ground_2 released and permanently renamed as ground

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

diff --git a/matita/matita/contribs/lambdadelta/ground_2/etc/ynat/ynat_rpm.etc b/matita/matita/contribs/lambdadelta/ground_2/etc/ynat/ynat_rpm.etc
deleted file mode 100644 (file)
index 51aa496..0000000
--- a/matita/matita/contribs/lambdadelta/ground_2/etc/ynat/ynat_rpm.etc
+++ /dev/null
@@ -1,51 +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/notation/relations/rplusminus_4.ma".
-include "ground_2/ynat/ynat_plus.ma".
-
-(* NATURAL NUMBERS WITH INFINITY ********************************************)
-
-(* algebraic x + y1 - y2 = z *)
-inductive yrpm (x:ynat) (y1:ynat) (y2:ynat): predicate ynat ≝
-| yrpm_ge: y2 ≤ y1 → yrpm x y1 y2 (x + (y1 - y2))
-| yrpm_lt: y1 < y2 → yrpm x y1 y2 (x - (y2 - y1))
-.
-
-interpretation "ynat 'algebraic plus-minus' (relational)"
-   'RPlusMinus x y1 y2 z = (yrpm x y1 y2 z).
-
-(* Basic inversion lemmas ***************************************************)
-
-lemma ypm_inv_ge: ∀x,y1,y2,z. x ⊞ y1 ⊟ y2 ≡ z →
-                  y2 ≤ y1 → z = x + (y1 - y2).
-#x #y1 #y2 #z * -z //
-#Hy12 #H elim (ylt_yle_false … H) -H //
-qed-.
-
-lemma ypm_inv_lt: ∀x,y1,y2,z. x ⊞ y1 ⊟ y2 ≡ z →
-                  y1 < y2 → z = x - (y2 - y1).
-#x #y1 #y2 #z * -z //
-#Hy21 #H elim (ylt_yle_false … H) -H //
-qed-.
-
-(* Advanced inversion lemmas ************************************************)
-
-lemma ypm_inv_le: ∀x,y1,y2,z. x ⊞ y1 ⊟ y2 ≡ z →
-                  y1 ≤ y2 → z = x - (y2 - y1).
-#x #y1 #y2 #z #H #Hy12 elim (yle_split_eq … Hy12) -Hy12 #Hy12
-[ /2 width=1 by ypm_inv_lt/
-| >(ypm_inv_ge … H) -H // destruct >yminus_refl //
-]
-qed-.