ground_2 released and permanently renamed as ground

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / etc / ynat_old / ynat_le.etc

diff --git a/matita/matita/contribs/lambdadelta/ground_2/etc/ynat_old/ynat_le.etc b/matita/matita/contribs/lambdadelta/ground_2/etc/ynat_old/ynat_le.etc
deleted file mode 100644 (file)
index bde84cf..0000000
--- a/matita/matita/contribs/lambdadelta/ground_2/etc/ynat_old/ynat_le.etc
+++ /dev/null
@@ -1,84 +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/star.ma".
-include "ground_2/ynat/ynat_iszero.ma".
-include "ground_2/ynat/ynat_pred.ma".
-
-(* INFINITARY NATURAL NUMBERS ***********************************************)
-
-(* order relation *)
-coinductive yle: relation ynat ≝
-| yle_O: ∀n. yle 0 n
-| yle_S: ∀m,n. yle m n → yle (⫯m) (⫯n)
-.
-
-interpretation "natural 'less or equal to'" 'leq x y = (yle x y).
-
-(* Inversion lemmas *********************************************************)
-
-fact yle_inv_O2_aux: ∀m,x. m ≤ x → x = 0 → m = 0.
-#m #x * -m -x //
-#m #x #_ #H elim (discr_YS_YO … H) (**) (* destructing lemma needed *)
-qed-.
-
-lemma yle_inv_O2: ∀m. m ≤ 0 → m = 0.
-/2 width =3 by yle_inv_O2_aux/ qed-.
-
-fact yle_inv_S1_aux: ∀x,y. x ≤ y → ∀m. x = ⫯m → ∃∃n. m ≤ n & y = ⫯n.
-#x #y * -x -y
-[ #y #m #H elim (discr_YO_YS … H) (**) (* destructing lemma needed *)
-| #x #y #Hxy #m #H destruct /2 width=3 by ex2_intro/
-] 
-qed-.
-
-lemma yle_inv_S1: ∀m,y.  ⫯m ≤ y → ∃∃n. m ≤ n & y = ⫯n.
-/2 width=3 by yle_inv_S1_aux/ qed-.
-
-lemma yle_inv_S: ∀m,n. ⫯m ≤ ⫯n → m ≤ n.
-#m #n #H elim (yle_inv_S1 … H) -H
-#x #Hx #H destruct //
-qed-.
-
-(* Properties ***************************************************************)
-
-let corec yle_refl: reflexive … yle ≝ ?.
-* [ @yle_O | #x @yle_S // ]
-qed.
-
-let corec yle_Y: ∀m. m ≤ ∞ ≝ ?.
-* [ @yle_O | #m <Y_rew @yle_S // ]
-qed.
-
-let corec yle_S_dx: ∀m,n. m ≤ n → m ≤ ⫯n ≝ ?.
-#m #n * -m -n [ #n @yle_O | #m #n #H @yle_S /2 width=1 by/ ]
-qed.
-
-lemma yle_refl_S_dx: ∀x. x ≤ ⫯x.
-/2 width=1 by yle_refl, yle_S_dx/ qed.
-
-lemma yle_pred_sn: ∀m,n. m ≤ n → ⫰m ≤ n ≝ ?.
-* // #m #n #H elim (yle_inv_S1 … H) -H
-#x #Hm #H destruct /2 width=1 by yle_S_dx/
-qed.
-
-lemma yle_refl_pred_sn: ∀x. ⫰x ≤ x.
-/2 width=1 by yle_refl, yle_pred_sn/ qed.
-
-let corec yle_trans: Transitive … yle ≝ ?.
-#x #y * -x -y [ #x #z #_ @yle_O ]
-#x #y #Hxy #z #H elim (yle_inv_S1 … H) -H
-#n #Hyz #H destruct
-@yle_S @(yle_trans … Hxy … Hyz) (**) (* cofix not guarded by constructors *)
-qed-.