helm/software/matita/tests/ng_bove.ma

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   3 (*      ||M||                                                             *)
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  14
  15 include "logic/pts.ma".
  16
  17 include "nat/minus.ma".
  18
  19 ninductive D: nat → Prop ≝
  20    D0: D O
  21  | Dn: ∀n. D (n - 2) → D n.
  22
  23 naxiom dow: ∀n,m.∀p: D n. n = S m → False.
  24 naxiom destr: ∀n. O = S n → False.
  25
  26 nlet rec f (n:nat) (p:D n) on p : nat ≝
  27  match n return λm. n=m → nat with
  28   [ O ⇒ λ_.O
  29   | S m ⇒ λH. f (n - 2) ?] (refl_eq ? n).
  30  ncases p in H
  31   [ #K; ncases (destr ? K)
  32   | #n0; #p; #H; nassumption ]
  33 nqed.