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14
15
16
17 include "logic/equality.ma".
18 include "nat/nat.ma".
19
20 axiom A : nat -> Type.
21 axiom B : nat -> Type.
22 axiom AB : \forall x. A  x = B x.
23
24 axiom eatA : ∀n. A n -> A O.
25 axiom eatB : ∀n. B n -> A O.
26
27 axiom jmcBA : ∀n,m.∀p:A n = B m.B m -> A n. 
28 axiom jmcAB : ∀n,m.∀p:A n = B m.A n -> B m.
29
30 coercion cic:/matita/tests/coercions_open/jmcAB.con.
31 coercion cic:/matita/tests/coercions_open/jmcBA.con.
32
33 axiom daemon : ∀x,y:A O.x = y.
34
35 alias num (instance 0) = "natural number".
36 lemma xx : ∀b:B 2.∀a:A 1.eatA ? b = eatB ? a.
37 intros; [3,5,7,9: apply AB|1: apply daemon];skip.
38 qed.