matita/matita/tests/unfold.ma

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  14
  15
  16
  17 include "coq.ma".
  18
  19 alias symbol "plus" (instance 0) = "Coq's natural plus".
  20 definition myplus \def \lambda x,y. x+y.
  21
  22 alias id "S" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/2)".
  23 lemma lem: \forall n. S (n + n) = (S n) + n.
  24  intro; reflexivity.
  25 qed.
  26
  27 theorem trivial: \forall n. S (myplus n n) = myplus (S n) n.
  28  unfold myplus in \vdash (\forall _.(? ? ? %)).
  29  intro.
  30  unfold myplus.
  31  rewrite > lem.
  32  reflexivity.
  33 qed.
  34
  35 (* This test needs to parse "uno" in the context of the hypothesis H,
  36    not in the context of the goal. *)
  37 alias id "O" = "cic:/Coq/Init/Datatypes/nat.ind#xpointer(1/1/1)".
  38 theorem t: let uno \def S O in uno + uno = S uno \to uno=uno.
  39  intros. unfold uno in H.
  40  reflexivity.
  41 qed.