ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / relocation / mr2_minus.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_minus.ma b/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_minus.ma
deleted file mode 100644 (file)
index 81544fe..0000000
--- a/matita/matita/contribs/lambdadelta/ground_2/relocation/mr2_minus.ma
+++ /dev/null
@@ -1,74 +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/rminus_3.ma".
-include "ground_2/relocation/mr2.ma".
-
-(* MULTIPLE RELOCATION WITH PAIRS *******************************************)
-
-inductive minuss: nat → relation mr2 ≝
-| minuss_nil: ∀i. minuss i (◊) (◊)
-| minuss_lt : ∀cs1,cs2,l,m,i. i < l → minuss i cs1 cs2 →
-              minuss i (❨l, m❩;cs1) (❨l - i, m❩;cs2)
-| minuss_ge : ∀cs1,cs2,l,m,i. l ≤ i → minuss (m + i) cs1 cs2 →
-              minuss i (❨l, m❩;cs1) cs2
-.
-
-interpretation "minus (multiple relocation with pairs)"
-   'RMinus cs1 i cs2 = (minuss i cs1 cs2).
-
-(* Basic inversion lemmas ***************************************************)
-
-fact minuss_inv_nil1_aux: ∀cs1,cs2,i. cs1 ▭ i ≘ cs2 → cs1 = ◊ → cs2 = ◊.
-#cs1 #cs2 #i * -cs1 -cs2 -i
-[ //
-| #cs1 #cs2 #l #m #i #_ #_ #H destruct
-| #cs1 #cs2 #l #m #i #_ #_ #H destruct
-]
-qed-.
-
-lemma minuss_inv_nil1: ∀cs2,i. ◊ ▭ i ≘ cs2 → cs2 = ◊.
-/2 width=4 by minuss_inv_nil1_aux/ qed-.
-
-fact minuss_inv_cons1_aux: ∀cs1,cs2,i. cs1 ▭ i ≘ cs2 →
-                           ∀l,m,cs. cs1 = ❨l, m❩;cs →
-                           l ≤ i ∧ cs ▭ m + i ≘ cs2 ∨
-                           ∃∃cs0. i < l & cs ▭ i ≘ cs0 &
-                                   cs2 = ❨l - i, m❩;cs0.
-#cs1 #cs2 #i * -cs1 -cs2 -i
-[ #i #l #m #cs #H destruct
-| #cs1 #cs #l1 #m1 #i1 #Hil1 #Hcs #l2 #m2 #cs2 #H destruct /3 width=3 by ex3_intro, or_intror/
-| #cs1 #cs #l1 #m1 #i1 #Hli1 #Hcs #l2 #m2 #cs2 #H destruct /3 width=1 by or_introl, conj/
-]
-qed-.
-
-lemma minuss_inv_cons1: ∀cs1,cs2,l,m,i. ❨l, m❩;cs1 ▭ i ≘ cs2 →
-                        l ≤ i ∧ cs1 ▭ m + i ≘ cs2 ∨
-                        ∃∃cs. i < l & cs1 ▭ i ≘ cs &
-                               cs2 = ❨l - i, m❩;cs.
-/2 width=3 by minuss_inv_cons1_aux/ qed-.
-
-lemma minuss_inv_cons1_ge: ∀cs1,cs2,l,m,i. ❨l, m❩;cs1 ▭ i ≘ cs2 →
-                           l ≤ i → cs1 ▭ m + i ≘ cs2.
-#cs1 #cs2 #l #m #i #H
-elim (minuss_inv_cons1 … H) -H * // #cs #Hil #_ #_ #Hli
-elim (lt_le_false … Hil Hli)
-qed-.
-
-lemma minuss_inv_cons1_lt: ∀cs1,cs2,l,m,i. ❨l, m❩;cs1 ▭ i ≘ cs2 →
-                           i < l →
-                           ∃∃cs. cs1 ▭ i ≘ cs & cs2 = ❨l - i, m❩;cs.
-#cs1 #cs2 #l #m #i #H elim (minuss_inv_cons1 … H) -H * /2 width=3 by ex2_intro/
-#Hli #_ #Hil elim (lt_le_false … Hil Hli)
-qed-.