update in ground

[helm.git] / matita / matita / contribs / lambdadelta / ground / relocation / gr_sor_coafter_ist_isf.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor_coafter_ist_isf.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor_coafter_ist_isf.ma
deleted file mode 100644 (file)
index 89b457f..0000000
--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sor_coafter_ist_isf.ma
+++ /dev/null
@@ -1,76 +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 "ground/relocation/gr_isf.ma".
-include "ground/relocation/gr_coafter_isi.ma".
-include "ground/relocation/gr_coafter_ist_isi.ma".
-include "ground/relocation/gr_sor_isi.ma".
-
-(* RELATIONAL UNION FOR GENERIC RELOCATION MAPS *****************************)
-
-(* Constructions with gr_coafter and gr_ist and gr_isf **********************)
-
-(*** coafter_sor *)
-lemma gr_sor_coafter_dx_tans:
-      ∀f. 𝐅❪f❫ → ∀f2. 𝐓❪f2❫ → ∀f1. f2 ~⊚ f1 ≘ f → ∀f1a,f1b. f1a ⋓ f1b ≘ f1 →
-      ∃∃fa,fb. f2 ~⊚ f1a ≘ fa & f2 ~⊚ f1b ≘ fb & fa ⋓ fb ≘ f.
-@gr_isf_ind
-[ #f #Hf #f2 #Hf2 #f1 #Hf #f1a #f1b #Hf1
-  lapply (gr_coafter_des_ist_sn_isi … Hf ??) -Hf // #H2f1
-  elim (gr_sor_inv_isi … Hf1) -Hf1 //
-  /3 width=5 by gr_coafter_isi_dx, gr_sor_idem, ex3_2_intro/
-| #f #_ #IH #f2 #Hf2 #f1 #H1 #f1a #f1b #H2
-  elim (gr_coafter_inv_push … H1) -H1 [1,3: * |*: // ]
-  [ #g2 #g1 #Hf #Hgf2 #Hgf1
-    elim (gr_sor_inv_push … H2) -H2 [ |*: // ] #ga #gb #Hg1
-    lapply (gr_ist_inv_push … Hf2 … Hgf2) -Hf2 #Hg2
-    elim (IH … Hf … Hg1) // -f1 -g1 -IH -Hg2
-    /3 width=11 by gr_coafter_refl, gr_sor_push_bi, ex3_2_intro/
-  | #g2 #Hf #Hgf2
-    lapply (gr_ist_inv_next … Hf2 … Hgf2) -Hf2 #Hg2
-    elim (IH … Hf … H2) // -f1 -IH -Hg2
-    /3 width=11 by gr_coafter_next, gr_sor_push_bi, ex3_2_intro/
-  ]
-| #f #_ #IH #f2 #Hf2 #f1 #H1 #f1a #f1b #H2
-  elim (gr_coafter_inv_next … H1) -H1 [ |*: // ] #g2 #g1 #Hf #Hgf2 #Hgf1
-  lapply (gr_ist_inv_push … Hf2 … Hgf2) -Hf2 #Hg2
-  elim (gr_sor_inv_next … H2) -H2 [1,3,4: * |*: // ] #ga #gb #Hg1
-  elim (IH … Hf … Hg1) // -f1 -g1 -IH -Hg2
-  /3 width=11 by gr_coafter_refl, gr_coafter_push, gr_sor_next_push, gr_sor_push_next, gr_sor_next_bi, ex3_2_intro/
-]
-qed-.
-
-(*** coafter_inv_sor *)
-lemma gr_sor_coafter_div:
-      ∀f. 𝐅❪f❫ → ∀f2. 𝐓❪f2❫ → ∀f1. f2 ~⊚ f1 ≘ f → ∀fa,fb. fa ⋓ fb ≘ f →
-      ∃∃f1a,f1b. f2 ~⊚ f1a ≘ fa & f2 ~⊚ f1b ≘ fb & f1a ⋓ f1b ≘ f1.
-@gr_isf_ind
-[ #f #Hf #f2 #Hf2 #f1 #H1f #fa #fb #H2f
-  elim (gr_sor_inv_isi … H2f) -H2f //
-  lapply (gr_coafter_des_ist_sn_isi … H1f ??) -H1f //
-  /3 width=5 by ex3_2_intro, gr_coafter_isi_dx, gr_sor_isi_bi_isi/
-| #f #_ #IH #f2 #Hf2 #f1 #H1 #fa #fb #H2
-  elim (gr_sor_inv_push … H2) -H2 [ |*: // ] #ga #gb #H2f
-  elim (gr_coafter_inv_push … H1) -H1 [1,3: * |*: // ] #g2 [ #g1 ] #H1f #Hgf2
-  [ lapply (gr_ist_inv_push … Hf2 … Hgf2) | lapply (gr_ist_inv_next … Hf2 … Hgf2) ] -Hf2 #Hg2
-  elim (IH … Hg2 … H1f … H2f) -f -Hg2
-  /3 width=11 by gr_sor_push_bi, ex3_2_intro, gr_coafter_refl, gr_coafter_next/
-| #f #_ #IH #f2 #Hf2 #f1 #H1 #fa #fb #H2
-  elim (gr_coafter_inv_next … H1) -H1 [ |*: // ] #g2 #g1 #H1f #Hgf2
-  lapply (gr_ist_inv_push … Hf2 … Hgf2) -Hf2 #Hg2
-  elim (gr_sor_inv_next … H2) -H2 [1,3,4: * |*: // ] #ga #gb #H2f
-  elim (IH … Hg2 … H1f … H2f) -f -Hg2
-  /3 width=11 by gr_sor_next_push, gr_sor_push_next, gr_sor_next_bi, ex3_2_intro, gr_coafter_refl, gr_coafter_push/
-]
-qed-.