proposition: Lemma telescope_prodf n m (f : nat -> F) : (forall k, n < k < m -> f k != 0) -> n < m -> \prod_(n <= k < m) (f k.+1 / f k) = f m / f n.
proof: Proof. move=> nz_f ltnm; apply: invr_inj; rewrite prodf_div !invf_div -prodf_div. by apply: telescope_prodr => // k /nz_f; rewrite unitfE. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)