Hey could somebody help me to prove the following law for Heyting valued models ( this is corollary 1.18 from Bells Boolean valued models and Independence proofs), which governs the assignment of Boolean truth values to formulas with restricted quantifiers.
Claim: For any B-formula $\phi(x)$ with one free variable $x$ and all $u \in V^H $,
$∥ \forall x \in u \phi(x) ∥ = \bigwedge (u(x) \to ∥\phi(x)∥) $
Thanks!