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A highly typed language we can prove things in
Coq GAP Python Shell
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Reimplementing a subset of Coq in Python

random notes

First order logic:

Theorem test : exists x : nat, x + 2 = 4.
Theorem test2 : forall y : nat, (exists x : nat, x = y).

Second order logic (quantifing over first order logic statements):

forall y : (fun x : nat -> nat)

Higher order on and so forth

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