# Contents

## Definition

A Heyting algebra is a distributive lattice $(L, \leq, \bot, \vee, \top, \wedge)$ with

• a function $\implies: L \times L to L$

• a family of dependent terms

$a:L, b:L \vdash (b \to a) \wedge a \leq b$
• a family of dependent terms

$a:L, b:L \vdash a \leq b \to (a \wedge b)$

representing the carteisan closed condition for the lattice.