--- a/src/HOL/Orderings.thy Fri Dec 11 14:43:55 2009 +0100
+++ b/src/HOL/Orderings.thy Fri Dec 11 14:43:56 2009 +0100
@@ -1257,45 +1257,4 @@
lemma le_funD: "f \<le> g \<Longrightarrow> f x \<le> g x"
unfolding le_fun_def by simp
-text {*
- Handy introduction and elimination rules for @{text "\<le>"}
- on unary and binary predicates
-*}
-
-lemma predicate1I:
- assumes PQ: "\<And>x. P x \<Longrightarrow> Q x"
- shows "P \<le> Q"
- apply (rule le_funI)
- apply (rule le_boolI)
- apply (rule PQ)
- apply assumption
- done
-
-lemma predicate1D [Pure.dest, dest]: "P \<le> Q \<Longrightarrow> P x \<Longrightarrow> Q x"
- apply (erule le_funE)
- apply (erule le_boolE)
- apply assumption+
- done
-
-lemma predicate2I [Pure.intro!, intro!]:
- assumes PQ: "\<And>x y. P x y \<Longrightarrow> Q x y"
- shows "P \<le> Q"
- apply (rule le_funI)+
- apply (rule le_boolI)
- apply (rule PQ)
- apply assumption
- done
-
-lemma predicate2D [Pure.dest, dest]: "P \<le> Q \<Longrightarrow> P x y \<Longrightarrow> Q x y"
- apply (erule le_funE)+
- apply (erule le_boolE)
- apply assumption+
- done
-
-lemma rev_predicate1D: "P x ==> P <= Q ==> Q x"
- by (rule predicate1D)
-
-lemma rev_predicate2D: "P x y ==> P <= Q ==> Q x y"
- by (rule predicate2D)
-
end