∀ n m, ¬(n = m) ⇒ ¬((n+1) = (m+1))

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

theorem not_eq_S : \forall (n:nat). \forall (m:nat). ((Not) ((eq) (nat) n m)) -> (Not) ((eq) (nat) ((S) n) ((S) m)).

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

not_eq_S : 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)) => connectives_sttfa_th.sttfa_Not(logic_sttfa_th.eq[nat_sttfa.sttfa_nat](nat_sttfa.sttfa_S(n))(nat_sttfa.sttfa_S(m))))))

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