Pensieve header: μ-calculus clippings - not to be executed.

hta[x_,y_,z_][λ[ω_, μ_]] := Module[{μx, Adμx},
μx = MakeLieSeries[D[μ, h[x]]];
Adμx = LieMorphism[{LW[y] -> Ad[ScaleLieSeries[-1,μx]][LW[z]]}];
λ[
AddCWSeries[StableApply[Adμx, ω], J[LW[y], μx]],
Collect[μ, _h, StableApply[Adμx,#]&]
]
];
hta[x_,y_][λ[ω_, μ_]] := λ[ω, μ] // hta[x,y,⟨"z"⟩] // LieMorphism[{LW["z"] -> LW[y]}];
dm[x_,y_,z_][λ_] := λ // hta[y,x] // tm[x,y,z] // hm[x,y,z];

Ad[x_] := adSeries[E^(-ad), x];

J[-1, ___] = MakeCWSeries[0];
J[n_, y_LW, μ_LieSeries, s_] := J[n,y,μ,s] = Module[
{sμ, μs},
sμ = ScaleLieSeries[s, μ];
μs=StableApply[LieMorphism[{y -> Ad[ScaleLieSeries[-1,sμ]][LW[z]]}], μ];
μs = μs // LieMorphism[{LW[z] -> y}];
IntegrateCWSeries[
AddCWSeries[
J[n-1, y, μ, s] // LieDerivation[{y -> b[μs, y]}],
div[y, μs ]
],
{s,0,s}
]
];
J[y_LW, μ_LieSeries] := J[y,μ] = Module[{cws,s},
cws=Unique[J];
cws[]=Hold[J[y,μ]];
cws[d_Integer] := cws[d] = J[d-1, y, μ, s][d] /. s->1;
CWSeries[cws]
];