Remark

Proposition 10 remains valid if H is a Lie quasi-subgroup.

We recall (Differentiable and Analytic Manifolds, R, 13.5.1) that, if V is an analytic manifold over K, $\mathscr{T}^{(\infty)}(V)$ has canonically a cogebra structure over K with a counit; the counit is the linear mapping of $\mathscr{T}^{(\infty)}(G)$ into K which associates with each element of $T_x^{(\infty)}(V)$ its constant term.