doc-src/TutorialI/Sets/sets.tex
changeset 11458 09a6c44a48ea
parent 11428 332347b9b942
child 11494 23a118849801
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   890 \[ \cdots \prec a@2 \prec a@1 \prec a@0. \]
   890 \[ \cdots \prec a@2 \prec a@1 \prec a@0. \]
   891 Well-foundedness can be hard to show. The various 
   891 Well-foundedness can be hard to show. The various 
   892 formulations are all complicated.  However,  often a relation
   892 formulations are all complicated.  However,  often a relation
   893 is well-founded by construction.  HOL provides
   893 is well-founded by construction.  HOL provides
   894 theorems concerning ways of constructing  a well-founded relation.  The
   894 theorems concerning ways of constructing  a well-founded relation.  The
   895 most familiar way is to specify a \bfindex{measure function}~\isa{f} into
   895 most familiar way is to specify a 
       
   896 \index{measure functions}\textbf{measure function}~\isa{f} into
   896 the natural numbers, when $\isa{x}\prec \isa{y}\iff \isa{f x} < \isa{f y}$;
   897 the natural numbers, when $\isa{x}\prec \isa{y}\iff \isa{f x} < \isa{f y}$;
   897 we write this particular relation as
   898 we write this particular relation as
   898 \isa{measure~f}.
   899 \isa{measure~f}.
   899 
   900 
   900 \begin{warn}
   901 \begin{warn}