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Variable Ack : nat -> nat -> nat.
Axiom Ack0 : forall m : nat, Ack 0 m = S m.
Axiom Ack1 : forall n : nat, Ack (S n) 0 = Ack n 1.
Axiom Ack2 : forall n m : nat, Ack (S n) (S m) = Ack n (Ack (S n) m).
Hint Rewrite Ack0 Ack1 Ack2 : base0.
Lemma ResAck0 : (Ack 2 2 = 7 -> False) -> False.
Proof.
intros.
autorewrite with base0 in H using try (apply H; reflexivity).
Qed.
Lemma ResAck1 : forall H:(Ack 2 2 = 7 -> False), True -> False.
Proof.
intros.
autorewrite with base0 in *.
apply H;reflexivity.
Qed.
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