proposition: Lemma irr1_rfix : (1%irr :=: rfix_mx aG G)%MS.
proof: Proof. rewrite [1%irr]unlock PackSocleK; apply/eqmxP. rewrite (component_mx_id principal_comp_subproof) andbT. have [I [W isoW ->]] := component_mx_def principal_comp_subproof. apply/sumsmx_subP=> i _; have [f _ hom_f <-]:= isoW i. by apply/rfix_mxP=> x Gx; rewrite -(hom_mxP hom_f) // (rfix_mxP G _). 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)