// This prints the left floatting menu

### Theoremprimes.let_clause_15311

Statement

∀ n m, O < m ⇒ n | m ⇒ ∀ d p, m = (n × (p+1)) ⇒ m = (n + (n × p))

Main Dependencies
definition
Theory

Statement

Theorem let_clause_15311 : forall (n:nat.nat), forall (m:nat.nat), (nat.lt nat.O m) -> (divides n m) -> forall (d:nat.nat), forall (p:nat.nat), (logic.eq (nat.nat) m (nat.times n (nat.S p))) -> logic.eq (nat.nat) m (nat.plus n (nat.times n p)).

Statement

theorem let_clause_15311 : \forall (n:nat). \forall (m:nat). ((lt) (O) m) -> ((divides) n m) -> \forall (d:nat). \forall (p:nat). ((eq) (nat) m ((times) n ((S) p))) -> (eq) (nat) m ((plus) n ((times) n p)).

Statement

theorem let_clause_15311 : forall (n:nat.nat) , forall (m:nat.nat) , ((((nat.lt_) ) ((nat.O) )) (m)) -> ((((primes.divides) ) (n)) (m)) -> forall (d:nat.nat) , forall (p:nat.nat) , ((((logic.eq_) (nat.nat)) (m)) ((((nat.times) ) (n)) (((nat.S) ) (p)))) -> (((logic.eq_) (nat.nat)) (m)) ((((nat.plus) ) (n)) ((((nat.times) ) (n)) (p))).

Statement

let_clause_15311 : LEMMA (FORALL(n:nat_sttfa_th.sttfa_nat):(FORALL(m:nat_sttfa_th.sttfa_nat):(nat_sttfa_th.lt(nat_sttfa_th.sttfa_O)(m) => (primes_sttfa.sttfa_divides(n)(m) => (FORALL(d:nat_sttfa_th.sttfa_nat):(FORALL(p:nat_sttfa_th.sttfa_nat):(logic_sttfa_th.eq[nat_sttfa_th.sttfa_nat](m)(nat_sttfa_th.times(n)(nat_sttfa_th.sttfa_S(p))) => logic_sttfa_th.eq[nat_sttfa_th.sttfa_nat](m)(nat_sttfa_th.plus(n)(nat_sttfa_th.times(n)(p))))))))))

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