equal
deleted
inserted
replaced
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 |