proposition: Lemma rker_mx_rsim n1 n2 (rG1 : reprG n1) (rG2 : reprG n2) : mx_rsim rG1 rG2 -> rker rG1 = rker rG2.
proof: Proof. case=> f def_n2; rewrite -{n2}def_n2 in f rG2 *. rewrite row_free_unit => injf homf. apply/setP=> x; rewrite !inE !mul1mx; apply: andb_id2l => Gx. by rewrite -(can_eq (mulmxK injf)) homf // -scalar_mxC (can_eq (mulKmx injf)). Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime) mathcomp(ssralg poly polydiv finset fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup matrix mxalgebra) mathcomp(mxpoly)