src/HOL/Lattices.thy
changeset 28823 dcbef866c9e2
parent 28692 a2bc5ce0c9fc
child 29223 e09c53289830
equal deleted inserted replaced
28822:7ca11ecbc4fb 28823:dcbef866c9e2
   289 subsection {* @{const min}/@{const max} on linear orders as
   289 subsection {* @{const min}/@{const max} on linear orders as
   290   special case of @{const inf}/@{const sup} *}
   290   special case of @{const inf}/@{const sup} *}
   291 
   291 
   292 lemma (in linorder) distrib_lattice_min_max:
   292 lemma (in linorder) distrib_lattice_min_max:
   293   "distrib_lattice (op \<le>) (op <) min max"
   293   "distrib_lattice (op \<le>) (op <) min max"
   294 proof unfold_locales
   294 proof
   295   have aux: "\<And>x y \<Colon> 'a. x < y \<Longrightarrow> y \<le> x \<Longrightarrow> x = y"
   295   have aux: "\<And>x y \<Colon> 'a. x < y \<Longrightarrow> y \<le> x \<Longrightarrow> x = y"
   296     by (auto simp add: less_le antisym)
   296     by (auto simp add: less_le antisym)
   297   fix x y z
   297   fix x y z
   298   show "max x (min y z) = min (max x y) (max x z)"
   298   show "max x (min y z) = min (max x y) (max x z)"
   299   unfolding min_def max_def
   299   unfolding min_def max_def