∀ a n m, (n + a) ≤ (m + a) ⇒ n ≤ m

Theorem le_plus_to_le_r : forall (a:nat), forall (n:nat), forall (m:nat), (le (plus n a) (plus m a)) -> le n m.

theorem le_plus_to_le_r : \forall (a:nat). \forall (n:nat). \forall (m:nat). ((le) ((plus) n a) ((plus) m a)) -> (le) n m.

theorem le_plus_to_le_r : forall (a:nat.nat) , forall (n:nat.nat) , forall (m:nat.nat) , ((((nat.le_) ) ((((nat.plus) ) (n)) (a))) ((((nat.plus) ) (m)) (a))) -> (((nat.le_) ) (n)) (m).

le_plus_to_le_r : LEMMA (FORALL(a:nat_sttfa.sttfa_nat):(FORALL(n:nat_sttfa.sttfa_nat):(FORALL(m:nat_sttfa.sttfa_nat):(nat_sttfa.le(nat_sttfa.plus(n)(a))(nat_sttfa.plus(m)(a)) => nat_sttfa.le(n)(m)))))

Printing for OpenTheory is not working at the moment.