equal
deleted
inserted
replaced
317 % |
317 % |
318 \begin{isamarkuptxt}% |
318 \begin{isamarkuptxt}% |
319 \begin{isabelle}% |
319 \begin{isabelle}% |
320 \ {\isadigit{1}}{\isachardot}\ {\isasymAnd}Xcoord\ Ycoord\ more{\isachardot}\isanewline |
320 \ {\isadigit{1}}{\isachardot}\ {\isasymAnd}Xcoord\ Ycoord\ more{\isachardot}\isanewline |
321 \isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymlbrakk}r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}\ {\isacharequal}\ r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isacharprime}{\isasymrparr}{\isacharsemicolon}\isanewline |
321 \isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymlbrakk}r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isasymrparr}\ {\isacharequal}\ r{\isasymlparr}Xcoord\ {\isacharcolon}{\isacharequal}\ a{\isacharprime}{\isasymrparr}{\isacharsemicolon}\isanewline |
322 \isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ \ \ }r\ {\isacharequal}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ more{\isasymrparr}{\isasymrbrakk}\isanewline |
322 \isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ \ }r\ {\isacharequal}\ {\isasymlparr}Xcoord\ {\isacharequal}\ Xcoord{\isacharcomma}\ Ycoord\ {\isacharequal}\ Ycoord{\isacharcomma}\ {\isasymdots}\ {\isacharequal}\ more{\isasymrparr}{\isasymrbrakk}\isanewline |
323 \isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymLongrightarrow}\ a\ {\isacharequal}\ a{\isacharprime}% |
323 \isaindent{\ {\isadigit{1}}{\isachardot}\ \ \ \ }{\isasymLongrightarrow}\ a\ {\isacharequal}\ a{\isacharprime}% |
324 \end{isabelle} Again, \isa{simp} finishes the proof. Because \isa{r} is now represented as |
324 \end{isabelle} Again, \isa{simp} finishes the proof. Because \isa{r} is now represented as |
325 an explicit record construction, the updates can be applied and the |
325 an explicit record construction, the updates can be applied and the |
326 record equality can be replaced by equality of the corresponding |
326 record equality can be replaced by equality of the corresponding |
327 fields (due to injectivity).% |
327 fields (due to injectivity).% |