Refinement of Specifications

A refinement S ⊑ T square-image-of-or-equals 𝑆 𝑇 S\sqsubseteq T of program specifications is proof that for all programs P 𝑃 P , P ⊨ S → P ⊨ T ⊨ 𝑃 𝑆 → 𝑃 ⊨ 𝑇 P\vDash S\to P\vDash T .

This is a version of the Exponential of Presheaves.