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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.