src/HOL/ex/Dedekind_Real.thy
changeset 54863 82acc20ded73
parent 54263 c4159fe6fa46
child 56544 b60d5d119489
equal deleted inserted replaced
54862:c65e5cbdbc97 54863:82acc20ded73
   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*}