update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sand.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_sand.ma
deleted file mode 100644 (file)
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--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sand.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 "ground/notation/relations/rintersection_3.ma".
-include "ground/relocation/gr_tl.ma".
-
-(* RELATIONAL INTERSECTION FOR GENERIC RELOCATION MAPS **********************)
-
-(*** sand *)
-coinductive gr_sand: relation3 gr_map gr_map gr_map ≝
-(*** sand_pp *)
-| gr_sand_push_bi (f1) (f2) (f) (g1) (g2) (g):
-  gr_sand f1 f2 f → ⫯f1 = g1 → ⫯f2 = g2 → ⫯f = g → gr_sand g1 g2 g
-(*** sand_np *)
-| gr_sand_next_push (f1) (f2) (f) (g1) (g2) (g):
-  gr_sand f1 f2 f → ↑f1 = g1 → ⫯f2 = g2 → ⫯f = g → gr_sand g1 g2 g
-(*** sand_pn *)
-| gr_sand_push_next (f1) (f2) (f) (g1) (g2) (g):
-  gr_sand f1 f2 f → ⫯f1 = g1 → ↑f2 = g2 → ⫯f = g → gr_sand g1 g2 g
-(*** sand_nn *)
-| gr_sand_next_bi (f1) (f2) (f) (g1) (g2) (g):
-  gr_sand f1 f2 f → ↑f1 = g1 → ↑f2 = g2 → ↑f = g → gr_sand g1 g2 g
-.
-
-interpretation
-  "relational intersection (generic relocation maps)"
-  'RIntersection f1 f2 f = (gr_sand f1 f2 f).
-
-(* Basic constructions ******************************************************)
-
-(*** sand_refl *)
-corec lemma gr_sand_idem:
-            ∀f. f ⋒ f ≘ f.
-#f cases (gr_map_split_tl f) #H
-[ @(gr_sand_push_bi … H H H)
-| @(gr_sand_next_bi … H H H)
-] -H //
-qed.
-
-(*** sand_sym *)
-corec lemma gr_sand_comm:
-            ∀f1,f2,f. f1 ⋒ f2 ≘ f → f2 ⋒ f1 ≘ f.
-#f1 #f2 #f * -f1 -f2 -f
-#f1 #f2 #f #g1 #g2 #g #Hf * * * -g1 -g2 -g
-[ @gr_sand_push_bi
-| @gr_sand_push_next
-| @gr_sand_next_push
-| @gr_sand_next_bi
-] /2 width=7 by/
-qed-.
-
-(* Basic inversions *********************************************************)
-
-(*** sand_inv_ppx *)
-lemma gr_sand_inv_push_bi:
-      ∀g1,g2,g. g1 ⋒ g2 ≘ g → ∀f1,f2. ⫯f1 = g1 → ⫯f2 = g2 →
-      ∃∃f. f1 ⋒ f2 ≘ f & ⫯f = g.
-#g1 #g2 #g * -g1 -g2 -g
-#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x1 #x2 #Hx1 #Hx2 destruct
-try (>(eq_inv_gr_push_bi … Hx1) -x1) try (>(eq_inv_gr_next_bi … Hx1) -x1)
-try elim (eq_inv_gr_push_next … Hx1) try elim (eq_inv_gr_next_push … Hx1)
-try (>(eq_inv_gr_push_bi … Hx2) -x2) try (>(eq_inv_gr_next_bi … Hx2) -x2)
-try elim (eq_inv_gr_push_next … Hx2) try elim (eq_inv_gr_next_push … Hx2)
-/2 width=3 by ex2_intro/
-qed-.
-
-(*** sand_inv_npx *)
-lemma gr_sand_inv_next_push:
-      ∀g1,g2,g. g1 ⋒ g2 ≘ g → ∀f1,f2. ↑f1 = g1 → ⫯f2 = g2 →
-      ∃∃f. f1 ⋒ f2 ≘ f & ⫯f = g.
-#g1 #g2 #g * -g1 -g2 -g
-#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x1 #x2 #Hx1 #Hx2 destruct
-try (>(eq_inv_gr_push_bi … Hx1) -x1) try (>(eq_inv_gr_next_bi … Hx1) -x1)
-try elim (eq_inv_gr_push_next … Hx1) try elim (eq_inv_gr_next_push … Hx1)
-try (>(eq_inv_gr_push_bi … Hx2) -x2) try (>(eq_inv_gr_next_bi … Hx2) -x2)
-try elim (eq_inv_gr_push_next … Hx2) try elim (eq_inv_gr_next_push … Hx2)
-/2 width=3 by ex2_intro/
-qed-.
-
-(*** sand_inv_pnx *)
-lemma gr_sand_inv_push_next:
-      ∀g1,g2,g. g1 ⋒ g2 ≘ g → ∀f1,f2. ⫯f1 = g1 → ↑f2 = g2 →
-      ∃∃f. f1 ⋒ f2 ≘ f & ⫯f = g.
-#g1 #g2 #g * -g1 -g2 -g
-#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x1 #x2 #Hx1 #Hx2 destruct
-try (>(eq_inv_gr_push_bi … Hx1) -x1) try (>(eq_inv_gr_next_bi … Hx1) -x1)
-try elim (eq_inv_gr_push_next … Hx1) try elim (eq_inv_gr_next_push … Hx1)
-try (>(eq_inv_gr_push_bi … Hx2) -x2) try (>(eq_inv_gr_next_bi … Hx2) -x2)
-try elim (eq_inv_gr_push_next … Hx2) try elim (eq_inv_gr_next_push … Hx2)
-/2 width=3 by ex2_intro/
-qed-.
-
-(*** sand_inv_nnx *)
-lemma gr_sand_inv_next_bi:
-      ∀g1,g2,g. g1 ⋒ g2 ≘ g → ∀f1,f2. ↑f1 = g1 → ↑f2 = g2 →
-      ∃∃f. f1 ⋒ f2 ≘ f & ↑f = g.
-#g1 #g2 #g * -g1 -g2 -g
-#f1 #f2 #f #g1 #g2 #g #Hf #H1 #H2 #H0 #x1 #x2 #Hx1 #Hx2 destruct
-try (>(eq_inv_gr_push_bi … Hx1) -x1) try (>(eq_inv_gr_next_bi … Hx1) -x1)
-try elim (eq_inv_gr_push_next … Hx1) try elim (eq_inv_gr_next_push … Hx1)
-try (>(eq_inv_gr_push_bi … Hx2) -x2) try (>(eq_inv_gr_next_bi … Hx2) -x2)
-try elim (eq_inv_gr_push_next … Hx2) try elim (eq_inv_gr_next_push … Hx2)
-/2 width=3 by ex2_intro/
-qed-.