Abstract
The theorem prover Isabelle has been used to axiomatise ZF set theory with natural deduction and to prove a number of theorems concerning functions. In particular, the well-founded recursion theorem has been derived, allowing the definition of functions over recursive types (such as the length and the append functions for lists). The theory of functions has been developed sufficiently within ZF to include PPλ, the theory of continuous functions forming the basis of LCF. Most of the theorems have been derived using backward proofs, with a small amount of automation.
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The work has been carried out at the Computer Laboratory of the University of Cambridge.
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Noel, P.A.J. Experimenting with Isabelle in ZF set theory. J Autom Reasoning 10, 15–58 (1993). https://doi.org/10.1007/BF00881863
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DOI: https://doi.org/10.1007/BF00881863