update for the article

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.ma
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--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_tdeq.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/rpx_rdeq.ma".
-include "basic_2/rt_computation/cpxs.ma".
-
-(* UNBOUND CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS **************)
-
-(* Properties with sort-irrelevant equivalence for terms ********************)
-
-lemma tdeq_cpxs_trans: ∀h,U1,T1. U1 ≛ T1 → ∀G,L,T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → 
-                       ∃∃U2. ⦃G,L⦄ ⊢ U1 ⬈*[h] U2 & U2 ≛ T2.
-#h #U1 #T1 #HUT1 #G #L #T2 #HT12 @(cpxs_ind … HT12) -T2 /2 width=3 by ex2_intro/
-#T #T2 #_ #HT2 * #U #HU1 #HUT elim (tdeq_cpx_trans … HUT … HT2) -T -T1
-/3 width=3 by ex2_intro, cpxs_strap1/
-qed-.
-
-(* Note: this requires tdeq to be symmetric *)
-(* Nasic_2A1: uses: cpxs_neq_inv_step_sn *)
-lemma cpxs_tdneq_fwd_step_sn: ∀h,G,L,T1,T2. ⦃G,L⦄ ⊢ T1 ⬈*[h] T2 → (T1 ≛ T2 → ⊥) →
-                              ∃∃T,T0. ⦃G,L⦄ ⊢ T1 ⬈[h] T & T1 ≛ T → ⊥ & ⦃G,L⦄ ⊢ T ⬈*[h] T0 & T0 ≛ T2.
-#h #G #L #T1 #T2 #H @(cpxs_ind_dx … H) -T1
-[ #H elim H -H //
-| #T1 #T0 #HT10 #HT02 #IH #Hn12
-  elim (tdeq_dec T1 T0) [ -HT10 -HT02 #H10 | -IH #Hn10 ]
-  [ elim IH -IH /3 width=3 by tdeq_trans/ -Hn12
-    #T3 #T4 #HT03 #Hn03 #HT34 #H42
-    elim (tdeq_cpx_trans … H10 … HT03) -HT03 #T5 #HT15 #H53
-    elim (tdeq_cpxs_trans … H53 … HT34) -HT34 #T6 #HT56 #H64
-    /5 width=8 by tdeq_canc_sn, (* 2x *) tdeq_trans, ex4_2_intro/
-  | /3 width=6 by ex4_2_intro/
-  ]
-]
-qed-.