"The fact that" operator
In [Zinoviev, 1973, p. 62 of 323] the symbol is defined as follows.
From any sentence one can form the term which reads "The fact that."
Representation in PLL
We will represent it as follows.
[:the-fact-that "X"]
We may capture the alternative representations of [:the-fact-that "X"] as follows.
[:bind "thing-to-explain" :to [:the-fact-that "X"]]
[:translation-of "thing-to-explain"
:in :english
:is "The fact that X"]
[:translation-of "thing-to-explain"
:in :russian
:is "Тот факт, что X"]
[:translation-of "thing-to-explain"
:in :latex
:is "\downarrow X"]
We assert that is a term.
[:bind "thing-to-test" :to [:the-fact-that "X"]]
[:assert-that ["thing-to-test" :is :term]]