∀ n m, n < m ⇒ ¬(n = m)

Theorem lt_to_not_eq : forall (n:nat), forall (m:nat), (lt n m) -> connectives.Not (logic.eq (nat) n m).

theorem lt_to_not_eq : \forall (n:nat). \forall (m:nat). ((lt) n m) -> (Not) ((eq) (nat) n m).

theorem lt_to_not_eq : forall (n:nat.nat) , forall (m:nat.nat) , ((((nat.lt_) ) (n)) (m)) -> ((connectives.Not) ) ((((logic.eq_) (nat.nat)) (n)) (m)).

lt_to_not_eq : LEMMA (FORALL(n:nat_sttfa.sttfa_nat):(FORALL(m:nat_sttfa.sttfa_nat):(nat_sttfa.lt(n)(m) => connectives_sttfa_th.sttfa_Not(logic_sttfa_th.eq[nat_sttfa.sttfa_nat](n)(m)))))

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