fact: Definition pid_mx {m n} r : 'M[R]_(m, n) := \matrix[pid_mx_key]_(i, j) ((i == j :> nat) && (i < r))%:R.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq choice) mathcomp(fintype finfun bigop finset fingroup perm order) mathcomp(div prime binomial ssralg countalg finalg zmodp)