diff --git a/Mathlib/Analysis/CStarAlgebra/CStarMatrix.lean b/Mathlib/Analysis/CStarAlgebra/CStarMatrix.lean
index 77b4e3543ccf29..169b4c3cf2215c 100644
--- a/Mathlib/Analysis/CStarAlgebra/CStarMatrix.lean
+++ b/Mathlib/Analysis/CStarAlgebra/CStarMatrix.lean
@@ -465,7 +465,7 @@ def toOneByOne [Unique n] [Semiring R] [AddCommMonoid A] [Mul A] [Star A] [Modul
 
 end basic
 
-variable [Fintype m] [NonUnitalCStarAlgebra A] [PartialOrder A] [StarOrderedRing A]
+variable [Fintype m] [NonUnitalCStarAlgebra A]
 
 /-- Interpret a `CStarMatrix m n A` as a continuous linear map acting on `C⋆ᵐᵒᵈ (n → A)`. -/
 noncomputable def toCLM : CStarMatrix m n A →ₗ[ℂ] C⋆ᵐᵒᵈ(A, m → A) →L[ℂ] C⋆ᵐᵒᵈ(A, n → A) where
@@ -526,7 +526,8 @@ lemma toCLM_apply_single_apply [DecidableEq m] {M : CStarMatrix m n A} {i : m} {
     (toCLM M) (equiv _ _ |>.symm <| Pi.single i a) j = a * M i j := by simp
 
 open WithCStarModule in
-lemma mul_entry_mul_eq_inner_toCLM [Fintype n] [DecidableEq m] [DecidableEq n]
+lemma mul_entry_mul_eq_inner_toCLM [PartialOrder A] [StarOrderedRing A]
+    [Fintype n] [DecidableEq m] [DecidableEq n]
     {M : CStarMatrix m n A} {i : m} {j : n} (a b : A) :
     a * M i j * star b
       = ⟪equiv _ _ |>.symm (Pi.single j b), toCLM M (equiv _ _ |>.symm <| Pi.single i a)⟫_A := by
@@ -541,7 +542,7 @@ lemma toCLM_injective : Function.Injective (toCLM (A := A) (m := m) (n := n)) :=
     ← toCLM_apply_single_apply]
   simp [h]
 
-variable [Fintype n]
+variable [PartialOrder A] [StarOrderedRing A] [Fintype n]
 
 open WithCStarModule in
 lemma inner_toCLM_conjTranspose_left {M : CStarMatrix m n A} {v : C⋆ᵐᵒᵈ(A, n → A)}
diff --git a/Mathlib/Analysis/Normed/Group/Basic.lean b/Mathlib/Analysis/Normed/Group/Basic.lean
index 6873c34837776c..00fcb182f449a7 100644
--- a/Mathlib/Analysis/Normed/Group/Basic.lean
+++ b/Mathlib/Analysis/Normed/Group/Basic.lean
@@ -103,40 +103,76 @@ class ContinuousENorm (E : Type*) [TopologicalSpace E] extends ENorm E where
 /-- An e-seminormed monoid is an additive monoid endowed with a continuous enorm.
 Note that we do not ask for the enorm to be positive definite:
 non-trivial elements may have enorm zero. -/
-class ESeminormedAddMonoid (E : Type*) [TopologicalSpace E]
-    extends ContinuousENorm E, AddMonoid E where
+class IsESeminormedAddMonoid (E : Type*) [TopologicalSpace E] [AddMonoid E]
+    extends ContinuousENorm E where
   enorm_zero : ‖(0 : E)‖ₑ = 0
   protected enorm_add_le : ∀ x y : E, ‖x + y‖ₑ ