equal
deleted
inserted
replaced
218 definition |
218 definition |
219 "(sup \<Colon> preal \<Rightarrow> preal \<Rightarrow> preal) = max" |
219 "(sup \<Colon> preal \<Rightarrow> preal \<Rightarrow> preal) = max" |
220 |
220 |
221 instance |
221 instance |
222 by intro_classes |
222 by intro_classes |
223 (auto simp add: inf_preal_def sup_preal_def min_max.sup_inf_distrib1) |
223 (auto simp add: inf_preal_def sup_preal_def max_min_distrib2) |
224 |
224 |
225 end |
225 end |
226 |
226 |
227 subsection{*Properties of Addition*} |
227 subsection{*Properties of Addition*} |
228 |
228 |
1553 |
1553 |
1554 definition |
1554 definition |
1555 "(sup \<Colon> real \<Rightarrow> real \<Rightarrow> real) = max" |
1555 "(sup \<Colon> real \<Rightarrow> real \<Rightarrow> real) = max" |
1556 |
1556 |
1557 instance |
1557 instance |
1558 by default (auto simp add: inf_real_def sup_real_def min_max.sup_inf_distrib1) |
1558 by default (auto simp add: inf_real_def sup_real_def max_min_distrib2) |
1559 |
1559 |
1560 end |
1560 end |
1561 |
1561 |
1562 |
1562 |
1563 subsection{*The Reals Form an Ordered Field*} |
1563 subsection{*The Reals Form an Ordered Field*} |