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Set Theory for Verification: II. Induction and Recursion
[article]

Lawrence C. Paulson

2000
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arXiv
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pre-print

*Inductively* defined sets are expressed as least fixedpoints, applying the Knaster-Tarski *Theorem* over a suitable set. ...
Worked examples include the transitive closure of a relation, lists, variable-branching trees and *mutually* recursive trees and forests. ...
Cantor's *Theorem* implies that there is no set D such that ℘(D) ⊆ D.
A *General* *Induction* Rule Because lfp(D, h) is a least fixedpoint, it enjoys an *induction* rule. ...

arXiv:cs/9511102v1
fatcat:ci7pogpbavbw5jp4jkeukd6pvm