matita/matita/contribs/lambdadelta/ground/etc/ynat_old/ynat_pred.etc

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   3 (*      ||M||                                                             *)
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   5 (*      ||T||                                                             *)
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  14
  15 include "ground_2/ynat/ynat.ma".
  16
  17 (* INFINITARY NATURAL NUMBERS ***********************************************)
  18
  19 (* the predecessor on ynat *)
  20 definition ypred: ynat → ynat ≝ λm. match m with
  21 [ YO   ⇒ 0
  22 | YS n ⇒ n
  23 ].
  24
  25 notation "hvbox( ⫰ term 55 T )"
  26    non associative with precedence 55
  27    for @{ 'Predecessor $T }.
  28
  29 interpretation "ynat predecessor" 'Predecessor m = (ypred m).
  30
  31 (* Properties ***************************************************************)
  32
  33 lemma ypred_S: ∀m. ⫰⫯m = m.
  34 // qed.
  35
  36 (* Inversion lemmas *********************************************************)
  37
  38 lemma YS_inj: ∀m,n. ⫯m = ⫯n → m = n.
  39 #m #n #H <(ypred_S m) <(ypred_S n) //
  40 qed-.