src/HOL/Orderings.thy
changeset 45931 99cf6e470816
parent 45893 e7dbb27c1308
child 46553 50a7e97fe653
     1.1 --- a/src/HOL/Orderings.thy	Mon Dec 19 14:41:08 2011 +0100
     1.2 +++ b/src/HOL/Orderings.thy	Mon Dec 19 14:41:08 2011 +0100
     1.3 @@ -1050,33 +1050,20 @@
     1.4  
     1.5  end
     1.6  
     1.7 -lemma min_leastL: "(!!x. least <= x) ==> min least x = least"
     1.8 +lemma min_absorb1: "x \<le> y \<Longrightarrow> min x y = x"
     1.9  by (simp add: min_def)
    1.10  
    1.11 -lemma max_leastL: "(!!x. least <= x) ==> max least x = x"
    1.12 +lemma max_absorb2: "x \<le> y ==> max x y = y"
    1.13  by (simp add: max_def)
    1.14  
    1.15 -lemma min_leastR: "(\<And>x\<Colon>'a\<Colon>order. least \<le> x) \<Longrightarrow> min x least = least"
    1.16 -by (simp add: min_def) (blast intro: antisym)
    1.17 -
    1.18 -lemma max_leastR: "(\<And>x\<Colon>'a\<Colon>order. least \<le> x) \<Longrightarrow> max x least = x"
    1.19 -by (simp add: max_def) (blast intro: antisym)
    1.20 -
    1.21 -lemma min_greatestL: "(\<And>x::'a::order. x \<le> greatest) \<Longrightarrow> min greatest x = x"
    1.22 -by (simp add: min_def) (blast intro: antisym)
    1.23 +lemma min_absorb2: "(y\<Colon>'a\<Colon>order) \<le> x \<Longrightarrow> min x y = y"
    1.24 +by (simp add:min_def)
    1.25  
    1.26 -lemma max_greatestL: "(\<And>x::'a::order. x \<le> greatest) \<Longrightarrow> max greatest x = greatest"
    1.27 -by (simp add: max_def) (blast intro: antisym)
    1.28 -
    1.29 -lemma min_greatestR: "(\<And>x. x \<le> greatest) \<Longrightarrow> min x greatest = x"
    1.30 -by (simp add: min_def)
    1.31 -
    1.32 -lemma max_greatestR: "(\<And>x. x \<le> greatest) \<Longrightarrow> max x greatest = greatest"
    1.33 +lemma max_absorb1: "(y\<Colon>'a\<Colon>order) \<le> x \<Longrightarrow> max x y = x"
    1.34  by (simp add: max_def)
    1.35  
    1.36  
    1.37  
    1.38 -
    1.39  subsection {* (Unique) top and bottom elements *}
    1.40  
    1.41  class bot = order +