# Homotopy Type Theory decidable universal quantifier > history (Rev #3)

## Definition

Given a decidable setoid $T$, a decidable universal quantifier on $T$ is a function $\forall x.(-)(x):(T \to \mathbb{2}) \to \mathbb{2}$ with a term

$p:\prod_{P:T \to \mathbb{2}} \left(\prod_{t:T} P(t) = 1\right) \to (\forall x.P(x) \equiv 1) \times \left(\left(\prod_{t:T} P(t) = 1\right) \to \emptyset \right) \to (\forall.P(x) \equiv 0)$