diff --git a/theories/base_logic/lib/proph_map.v b/theories/base_logic/lib/proph_map.v
index f4ead7f01b8ea0e92e3045a9f5a72efaf796eef9..1158cd502259be76be9d0af2917ae52c5ac74b7c 100644
--- a/theories/base_logic/lib/proph_map.v
+++ b/theories/base_logic/lib/proph_map.v
@@ -134,10 +134,8 @@ Section proph_map.
     rewrite proph_eq /proph_def. iIntros "Hp1 Hp2".
     iCombine "Hp1 Hp2" as "Hp".
     iDestruct (own_valid with "Hp") as %Hp.
-    (* FIXME: [apply auth_frag_valid in Hp] and
-       [rewrite ->auth_frag_valid in Hp] both should work but do not. *)
-    move:Hp. rewrite auth_frag_valid singleton_valid=>Hp.
-    done.
+    (* FIXME: FIXME(Coq #6294): needs new unification *)
+    move:Hp. rewrite auth_frag_valid singleton_valid //.
   Qed.
 
   Lemma proph_map_new_proph p ps pvs :
@@ -169,7 +167,8 @@ Section proph_map.
     assert (vs = v :: proph_list_resolves pvs p) as ->.
     { rewrite (Hres p vs HR). simpl. by rewrite decide_True. }
     iMod (own_update_2 with "H● Hp") as "[H● H◯]".
-    { eapply auth_update. apply: singleton_local_update.
+    { (* FIXME: FIXME(Coq #6294): needs new unification *)
+      eapply auth_update. apply: singleton_local_update.
       - by rewrite /to_proph_map lookup_fmap HR.
       - by apply (exclusive_local_update _ (Excl (proph_list_resolves pvs p : list (leibnizC V)))). }
     rewrite /to_proph_map -fmap_insert.
diff --git a/theories/heap_lang/lib/counter.v b/theories/heap_lang/lib/counter.v
index cde2c0b41a6e2354cebc9610193d42884d74db07..3d46fbd6e5d1a2457353e6c340eb03feaebd9c3a 100644
--- a/theories/heap_lang/lib/counter.v
+++ b/theories/heap_lang/lib/counter.v
@@ -60,8 +60,9 @@ Section mono_proof.
       wp_cas_suc. iModIntro. iSplitL "Hl Hγ".
       { iNext. iExists (S c). rewrite Nat2Z.inj_succ Z.add_1_l. by iFrame. }
       wp_if. iApply "HΦ"; iExists γ; repeat iSplit; eauto.
-      iApply (own_mono with "Hγf"). apply: auth_frag_mono.
-      by apply mnat_included, le_n_S.
+      iApply (own_mono with "Hγf").
+      (* FIXME: FIXME(Coq #6294): needs new unification *)
+      apply: auth_frag_mono. by apply mnat_included, le_n_S.
     - wp_cas_fail; first (by intros [= ?%Nat2Z.inj]). iModIntro.
       iSplitL "Hl Hγ"; [iNext; iExists c'; by iFrame|].
       wp_if. iApply ("IH" with "[Hγf] [HΦ]"); last by auto.
diff --git a/theories/program_logic/ownp.v b/theories/program_logic/ownp.v
index 4b4b4a9a20292fc6b99b4da7e912cb5f0dee4222..c57af7bba3ca6202ef6cfddec5a0b6d710803990 100644
--- a/theories/program_logic/ownp.v
+++ b/theories/program_logic/ownp.v
@@ -118,8 +118,8 @@ Section lifting.
       iModIntro; iSplit; [by destruct s|]; iNext; iIntros (e2 σ2 efs Hstep).
       iDestruct "Hσκs" as "Hσ". rewrite /ownP.
       iMod (own_update_2 with "Hσ Hσf") as "[Hσ Hσf]".
-      { apply auth_update. apply: option_local_update.
-         by apply: (exclusive_local_update _ (Excl σ2)). }
+      { apply auth_update. apply option_local_update.
+         by apply (exclusive_local_update _ (Excl σ2)). }
       iFrame "Hσ". iApply ("H" with "[]"); eauto with iFrame.
   Qed.