Suppose we are given functions $u_{a,b},v_{a,b}:V_{a,b}\rightarrow\mathbin{\mathbb{R}}$ for all $a,b\in\mathbin{\mathbb{R}}$ satisfying part (ii) of Assumption 7.1. Define $3$-folds $N_{a,b,c}$ in $U$ for $a,b,c\in\mathbin{\mathbb{R}}$ by (54). Then $N_{a,b,c}\cap N_{a^{\prime},b^{\prime},c^{\prime}}=\emptyset$ unless $(a,b,c)=(a^{\prime},b^{\prime},c^{\prime})$.