update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sdj.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_sdj.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/parallel_2.ma".
-include "ground/relocation/gr_tl.ma".
-
-(* DISJOINTNESS FOR GENERIC RELOCATION MAPS *********************************)
-
-(*** sdj *)
-coinductive gr_sdj: relation gr_map ≝
-(*** sdj_pp *)
-| gr_sdj_push_bi (f1) (f2) (g1) (g2):
-  gr_sdj f1 f2 → ⫯f1 = g1 → ⫯f2 = g2 → gr_sdj g1 g2
-(*** sdj_np *)
-| gr_sdj_next_push (f1) (f2) (g1) (g2):
-  gr_sdj f1 f2 → ↑f1 = g1 → ⫯f2 = g2 → gr_sdj g1 g2
-(*** sdj_pn *)
-| gr_sdj_push_next (f1) (f2) (g1) (g2):
-  gr_sdj f1 f2 → ⫯f1 = g1 → ↑f2 = g2 → gr_sdj g1 g2
-.
-
-interpretation
-  "disjointness (generic relocation maps)"
-  'Parallel f1 f2 = (gr_sdj f1 f2).
-
-(* Basic constructions ******************************************************)
-
-(*** sdj_sym *)
-corec lemma gr_sdj_sym:
-            symmetric … gr_sdj.
-#f1 #f2 * -f1 -f2
-#f1 #f2 #g1 #g2 #Hf #H1 #H2
-[ @(gr_sdj_push_bi … H2 H1)
-| @(gr_sdj_push_next … H2 H1)
-| @(gr_sdj_next_push … H2 H1)
-] -g2 -g1
-/2 width=1 by/
-qed-.
-
-(* Basic inversions *********************************************************)
-
-(*** sdj_inv_pp *)
-lemma gr_sdj_inv_push_bi:
-      ∀g1,g2. g1 ∥ g2 → ∀f1,f2. ⫯f1 = g1 → ⫯f2 = g2 → f1 ∥ f2.
-#g1 #g2 * -g1 -g2
-#f1 #f2 #g1 #g2 #H #H1 #H2 #x1 #x2 #Hx1 #Hx2 destruct
-[ lapply (eq_inv_gr_push_bi … Hx1) -Hx1
-  lapply (eq_inv_gr_push_bi … Hx2) -Hx2 //
-| elim (eq_inv_gr_push_next … Hx1)
-| elim (eq_inv_gr_push_next … Hx2)
-]
-qed-.
-
-(*** sdj_inv_np *)
-lemma gr_sdj_inv_next_push:
-      ∀g1,g2. g1 ∥ g2 → ∀f1,f2. ↑f1 = g1 → ⫯f2 = g2 → f1 ∥ f2.
-#g1 #g2 * -g1 -g2
-#f1 #f2 #g1 #g2 #H #H1 #H2 #x1 #x2 #Hx1 #Hx2 destruct
-[ elim (eq_inv_gr_next_push … Hx1)
-| lapply (eq_inv_gr_next_bi … Hx1) -Hx1
-  lapply (eq_inv_gr_push_bi … Hx2) -Hx2 //
-| elim (eq_inv_gr_push_next … Hx2)
-]
-qed-.
-
-(*** sdj_inv_pn *)
-lemma gr_sdj_inv_push_next:
-      ∀g1,g2. g1 ∥ g2 → ∀f1,f2. ⫯f1 = g1 → ↑f2 = g2 → f1 ∥ f2.
-#g1 #g2 * -g1 -g2
-#f1 #f2 #g1 #g2 #H #H1 #H2 #x1 #x2 #Hx1 #Hx2 destruct
-[ elim (eq_inv_gr_next_push … Hx2)
-| elim (eq_inv_gr_push_next … Hx1)
-| lapply (eq_inv_gr_push_bi … Hx1) -Hx1
-  lapply (eq_inv_gr_next_bi … Hx2) -Hx2 //
-]
-qed-.
-
-(*** sdj_inv_nn *)
-lemma gr_sdj_inv_next_bi:
-      ∀g1,g2. g1 ∥ g2 → ∀f1,f2. ↑f1 = g1 → ↑f2 = g2 → ⊥.
-#g1 #g2 * -g1 -g2
-#f1 #f2 #g1 #g2 #H #H1 #H2 #x1 #x2 #Hx1 #Hx2 destruct
-[ elim (eq_inv_gr_next_push … Hx1)
-| elim (eq_inv_gr_next_push … Hx2)
-| elim (eq_inv_gr_next_push … Hx1)
-]
-qed-.
-
-(* Advanced inversions ******************************************************)
-
-(*** sdj_inv_nx *)
-lemma gr_sdj_inv_next_sn:
-      ∀g1,g2. g1 ∥ g2 → ∀f1. ↑f1 = g1 →
-      ∃∃f2. f1 ∥ f2 & ⫯f2 = g2.
-#g1 #g2 elim (gr_map_split_tl g2) #H2 #H #f1 #H1
-[ lapply (gr_sdj_inv_next_push … H … H1 H2) -H /2 width=3 by ex2_intro/
-| elim (gr_sdj_inv_next_bi … H … H1 H2)
-]
-qed-.
-
-(*** sdj_inv_xn *)
-lemma gr_sdj_inv_next_dx:
-      ∀g1,g2. g1 ∥ g2 → ∀f2. ↑f2 = g2 →
-      ∃∃f1. f1 ∥ f2 & ⫯f1 = g1.
-#g1 #g2 elim (gr_map_split_tl g1) #H1 #H #f2 #H2
-[ lapply (gr_sdj_inv_push_next … H … H1 H2) -H /2 width=3 by ex2_intro/
-| elim (gr_sdj_inv_next_bi … H … H1 H2)
-]
-qed-.
-
-(*** sdj_inv_xp *)
-lemma gr_sdj_inv_push_dx:
-      ∀g1,g2. g1 ∥ g2 → ∀f2. ⫯f2 = g2 →
-      ∨∨ ∃∃f1. f1 ∥ f2 & ⫯f1 = g1
-       | ∃∃f1. f1 ∥ f2 & ↑f1 = g1.
-#g1 #g2 elim (gr_map_split_tl g1) #H1 #H #f2 #H2
-[ lapply (gr_sdj_inv_push_bi … H … H1 H2)
-| lapply (gr_sdj_inv_next_push … H … H1 H2)
-] -H -H2
-/3 width=3 by ex2_intro, or_introl, or_intror/
-qed-.
-
-(*** sdj_inv_px *)
-lemma gr_sdj_inv_push_sn:
-      ∀g1,g2. g1 ∥ g2 → ∀f1. ⫯f1 = g1 →
-      ∨∨ ∃∃f2. f1 ∥ f2 & ⫯f2 = g2
-       | ∃∃f2. f1 ∥ f2 & ↑f2 = g2.
-#g1 #g2 elim (gr_map_split_tl g2) #H2 #H #f1 #H1
-[ lapply (gr_sdj_inv_push_bi … H … H1 H2)
-| lapply (gr_sdj_inv_push_next … H … H1 H2)
-] -H -H1
-/3 width=3 by ex2_intro, or_introl, or_intror/
-qed-.