proposition: Lemma mxsimpleP U : [/\ mxmodule U, U != 0 & ~ mxnonsimple U] <-> mxsimple U.
proof: Proof. do [split => [] [modU nzU simU]; split] => // [V modV sVU nzV | [V]]. apply/idPn; rewrite -(ltn_leqif (mxrank_leqif_sup sVU)) => ltVU. by case: simU; exists V; apply/and4P. by case/and4P=> modV sVU nzV; apply/negP; rewrite -leqNgt mxrankS ?simU. 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)