proposition: Fact c_incr (n m i : int) : 0 <= n -> 0 <= i -> i <= n -> n <= m -> c n i <= c m i.
proof: Proof. case: n m i => [] // n [] // m [] // i _ _ lein lenm; rewrite /c. rewrite -!PoszD !binz_nat_nat -!expfzMl -!rmorphM /= !exprz_pintl // ler_nat. by apply: leq_mul; apply: leq_mul; apply: leq_bin2l; lia. Qed.
imports: mathcomp(all_ssreflect all_algebra) tactics binomialz seq_defs