ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / etc / ynat / ynat_min.etc

diff --git a/matita/matita/contribs/lambdadelta/ground_2/etc/ynat/ynat_min.etc b/matita/matita/contribs/lambdadelta/ground_2/etc/ynat/ynat_min.etc
deleted file mode 100644 (file)
index 96b8f2a..0000000
--- a/matita/matita/contribs/lambdadelta/ground_2/etc/ynat/ynat_min.etc
+++ /dev/null
@@ -1,52 +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/ynat/ynat_plus.ma".
-
-(* NATURAL NUMBERS WITH INFINITY ********************************************)
-
-fact ymin_pre_dx_aux: ∀x,y. y ≤ x → x - (x - y) ≤ y.
-#x #y * -x -y
-[ #x #y #Hxy >yminus_inj
- /3 width=4 by yle_inj, monotonic_le_minus_l/
-| * //
-]
-qed-.
-
-lemma ymin_pre_sn: ∀x,y. x ≤ y → x - (x - y) = x.
-#x #y * -x -y //
-#x #y #Hxy >yminus_inj >(eq_minus_O … Hxy) -Hxy //
-qed-.
-
-lemma ymin_pre_i_dx: ∀x,y. x - (x - y) ≤ y.
-#x #y elim (yle_split x y) /2 width=1 by ymin_pre_dx_aux/
-#Hxy >(ymin_pre_sn … Hxy) //
-qed.
-
-lemma ymin_pre_i_sn: ∀x,y. x - (x - y) ≤ x.
-// qed.
-
-lemma ymin_pre_dx: ∀x,y. y ≤ yinj x → yinj x - (yinj x - y) = y.
-#x #y #H elim (yle_inv_inj2 … H) -H
-#z #Hzx #H destruct >yminus_inj
-/3 width=4 by minus_le_minus_minus_comm, eq_f/
-qed-.
-
-lemma ymin_pre_e: ∀z,x. z ≤ yinj x → ∀y. z ≤ y →
-                  z ≤ yinj x - (yinj x - y).
-#z #x #Hzx #y #Hzy elim (yle_split x y)
-[ #H >(ymin_pre_sn … H) -y //
-| #H >(ymin_pre_dx … H) -x //
-]
-qed.