diff --git a/src/Init/Grind/Ring/Envelope.lean b/src/Init/Grind/Ring/Envelope.lean
index b93b17551c..2ad8b2e3fa 100644
--- a/src/Init/Grind/Ring/Envelope.lean
+++ b/src/Init/Grind/Ring/Envelope.lean
@@ -330,7 +330,7 @@ theorem toQ_inj [AddRightCancel α] {a b : α} : toQ a = toQ b → a = b := by
   obtain ⟨k, h₁⟩ := h₁
   exact AddRightCancel.add_right_cancel a b k h₁
 
-instance [Semiring α] [AddRightCancel α] [NoNatZeroDivisors α] : NoNatZeroDivisors (OfSemiring.Q α) where
+instance (priority := high) [Semiring α] [AddRightCancel α] [NoNatZeroDivisors α] : NoNatZeroDivisors (OfSemiring.Q α) where
   no_nat_zero_divisors := by
     intro k a b h₁ h₂
     replace h₂ : mul (natCast k) a = mul (natCast k) b := h₂
@@ -346,7 +346,7 @@ instance [Semiring α] [AddRightCancel α] [NoNatZeroDivisors α] : NoNatZeroDiv
     replace h₂ := NoNatZeroDivisors.no_nat_zero_divisors k (a₁ + b₂) (a₂ + b₁) h₁ h₂
     apply Quot.sound; simp [r]; exists 0; simp [h₂]
 
-instance {p} [Semiring α] [AddRightCancel α] [IsCharP α p] : IsCharP (OfSemiring.Q α) p where
+instance (priority := high) {p} [Semiring α] [AddRightCancel α] [IsCharP α p] : IsCharP (OfSemiring.Q α) p where
   ofNat_ext_iff := by
     intro x y
     constructor
@@ -366,7 +366,7 @@ instance {p} [Semiring α] [AddRightCancel α] [IsCharP α p] : IsCharP (OfSemir
       apply Quot.sound
       exists 0; simp [← Semiring.ofNat_eq_natCast, this]
 
-instance [LE α] [IsPreorder α] [OrderedAdd α] : LE (OfSemiring.Q α) where
+instance (priority := high) [LE α] [IsPreorder α] [OrderedAdd α] : LE (OfSemiring.Q α) where
   le a b := Q.liftOn₂ a b (fun (a, b) (c, d) => a + d ≤ b + c)
     (by intro (a₁, b₁) (a₂, b₂) (a₃, b₃) (a₄, b₄)
         simp; intro k₁ h₁ k₂ h₂
@@ -382,14 +382,14 @@ instance [LE α] [IsPreorder α] [OrderedAdd α] : LE (OfSemiring.Q α) where
         rw [this]; clear this
         rw [← OrderedAdd.add_le_left_iff])
 
-instance [LE α] [IsPreorder α] [OrderedAdd α] : LT (OfSemiring.Q α) where
+instance (priority := high) [LE α] [IsPreorder α] [OrderedAdd α] : LT (OfSemiring.Q α) where
   lt a b := a ≤ b ∧ ¬b ≤ a
 
 @[local simp] theorem mk_le_mk [LE α] [IsPreorder α] [OrderedAdd α] {a₁ a₂ b₁ b₂ : α}  :
     Q.mk (a₁, a₂) ≤ Q.mk (b₁, b₂) ↔ a₁ + b₂ ≤ a₂ + b₁ := by
   rfl
 
-instance [LE α] [IsPreorder α] [OrderedAdd α] : IsPreorder (OfSemiring.Q α) where
+instance (priority := high) [LE α] [IsPreorder α] [OrderedAdd α] : IsPreorder (OfSemiring.Q α) where
   le_refl a := by
     obtain ⟨⟨a₁, a₂⟩⟩ := a
     change Q.mk _ ≤ Q.mk _
@@ -424,7 +424,7 @@ theorem toQ_le [LE α] [IsPreorder α] [OrderedAdd α] {a b : α} : toQ a ≤ to
 theorem toQ_lt [LE α] [LT α] [LawfulOrderLT α] [IsPreorder α] [OrderedAdd α] {a b : α} : toQ a < toQ b ↔ a < b := by
   simp [lt_iff_le_and_not_ge]
 
