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### Theoremprimes.divides_to_dividesb_true

Statement

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

Main Dependencies

Statement

Theorem divides_to_dividesb_true : forall (n:nat.nat), forall (m:nat.nat), (nat.lt nat.O n) -> (divides n m) -> logic.eq (bool.bool) (dividesb n m) bool.true.

Statement

theorem divides_to_dividesb_true : \forall (n:nat). \forall (m:nat). ((lt) (O) n) -> ((divides) n m) -> (eq) (bool) ((dividesb) n m) (true) .

Statement

theorem divides_to_dividesb_true : forall (n:nat.nat) , forall (m:nat.nat) , ((((nat.lt_) ) ((nat.O) )) (n)) -> ((((primes.divides) ) (n)) (m)) -> (((logic.eq_) (bool.bool)) ((((primes.dividesb) ) (n)) (m))) ((bool.true) ).

Statement

divides_to_dividesb_true : 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) => (primes_sttfa.sttfa_divides(n)(m) => logic_sttfa_th.eq[bool_sttfa_th.sttfa_bool](primes_sttfa.dividesb(n)(m))(bool_sttfa_th.sttfa_true)))))

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