ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / mr2_at.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_at.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_at.ma
deleted file mode 100644 (file)
index d2a2499..0000000
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_at.ma
+++ /dev/null
@@ -1,84 +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_2/notation/relations/rat_3.ma".
-include "ground_2/relocation/mr2.ma".
-
-(* MULTIPLE RELOCATION WITH PAIRS *******************************************)
-
-inductive at: mr2 → relation nat ≝
-| at_nil: ∀i. at (◊) i i
-| at_lt : ∀cs,l,m,i1,i2. i1 < l →
-          at cs i1 i2 → at (❨l, m❩;cs) i1 i2
-| at_ge : ∀cs,l,m,i1,i2. l ≤ i1 →
-          at cs (i1 + m) i2 → at (❨l, m❩;cs) i1 i2
-.
-
-interpretation "application (multiple relocation with pairs)"
-   'RAt i1 cs i2 = (at cs i1 i2).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact at_inv_nil_aux: ∀cs,i1,i2. @❪i1, cs❫ ≘ i2 → cs = ◊ → i1 = i2.
-#cs #i1 #i2 * -cs -i1 -i2
-[ //
-| #cs #l #m #i1 #i2 #_ #_ #H destruct
-| #cs #l #m #i1 #i2 #_ #_ #H destruct
-]
-qed-.
-
-lemma at_inv_nil: ∀i1,i2. @❪i1, ◊❫ ≘ i2 → i1 = i2.
-/2 width=3 by at_inv_nil_aux/ qed-.
-
-fact at_inv_cons_aux: ∀cs,i1,i2. @❪i1, cs❫ ≘ i2 →
-                      ∀l,m,cs0. cs = ❨l, m❩;cs0 →
-                      i1 < l ∧ @❪i1, cs0❫ ≘ i2 ∨
-                      l ≤ i1 ∧ @❪i1 + m, cs0❫ ≘ i2.
-#cs #i1 #i2 * -cs -i1 -i2
-[ #i #l #m #cs #H destruct
-| #cs1 #l1 #m1 #i1 #i2 #Hil1 #Hi12 #l2 #m2 #cs2 #H destruct /3 width=1 by or_introl, conj/
-| #cs1 #l1 #m1 #i1 #i2 #Hli1 #Hi12 #l2 #m2 #cs2 #H destruct /3 width=1 by or_intror, conj/
-]
-qed-.
-
-lemma at_inv_cons: ∀cs,l,m,i1,i2. @❪i1, ❨l, m❩;cs❫ ≘ i2 →
-                   i1 < l ∧ @❪i1, cs❫ ≘ i2 ∨
-                   l ≤ i1 ∧ @❪i1 + m, cs❫ ≘ i2.
-/2 width=3 by at_inv_cons_aux/ qed-.
-
-lemma at_inv_cons_lt: ∀cs,l,m,i1,i2. @❪i1, ❨l, m❩;cs❫ ≘ i2 →
-                      i1 < l → @❪i1, cs❫ ≘ i2.
-#cs #l #m #i1 #m2 #H
-elim (at_inv_cons … H) -H * // #Hli1 #_ #Hi1l
-elim (lt_le_false … Hi1l Hli1)
-qed-.
-
-lemma at_inv_cons_ge: ∀cs,l,m,i1,i2. @❪i1, ❨l, m❩;cs❫ ≘ i2 →
-                      l ≤ i1 → @❪i1 + m, cs❫ ≘ i2.
-#cs #l #m #i1 #m2 #H
-elim (at_inv_cons … H) -H * // #Hi1l #_ #Hli1
-elim (lt_le_false … Hi1l Hli1)
-qed-.
-
-(* Main properties **********************************************************)
-
-theorem at_mono: ∀cs,i,i1. @❪i, cs❫ ≘ i1 → ∀i2. @❪i, cs❫ ≘ i2 → i1 = i2.
-#cs #i #i1 #H elim H -cs -i -i1
-[ #i #x #H <(at_inv_nil … H) -x //
-| #cs #l #m #i #i1 #Hil #_ #IHi1 #x #H
-  lapply (at_inv_cons_lt … H Hil) -H -Hil /2 width=1 by/
-| #cs #l #m #i #i1 #Hli #_ #IHi1 #x #H
-  lapply (at_inv_cons_ge … H Hli) -H -Hli /2 width=1 by/
-]
-qed-.