Provenprovable

Provenprovable is a neologism used to describe a proposition for which a valid proof exists within a given formal system and the proof itself can be verified by a proof-checking process. The term emphasizes two aspects: the existence of a proof and the ability to confirm that proof within the same or a related formal framework.

In practice, the idea of provenprovable appears in discussions about formal verification and proof assistants. A statement is considered provenprovable with respect to a formal environment if its proof has been encoded in a formal language and checked by the system’s verification kernel, such as those used by Coq, Lean, or Isabelle. This highlights the reliability of automated checking and the reproducibility of formal proofs.

The concept is not part of standard mathematical nomenclature, and its exact meaning can vary by context. It depends on the choice of base system and the level of verification required. Because formal systems differ in strength and axioms, a statement might be provenprovable in one framework but not in another. Gödelian considerations remind readers that, in any sufficiently strong system, there are true statements that are not provable within that system, which can influence how one interprets provenprovability across different formal settings.

See also: formal verification, proof assistant, proof checking, mathematical proof, meta-mathematics.