--- a/src/HOL/Library/While_Combinator.thy Mon Jan 10 14:13:23 2022 +0100
+++ b/src/HOL/Library/While_Combinator.thy Mon Jan 10 21:34:09 2022 +0100
@@ -239,6 +239,15 @@
apply blast
done
+text \<open>Combine invariant preservation and variant decrease in one goal:\<close>
+theorem while_rule2:
+ "[| P s;
+ !!s. [| P s; b s |] ==> P (c s) \<and> (c s, s) \<in> r;
+ !!s. [| P s; \<not> b s |] ==> Q s;
+ wf r |] ==>
+ Q (while b c s)"
+using while_rule[of P] by metis
+
text\<open>Proving termination:\<close>
theorem wf_while_option_Some: