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better test for church numerals
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14
15 set "baseuri" "cic:/matita/nat/bad_induction".
16
17 include "nat/nat.ma".
18
19 include "logic/equality.ma".
20
21 axiom bad_ind : ∀P : nat -> Prop. ∀n.(n = O -> P n) -> (∀n.P n -> P (S n)) -> P n.
22
23 theorem absurd: ∀n. n = O.
24   intros.
25   letin P ≝ (λx:nat. n = O).
26   apply (bad_ind P n); simplify; intros; autobatch.
27 qed.