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

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  14
  15 include "ground/notation/functions/downarrow_1.ma".
  16 include "ground/arith/pnat_dis.ma".
  17 include "ground/arith/nat.ma".
  18
  19 (* PREDECESSOR FOR NON-NEGATIVE INTEGERS ************************************)
  20
  21 (*** pred *)
  22 definition npred (m): nat ≝ match m with
  23 [ nzero  ⇒ 𝟎
  24 | ninj p ⇒ pdis … (𝟎) ninj p
  25 ].
  26
  27 interpretation
  28   "predecessor (non-negative integers)"
  29   'DownArrow m = (npred m).
  30
  31 (* Basic constructions ******************************************************)
  32
  33 (*** pred_O *)
  34 lemma npred_zero: 𝟎 = ↓𝟎.
  35 // qed.