∀ n m, ¬(n = m) ⇒ n ≤ m ⇒ n < m

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

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

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

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

Printing for OpenTheory is not working at the moment.