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New Foundations is consistent – a difficult mathematical proof proved using Lean
A digitisation of Randall Holmes’ proof
In this repository, we use the interactive theorem prover Lean to verify the difficult part of his proof, thus proving that New Foundations is indeed consistent. We have formally constructed a model of TTT in Lean, thus proving (on paper) that New Foundations is consistent, or in short, Con(NF). Every definition and theorem in mathlib and this project have been checked by Lean’s trusted kernel, which computationally verifies that the proofs we have constructed are indeed correct.
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