helm/software/matita/tests/ng_commands.ma

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  14
  15 include "nat/plus.ma".
  16
  17 ndefinition thesis0: ∀A:Type.Type ≝ λA. A → A.
  18
  19 ndefinition thesis: ∀A:Type.Type ≝ λA. ?.
  20  napply (A → A);
  21 nqed.
  22
  23 ntheorem foo: ∀A:Type.thesis A.#A;#x;napply x;
  24 nqed.
  25
  26 ntheorem goo: ∀A:Type.A → A. #A; napply (foo ?);
  27 nqed.
  28
  29 naxiom NP: Prop.
  30
  31 ndefinition Q: Prop ≝ NP.
  32
  33 nlet rec nzero (n:nat) : nat ≝
  34  match n with
  35   [ O ⇒ O
  36   | S m ⇒ nzero m].
  37
  38 ntheorem nzero_ok: nzero (S (S O)) = O.
  39  napply (refl_eq ? O);
  40 nqed.
  41
  42 (*
  43 ninductive nnat: Type ≝
  44    nO: nnat
  45  | nS: nnat → nnat.
  46 *)
  47
  48 (* testare anche i record e le ricorsioni/coricorsioni/(co)induttivi MUTUI *)
  49
  50 (*
  51 nrecord pair: Type ≝ { l: pair; r: pair }.
  52 *)