proposition: Lemma DadeE alpha a u : a \in A -> u \in dd1 a -> alpha^\tau u = alpha a.
proof: Proof. move=> Aa Ha_u; rewrite cfunElock. have [b /= /andP[Ab Hb_u] | ] := pickP; last by move/(_ a); rewrite Aa Ha_u. have [|x Lx ->] := Dade_support1_TI Aa Ab; last by rewrite cfunJ. by apply/pred0Pn; exists u; rewrite /= Ha_u. Qed.
imports: HB(structures) mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq path div choice) mathcomp(fintype tuple finfun bigop prime ssralg poly finset center) mathcomp(fingroup morphism perm automorphism quotient action zmodp) mathcomp(gfunctor gproduct cyclic pgroup frobenius ssrnum) mathcomp(matrix mxalgebra mxrepresentation vector algC classfun character) mathcomp(inertia vcharacter) odd_order(PFsection1)