proposition: Lemma isometry_raddf_inj U (tau : {additive 'CF(L) -> 'CF(G)}) : {in U &, isometry tau} -> {in U &, forall u v, u - v \in U} -> {in U &, injective tau}.
proof: Proof. move=> Itau linU phi psi Uphi Upsi /eqP; rewrite -subr_eq0 -raddfB. by rewrite -cfnorm_eq0 Itau ?linU // cfnorm_eq0 subr_eq0 => /eqP. Qed.
imports: HB(structures) mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat seq path) mathcomp(div choice fintype tuple finfun bigop prime order) mathcomp(ssralg poly finset fingroup morphism perm) mathcomp(automorphism quotient finalg action gproduct) mathcomp(zmodp commutator cyclic center pgroup sylow) mathcomp(matrix vector falgebra ssrnum algC algnum) mathcomp(archimedean)