Reinforced Large Language Model is a formal theorem prover

Theorem formalization and proof are fundamental processes in mathematics and computer science that involve expressing mathematical statements in a precise, unambiguous language and rigorously demonstrating their truth or validity. Formalization typically begins by translating an informal mathematical theorem into a formal logical system, where every term, assumption, and conclusion is explicitly defined using axioms, rules of inference, and symbolic notation. This ensures that the statement is free from ambiguity and can be manipulated systematically. Once formalized, the proof process involves constructing a sequence of logically valid steps, starting from agreed-upon axioms or previously proven theorems, to establish the desired result. Proofs can range from simple direct arguments to complex constructions involving advanced techniques like induction, contradiction, or model theory.