proposition: Lemma subset_coherent_with S1 S2 A tau (tau1 : {additive 'CF(L) -> 'CF(G)}) : {subset S1 <= S2} -> coherent_with S2 A tau tau1 -> coherent_with S1 A tau tau1.
proof: Proof. move=> /zchar_subset sS12 [Itau1 Dtau1]. by split=> [|xi /sS12/Dtau1//]; apply: sub_iso_to Itau1. Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq path div choice fintype) mathcomp(tuple finfun bigop order prime ssralg poly finset center) mathcomp(fingroup morphism perm automorphism quotient action zmodp) mathcomp(gfunctor gproduct cyclic pgroup frobenius) mathcomp(matrix mxalgebra mxrepresentation vector ssrint) mathcomp(ssrnum algC classfun character inertia vcharacter) odd_order(PFsection1 PFsection2 PFsection3 PFsection4)