update in ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sle.ma b/matita/matita/contribs/lambdadelta/ground/relocation/gr_sle.ma
deleted file mode 100644 (file)
index 74c1578..0000000
--- a/matita/matita/contribs/lambdadelta/ground/relocation/gr_sle.ma
+++ /dev/null
@@ -1,162 +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_tl.ma".
-
-(* INCLUSION FOR GENERIC RELOCATION MAPS ************************************)
-
-(*** sle *)
-coinductive gr_sle: relation gr_map ≝
-(*** sle_push *)
-| gr_sle_push (f1) (f2) (g1) (g2):
-  gr_sle f1 f2 → ⫯f1 = g1 → ⫯f2 = g2 → gr_sle g1 g2
-(*** sle_next *)
-| gr_sle_next (f1) (f2) (g1) (g2):
-  gr_sle f1 f2 → ↑f1 = g1 → ↑f2 = g2 → gr_sle g1 g2
-(*** sle_weak *)
-| gr_sle_weak (f1) (f2) (g1) (g2):
-  gr_sle f1 f2 → ⫯f1 = g1 → ↑f2 = g2 → gr_sle g1 g2
-.
-
-interpretation
-  "inclusion (generic relocation maps)"
-  'subseteq f1 f2 = (gr_sle f1 f2).
-
-(* Basic constructions ******************************************************)
-
-(*** sle_refl *)
-corec lemma gr_sle_refl:
-            reflexive … gr_sle.
-#f cases (gr_map_split_tl f) #H
-[ @(gr_sle_push … H H) | @(gr_sle_next … H H) ] -H //
-qed.
-
-(* Basic inversions *********************************************************)
-
-(*** sle_inv_xp *)
-lemma gr_sle_inv_push_dx:
-      ∀g1,g2. g1 ⊆ g2 → ∀f2. ⫯f2 = g2 →
-      ∃∃f1. f1 ⊆ f2 & ⫯f1 = g1.
-#g1 #g2 * -g1 -g2
-#f1 #f2 #g1 #g2 #H #H1 #H2 #x2 #Hx2 destruct
-[ lapply (eq_inv_gr_push_bi … Hx2) -Hx2 /2 width=3 by ex2_intro/ ]
-elim (eq_inv_gr_push_next … Hx2)
-qed-.
-
-(*** sle_inv_nx *)
-lemma gr_sle_inv_next_sn:
-      ∀g1,g2. g1 ⊆ g2 → ∀f1. ↑f1 = g1 →
-      ∃∃f2. f1 ⊆ f2 & ↑f2 = g2.
-#g1 #g2 * -g1 -g2
-#f1 #f2 #g1 #g2 #H #H1 #H2 #x1 #Hx1 destruct
-[2: lapply (eq_inv_gr_next_bi … Hx1) -Hx1 /2 width=3 by ex2_intro/ ]
-elim (eq_inv_gr_next_push … Hx1)
-qed-.
-
-(*** sle_inv_pn *)
-lemma gr_sle_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-.
-
-(* Advanced inversions ******************************************************)
-
-(*** sle_inv_pp *)
-lemma gr_sle_inv_push_bi:
-      ∀g1,g2. g1 ⊆ g2 → ∀f1,f2. ⫯f1 = g1 → ⫯f2 = g2 → f1 ⊆ f2.
-#g1 #g2 #H #f1 #f2 #H1 #H2
-elim (gr_sle_inv_push_dx … H … H2) -g2 #x1 #H #Hx1 destruct
-lapply (eq_inv_gr_push_bi … Hx1) -Hx1 //
-qed-.
-
-(*** sle_inv_nn *)
-lemma gr_sle_inv_next_bi:
-      ∀g1,g2. g1 ⊆ g2 → ∀f1,f2. ↑f1 = g1 → ↑f2 = g2 → f1 ⊆ f2.
-#g1 #g2 #H #f1 #f2 #H1 #H2
-elim (gr_sle_inv_next_sn … H … H1) -g1 #x2 #H #Hx2 destruct
-lapply (eq_inv_gr_next_bi … Hx2) -Hx2 //
-qed-.
-
-(*** sle_inv_px *)
-lemma gr_sle_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_sle_inv_push_bi … H … H1 H2)
-| lapply (gr_sle_inv_push_next … H … H1 H2)
-] -H -H1
-/3 width=3 by ex2_intro, or_introl, or_intror/
-qed-.
-
-(*** sle_inv_xn *)
-lemma gr_sle_inv_next_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_sle_inv_push_next … H … H1 H2)
-| lapply (gr_sle_inv_next_bi … H … H1 H2)
-] -H -H2
-/3 width=3 by ex2_intro, or_introl, or_intror/
-qed-.
-
-(* Constructions with gr_tl *************************************************)
-
-(*** sle_px_tl *)
-lemma gr_sle_push_sn_tl:
-      ∀g1,g2. g1 ⊆ g2 → ∀f1. ⫯f1 = g1 → f1 ⊆ ⫰g2.
-#g1 #g2 #H #f1 #H1
-elim (gr_sle_inv_push_sn … H … H1) -H -H1 * //
-qed.
-
-(*** sle_xn_tl *)
-lemma gr_sle_next_dx_tl:
-      ∀g1,g2. g1 ⊆ g2 → ∀f2. ↑f2 = g2 → ⫰g1 ⊆ f2.
-#g1 #g2 #H #f2 #H2
-elim (gr_sle_inv_next_dx … H … H2) -H -H2 * //
-qed.
-
-(*** sle_tl *)
-lemma gr_sle_tl:
-      ∀f1,f2. f1 ⊆ f2 → ⫰f1 ⊆ ⫰f2.
-#f1 elim (gr_map_split_tl f1) #H1 #f2 #H
-[ lapply (gr_sle_push_sn_tl … H … H1) -H //
-| elim (gr_sle_inv_next_sn … H … H1) -H //
-]
-qed.
-
-(* Inversions with gr_tl ****************************************************)
-
-(*** sle_inv_tl_sn *)
-lemma gr_sle_inv_tl_sn:
-      ∀f1,f2. ⫰f1 ⊆ f2 → f1 ⊆ ↑f2.
-#f1 elim (gr_map_split_tl f1) #H #f2 #Hf12
-/2 width=5 by gr_sle_next, gr_sle_weak/
-qed-.
-
-(*** sle_inv_tl_dx *)
-lemma gr_sle_inv_tl_dx:
-      ∀f1,f2. f1 ⊆ ⫰f2 → ⫯f1 ⊆ f2.
-#f1 #f2 elim (gr_map_split_tl f2) #H #Hf12
-/2 width=5 by gr_sle_push, gr_sle_weak/
-qed-.