proposition: Lemma FTtype_P1max : (M \in 'M_'P1) = (2 < FTtype M <= 5).
proof: Proof. rewrite 2!ltn_neqAle -!andbA FTtype_range andbT eq_sym -FTtype_P2max. rewrite eq_sym -FTtype_Pmax in_setD inE. by case: (M \in _); rewrite ?andbT ?andbF ?negbK. 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)