proposition: Lemma FTtype_P2max : (M \in 'M_'P2) = (FTtype M == 2).
proof: Proof. have [[U K] /= complU] := kappa_witness. rewrite (sameP (P2maxP maxM complU) andP) -(trivgFmax maxM complU) FTtype_Fmax. have [-> // | notMtype1] := altP eqP. have ntK: K :!=: 1 by rewrite -(trivgFmax maxM complU) FTtype_Fmax. have [_ [//|defM' _] _ _ _] := kappa_structure maxM complU. do [rewrite /FTtype; case: ifP => // _] in notMtype1 *. rewrite -cardG_gt1 eqEcard Msigma_der1 //= -(sdprod_card defM') -ltnNge. rewrite -(@ltn_pmul2l #|M`_\sigma|) ?cardG_gt0 //= muln1. by case: leqP => // _; do 2!case: ifP=> //. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq div path fintype) mathcomp(bigop finset prime fingroup morphism perm automorphism quotient) mathcomp(action gproduct gfunctor pgroup cyclic center commutator) mathcomp(gseries nilpotent sylow abelian maximal hall frobenius) odd_order(BGsection1 BGsection2 BGsection3 BGsection4 BGsection5) odd_order(BGsection6 BGsection7 BGsection9 BGsection10 BGsection12) odd_order(BGsection13 BGsection14 BGsection15)