Proposition: Double ordering

Both $F\gtrsim G$ and $G\gtrsim F$ hold exactly when their actual functional supports have no causally related pair in either direction. In particular those supports are disjoint, with neither null relation nor coincidence.

Proof. The two equations respectively exclude $a\in J^{-}(b)$ and $b\in J^{-}(a)$ for support points. Reflexivity excludes coincidence.