proposition: Lemma eqr_div x y z t : y != 0 -> t != 0 -> (x / y == z / t) = (x * t == z * y).
proof: Proof. move=> yD0 tD0; rewrite -[x in RHS](divfK yD0) -[z in RHS](divfK tD0) mulrAC. by apply/eqP/eqP => [->|/(mulIf yD0)/(mulIf tD0)]. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat div seq) mathcomp(choice fintype finfun bigop prime binomial)