milestone update in ground_2 and basic_2A

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / multiple / mr2.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2.ma b/matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2.ma
deleted file mode 100644 (file)
index 34f1691..0000000
--- a/matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2.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 "basic_2A/notation/relations/rat_3.ma".
-include "basic_2A/grammar/term_vector.ma".
-
-(* MULTIPLE RELOCATION WITH PAIRS *******************************************)
-
-inductive at: list2 nat nat → 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
-lapply (le_to_lt_to_lt … Hli1 Hi1l) -Hli1 -Hi1l #Hl
-elim (lt_refl_false … Hl)
-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
-lapply (le_to_lt_to_lt … Hli1 Hi1l) -Hli1 -Hi1l #Hl
-elim (lt_refl_false … Hl)
-qed-.