A proof system is a formal framework used in mathematics and computer science to establish the validity of statements or propositions. It consists of a set of rules and axioms that allow one to derive conclusions from premises. Proof systems are essential for verifying the correctness of algorithms and ensuring that logical reasoning is sound. There are various types of proof systems, including natural deduction, sequent calculus, and axiomatic systems. Each type has its own methodology for constructing proofs. These systems are foundational in fields like logic, theoretical computer science, and mathematics, providing a structured approach to problem-solving and reasoning.