The Lean Homotopy Type Theory Library ===================================== The Lean homotopy type theory library is contained in the following modules and directories: * [init](init/init.md) : constants and theorems needed for low-level system operations * [types](types/types.md) : concrete datatypes and type constructors * [hit](hit/hit.md): higher inductive types * [algebra](algebra/algebra.md) : algebraic structures Lean's homotopy type theory kernel is a version of Martin-Löf Type Theory with: * universe polymorphism * a non-cumulative hierarchy of universes, `Type 0`, `Type 1`, ... * inductively defined types Note that there is no proof-irrelevant or impredicative universe. By default, the univalence axiom is declared on initialization. See also the [standard library](../library/library.md).