chore(builtin/Nat): use iff
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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@ -36,7 +36,7 @@ axiom add_zeror (a : Nat) : a + 0 = a
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axiom add_succr (a b : Nat) : a + (b + 1) = (a + b) + 1
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axiom mul_zeror (a : Nat) : a * 0 = 0
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axiom mul_succr (a b : Nat) : a * (b + 1) = a * b + a
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axiom le_def (a b : Nat) : a ≤ b = ∃ c, a + c = b
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axiom le_def (a b : Nat) : a ≤ b ⟷ ∃ c, a + c = b
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axiom induction {P : Nat → Bool} (H1 : P 0) (H2 : ∀ (n : Nat) (iH : P n), P (n + 1)) : ∀ a, P a
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theorem induction_on {P : Nat → Bool} (a : Nat) (H1 : P 0) (H2 : ∀ (n : Nat) (iH : P n), P (n + 1)) : P a
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