∀ n, leibniz (λm. m + (n × m)) (times_body (n+1))

Theorem sym_eq_times_body_S : forall (n:nat), leibniz.leibniz (nat -> nat) (fun (m:nat) => plus m (times n m)) (times_body (S n)).

theorem sym_eq_times_body_S : \forall (n:nat). (leibniz) (nat -> nat) (\lambda m : nat. (plus) m ((times) n m)) ((times_body) ((S) n)).

theorem sym_eq_times_body_S : forall (n:nat.nat) , (((leibniz.leibniz) ((nat.nat) -> nat.nat)) (fun (m : nat.nat) , (((nat.plus) ) (m)) ((((nat.times) ) (n)) (m)))) (((nat.times_body) ) (((nat.S) ) (n))).

sym_eq_times_body_S : LEMMA (FORALL(n:nat_sttfa.sttfa_nat):leibniz_sttfa_th.leibniz[[nat_sttfa.sttfa_nat -> nat_sttfa.sttfa_nat]]((LAMBDA(m:nat_sttfa.sttfa_nat):nat_sttfa.plus(m)(nat_sttfa.times(n)(m))))(nat_sttfa.times_body(nat_sttfa.sttfa_S(n))))

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