proposition: Lemma exp_quo_lessn r1 (p1 q1 p2 q2 : nat) : (0 < q1)%N -> (0 < q2)%N -> 1 <= r1 -> (p1 * q2 <= p2 * q1)%N -> exp_quo r1 p1 q1 <= exp_quo r1 p2 q2.
proof: Proof. move => Hq1 Hq2 H1r Hle. have H0r : 0 <= r1 by apply/le_trans/H1r/ler01. by rewrite exp_quo_lessE // exp_incr_expp ?ler1q. Qed.
imports: mathcomp(all_ssreflect all_algebra all_field) extra_mathcomp posnum hanson_elem_arith