framelemma

Framelemma is a term used in mathematical and logical literature to denote a lemma associated with the concept of a frame. The precise meaning varies by discipline, and there is no single universally agreed definition. In lattice theory and locale theory, a frame is a complete lattice satisfying the infinite distributive law a ∧ (∨ S) = ∨ {a ∧ s : s ∈ S}. A frame lemma in this setting would typically concern the behavior of frame homomorphisms, subframes, or nuclei. For example, such a lemma might characterize when a homomorphism preserves arbitrary joins and finite meets, or how a sublocale arises from a nucleus and how points of the frame relate to maps into the two-element frame. In locale-theoretic language, frame lemmas help connect algebraic presentations of a space with its geometric or topological content.

In computer science and formal logic, related ideas appear under the Frame Rule or frame properties in separation logic. A frame lemma here would be a supporting result showing that a program fragment's correctness is preserved when additional, disjoint resources are added to the state. The exact statement depends on the chosen formalism and the resource model.

See also: Frame (mathematics), Locale, Frame rule, Separation logic, Lattice theory.