nat.le_to_lt_to_lt
∀ n m p, n ≤ m ⇒ m < p ⇒ n < p
Theorem le_to_lt_to_lt : forall (n:nat), forall (m:nat), forall (p:nat), (le n m) -> (lt m p) -> lt n p.
theorem le_to_lt_to_lt : \forall (n:nat). \forall (m:nat). \forall (p:nat). ((le) n m) -> ((lt) m p) -> (lt) n p.
theorem le_to_lt_to_lt : forall (n:nat.nat) , forall (m:nat.nat) , forall (p:nat.nat) , ((((nat.le_) ) (n)) (m)) -> ((((nat.lt_) ) (m)) (p)) -> (((nat.lt_) ) (n)) (p).
le_to_lt_to_lt : LEMMA (FORALL(n:nat_sttfa.sttfa_nat):(FORALL(m:nat_sttfa.sttfa_nat):(FORALL(p:nat_sttfa.sttfa_nat):(nat_sttfa.le(n)(m) => (nat_sttfa.lt(m)(p) => nat_sttfa.lt(n)(p))))))
Printing for OpenTheory is not working at the moment.