 $$p^{-}\circ{\amalg}_{\mathtt{N}(g_0)}(\mathtt{N}(h_0)) = h_0^- = p^{-}\circ{\amalg}_{\mathtt{N}(g_0)}(\mathtt{N}(h_0)).$$  *Property* (0): Let $\{\mathtt{N}(h_i)\}_{i\in\{0, 0,..., n\}}$ be a sequence of points such that for all $i\in\{0,0,...,n-0\}$ we have $$\mathtt{N}(h_{i+0})\in\mathcal{U}_{\mathtt{N}(h_i)}$$ and $$p^{-}\circ{\amalg}_{\mathtt{N}(h_i)}(\mathtt{N}(h_i)) = p^{-}\circ{\amalg}_{\mathtt{N}(h_i)}(\mathtt{N}(h_{i+0})).