Formalizing the zigzag construction of path spaces of pushouts

A recent pre-print of Wärn gives a novel pen-and-paper construction of a type family characterizing the path spaces of an arbitrary pushout, and a natural language argument for its correctness. We present the first formalization of the construction and a proof that it is fiberwise equivalent to the path spaces. The formalization is carried out in axiomatic homotopy type theory, using the Agda proof assistant and the agda-unimath library.