A **Formal Proof** is a ~~set~~finite sequence of steps from axiom(s) or previous derived proof(s) which strictly follow the allowed rules of inference of the mathematical system in which it exists. They are used to establish statements as true within a mathematical framework in a way which can be independently verified with extremely high certainty, with the most reliable flavor of proof being machine-checked proofs generated by proof assistants since they have even less room for human error.

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Formal Proofis a~~set~~finite sequence of steps from axiom(s) or previous derived proof(s) which strictly follow the allowed rules of inference of the mathematical system in which it exists. They are used to establish statements as true within a mathematical framework in a way which can be independently verified with extremely high certainty, with the most reliable flavor of proof being machine-checked proofs generated by proof assistants since they have even less room for human error.