TY - INPR
A1 - Gramlich, Bernhard
T1 - A Note on a Parameterized Version of the Well-Founded Induction Principle
N2 - The well-known and powerful proof principle by well-founded induction says that for verifying \(\forall x : P (x)\) for some property \(P\) it suffices to show \(\forall x : [[\forall y < x :P (y)] \Rightarrow P (x)] \) , provided \(<\) is a well-founded partial ordering on the domainof interest. Here we investigate a more general formulation of this proof principlewhich allows for a kind of parameterized partial orderings \(<_x\) which naturallyarises in some cases. More precisely, we develop conditions under which theparameterized proof principle \(\forall x : [[\forall y <_x x : P (y)] \Rightarrow P (x)]\) is sound in thesense that \(\forall x : [[\forall y <_x x : P (y)] \Rightarrow P (x)] \Rightarrow \forall x : P (x)\) holds, and givecounterexamples demonstrating that these conditions are indeed essential.
T3 - SEKI Report - 95,8
Y1 - 1995
UR - https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/378
UR - https://nbn-resolving.org/urn:nbn:de:hbz:386-kluedo-3499
ER -