SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\WKO4"];

<< FreeLie.m;
<< AwCalculus.m;
$SeriesShowDegree=4;

x=LW@"x"; y=LW@"y";
{α,β,γ} = LS /@ {x+b[x,y], y-b[x,b[x,y]], x+y-2b[x,y]}

{λ=⟨x->α, y -> β⟩, γ // (Subscript[D, λ])}

λ1=λ; λ2=⟨x->β, y-> γ⟩; tb[λ1,λ2]

j[λ]

div[λ]

(Subscript[div, y])[(Subscript[λ, y])]

(Subscript[div, y])[x+y]

τ=FreeLie`Private`τ

τ[y,y]

tr[AW["y"]]

tr["y"]

lhs=j[(Subscript[BCH, tb])[λ1, λ2]]; rhs=j[λ1] + (E^(Subscript[D, λ1]))[j[λ2]];
{lhs, (lhs≡rhs)@{8}}