more additions and corrections for the article

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_drops.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_drops.ma
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--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_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/rdsx_length.ma".
-include "basic_2/rt_computation/rdsx_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 rdsx_lifts (h) (G): d_liftable1_isuni … (λL,T. G ⊢ ⬈*[h,T] 𝐒⦃L⦄).
-#h #G #K #T #H @(rdsx_ind … H) -K
-#K1 #_ #IH #b #f #L1 #HLK1 #Hf #U #HTU @rdsx_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 rdsx_inv_lifts (h) (G): d_deliftable1_isuni … (λL,T. G ⊢ ⬈*[h,T] 𝐒⦃L⦄).
-#h #G #L #U #H @(rdsx_ind … H) -L
-#L1 #_ #IH #b #f #K1 #HLK1 #Hf #T #HTU @rdsx_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 rdsx_lref_atom (h) (G): ∀L,i. ⬇*[Ⓕ,𝐔❴i❵] L ≘ ⋆ → G ⊢ ⬈*[h,#i] 𝐒⦃L⦄.
-#h #G #L1 #i #HL1
-@(rdsx_lifts … (#0) … HL1) -HL1 //
-qed.
-
-(* Basic_2A1: uses: lsx_lref_skip *)
-lemma rdsx_lref_unit (h) (G): ∀I,L,K,i. ⬇*[i] L ≘ K.ⓤ{I} → G ⊢ ⬈*[h,#i] 𝐒⦃L⦄.
-#h #G #I #L1 #K1 #i #HL1
-@(rdsx_lifts … (#0) … HL1) -HL1 //
-qed.
-
-(* Advanced forward lemmas **************************************************)
-
-(* Basic_2A1: uses: lsx_fwd_lref_be *)
-lemma rdsx_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 (rdsx_inv_lifts … HL … HLK … (#0) ?) -L
-/2 width=2 by rdsx_fwd_pair/
-qed-.