matita/matita/contribs/lambdadelta/ground/arith/ynat_le_lminus_succ.ma

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  14
  15 include "ground/arith/ynat_succ.ma".
  16 include "ground/arith/ynat_le_lminus.ma".
  17
  18 (* ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY ****************************)
  19
  20 (* Constructions with ylminus and ysucc *************************************)
  21
  22 (*** yminus_succ1_inj *)
  23 lemma ylminus_succ_sn (x) (n):
  24       yinj_nat n ≤ x → ↑(x - n) = ↑x - n.
  25 #x @(ynat_split_nat_inf … x) -x //
  26 #m #n #Hnm
  27 <ylminus_inj_sn <ysucc_inj <ysucc_inj <ylminus_inj_sn
  28 <nminus_succ_sn /2 width=1 by yle_inv_inj_bi/
  29 qed-.