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

## Definition

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

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