more additions and corrections for the article

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rsx_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 "static_2/static/rdeq_drops.ma".
+include "basic_2/rt_transition/lpx_drops.ma".
+include "basic_2/rt_computation/rsx_length.ma".
+include "basic_2/rt_computation/rsx_fqup.ma".
+
+(* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
+
+(* Properties with generic relocation ***************************************)
+
+(* Note: this uses length *)
+(* Basic_2A1: uses: lsx_lift_le lsx_lift_ge *)
+lemma rsx_lifts (h) (G): d_liftable1_isuni … (λL,T. G ⊢ ⬈*[h,T] 𝐒⦃L⦄).
+#h #G #K #T #H @(rsx_ind … H) -K
+#K1 #_ #IH #b #f #L1 #HLK1 #Hf #U #HTU @rsx_intro
+#L2 #HL12 #HnL12 elim (lpx_drops_conf … HLK1 … HL12) 
+/5 width=9 by rdeq_lifts_bi, lpx_fwd_length/
+qed-.
+
+(* Inversion lemmas on relocation *******************************************)
+
+(* Basic_2A1: uses: lsx_inv_lift_le lsx_inv_lift_be lsx_inv_lift_ge *)
+lemma rsx_inv_lifts (h) (G): d_deliftable1_isuni … (λL,T. G ⊢ ⬈*[h,T] 𝐒⦃L⦄).
+#h #G #L #U #H @(rsx_ind … H) -L
+#L1 #_ #IH #b #f #K1 #HLK1 #Hf #T #HTU @rsx_intro
+#K2 #HK12 #HnK12 elim (drops_lpx_trans … HLK1 … HK12) -HK12
+/4 width=10 by rdeq_inv_lifts_bi/
+qed-.
+
+(* Advanced properties ******************************************************)
+
+(* Basic_2A1: uses: lsx_lref_free *)
+lemma rsx_lref_atom (h) (G): ∀L,i. ⬇*[Ⓕ,𝐔❴i❵] L ≘ ⋆ → G ⊢ ⬈*[h,#i] 𝐒⦃L⦄.
+#h #G #L1 #i #HL1
+@(rsx_lifts … (#0) … HL1) -HL1 //
+qed.
+
+(* Basic_2A1: uses: lsx_lref_skip *)
+lemma rsx_lref_unit (h) (G): ∀I,L,K,i. ⬇*[i] L ≘ K.ⓤ{I} → G ⊢ ⬈*[h,#i] 𝐒⦃L⦄.
+#h #G #I #L1 #K1 #i #HL1
+@(rsx_lifts … (#0) … HL1) -HL1 //
+qed.
+
+(* Advanced forward lemmas **************************************************)
+
+(* Basic_2A1: uses: lsx_fwd_lref_be *)
+lemma rsx_fwd_lref_pair (h) (G):
+      ∀L,i. G ⊢ ⬈*[h,#i] 𝐒⦃L⦄ →
+      ∀I,K,V. ⬇*[i] L ≘ K.ⓑ{I}V → G ⊢ ⬈*[h,V] 𝐒⦃K⦄.
+#h #G #L #i #HL #I #K #V #HLK
+lapply (rsx_inv_lifts … HL … HLK … (#0) ?) -L
+/2 width=2 by rsx_fwd_pair/
+qed-.