matita/matita/contribs/lambdadelta/ground_2/ynat/ynat.ma

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  14
  15 include "arithmetics/nat.ma".
  16 include "ground_2/notation/constructors/infinity_0.ma".
  17
  18 (* NATURAL NUMBERS WITH INFINITY ********************************************)
  19
  20 (* the type of natural numbers with infinity *)
  21 inductive ynat: Type[0] ≝
  22 | yinj: nat → ynat
  23 | Y   : ynat
  24 .
  25
  26 coercion yinj.
  27
  28 interpretation "ynat infinity" 'Infinity = Y.
  29
  30 (* Inversion lemmas *********************************************************)
  31
  32 lemma yinj_inj: ∀m,n. yinj m = yinj n → m = n.
  33 #m #n #H destruct //
  34 qed-.