milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / multiple / mr2_minus.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2_minus.ma b/matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2_minus.ma
deleted file mode 100644 (file)
index 8eb1a55..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2_minus.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 "basic_2A/notation/relations/rminus_3.ma".
-include "basic_2A/multiple/mr2.ma".
-
-(* MULTIPLE RELOCATION WITH PAIRS *******************************************)
-
-inductive minuss: nat → relation (list2 nat nat) ≝
-| 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
-lapply (lt_to_le_to_lt … Hil Hli) -Hil -Hli #Hi
-elim (lt_refl_false … Hi)
-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 lapply (lt_to_le_to_lt … Hil Hli) -Hil -Hli
-#Hi elim (lt_refl_false … Hi)
-qed-.