update in lambdadelta

[helm.git] / matita / matita / contribs / lambdadelta / basic_2A / multiple / mr2_mr2.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2_mr2.ma b/matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2_mr2.ma
new file mode 100644 (file)
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+++ b/matita/matita/contribs/lambdadelta/basic_2A/multiple/mr2_mr2.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/multiple/mr2.ma".
+
+(* MULTIPLE RELOCATION WITH PAIRS *******************************************)
+
+(* 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-.