# Homotopy Type Theory identity type (Rev #2, changes)

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## Idea

The identity type has elements that are witnesses to the “sameness” of elements.

## Definition

The identity type $=_A : A \to A \to \mathcal{U}$ can be defined as the inductive type? with the following constructor: * for any $a:A$, an element $refl_A: a=_A a$