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

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  14
  15 include "ground/arith/nat_succ.ma".
  16 include "ground/arith/nat_pred.ma".
  17
  18 (* PREDECESSOR FOR NON-NEGATIVE INTEGERS ************************************)
  19
  20 (* Constructions with nsucc *************************************************)
  21
  22 (*** pred_Sn pred_S *)
  23 lemma npred_succ (n): n = ↓↑n.
  24 * //
  25 qed.
  26
  27 (* Inversions with nsucc ****************************************************)
  28
  29 (*** nat_split *)
  30 lemma nat_split_zero_pos (n): ∨∨ 𝟎 = n | n = ↑↓n.
  31 #n @(nat_ind_succ … n) -n
  32 /2 width=1 by or_introl, or_intror/
  33 qed-.