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We describe a formal proof of the independence of the continuum hypothesis($\mathsf{CH}$) in the Lean theorem prover. We use Boolean-valued models togive forcing arguments for both directions, using Cohen forcing for theconsistency of $\neg \mathsf{CH}$ and a $\sigma$-closed forcing for theconsistency of $\mathsf{CH}$.

A Formal Proof of the Independence of the Continuum Hypothesis