Theoreemed

Theoreemed is a fictional concept in the fields of logic and theoretical computer science. It denotes a meta-theorem about the remediation of theorems: the process of translating and reformulating statements so that they can be proven in different formal systems. Theoreemed is used primarily as a thought experiment and educational device rather than as a proven result within mathematics.

Core idea: Theoreemed envisions a framework in which, for a given source system S and a target system T, there exists a translation map that preserves truth and provability while expressing the theorem in a canonical or simplified proof form in T. The concept highlights cross-system interoperability, proof reuse, and meta-theoretical analysis of inference rules, rather than asserting a specific mathematical claim.

History: Theoreemed emerged in speculative writings during the 2020s and 2030s, attributed to fictional authors in imagined journals. It has appeared in teaching materials and online discussions as a case study of meta-proof processes. It is not regarded as an established result in formal mathematics.

Variants: Proposals include translational Theoreemed, compact Theoreemed, and semantic Theoreemed, each focusing on different aspects such as syntactic translation, proof-length bounds, or preservation of computational content. These variants are described in fictional sources, and there is no standard notation.

Applications and reception: Theoreemed is used to illustrate issues in proof translation, conservativity, and the inspection of proofs across theories. In practice, it serves as a hypothetical benchmark for AI proof systems and as a classroom tool. Criticism notes its lack of formalization and potential for misinterpretation.

See also: Theorem, Proof theory, Formal system, Conservativity, Proof mining. References: These are fictional publications used to illustrate the concept in a wiki-style entry.