-instance [LE α] [IsPreorder α] [OrderedAdd α] : OrderedAdd (OfSemiring.Q α) where
+instance (priority := high) [LE α] [IsPreorder α] [OrderedAdd α] : OrderedAdd (OfSemiring.Q α) where
   add_le_left_iff := by
     intro a b c
     obtain ⟨⟨a₁, a₂⟩⟩ := a
@@ -438,7 +438,7 @@ instance [LE α] [IsPreorder α] [OrderedAdd α] : OrderedAdd (OfSemiring.Q α)
     rw [← OrderedAdd.add_le_left_iff]
 
 -- This perhaps works in more generality than `ExistsAddOfLT`?
-instance [LE α] [LT α] [LawfulOrderLT α] [IsPreorder α] [OrderedRing α] [ExistsAddOfLT α] : OrderedRing (OfSemiring.Q α) where
+instance (priority := high) [LE α] [LT α] [LawfulOrderLT α] [IsPreorder α] [OrderedRing α] [ExistsAddOfLT α] : OrderedRing (OfSemiring.Q α) where
   zero_lt_one := by
     rw [← toQ_ofNat, ← toQ_ofNat, toQ_lt]
     exact OrderedRing.zero_lt_one
@@ -511,7 +511,16 @@ def ofCommSemiring : CommRing (OfSemiring.Q α) :=
   { OfSemiring.ofSemiring with
     mul_comm := mul_comm }
 
-attribute [instance] ofCommSemiring
+attribute [instance high] ofCommSemiring
+instance (priority := high) [CommRing (OfSemiring.Q α)] : Add (OfSemiring.Q α) := by infer_instance
+instance (priority := high) [CommRing (OfSemiring.Q α)] : Sub (OfSemiring.Q α) := by infer_instance
+instance (priority := high) [CommRing (OfSemiring.Q α)] : Mul (OfSemiring.Q α) := by infer_instance
+instance (priority := high) [CommRing (OfSemiring.Q α)] : Neg (OfSemiring.Q α) := by infer_instance
+instance (priority := high) [CommRing (OfSemiring.Q α)] : OfNat (OfSemiring.Q α) n := by infer_instance
+attribute [local instance] Semiring.natCast Ring.intCast
+instance (priority := high) [CommRing (OfSemiring.Q α)] : NatCast (OfSemiring.Q α) := by infer_instance
+instance (priority := high) [CommRing (OfSemiring.Q α)] : IntCast (OfSemiring.Q α) := by infer_instance
+instance (priority := high) [CommRing (OfSemiring.Q α)] : HPow (OfSemiring.Q α) Nat (OfSemiring.Q α) := by infer_instance
 
