proposition: Lemma Clifford_iso2 x U V : mx_iso rH U V -> x \in G -> mx_iso rH (U *m rG x) (V *m rG x).
proof: Proof. case=> [f injf homUf defV] Gx; have Gx' := groupVr Gx. pose fx := rG (x^-1)%g *m f *m rG x; exists fx; last 1 first. - by rewrite !mulmxA repr_mxK //; apply: eqmxMr. - by rewrite !unitmx_mul andbC !repr_mx_unit. apply/hom_mxP=> h Hh; have Gh := subsetP sHG h Hh. rewrite -(mulmxA U) -repr_mxM // conjgCV repr_mxM ?groupJ // !mulmxA. rewrite !repr_mxK // (hom_mxP homUf) -?mem_conjg ?(normsP nHG) //=. by rewrite !repr_mxM ?invgK ?groupM // !mulmxA repr_mxKV. 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)