diff -r 8e2285baadba -r 84e6f9b542e2 src/HOL/Orderings.thy
--- a/src/HOL/Orderings.thy	Wed May 25 10:57:07 2022 +0100
+++ b/src/HOL/Orderings.thy	Wed May 25 14:39:46 2022 +0200
@@ -1060,6 +1060,15 @@
 
 subsection \<open>Monotonicity\<close>
 
+definition monotone :: "('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('b \<Rightarrow> 'b \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> bool"
+  where "monotone orda ordb f \<longleftrightarrow> (\<forall>x y. orda x y \<longrightarrow> ordb (f x) (f y))"
+
+lemma monotoneI[intro?]: "(\<And>x y. orda x y \<Longrightarrow> ordb (f x) (f y)) \<Longrightarrow> monotone orda ordb f"
+  unfolding monotone_def by iprover
+
+lemma monotoneD[dest?]: "monotone orda ordb f \<Longrightarrow> orda x y \<Longrightarrow> ordb (f x) (f y)"
+  unfolding monotone_def by iprover
+
 context order
 begin