Formal Proof of Contract Theorem in First-Order Logic in Coq

This paper uses the theorem proving tool Coq to complete the formal description and proof of the contract theorem in the field of first-order logic. The contract theorem elaborates the link between variable assignments and the outcomes of term assignments, or the computed result of a formula’s satisfaction relationship. We also provide comprehensive explanations of fundamental concepts in first-order logic, encompassing variables, formulas, and satisfiable relations. The successful verification of the Contract Theorem serves as a vital step towards substantiating the validity of first-order logic formulas and culminating in the creation of a comprehensive logical framework. Through this proof, we emphasize Coq’s remarkable capabilities in automated induction, as well as its interactive and intelligent nature in facilitating machine-based mathematical theorem proofs.