// This prints the left floatting menu
Dedukti    Load Matita      Load Coq         Load Lean        Load PVS         Load OpenTheory Load
Dedukti-jumb

Theorem

nat.not_le_to_leb_false

Statement

∀ n m, ¬(n ≤ m) ⇒ (leb n m) = false

Main Dependencies
Theory

Coq-Jumb
Statement

Theorem not_le_to_leb_false : forall (n:nat), forall (m:nat), (connectives.Not (le n m)) -> logic.eq (bool.bool) (leb n m) bool.false.



Matita-Jumb
Statement

theorem not_le_to_leb_false : \forall (n:nat). \forall (m:nat). ((Not) ((le) n m)) -> (eq) (bool) ((leb) n m) (false) .



Lean-jumb
Statement

theorem not_le_to_leb_false : forall (n:nat.nat) , forall (m:nat.nat) , (((connectives.Not) ) ((((nat.le_) ) (n)) (m))) -> (((logic.eq_) (bool.bool)) ((((nat.leb) ) (n)) (m))) ((bool.false) ).



PVS-jumb

Statement

not_le_to_leb_false : LEMMA (FORALL(n:nat_sttfa.sttfa_nat):(FORALL(m:nat_sttfa.sttfa_nat):(connectives_sttfa_th.sttfa_Not(nat_sttfa.le(n)(m)) => logic_sttfa_th.eq[bool_sttfa_th.sttfa_bool](nat_sttfa.leb(n)(m))(bool_sttfa_th.sttfa_false))))



OpenTheory

Printing for OpenTheory is not working at the moment.