propagating the arithmetics library, partial commit

[helm.git] / matita / matita / contribs / lambdadelta / ground / arith / ynat_lt_minus1.ma

diff --git a/matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_minus1.ma b/matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_minus1.ma
deleted file mode 100644 (file)
index 9ab5aa7..0000000
--- a/matita/matita/contribs/lambdadelta/ground/arith/ynat_lt_minus1.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 "ground/arith/nat_lt_minus.ma".
-include "ground/arith/ynat_minus1.ma".
-include "ground/arith/ynat_lt.ma".
-
-(* STRICT ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY *********************)
-
-(* Constructions with yminus1 ***********************************************)
-
-(*** ylt_to_minus *)
-lemma ylt_zero_minus1 (m) (y):
-      yinj_nat m < y → 𝟎 < y - m.
-#m #y @(ynat_split_nat_inf … y) -y //
-#n #Hmn <yminus1_inj_sn >yinj_nat_zero >(nminus_refl m)
-/4 width=1 by ylt_inj, ylt_inv_inj_bi, nlt_minus_bi_dx/
-qed.
-
-(* Inversions with yminus1 **************************************************)
-
-(*** yminus_to_lt *)
-lemma ylt_inv_zero_minus1 (m) (y):
-      (𝟎) < y - m → yinj_nat m < y.
-#m #y @(ynat_split_nat_inf … y) -y //
-#n <yminus1_inj_sn >yinj_nat_zero >(nminus_refl m) #Hmm
-/4 width=2 by ylt_inv_inj_bi, ylt_inj, nlt_inv_minus_bi_dx/
-qed-.
-
-(* Destructions with yminus1 ************************************************)
-
-(*** yminus_pred *)
-lemma yminus1_pred_bi (x:ynat) (n):
-      (𝟎) < x → 𝟎 < n → x - n = ↓x - ↓n.
-#x @(ynat_split_nat_inf … x) -x //
-#m #n >yinj_nat_zero
-#Hm #Hn <yminus1_inj_sn <ypred_inj <yminus1_inj_sn
-<nminus_pred_bi /2 width=1 by ylt_inv_inj_bi/
-qed-.