add complementary lemmas for {min,max}_least
authornoschinl
Thu Dec 15 16:10:44 2011 +0100 (2011-12-15)
changeset 45893e7dbb27c1308
parent 45892 8dcf6692433f
child 45895 36f3f0010b7d
add complementary lemmas for {min,max}_least
src/HOL/Orderings.thy
     1.1 --- a/src/HOL/Orderings.thy	Thu Dec 15 15:55:39 2011 +0100
     1.2 +++ b/src/HOL/Orderings.thy	Thu Dec 15 16:10:44 2011 +0100
     1.3 @@ -1057,14 +1057,24 @@
     1.4  by (simp add: max_def)
     1.5  
     1.6  lemma min_leastR: "(\<And>x\<Colon>'a\<Colon>order. least \<le> x) \<Longrightarrow> min x least = least"
     1.7 -apply (simp add: min_def)
     1.8 -apply (blast intro: antisym)
     1.9 -done
    1.10 +by (simp add: min_def) (blast intro: antisym)
    1.11  
    1.12  lemma max_leastR: "(\<And>x\<Colon>'a\<Colon>order. least \<le> x) \<Longrightarrow> max x least = x"
    1.13 -apply (simp add: max_def)
    1.14 -apply (blast intro: antisym)
    1.15 -done
    1.16 +by (simp add: max_def) (blast intro: antisym)
    1.17 +
    1.18 +lemma min_greatestL: "(\<And>x::'a::order. x \<le> greatest) \<Longrightarrow> min greatest x = x"
    1.19 +by (simp add: min_def) (blast intro: antisym)
    1.20 +
    1.21 +lemma max_greatestL: "(\<And>x::'a::order. x \<le> greatest) \<Longrightarrow> max greatest x = greatest"
    1.22 +by (simp add: max_def) (blast intro: antisym)
    1.23 +
    1.24 +lemma min_greatestR: "(\<And>x. x \<le> greatest) \<Longrightarrow> min x greatest = x"
    1.25 +by (simp add: min_def)
    1.26 +
    1.27 +lemma max_greatestR: "(\<And>x. x \<le> greatest) \<Longrightarrow> max x greatest = greatest"
    1.28 +by (simp add: max_def)
    1.29 +
    1.30 +
    1.31  
    1.32  
    1.33  subsection {* (Unique) top and bottom elements *}