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(* Specifications: *)
Lemma lt_q_qbr : forall b q r : nat, 0 < r -> one < b -> q < q * b + r.
Hint Resolve lt_q_qbr: arith.
Lemma lt_O_q : forall b q r : nat, b < q * b + r -> 0 < r -> r < b -> 0 < q.