The notes state that a Kantian equilibrium requires that no agent i be able to gain by deviating away from his equilibrium action and towards some other action supposing that everyone else deviates analogously in the sense of scaling his action by the same factor as agent i.
Kantian Welfare Theorem:
Suppose that externalities are either all positive or all negative. Then, any Kantian equilibrium x with x>= 0 is Pareto efficient.
The proof in the notes consider the case of positive externalities, what would be the case of negative externalities?