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

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

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

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

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

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