nat.le_plus_to_le
∀ a n m, (a + n) ≤ (a + m) ⇒ n ≤ m
Theorem le_plus_to_le : forall (a:nat), forall (n:nat), forall (m:nat), (le (plus a n) (plus a m)) -> le n m.
theorem le_plus_to_le : \forall (a:nat). \forall (n:nat). \forall (m:nat). ((le) ((plus) a n) ((plus) a m)) -> (le) n m.
theorem le_plus_to_le : forall (a:nat.nat) , forall (n:nat.nat) , forall (m:nat.nat) , ((((nat.le_) ) ((((nat.plus) ) (a)) (n))) ((((nat.plus) ) (a)) (m))) -> (((nat.le_) ) (n)) (m).
le_plus_to_le : 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(a)(n))(nat_sttfa.plus(a)(m)) => nat_sttfa.le(n)(m)))))
Printing for OpenTheory is not working at the moment.