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replaced
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 |
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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} |