∀ n m, O < m ⇒ (mod n m) < m

Theorem lt_mod_m_m : forall (n:nat.nat), forall (m:nat.nat), (nat.lt nat.O m) -> nat.lt (mod n m) m.

theorem lt_mod_m_m : \forall (n:nat). \forall (m:nat). ((lt) (O) m) -> (lt) ((mod) n m) m.

theorem lt_mod_m_m : forall (n:nat.nat) , forall (m:nat.nat) , ((((nat.lt_) ) ((nat.O) )) (m)) -> (((nat.lt_) ) ((((div_mod.mod) ) (n)) (m))) (m).

lt_mod_m_m : LEMMA (FORALL(n:nat_sttfa_th.sttfa_nat):(FORALL(m:nat_sttfa_th.sttfa_nat):(nat_sttfa_th.lt(nat_sttfa_th.sttfa_O)(m) => nat_sttfa_th.lt(div_mod_sttfa.mod(n)(m))(m))))

Printing for OpenTheory is not working at the moment.