proposition: Lemma gen_mulVr x : x != 0 -> genV x * x = 1.
proof: Proof. rewrite -(inj_eq mxval_inj) mxval0. move/(mx_Schur irrG (mxval_centg x)) => u_x. by apply: mxval_inj; rewrite mxvalM mxval_genV mxval1 mulVmx. 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)