doc-src/TutorialI/Sets/sets.tex
changeset 10978 5eebea8f359f
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   869 Here \isa{wf\ r} expresses that the relation~\isa{r} is well-founded.
   869 Here \isa{wf\ r} expresses that the relation~\isa{r} is well-founded.
   870 
   870 
   871 Many familiar induction principles are instances of this rule. 
   871 Many familiar induction principles are instances of this rule. 
   872 For example, the predecessor relation on the natural numbers 
   872 For example, the predecessor relation on the natural numbers 
   873 is well-founded; induction over it is mathematical induction. 
   873 is well-founded; induction over it is mathematical induction. 
   874 The `tail of' relation on lists is well-founded; induction over 
   874 The ``tail of'' relation on lists is well-founded; induction over 
   875 it is structural induction. 
   875 it is structural induction. 
   876 
   876 
   877 Well-foundedness can be difficult to show. The various 
   877 Well-foundedness can be difficult to show. The various 
   878 formulations are all complicated.  However,  often a relation
   878 formulations are all complicated.  However,  often a relation
   879 is well-founded by construction.  HOL provides
   879 is well-founded by construction.  HOL provides