Mizar Correctness Proofs of Generic Fraction Field Arithmetic
We propose the Mizar system as a theorem prover capable of verifying generic algebraic algorithms on an appropriate abstract level. The main advantage of the Mizar theorem prover is its special proof script language that enables textbook style presentation of proofs, hence allowing proofs in the language of algebra.
Using Mizar we were able to give a rigorous machine assisted correctness proof of a generic version of the Brown/Henrici arithmetic in the field of fractions over arbitrary gcd domains.
KeywordsIntegral Domain Great Common Divisor Natural Deduction Correctness Proof Addition Algorithm
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