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

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  14
  15 include "ground_2/notation.ma".
  16 include "ground_2/xoa_props.ma".
  17 include "ground_2/ynat/ynat.ma".
  18
  19 (* INFINITARY NATURAL NUMBERS ***********************************************)
  20
  21 (* "is_zero" predicate *)
  22 definition yzero: predicate ynat ≝ λx. match x with
  23 [ YO   ⇒ ⊤
  24 | YS _ ⇒ ⊥
  25 ].
  26
  27 (* Inversion lemmas *********************************************************)
  28
  29 lemma discr_YS_YO: ∀n. ⫯n = 0 → ⊥.
  30 #n #H change with (yzero (⫯n))
  31 >H -H //
  32 qed-.
  33
  34 lemma discr_YO_YS: ∀n. ynat_of_nat 0 = ⫯n → ⊥. (**) (* explicit coercion *)
  35 /2 width=2 by discr_YS_YO/ qed-.