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### Theoremprimes.dividesb_false_to_not_divides

Statement

∀ n m, (dividesb n m) = false ⇒ ¬(n | m)

Main Dependencies

Statement

Theorem dividesb_false_to_not_divides : forall (n:nat.nat), forall (m:nat.nat), (logic.eq (bool.bool) (dividesb n m) bool.false) -> connectives.Not (divides n m).

Statement

theorem dividesb_false_to_not_divides : \forall (n:nat). \forall (m:nat). ((eq) (bool) ((dividesb) n m) (false) ) -> (Not) ((divides) n m).

Statement

theorem dividesb_false_to_not_divides : forall (n:nat.nat) , forall (m:nat.nat) , ((((logic.eq_) (bool.bool)) ((((primes.dividesb) ) (n)) (m))) ((bool.false) )) -> ((connectives.Not) ) ((((primes.divides) ) (n)) (m)).

Statement

dividesb_false_to_not_divides : LEMMA (FORALL(n:nat_sttfa_th.sttfa_nat):(FORALL(m:nat_sttfa_th.sttfa_nat):(logic_sttfa_th.eq[bool_sttfa_th.sttfa_bool](primes_sttfa.dividesb(n)(m))(bool_sttfa_th.sttfa_false) => connectives_sttfa_th.sttfa_Not(primes_sttfa.sttfa_divides(n)(m)))))

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