 /-
 Remark: `↑a` is notation for `OfSemiring.toQ a`.
diff --git a/tests/elab/info_trees.lean b/tests/elab/info_trees.lean
index a99967b144..a1bedbd9f5 100644
--- a/tests/elab/info_trees.lean
+++ b/tests/elab/info_trees.lean
@@ -62,7 +62,7 @@ info: • [Command] @ ⟨79, 0⟩-⟨79, 40⟩ @ Lean.Elab.Command.elabDeclarati
                   ⊢ 0 ≤ n
                   after no goals
                   • [Term] Nat.zero_le n : 0 ≤ n @ ⟨1, 1⟩†-⟨1, 1⟩† @ Lean.Elab.Term.elabApp
-                    • [Completion-Id] Nat.zero_le : some LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) _uniq.35.3 @ ⟨1, 0⟩†-⟨1, 0⟩†
+                    • [Completion-Id] Nat.zero_le : some LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) _uniq.47.3 @ ⟨1, 0⟩†-⟨1, 0⟩†
                     • [Term] Nat.zero_le : ∀ (n : Nat), 0 ≤ n @ ⟨1, 0⟩†-⟨1, 0⟩†
                     • [Term] n : Nat @ ⟨1, 5⟩†-⟨1, 5⟩† @ Lean.Elab.Term.elabIdent
                       • [Completion-Id] n : some Nat @ ⟨1, 5⟩†-⟨1, 5⟩†
diff --git a/tests/elab/setOptionTermTactic.lean.out.expected b/tests/elab/setOptionTermTactic.lean.out.expected
index 1878862a00..232078aef5 100644
--- a/tests/elab/setOptionTermTactic.lean.out.expected
+++ b/tests/elab/setOptionTermTactic.lean.out.expected
@@ -1,8 +1,8 @@
 [Meta.synthInstance] 💥️ OfNat ?m 1
   [Meta.synthInstance] new goal OfNat ?m 1
-    [Meta.synthInstance.instances] #[@Lean.Grind.Semiring.ofNat, @One.toOfNat1, @Int16.instOfNat, @UInt64.instOfNat, @Rat.instOfNat, @Int8.instOfNat, @instOfNatFloat, @BitVec.instOfNat, Dyadic.instOfNat, @Int64.instOfNat, @instOfNat, @Id.instOfNat, @UInt16.instOfNat, instOfNatNat, @UInt32.instOfNat, @UInt8.instOfNat, @Fin.instOfNat, @ISize.instOfNat, @instOfNatFloat32, @Int32.instOfNat, @USize.instOfNat]
-  [Meta.synthInstance.apply] 💥️ apply @USize.instOfNat to OfNat ?m 1
-    [Meta.synthInstance.tryResolve] 💥️ OfNat ?m 1 ≟ OfNat USize ?m
+    [Meta.synthInstance.instances] #[@Lean.Grind.Semiring.ofNat, @One.toOfNat1, @Int16.instOfNat, @UInt64.instOfNat, @Rat.instOfNat, @Int8.instOfNat, @instOfNatFloat, @BitVec.instOfNat, Dyadic.instOfNat, @Int64.instOfNat, @instOfNat, @Id.instOfNat, @UInt16.instOfNat, instOfNatNat, @UInt32.instOfNat, @UInt8.instOfNat, @Fin.instOfNat, @ISize.instOfNat, @instOfNatFloat32, @Int32.instOfNat, @USize.instOfNat, @Lean.Grind.CommRing.OfCommSemiring.instOfNatQ]
+  [Meta.synthInstance.apply] 💥️ apply @Lean.Grind.CommRing.OfCommSemiring.instOfNatQ to OfNat ?m 1
+    [Meta.synthInstance.tryResolve] 💥️ OfNat ?m 1 ≟ OfNat (Lean.Grind.Ring.OfSemiring.Q ?m) ?m
 [Meta.Tactic.simp.rewrite] Nat.add_succ:1000:
       x + 1
     ==>
diff --git a/tests/lean/interactive/completionPrefixIssue.lean.expected.out b/tests/lean/interactive/completionPrefixIssue.lean.expected.out
index 42557a5dc8..3b795c3afb 100644
--- a/tests/lean/interactive/completionPrefixIssue.lean.expected.out
+++ b/tests/lean/interactive/completionPrefixIssue.lean.expected.out
@@ -3,7 +3,7 @@
 {"items":
  [{"label": "veryLongDefinitionName",
    "kind": 6,
-   "data": ["file:///completionPrefixIssue.lean", 1, 64, 0, "f_uniq.39"]},
+   "data": ["file:///completionPrefixIssue.lean", 1, 64, 0, "f_uniq.51"]},
   {"label": "veryLongDefinitionNameVeryLongDefinitionName",
    "kind": 21,
    "data":
@@ -17,7 +17,7 @@ Resolution of veryLongDefinitionName:
 {"label": "veryLongDefinitionName",
  "kind": 6,
  "detail": "Nat",
- "data": ["file:///completionPrefixIssue.lean", 1, 64, 0, "f_uniq.39"]}
+ "data": ["file:///completionPrefixIssue.lean", 1, 64, 0, "f_uniq.51"]}
 Resolution of veryLongDefinitionNameVeryLongDefinitionName:
 {"label": "veryLongDefinitionNameVeryLongDefinitionName",
  "kind": 21,
diff --git a/tests/pkg/module/Module/Imported.lean b/tests/pkg/module/Module/Imported.lean
index 30636ba7a9..5baa85dcdb 100644
--- a/tests/pkg/module/Module/Imported.lean
+++ b/tests/pkg/module/Module/Imported.lean
@@ -28,6 +28,7 @@ Note: The following definitions were not unfolded because their definition is no
 #guard_msgs in
 example : f = 1 := rfl
 
+set_option pp.mvars.anonymous false in
 /--
 error: Tactic `apply` failed: could not unify the conclusion of `@rfl`
   ?a = ?a
@@ -35,7 +36,7 @@ with the goal
   f = 1
 
 Note: The full type of `@rfl` is
-  ∀ {α : Sort ?u.121} {a : α}, a = a
+  ∀ {α : Sort _} {a : α}, a = a
 
 Note: The following definitions were not unfolded because their definition is not exposed:
   f ↦ 1