∀ n m, ¬(n = m) ⇒ (n = m) = false

Theorem not_eq_to_eqb_false : forall (n:nat), forall (m:nat), (connectives.Not (logic.eq (nat) n m)) -> logic.eq (bool.bool) (eqb n m) bool.false.

theorem not_eq_to_eqb_false : \forall (n:nat). \forall (m:nat). ((Not) ((eq) (nat) n m)) -> (eq) (bool) ((eqb) n m) (false) .

theorem not_eq_to_eqb_false : forall (n:nat.nat) , forall (m:nat.nat) , (((connectives.Not) ) ((((logic.eq_) (nat.nat)) (n)) (m))) -> (((logic.eq_) (bool.bool)) ((((nat.eqb) ) (n)) (m))) ((bool.false) ).

not_eq_to_eqb_false : 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)) => logic_sttfa_th.eq[bool_sttfa_th.sttfa_bool](nat_sttfa.eqb(n)(m))(bool_sttfa_th.sttfa_false))))

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