How to implement exist some x, all x these higher order logic in F#?

http://www.cl.cam.ac.uk/~mjcg/OGI/Notes/HOL.pdf
how to implement exist some x, all x these higher order logic in F#?
where can find the example of open source code have these implementation?
computing nightmare

i do not know the whole code.
i just imagine all x is just a full one in logic table
i guess that there are two cases
for example,
case 1
Or(All x, B)
1 0 -> 1
1 1 -> 1
1 0 -> 1
1 1 -> 1
case 2
All x such that B and C
v x And(B, C)
And(Or(v x , B), Or(v x, C))
1 0
1 1
1 0
1 1
becomes
1
1
1
1
but all these just my guess, i still do not know how all x works in logic table
is there open source example code in github show all x and exist some?
exist some in logic table
0 or 1 or 1 or 1
1 0 1 1
1 1 0 1
1 1 1 0
computing nightmare

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