proposition: Lemma cfDetIsom aT rT (G : {group aT}) (R : {group rT}) (f : {morphism G >-> rT}) (isoGR : isom G R f) phi : cfDet (cfIsom isoGR phi) = cfIsom isoGR (cfDet phi).
proof: Proof. rewrite unlock rmorph_prod (reindex (isom_Iirr isoGR)); last first. by exists (isom_Iirr (isom_sym isoGR)) => i; rewrite ?isom_IirrK ?isom_IirrKV. apply: eq_bigr=> i; rewrite -!cfDetRepr !irrRepr isom_IirrE rmorphXn cfIsom_iso. by rewrite /= ![in cfIsom _]unlock cfDetMorph ?cfRes_char ?cfDetRes ?irr_char. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype choice ssrnat seq) mathcomp(path div fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset gproduct fingroup morphism) mathcomp(perm automorphism quotient finalg action zmodp) mathcomp(commutator cyclic center pgroup nilpotent sylow) mathcomp(abelian matrix mxalgebra mxpoly mxrepresentation) mathcomp(vector ssrnum algC classfun archimedean)