∀ n m p, O < p ⇒ ∀ x2515 x2516, x2515 = ((mod x2515 x2516) + (x2516 × (div x2515 x2516)))

Theorem let_clause_1034 : forall (n:nat.nat), forall (m:nat.nat), forall (p:nat.nat), (nat.lt nat.O p) -> forall (x2515:nat.nat), forall (x2516:nat.nat), logic.eq (nat.nat) x2515 (nat.plus (div_mod.mod x2515 x2516) (nat.times x2516 (div_mod.div x2515 x2516))).

theorem let_clause_1034 : \forall (n:nat). \forall (m:nat). \forall (p:nat). ((lt) (O) p) -> \forall (x2515:nat). \forall (x2516:nat). (eq) (nat) x2515 ((plus) ((mod) x2515 x2516) ((times) x2516 ((div) x2515 x2516))).

theorem let_clause_1034 : forall (n:nat.nat) , forall (m:nat.nat) , forall (p:nat.nat) , ((((nat.lt_) ) ((nat.O) )) (p)) -> forall (x2515:nat.nat) , forall (x2516:nat.nat) , (((logic.eq_) (nat.nat)) (x2515)) ((((nat.plus) ) ((((div_mod.mod) ) (x2515)) (x2516))) ((((nat.times) ) (x2516)) ((((div_mod.div) ) (x2515)) (x2516)))).

let_clause_1034 : LEMMA (FORALL(n:nat_sttfa_th.sttfa_nat):(FORALL(m:nat_sttfa_th.sttfa_nat):(FORALL(p:nat_sttfa_th.sttfa_nat):(nat_sttfa_th.lt(nat_sttfa_th.sttfa_O)(p) => (FORALL(x2515:nat_sttfa_th.sttfa_nat):(FORALL(x2516:nat_sttfa_th.sttfa_nat):logic_sttfa_th.eq[nat_sttfa_th.sttfa_nat](x2515)(nat_sttfa_th.plus(div_mod_sttfa_th.mod(x2515)(x2516))(nat_sttfa_th.times(x2516)(div_mod_sttfa_th.div(x2515)(x2516))))))))))

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