milestone update in ground, partial commit

[helm.git] / matita / matita / contribs / lambdadelta / ground / lib / arith_2b.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/lib/arith_2b.ma b/matita/matita/contribs/lambdadelta/ground/lib/arith_2b.ma
deleted file mode 100644 (file)
index f9df115..0000000
--- a/matita/matita/contribs/lambdadelta/ground/lib/arith_2b.ma
+++ /dev/null
@@ -1,44 +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/lib/arith.ma".
-
-(* ARITHMETICAL PROPERTIES FOR λδ-2B ****************************************)
-
-lemma arith_l4 (m11) (m12) (m21) (m22):
-               m21+m22-(m11+m12) = m21-m11-m12+(m22-(m11-m21)-(m12-(m21-m11))).
-#m11 #m12 #m21 #m22 >minus_plus
-elim (le_or_ge (m11+m12) m21) #Hm1121
-[ lapply (transitive_le m11 ??? Hm1121) // #Hm121
-  lapply (le_plus_to_minus_l … Hm1121) #Hm12211
-  <plus_minus // @eq_f2 // >(eq_minus_O m11 ?) // >(eq_minus_O m12 ?) //
-| >(eq_minus_O m21 ?) // <plus_O_n <minus_plus <commutative_plus
-  elim (le_or_ge m11 m21) #Hm121
-  [ lapply (le_plus_to_minus_comm … Hm1121) #Hm2112
-    >(eq_minus_O m11 ?) // <plus_minus_associative // <minus_le_minus_minus_comm //
-  | >(eq_minus_O m21 ?) // <minus_le_minus_minus_comm //
-  ]
-]
-qed.
-
-lemma arith_l3 (m) (n1) (n2): n1+n2-m = n1-m+(n2-(m-n1)).
-// qed.
-
-lemma arith_l2 (n1) (n2): ↑n2-n1 = 1-n1+(n2-(n1-1)).
-#n1 #n2 <arith_l3 //
-qed.
-
-lemma arith_l1: ∀x. 1 = 1-x+(x-(x-1)).
-#x <arith_l2 //
-qed.