proposition: Lemma rank_irr1 : \rank 1%irr = 1.
proof: Proof. apply/eqP; rewrite eqn_leq lt0n mxrank_eq0 nz_socle andbT. by rewrite irr1_rfix rfix_regular rank_leq_row. 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)