matita/tests/bad_induction.ma

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  14
  15
  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; unfold; autobatch.
  27 qed.