equal
deleted
inserted
replaced
464 moreover note total |
464 moreover note total |
465 ultimately show ?thesis by blast |
465 ultimately show ?thesis by blast |
466 qed |
466 qed |
467 qed |
467 qed |
468 |
468 |
469 subsubsection \<open>Total order \<open><=\<close> on @{typ int}\<close> |
469 subsubsection \<open>Total order \<open><=\<close> on \<^typ>\<open>int\<close>\<close> |
470 |
470 |
471 interpretation int: dpo "(<=) :: [int, int] => bool" |
471 interpretation int: dpo "(<=) :: [int, int] => bool" |
472 rewrites "(dpo.less (<=) (x::int) y) = (x < y)" |
472 rewrites "(dpo.less (<=) (x::int) y) = (x < y)" |
473 txt \<open>We give interpretation for less, but not \<open>is_inf\<close> and \<open>is_sub\<close>.\<close> |
473 txt \<open>We give interpretation for less, but not \<open>is_inf\<close> and \<open>is_sub\<close>.\<close> |
474 proof - |
474 proof - |
520 thm int.meet_left text \<open>from dlat\<close> |
520 thm int.meet_left text \<open>from dlat\<close> |
521 thm int.meet_distr text \<open>from ddlat\<close> |
521 thm int.meet_distr text \<open>from ddlat\<close> |
522 thm int.less_total text \<open>from dlo\<close> |
522 thm int.less_total text \<open>from dlo\<close> |
523 |
523 |
524 |
524 |
525 subsubsection \<open>Total order \<open><=\<close> on @{typ nat}\<close> |
525 subsubsection \<open>Total order \<open><=\<close> on \<^typ>\<open>nat\<close>\<close> |
526 |
526 |
527 interpretation nat: dpo "(<=) :: [nat, nat] => bool" |
527 interpretation nat: dpo "(<=) :: [nat, nat] => bool" |
528 rewrites "dpo.less (<=) (x::nat) y = (x < y)" |
528 rewrites "dpo.less (<=) (x::nat) y = (x < y)" |
529 txt \<open>We give interpretation for less, but not \<open>is_inf\<close> and \<open>is_sub\<close>.\<close> |
529 txt \<open>We give interpretation for less, but not \<open>is_inf\<close> and \<open>is_sub\<close>.\<close> |
530 proof - |
530 proof - |
571 thm nat.meet_left text \<open>from dlat\<close> |
571 thm nat.meet_left text \<open>from dlat\<close> |
572 thm nat.meet_distr text \<open>from ddlat\<close> |
572 thm nat.meet_distr text \<open>from ddlat\<close> |
573 thm nat.less_total text \<open>from ldo\<close> |
573 thm nat.less_total text \<open>from ldo\<close> |
574 |
574 |
575 |
575 |
576 subsubsection \<open>Lattice \<open>dvd\<close> on @{typ nat}\<close> |
576 subsubsection \<open>Lattice \<open>dvd\<close> on \<^typ>\<open>nat\<close>\<close> |
577 |
577 |
578 interpretation nat_dvd: dpo "(dvd) :: [nat, nat] => bool" |
578 interpretation nat_dvd: dpo "(dvd) :: [nat, nat] => bool" |
579 rewrites "dpo.less (dvd) (x::nat) y = (x dvd y & x ~= y)" |
579 rewrites "dpo.less (dvd) (x::nat) y = (x dvd y & x ~= y)" |
580 txt \<open>We give interpretation for less, but not \<open>is_inf\<close> and \<open>is_sub\<close>.\<close> |
580 txt \<open>We give interpretation for less, but not \<open>is_inf\<close> and \<open>is_sub\<close>.\<close> |
581 proof - |
581 proof - |