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



Given a decidable setoid TT, a decidable universal quantifier on TT is a function x.()(x):(T𝟚)𝟚\forall x.(-)(x):(T \to \mathbb{2}) \to \mathbb{2} with a term

p: P:T𝟚( t:TP(t)=1)(x.P(x)1)×(( t:TP(t)=1))(.P(x)0)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)

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