equal
deleted
inserted
replaced
1860 |
1860 |
1861 text \<open>Misc\<close> |
1861 text \<open>Misc\<close> |
1862 |
1862 |
1863 definition pairwise :: "('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> 'a set \<Rightarrow> bool" |
1863 definition pairwise :: "('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> 'a set \<Rightarrow> bool" |
1864 where "pairwise R S \<longleftrightarrow> (\<forall>x \<in> S. \<forall>y \<in> S. x \<noteq> y \<longrightarrow> R x y)" |
1864 where "pairwise R S \<longleftrightarrow> (\<forall>x \<in> S. \<forall>y \<in> S. x \<noteq> y \<longrightarrow> R x y)" |
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1865 |
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1866 lemma pairwise_alt: "pairwise R S \<longleftrightarrow> (\<forall>x\<in>S. \<forall>y\<in>S-{x}. R x y)" |
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1867 by (auto simp add: pairwise_def) |
1865 |
1868 |
1866 lemma pairwise_trivial [simp]: "pairwise (\<lambda>i j. j \<noteq> i) I" |
1869 lemma pairwise_trivial [simp]: "pairwise (\<lambda>i j. j \<noteq> i) I" |
1867 by (auto simp: pairwise_def) |
1870 by (auto simp: pairwise_def) |
1868 |
1871 |
1869 lemma pairwiseI [intro?]: |
1872 lemma pairwiseI [intro?]: |