--- a/src/HOL/Lifting.thy Tue Feb 25 19:07:14 2014 +0100
+++ b/src/HOL/Lifting.thy Tue Feb 25 19:07:40 2014 +0100
@@ -296,7 +296,10 @@
shows "x = y"
using assms by (simp add: invariant_def)
-lemma fun_rel_eq_invariant:
+lemma fun_rel_eq_invariant: "(op= ===> Lifting.invariant P) = Lifting.invariant (\<lambda>f. \<forall>x. P(f x))"
+unfolding invariant_def fun_rel_def by auto
+
+lemma fun_rel_invariant_rel:
shows "((invariant R) ===> S) = (\<lambda>f g. \<forall>x. R x \<longrightarrow> S (f x) (g x))"
by (auto simp add: invariant_def fun_rel_def)