proposition: Lemma cfker_repr n (rG : mx_representation algC G n) : cfker (cfRepr rG) = rker rG.
proof: Proof. apply/esym/setP=> x; rewrite inE mul1mx /=. case Gx: (x \in G); last by rewrite inE Gx. apply/eqP/idP=> Kx; last by rewrite max_cfRepr_mx1 // cfker1. rewrite inE Gx; apply/forallP=> y; rewrite !cfunE !mulrb groupMl //. by case: ifP => // Gy; rewrite repr_mxM // Kx mul1mx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype choice ssrnat seq) mathcomp(path div fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset gproduct fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup nilpotent sylow) mathcomp(abelian matrix mxalgebra mxpoly mxrepresentation) mathcomp(vector ssrnum algC classfun archimedean)