cpxs_lfpx completed

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/cpxs_drops.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_drops.ma".
+include "basic_2/rt_computation/cpxs.ma".
+
+(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL RT-COMPUTATION FOR TERMS ************)
+
+(* Advanced properties ******************************************************)
+
+lemma cpxs_delta: ∀h,I,G,K,V1,V2. ⦃G, K⦄ ⊢ V1 ⬈*[h] V2 →
+                  ∀W2. ⬆*[1] V2 ≡ W2 → ⦃G, K.ⓑ{I}V1⦄ ⊢ #0 ⬈*[h] W2.
+#h #I #G #K #V1 #V2 #H @(cpxs_ind … H) -V2
+[ /3 width=3 by cpx_cpxs, cpx_delta/
+| #V #V2 #_ #HV2 #IH #W2 #HVW2
+  elim (lifts_total V (𝐔❴1❵)) #W #HVW
+  elim (cpx_lifts … HV2 (Ⓣ) … (K.ⓑ{I}V1) … HVW) -HV2
+  [ #V0 #HV20 <(lifts_mono … HVW2 … HV20) -V2 -V0 /3 width=3 by cpxs_strap1/
+  | /3 width=1 by drops_refl, drops_drop/
+  ]
+]
+qed.
+
+lemma cpxs_lref: ∀h,I,G,K,V,T,i. ⦃G, K⦄ ⊢ #i ⬈*[h] T →
+                 ∀U. ⬆*[1] T ≡ U → ⦃G, K.ⓑ{I}V⦄ ⊢ #⫯i ⬈*[h] U.
+#h #I #G #K #V #T #i #H @(cpxs_ind … H) -T
+[ /3 width=3 by cpx_cpxs, cpx_lref/
+| #T0 #T #_ #HT2 #IH #U #HTU
+  elim (lifts_total T0 (𝐔❴1❵)) #U0 #HTU0
+  elim (cpx_lifts … HT2 (Ⓣ) … (K.ⓑ{I}V) … HTU0) -HT2
+  [ #X #HTX <(lifts_mono … HTU … HTX) -T -X /3 width=3 by cpxs_strap1/
+  | /3 width=1 by drops_refl, drops_drop/
+  ]
+]
+qed.
+
+(* Basic_2A1: was: cpxs_delta *)
+lemma cpxs_delta_drops: ∀h,I,G,L,K,V1,V2,i.
+                        ⬇*[i] L ≡ K.ⓑ{I}V1 → ⦃G, K⦄ ⊢ V1 ⬈*[h] V2 →
+                        ∀W2. ⬆*[⫯i] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ⬈*[h] W2.
+#h #I #G #L #K #V1 #V2 #i #HLK #H @(cpxs_ind … H) -V2
+[ /3 width=7 by cpx_cpxs, cpx_delta_drops/
+| #V #V2 #_ #HV2 #IH #W2 #HVW2
+  elim (lifts_total V (𝐔❴⫯i❵)) #W #HVW
+  elim (cpx_lifts … HV2 (Ⓣ) … L … HVW) -HV2
+  [ #V0 #HV20 <(lifts_mono … HVW2 … HV20) -V2 -V0 /3 width=3 by cpxs_strap1/
+  | /2 width=3 by drops_isuni_fwd_drop2/ 
+  ]
+]
+qed.
+(*
+(* Advanced inversion lemmas ************************************************)
+
+lemma cpxs_inv_lref1: ∀h,o,G,L,T2,i. ⦃G, L⦄ ⊢ #i ⬈*[h, o] T2 →
+                      T2 = #i ∨
+                      ∃∃I,K,V1,T1. ⬇[i] L ≡ K.ⓑ{I}V1 & ⦃G, K⦄ ⊢ V1 ⬈*[h, o] T1 &
+                                   ⬆[0, i+1] T1 ≡ T2.
+#h #o #G #L #T2 #i #H @(cpxs_ind … H) -T2 /2 width=1 by or_introl/
+#T #T2 #_ #HT2 *
+[ #H destruct
+  elim (cpx_inv_lref1 … HT2) -HT2 /2 width=1 by or_introl/
+  * /4 width=7 by cpx_cpxs, ex3_4_intro, or_intror/
+| * #I #K #V1 #T1 #HLK #HVT1 #HT1
+  lapply (drop_fwd_drop2 … HLK) #H0LK
+  elim (cpx_inv_lift1 … HT2 … H0LK … HT1) -H0LK -T
+  /4 width=7 by cpxs_strap1, ex3_4_intro, or_intror/
+]
+qed-.
+
+(* Relocation properties ****************************************************)
+
+lemma cpxs_lift: ∀h,o,G. d_liftable (cpxs h o G).
+/3 width=10 by cpx_lift, cpxs_strap1, d_liftable_LTC/ qed.
+
+lemma cpxs_inv_lift1: ∀h,o,G. d_deliftable_sn (cpxs h o G).
+/3 width=6 by d_deliftable_sn_LTC, cpx_inv_lift1/
+qed-.
+*)