beam2d / coq-zf

Zeromelo-Fraenkel set theory in Coq

This is a self-study project of implementing ZF axioms in Coq.

• ZF.v defines the axioms of ZF.
• Aczel.v implements the axioms.

The following axioms are used to implement them.

• Predicate extensionality ∀ P Q, (∀ a, P a ↔ Q a) → P = Q is used to prove set equalities.
• Functional choice: ∀ R, (∀ x, ∃ y, R x y) → ∃ f, ∀ x, R x (f x) is used to implement the axiom of replacement.

See [https://www.ps.uni-saarland.de/settheory.html] for the resources I consulted.