more additions and corrections for the article

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

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_csx.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_csx.ma
deleted file mode 100644 (file)
index f6c85a0..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/rdsx_csx.ma
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@@ -1,72 +0,0 @@
-(**************************************************************************)
-(*       ___                                                              *)
-(*      ||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_computation/csx_lsubr.ma".
-include "basic_2/rt_computation/csx_cpxs.ma".
-include "basic_2/rt_computation/lsubsx_rdsx.ma".
-
-(* STRONGLY NORMALIZING REFERRED LOCAL ENV.S FOR UNBOUND RT-TRANSITION ******)
-
-(* Advanced properties ******************************************************)
-
-(* Basic_2A1: uses: lsx_lref_be_lpxs *)
-lemma rdsx_pair_lpxs (h) (G):
-                     ∀K1,V. ⦃G,K1⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ →
-                     ∀K2. G ⊢ ⬈*[h,V] 𝐒⦃K2⦄ → ⦃G,K1⦄ ⊢ ⬈*[h] K2 →
-                     ∀I. G ⊢ ⬈*[h,#0] 𝐒⦃K2.ⓑ{I}V⦄.
-#h #G #K1 #V #H
-@(csx_ind_cpxs … H) -V #V0 #_ #IHV0 #K2 #H
-@(rdsx_ind … H) -K2 #K0 #HK0 #IHK0 #HK10 #I
-@rdsx_intro #Y #HY #HnY
-elim (lpx_inv_pair_sn … HY) -HY #K2 #V2 #HK02 #HV02 #H destruct
-elim (tdeq_dec V0 V2) #HnV02 destruct [ -IHV0 -HV02 -HK0 | -IHK0 -HnY ]
-[ /5 width=5 by rdsx_rdeq_trans, lpxs_step_dx, rdeq_pair/
-| @(IHV0 … HnV02) -IHV0 -HnV02
-  [ /2 width=3 by lpxs_cpx_trans/
-  | /3 width=3 by rdsx_lpx_trans, rdsx_cpx_trans/
-  | /2 width=3 by lpxs_step_dx/
-  ]
-]
-qed.
-
-(* Basic_2A1: uses: lsx_lref_be *)
-lemma rdsx_lref_pair_drops (h) (G):
-                           ∀K,V. ⦃G,K⦄ ⊢ ⬈*[h] 𝐒⦃V⦄ → G ⊢ ⬈*[h,V] 𝐒⦃K⦄ →
-                           ∀I,i,L. ⬇*[i] L ≘ K.ⓑ{I}V → G ⊢ ⬈*[h,#i] 𝐒⦃L⦄.
-#h #G #K #V #HV #HK #I #i elim i -i
-[ #L #H >(drops_fwd_isid … H) -H /2 width=3 by rdsx_pair_lpxs/
-| #i #IH #L #H
-  elim (drops_inv_bind2_isuni_next … H) -H // #J #Y #HY #H destruct
-  @(rdsx_lifts … (𝐔❴1❵)) /3 width=6 by drops_refl, drops_drop/ (**) (* full auto fails *)
-]
-qed.
-
-(* Main properties **********************************************************)
-
-(* Basic_2A1: uses: csx_lsx *)
-theorem csx_rdsx (h): ∀G,L,T. ⦃G,L⦄ ⊢ ⬈*[h] 𝐒⦃T⦄ → G ⊢ ⬈*[h,T] 𝐒⦃L⦄.
-#h #G #L #T @(fqup_wf_ind_eq (Ⓕ) … G L T) -G -L -T
-#Z #Y #X #IH #G #L * * //
-[ #i #HG #HL #HT #H destruct
-  elim (csx_inv_lref … H) -H [ |*: * ]
-  [ /2 width=1 by rdsx_lref_atom/
-  | /2 width=3 by rdsx_lref_unit/
-  | /4 width=6 by rdsx_lref_pair_drops, fqup_lref/
-  ]
-| #p #I #V #T #HG #HL #HT #H destruct
-  elim (csx_fwd_bind_unit … H Void) -H /3 width=1 by rdsx_bind_void/
-| #I #V #T #HG #HL #HT #H destruct
-  elim (csx_fwd_flat … H) -H /3 width=1 by rdsx_flat/
-]
-qed.