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

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  14
  15 include "ground/arith/nat_pred_succ.ma".
  16 include "ground/arith/ynat_succ.ma".
  17 include "ground/arith/ynat_pred.ma".
  18
  19 (* PREDECESSOR FOR NON-NEGATIVE INTEGERS WITH INFINITY **********************)
  20
  21 (* Constructions with ysucc *************************************************)
  22
  23 (*** ypred_succ ypred_S *)
  24 lemma ypred_succ (x): x = ↓↑x.
  25 #x @(ynat_split_nat_inf … x) -x //
  26 qed.
  27
  28 (* Inversions with ysucc ****************************************************)
  29
  30 (*** ynat_cases *)
  31 lemma ynat_split_zero_pos (x): ∨∨ 𝟎 = x | x = ↑↓x.
  32 #x @(ynat_split_nat_inf … x) -x //
  33 #n elim (nat_split_zero_pos n)
  34 /2 width=1 by or_introl, or_intror/
  35 qed-.