# Intersections of four lines with two others have same cross ratio - any other line intersecting three of the original ones interects the fourth!

Follow-Up on this.

Given four lines $l_1, l_2, l_3, l_4 \in \mathbb{RP}^3$ and two others $s, t$ such that each four intersections have the same cross ratio, namely $$(l_1 \cap s, l_2 \cap s, l_3 \cap s, l_4 \cap s) = (l_1 \cap t, l_2 \cap t, l_3 \cap t, l_4 \cap t)$$

If another line $r$ intersect $l_1, l_2, l_3$, does it intersect $l_4$ aswell? Why?