doc-src/TutorialI/Types/numerics.tex
changeset 11161 166f7d87b37f
parent 11148 79aa2932b2d7
child 11174 96a533d300a6
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11160:e0ab13bec5c8 11161:166f7d87b37f
   181 \rulename{DIVISION_BY_ZERO_MOD}
   181 \rulename{DIVISION_BY_ZERO_MOD}
   182 \end{isabelle}
   182 \end{isabelle}
   183 As a concession to convention, these equations are not installed as default
   183 As a concession to convention, these equations are not installed as default
   184 simplification rules but are merely used to remove nonzero-divisor
   184 simplification rules but are merely used to remove nonzero-divisor
   185 hypotheses by case analysis.  In \isa{div_mult_mult1} above, one of
   185 hypotheses by case analysis.  In \isa{div_mult_mult1} above, one of
   186 the two divisors (namely~\isa{c}) must be still be nonzero.
   186 the two divisors (namely~\isa{c}) must still be nonzero.
   187 
   187 
   188 The \textbf{divides} relation has the standard definition, which
   188 The \textbf{divides} relation has the standard definition, which
   189 is overloaded over all numeric types: 
   189 is overloaded over all numeric types: 
   190 \begin{isabelle}
   190 \begin{isabelle}
   191 m\ dvd\ n\ \isasymequiv\ {\isasymexists}k.\ n\ =\ m\ *\ k
   191 m\ dvd\ n\ \isasymequiv\ {\isasymexists}k.\ n\ =\ m\ *\ k