_inv_pair … H) -H
+    #_ #H elim (tdeq_inv_pair … H) -H
+    #_ /4 width=1 by tdeq_pair/
+  ]
+| -IHT1 -H2 #q #V0 #W0 #W2 #T0 #T2 #HLV0 #HLW02 #HLT02 #H1 #H3 destruct
+  lapply (lsubr_cpx_trans … HLT02 (L.ⓓⓝW0.V) ?) -HLT02
+  /4 width=5 by csx_cpx_trans, cpx_bind, cpx_flat, lsubr_beta/
+| -HT1 -IHT1 -H2 #q #V0 #V1 #W0 #W1 #T0 #T3 #_ #_ #_ #_ #H destruct
+]
+qed-.
+
+(* Basic_1: was just: sn3_beta *)
+lemma csx_appl_beta: ∀h,o,p,G,L,V,W,T. ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓓ{p}ⓝW.V.T⦄ → ⦃G, L⦄ ⊢ ⬈*[h, o] 𝐒⦃ⓐV.ⓛ{p}W.T⦄.
+/2 width=3 by csx_appl_beta_aux/ qed.