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

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  14
  15 include "ground/arith/ynat_le_pred_succ.ma".
  16 include "ground/arith/ynat_lt_pred_succ.ma".
  17
  18 (* STRICT ORDER FOR NON-NEGATIVE INTEGERS WITH INFINITY *********************)
  19
  20 (* Constructions with yle and ypred and ysucc *******************************)
  21
  22 (*** yle_inv_succ_sn_lt yle_inv_succ1_lt *)
  23 lemma le_succ_sn_ylt (x) (y):
  24       ↑x ≤ y → ∧∧ x ≤ ↓y & 𝟎 < y.
  25 #x #y #H elim (yle_inv_succ_sn … H) -H
  26 /4 width=2 by ylt_zero_sn, conj/
  27 qed-.