- first results on cpx (dericed from those on cpg)

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_transition/cpx_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/cpg_drops.ma".
+include "basic_2/rt_transition/cpx.ma".
+
+(* UNCOUNTED CONTEXT-SENSITIVE PARALLEL REDUCTION FOR TERMS *****************)
+
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: was: cpx_delta *)
+lemma cpx_delta_drops: ∀h,I,G,L,K,V,V2,W2,i.
+                       ⬇*[i] L ≡ K.ⓑ{I}V → ⦃G, K⦄ ⊢ V ➡[h] V2 →
+                       ⬆*[⫯i] V2 ≡ W2 → ⦃G, L⦄ ⊢ #i ➡[h] W2.
+#h * #G #L #K #V #V2 #W2 #i #HLK *
+/3 width=7 by cpg_ell_drops, cpg_delta_drops, ex_intro/
+qed.
+
+(* Advanced inversion lemmas ************************************************)
+
+(* Basic_2A1: was: cpx_inv_atom1 *)
+lemma cpx_inv_atom1_drops: ∀h,I,G,L,T2. ⦃G, L⦄ ⊢ ⓪{I} ➡[h] T2 →
+                           ∨∨ T2 = ⓪{I}
+                            | ∃∃s. T2 = ⋆(next h s) & I = Sort s
+                            | ∃∃J,K,V,V2,i. ⬇*[i] L ≡ K.ⓑ{J}V & ⦃G, K⦄ ⊢ V ➡[h] V2 &
+                                            ⬆*[⫯i] V2 ≡ T2 & I = LRef i.
+#h #I #G #L #T2 * #c #H elim (cpg_inv_atom1_drops … H) -H *
+/4 width=9 by or3_intro0, or3_intro1, or3_intro2, ex4_5_intro, ex2_intro, ex_intro/
+qed-.
+
+(* Basic_2A1: was: cpx_inv_lref1 *)
+lemma cpx_inv_lref1_drops: ∀h,G,L,T2,i. ⦃G, L⦄ ⊢ #i ➡[h] T2 →
+                           T2 = #i ∨
+                           ∃∃J,K,V,V2. ⬇*[i] L ≡ K. ⓑ{J}V & ⦃G, K⦄ ⊢ V ➡[h] V2 &
+                                       ⬆*[⫯i] V2 ≡ T2.
+#h #G #L #T1 #i * #c #H elim (cpg_inv_lref1_drops … H) -H *
+/4 width=7 by ex3_4_intro, ex_intro, or_introl, or_intror/
+qed-.
+
+(* Properties with generic slicing for local environments *******************)
+
+(* Basic_2A1: includes: cpx_lift *)
+lemma cpx_lifts: ∀h,G. d_liftable2 (cpx h G).
+#h #G #K #T1 #T2 * #cT #HT12 #b #f #L #HLK #U1 #HTU1
+elim (cpg_lifts … HT12 … HLK … HTU1) -K -T1
+/3 width=4 by ex2_intro, ex_intro/
+qed-.
+
+(* Inversion lemmas with generic slicing for local environments *************)
+
+(* Basic_2A1: includes: cpx_inv_lift1 *)
+lemma cpx_inv_lift1: ∀h,G. d_deliftable2_sn (cpx h G).
+#h #G #L #U1 #U2 * #cU #HU12 #b #f #K #HLK #T1 #HTU1
+elim (cpg_inv_lifts1 … HU12 … HLK … HTU1) -L -U1
+/3 width=4 by ex2_intro, ex_intro/
+qed-.