27 \ \ % |
27 \ \ % |
28 \endisadelimvisible |
28 \endisadelimvisible |
29 % |
29 % |
30 \isatagvisible |
30 \isatagvisible |
31 \isacommand{interpretation}\isamarkupfalse% |
31 \isacommand{interpretation}\isamarkupfalse% |
32 \ int{\isacharcolon}\ partial{\isacharunderscore}order\ {\isachardoublequoteopen}op\ {\isasymle}\ {\isacharcolon}{\isacharcolon}\ {\isacharbrackleft}int{\isacharcomma}\ int{\isacharbrackright}\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline |
32 \ int{\isaliteral{3A}{\isacharcolon}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{22}{\isachardoublequoteopen}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ {\isaliteral{5B}{\isacharbrackleft}}int{\isaliteral{2C}{\isacharcomma}}\ int{\isaliteral{5D}{\isacharbrackright}}\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
33 \ \ \ \ \isakeyword{where}\ {\isachardoublequoteopen}partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasymle}\ {\isacharparenleft}x{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ y\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharless}\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline |
33 \ \ \ \ \isakeyword{where}\ {\isaliteral{22}{\isachardoublequoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}int{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3C}{\isacharless}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
34 \ \ \isacommand{proof}\isamarkupfalse% |
34 \ \ \isacommand{proof}\isamarkupfalse% |
35 \ {\isacharminus}% |
35 \ {\isaliteral{2D}{\isacharminus}}% |
36 \begin{isamarkuptxt}% |
36 \begin{isamarkuptxt}% |
37 \normalsize The goals are now: |
37 \normalsize The goals are now: |
38 \begin{isabelle}% |
38 \begin{isabelle}% |
39 \ {\isadigit{1}}{\isachardot}\ partial{\isacharunderscore}order\ op\ {\isasymle}\isanewline |
39 \ {\isadigit{1}}{\isaliteral{2E}{\isachardot}}\ partial{\isaliteral{5F}{\isacharunderscore}}order\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\isanewline |
40 \ {\isadigit{2}}{\isachardot}\ partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasymle}\ x\ y\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharless}\ y{\isacharparenright}% |
40 \ {\isadigit{2}}{\isaliteral{2E}{\isachardot}}\ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ x\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3C}{\isacharless}}\ y{\isaliteral{29}{\isacharparenright}}% |
41 \end{isabelle} |
41 \end{isabelle} |
42 The proof that~\isa{{\isasymle}} is a partial order is as above.% |
42 The proof that~\isa{{\isaliteral{5C3C6C653E}{\isasymle}}} is a partial order is as above.% |
43 \end{isamarkuptxt}% |
43 \end{isamarkuptxt}% |
44 \isamarkuptrue% |
44 \isamarkuptrue% |
45 \ \ \ \ \isacommand{show}\isamarkupfalse% |
45 \ \ \ \ \isacommand{show}\isamarkupfalse% |
46 \ {\isachardoublequoteopen}partial{\isacharunderscore}order\ {\isacharparenleft}op\ {\isasymle}\ {\isacharcolon}{\isacharcolon}\ int\ {\isasymRightarrow}\ int\ {\isasymRightarrow}\ bool{\isacharparenright}{\isachardoublequoteclose}\isanewline |
46 \ {\isaliteral{22}{\isachardoublequoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order\ {\isaliteral{28}{\isacharparenleft}}op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ int\ {\isaliteral{5C3C52696768746172726F773E}{\isasymRightarrow}}\ bool{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
47 \ \ \ \ \ \ \isacommand{by}\isamarkupfalse% |
47 \ \ \ \ \ \ \isacommand{by}\isamarkupfalse% |
48 \ unfold{\isacharunderscore}locales\ auto% |
48 \ unfold{\isaliteral{5F}{\isacharunderscore}}locales\ auto% |
49 \begin{isamarkuptxt}% |
49 \begin{isamarkuptxt}% |
50 \normalsize The second goal is shown by unfolding the |
50 \normalsize The second goal is shown by unfolding the |
51 definition of \isa{partial{\isacharunderscore}order{\isachardot}less}.% |
51 definition of \isa{partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less}.% |
52 \end{isamarkuptxt}% |
52 \end{isamarkuptxt}% |
53 \isamarkuptrue% |
53 \isamarkuptrue% |
54 \ \ \ \ \isacommand{show}\isamarkupfalse% |
54 \ \ \ \ \isacommand{show}\isamarkupfalse% |
55 \ {\isachardoublequoteopen}partial{\isacharunderscore}order{\isachardot}less\ op\ {\isasymle}\ {\isacharparenleft}x{\isacharcolon}{\isacharcolon}int{\isacharparenright}\ y\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharless}\ y{\isacharparenright}{\isachardoublequoteclose}\isanewline |
55 \ {\isaliteral{22}{\isachardoublequoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}\ {\isaliteral{28}{\isacharparenleft}}x{\isaliteral{3A}{\isacharcolon}}{\isaliteral{3A}{\isacharcolon}}int{\isaliteral{29}{\isacharparenright}}\ y\ {\isaliteral{3D}{\isacharequal}}\ {\isaliteral{28}{\isacharparenleft}}x\ {\isaliteral{3C}{\isacharless}}\ y{\isaliteral{29}{\isacharparenright}}{\isaliteral{22}{\isachardoublequoteclose}}\isanewline |
56 \ \ \ \ \ \ \isacommand{unfolding}\isamarkupfalse% |
56 \ \ \ \ \ \ \isacommand{unfolding}\isamarkupfalse% |
57 \ partial{\isacharunderscore}order{\isachardot}less{\isacharunderscore}def\ {\isacharbrackleft}OF\ {\isacharbackquoteopen}partial{\isacharunderscore}order\ op\ {\isasymle}{\isacharbackquoteclose}{\isacharbrackright}\isanewline |
57 \ partial{\isaliteral{5F}{\isacharunderscore}}order{\isaliteral{2E}{\isachardot}}less{\isaliteral{5F}{\isacharunderscore}}def\ {\isaliteral{5B}{\isacharbrackleft}}OF\ {\isaliteral{60}{\isacharbackquoteopen}}partial{\isaliteral{5F}{\isacharunderscore}}order\ op\ {\isaliteral{5C3C6C653E}{\isasymle}}{\isaliteral{60}{\isacharbackquoteclose}}{\isaliteral{5D}{\isacharbrackright}}\isanewline |
58 \ \ \ \ \ \ \isacommand{by}\isamarkupfalse% |
58 \ \ \ \ \ \ \isacommand{by}\isamarkupfalse% |
59 \ auto\isanewline |
59 \ auto\isanewline |
60 \ \ \isacommand{qed}\isamarkupfalse% |
60 \ \ \isacommand{qed}\isamarkupfalse% |
61 % |
61 % |
62 \endisatagvisible |
62 \endisatagvisible |