Involutive moving frames II; The Lie-Tresse theorem

This paper continues the project, begun in [1], of harmonizing Cartan's classical equivalence method and modern equivariant moving frame a framework dubbed involutive frames. As an attestation fruitfulness our framework, we obtain new, constructive intuitive proof Lie-Tresse theorem (Fundamental basis theorem) first general upper bound on minimal number generating differential invariants for Lie pseudo-groups. Further, demonstrate computational advantages this by studying problem order PDE two independent variables one dependent variable under point transformations.