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Dedukti-jumb

Theorem

nat.not_le_to_not_le_S_S

Statement

∀ n m, ¬(n ≤ m) ⇒ ¬((n+1) ≤ (m+1))

Main Dependencies
Theory
Coq-Jumb
Statement

Theorem not_le_to_not_le_S_S : forall (n:nat), forall (m:nat), (connectives.Not (le n m)) -> connectives.Not (le (S n) (S m)).


Matita-Jumb
Statement

theorem not_le_to_not_le_S_S : \forall (n:nat). \forall (m:nat). ((Not) ((le) n m)) -> (Not) ((le) ((S) n) ((S) m)).


Lean-jumb
Statement

theorem not_le_to_not_le_S_S : forall (n:nat.nat) , forall (m:nat.nat) , (((connectives.Not) ) ((((nat.le_) ) (n)) (m))) -> ((connectives.Not) ) ((((nat.le_) ) (((nat.S) ) (n))) (((nat.S) ) (m))).


PVS-jumb
Statement

not_le_to_not_le_S_S : LEMMA (FORALL(n:nat_sttfa.sttfa_nat):(FORALL(m:nat_sttfa.sttfa_nat):(connectives_sttfa_th.sttfa_Not(nat_sttfa.le(n)(m)) => connectives_sttfa_th.sttfa_Not(nat_sttfa.le(nat_sttfa.sttfa_S(n))(nat_sttfa.sttfa_S(m))))))


OpenTheory

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