diff --git a/thys/Gromov_Hyperbolicity/Eexp_Eln.thy b/thys/Gromov_Hyperbolicity/Eexp_Eln.thy
index be2252bacd951cb0036762661c0797d811ebe69a_dGh5cy9Hcm9tb3ZfSHlwZXJib2xpY2l0eS9FZXhwX0Vsbi50aHk=..1282d34fd48c74fa27990d0b04a90e9c45afbc39_dGh5cy9Hcm9tb3ZfSHlwZXJib2xpY2l0eS9FZXhwX0Vsbi50aHk= 100644
--- a/thys/Gromov_Hyperbolicity/Eexp_Eln.thy
+++ b/thys/Gromov_Hyperbolicity/Eexp_Eln.thy
@@ -19,7 +19,7 @@
 | "ennexp (\<infinity>) = \<infinity>"
 | "ennexp (-\<infinity>) = 0"
 by (auto intro: ereal_cases)
-termination by standard (rule wf_empty)
+termination by standard (rule wf_on_bot)
 
 lemma ennexp_0 [simp]:
   "ennexp 0 = 1"
@@ -29,7 +29,7 @@
 "eln (ennreal r) = (if r \<le> 0 then -\<infinity> else ereal (ln r))"
 | "eln (\<infinity>) = \<infinity>"
 by (auto intro: ennreal_cases, metis ennreal_eq_0_iff, simp add: ennreal_neg)
-termination by standard (rule wf_empty)
+termination by standard (rule wf_on_bot)
 
 lemma eln_simps [simp]:
   "eln 0 = -\<infinity>"
diff --git a/thys/Gromov_Hyperbolicity/Gromov_Boundary.thy b/thys/Gromov_Hyperbolicity/Gromov_Boundary.thy
index be2252bacd951cb0036762661c0797d811ebe69a_dGh5cy9Hcm9tb3ZfSHlwZXJib2xpY2l0eS9Hcm9tb3ZfQm91bmRhcnkudGh5..1282d34fd48c74fa27990d0b04a90e9c45afbc39_dGh5cy9Hcm9tb3ZfSHlwZXJib2xpY2l0eS9Hcm9tb3ZfQm91bmRhcnkudGh5 100644
--- a/thys/Gromov_Hyperbolicity/Gromov_Boundary.thy
+++ b/thys/Gromov_Hyperbolicity/Gromov_Boundary.thy
@@ -2701,7 +2701,7 @@
   | "to_real_Gromov_completion (\<infinity>) = abs_Gromov_completion (\<lambda>n. n)"
   | "to_real_Gromov_completion (-\<infinity>) = abs_Gromov_completion (\<lambda>n. -n)"
 by (auto intro: ereal_cases)
-termination by standard (rule wf_empty)
+termination by standard (rule wf_on_bot)
 
 text \<open>To prove the bijectivity, we prove by hand injectivity and surjectivity using the above
 lemmas.\<close>
diff --git a/thys/JinjaThreads/Compiler/Compiler1.thy b/thys/JinjaThreads/Compiler/Compiler1.thy
index be2252bacd951cb0036762661c0797d811ebe69a_dGh5cy9KaW5qYVRocmVhZHMvQ29tcGlsZXIvQ29tcGlsZXIxLnRoeQ==..1282d34fd48c74fa27990d0b04a90e9c45afbc39_dGh5cy9KaW5qYVRocmVhZHMvQ29tcGlsZXIvQ29tcGlsZXIxLnRoeQ== 100644
--- a/thys/JinjaThreads/Compiler/Compiler1.thy
+++ b/thys/JinjaThreads/Compiler/Compiler1.thy
@@ -57,7 +57,7 @@
 by pat_completeness auto
 termination
 apply(relation "case_sum (\<lambda>p. size (snd p)) (\<lambda>p. size_list size (snd p)) <*mlex*> {}")
-apply(rule wf_mlex[OF wf_empty])
+apply(rule wf_mlex[OF wf_on_bot])
 apply(rule mlex_less, simp)+
 done
 
diff --git a/thys/JinjaThreads/Compiler/TypeComp.thy b/thys/JinjaThreads/Compiler/TypeComp.thy
index be2252bacd951cb0036762661c0797d811ebe69a_dGh5cy9KaW5qYVRocmVhZHMvQ29tcGlsZXIvVHlwZUNvbXAudGh5..1282d34fd48c74fa27990d0b04a90e9c45afbc39_dGh5cy9KaW5qYVRocmVhZHMvQ29tcGlsZXIvVHlwZUNvbXAudGh5 100644
--- a/thys/JinjaThreads/Compiler/TypeComp.thy
+++ b/thys/JinjaThreads/Compiler/TypeComp.thy
@@ -169,7 +169,7 @@
 by pat_completeness simp_all
 termination
 apply(relation "case_sum (\<lambda>p. size (snd (snd (snd p)))) (\<lambda>p. size_list size (snd (snd (snd p)))) <*mlex*> {}")
-apply(rule wf_mlex[OF wf_empty])
+apply(rule wf_mlex[OF wf_on_bot])
 apply(rule mlex_less, simp)+
 done
 
diff --git a/thys/Signature_Groebner/Signature_Groebner.thy b/thys/Signature_Groebner/Signature_Groebner.thy
index be2252bacd951cb0036762661c0797d811ebe69a_dGh5cy9TaWduYXR1cmVfR3JvZWJuZXIvU2lnbmF0dXJlX0dyb2VibmVyLnRoeQ==..1282d34fd48c74fa27990d0b04a90e9c45afbc39_dGh5cy9TaWduYXR1cmVfR3JvZWJuZXIvU2lnbmF0dXJlX0dyb2VibmVyLnRoeQ== 100644
--- a/thys/Signature_Groebner/Signature_Groebner.thy
+++ b/thys/Signature_Groebner/Signature_Groebner.thy
@@ -7511,7 +7511,7 @@
   shows "rb_aux_dom args"
 proof -
   let ?rel = "rb_aux_term <*lex*> ({}::(nat \<times> nat) set)"
-  from wf_rb_aux_term wf_empty have "wf ?rel" ..
+  from wf_rb_aux_term wf_on_bot have "wf ?rel" ..
   thus ?thesis using assms
   proof (induct args)
     case (less args)
diff --git a/thys/Skip_Lists/Skip_List.thy b/thys/Skip_Lists/Skip_List.thy
index be2252bacd951cb0036762661c0797d811ebe69a_dGh5cy9Ta2lwX0xpc3RzL1NraXBfTGlzdC50aHk=..1282d34fd48c74fa27990d0b04a90e9c45afbc39_dGh5cy9Ta2lwX0xpc3RzL1NraXBfTGlzdC50aHk= 100644
--- a/thys/Skip_Lists/Skip_List.thy
+++ b/thys/Skip_Lists/Skip_List.thy
@@ -571,7 +571,7 @@
 proof (relation "(\<lambda>(A,f,l,a,b). card A) <*mlex*> (\<lambda>(A,f,l,a,b). Max (f ` A) - l) <*mlex*> {}", goal_cases)
   case 1
   then show ?case
-    by(intro wf_mlex wf_empty)
+    by(intro wf_mlex wf_on_bot)
 next
   case 2
   then show ?case
@@ -607,7 +607,7 @@
        goal_cases)
   case 1
   then show ?case
-    by(intro wf_mlex wf_empty)
+    by(intro wf_mlex wf_on_bot)
 next
   case 2
   then show ?case