proposition: Lemma mx_Schur_inj U f : mxsimple U -> (U <= dom_hom_mx f)%MS -> U *m f != 0 -> (U :&: kermx f)%MS = 0.
proof: Proof. case=> [modU _ simU] homUf nzUf; apply/eqP; apply: contraR nzUf => nz_ker. rewrite (sameP eqP sub_kermxP) (sameP capmx_idPl eqmxP) simU ?capmxSl //. exact: kermx_hom_module. 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)