Explore the proof

Blueprint

Every statement paired with its Lean counterpart, with an interactive dependency graph; completion status is computed directly from the Lean code.

Lean API documentation

doc-gen4 pages for every declaration in the formalization; dependency links resolve to the public Mathlib docs.

Lean formalizations

The presentation has been formalized twice, in two separate Lean projects.

David Roe's formalization Complete

An end-to-end Lean proof of the presentation theorem with no sorry placeholders. Lean treats nine named mathematical results from the literature as given, with a specific citation recorded for each.

David Turturean's formalization

A second Lean proof, begun independently and preserved in two stages.

Contains no sorry placeholders and uses no Lean code from Roe's project. Lean treats six published results and four project-specific steps as given; the release lists all ten. On this site: blueprint · API documentation.

Proves four remaining steps using a documented adaptation from Roe's formalization. Its seven remaining external mathematical inputs are each tied to published literature.