proposition: Lemma mx_rsim_scalar n1 n2 (rG1 : reprG n1) (rG2 : reprG n2) x c : x \in G -> mx_rsim rG1 rG2 -> rG1 x = c%:M -> rG2 x = c%:M.
proof: Proof. move=> Gx /mx_rsim_sym[B _ Bfree rG2_B] rG1x. by apply: (row_free_inj Bfree); rewrite rG2_B // rG1x scalar_mxC. 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)