update in ground_2 and basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_transition / cpt_cpm.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt_cpm.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpt_cpm.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/cpm_drops.ma".
+include "basic_2/rt_transition/cpt_drops.ma".
+
+(* T-BOUND CONTEXT-SENSITIVE PARALLEL T-TRANSITION FOR TERMS ****************)
+
+(* Properties with t-bound rt-transition for terms **************************)
+
+lemma cpm_cpt_cpr (h) (n) (G) (L):
+      ∀T1,T2. ⦃G,L⦄ ⊢ T1 ➡[n,h] T2 →
+      ∃∃T0. ⦃G,L⦄ ⊢ T1 ⬆[h,n] T0 & ⦃G,L⦄ ⊢ T0 ➡[h] T2.
+#h #n #G #L #T1 #T2 #H
+@(cpm_ind … H) -n -G -L -T1 -T2
+[ #I #G #L /2 width=3 by ex2_intro/
+| #G #L #s /3 width=3 by cpm_sort, ex2_intro/
+| #n #G #K #V1 #V2 #W2 #_ * #V0 #HV10 #HV02 #HVW2
+  elim (lifts_total V0 (𝐔❴1❵)) #W0 #HVW0
+  lapply (cpm_lifts_bi … HV02 (Ⓣ) … (K.ⓓV1) … HVW0 … HVW2) -HVW2
+  [ /3 width=1 by drops_refl, drops_drop/ ] -HV02 #HW02
+  /3 width=3 by cpt_delta, ex2_intro/
+| #n #G #K #V1 #V2 #W2 #_ * #V0 #HV10 #HV02 #HVW2
+  elim (lifts_total V0 (𝐔❴1❵)) #W0 #HVW0
+  lapply (cpm_lifts_bi … HV02 (Ⓣ) … (K.ⓛV1) … HVW0 … HVW2) -HVW2
+  [ /3 width=1 by drops_refl, drops_drop/ ] -HV02 #HW02
+  /3 width=3 by cpt_ell, ex2_intro/
+| #n #I #G #K #T2 #U2 #i #_ * #T0 #HT0 #HT02 #HTU2
+  elim (lifts_total T0 (𝐔❴1❵)) #U0 #HTU0
+  lapply (cpm_lifts_bi … HT02 (Ⓣ) … (K.ⓘ{I}) … HTU0 … HTU2) -HTU2
+  [ /3 width=1 by drops_refl, drops_drop/ ] -HT02 #HU02
+  /3 width=3 by cpt_lref, ex2_intro/
+| #n #p #I #G #L #V1 #V2 #T1 #T2 #HV12 #_ #_ * #T0 #HT10 #HT02
+  /3 width=5 by cpt_bind, cpm_bind, ex2_intro/
+| #n #G #L #V1 #V2 #T1 #T2 #HV12 #_ #_ * #T0 #HT10 #HT02
+  /3 width=5 by cpt_appl, cpm_appl, ex2_intro/
+| #n #G #L #V1 #V2 #T1 #T2 #_ #_ * #V0 #HV10 #HV02 * #T0 #HT10 #HT02
+  /3 width=5 by cpt_cast, cpm_cast, ex2_intro/
+| #n #G #L #V #U1 #T1 #T2 #HTU1 #_ * #T0 #HT10 #HT02
+  elim (cpt_lifts_sn … HT10 (Ⓣ) … (L.ⓓV) … HTU1) -T1
+  [| /3 width=1 by drops_refl, drops_drop/ ] #U0 #HTU0 #HU10
+  /3 width=6 by cpt_bind, cpm_zeta, ex2_intro/
+| #n #G #L #U #T1 #T2 #_ * #T0 #HT10 #HT02
+| #n #G #L #U1 #U2 #T #_ * #U0 #HU10 #HU02
+  /3 width=3 by cpt_ee, ex2_intro/
+| #n #p #G #L #V1 #V2 #W1 #W2 #T1 #T2 #HV12 #HW12 #_ #_ #_ * #T0 #HT10 #HT02
+  /4 width=7 by cpt_appl, cpt_bind, cpm_beta, ex2_intro/
+| #n #p #G #L #V1 #V2 #V0 #W1 #W2 #T1 #T2 #HV12 #HW12 #_ #_ #_ * #T0 #HT10 #HT02 #HV20
+  /4 width=9 by cpt_appl, cpt_bind, cpm_theta, ex2_intro/
+]
+
+(* Forward lemmas with t-bound rt-transition for terms **********************)
+
+lemma cpt_fwd_cpm (h) (n) (G) (L):
+      ∀T1,T2. ⦃G,L⦄ ⊢ T1 ⬆[h,n] T2 → ⦃G,L⦄ ⊢ T1 ➡[n,h] T2.
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