∀ n, leibniz (λm. (n + m)+1) (plus_body (n+1))

Theorem sym_eq_plus_body_S : forall (n:nat), leibniz.leibniz (nat -> nat) (fun (m:nat) => S (plus n m)) (plus_body (S n)).

theorem sym_eq_plus_body_S : \forall (n:nat). (leibniz) (nat -> nat) (\lambda m : nat. (S) ((plus) n m)) ((plus_body) ((S) n)).

theorem sym_eq_plus_body_S : forall (n:nat.nat) , (((leibniz.leibniz) ((nat.nat) -> nat.nat)) (fun (m : nat.nat) , ((nat.S) ) ((((nat.plus) ) (n)) (m)))) (((nat.plus_body) ) (((nat.S) ) (n))).

sym_eq_plus_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.sttfa_S(nat_sttfa.plus(n)(m))))(nat_sttfa.plus_body(nat_sttfa.sttfa_S(n))))

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