equal
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inserted
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223 0)\ \isasymand \ (\isasymforall d.\ a\ =\ b+d\ \isasymlongrightarrow \ P\ |
223 0)\ \isasymand \ (\isasymforall d.\ a\ =\ b+d\ \isasymlongrightarrow \ P\ |
224 d)) |
224 d)) |
225 \rulename{nat_diff_split} |
225 \rulename{nat_diff_split} |
226 \end{isabelle} |
226 \end{isabelle} |
227 For example, it proves the following fact, which lies outside the scope of |
227 For example, it proves the following fact, which lies outside the scope of |
228 linear arithmetic: |
228 linear arithmetic:\REMARK{replace by new example!} |
229 \begin{isabelle} |
229 \begin{isabelle} |
230 \isacommand{lemma}\ "(n-1)*(n+1)\ =\ n*n\ -\ 1"\isanewline |
230 \isacommand{lemma}\ "(n-1)*(n+1)\ =\ n*n\ -\ 1"\isanewline |
231 \isacommand{apply}\ (simp\ split:\ nat_diff_split)\isanewline |
231 \isacommand{apply}\ (simp\ split:\ nat_diff_split)\isanewline |
232 \isacommand{done} |
232 \isacommand{done} |
233 \end{isabelle} |
233 \end{isabelle} |