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

Theorem

nat.le_plus_to_minus_r

Statement

∀ a b c, (a + b) ≤ c ⇒ a ≤ (c - b)

Main Dependencies
Theory

Coq-Jumb
Statement

Theorem le_plus_to_minus_r : forall (a:nat), forall (b:nat), forall (c:nat), (le (plus a b) c) -> le a (minus c b).



Matita-Jumb
Statement

theorem le_plus_to_minus_r : \forall (a:nat). \forall (b:nat). \forall (c:nat). ((le) ((plus) a b) c) -> (le) a ((minus) c b).



Lean-jumb
Statement

theorem le_plus_to_minus_r : forall (a:nat.nat) , forall (b:nat.nat) , forall (c:nat.nat) , ((((nat.le_) ) ((((nat.plus) ) (a)) (b))) (c)) -> (((nat.le_) ) (a)) ((((nat.minus) ) (c)) (b)).



PVS-jumb

Statement

le_plus_to_minus_r : LEMMA (FORALL(a:nat_sttfa.sttfa_nat):(FORALL(b:nat_sttfa.sttfa_nat):(FORALL(c:nat_sttfa.sttfa_nat):(nat_sttfa.le(nat_sttfa.plus(a)(b))(c) => nat_sttfa.le(a)(nat_sttfa.minus(c)(b))))))



OpenTheory

Printing for OpenTheory is not working at the moment.