Slemma

Slemma is a term sometimes used in mathematical and computational literature to denote a type of auxiliary proposition that serves as a stepping stone toward a larger result, with the distinctive feature of encoding a specific semantic or structural constraint.

In formal proofs, a slemma is proven separately and then applied to establish more complex theorems. It typically asserts that a property holds for all objects meeting a predicate within a particular framework, and its proof is reusable across related problems. For example, in a formal verification setting, a slemma might state that if an input satisfies a precondition, then a function preserves a safety invariant; this allows the main theorem to be proved by chaining the slemma's result with other arguments.

The term is a portmanteau of lemma with possible roots in semantic or structural, reflecting its role as a semantically constrained lemma. It is not widely standardized and appears primarily in discussions aimed at proof organization rather than as a formal, universal notion.

See also: lemma, theorem, corollary, invariant, formal verification.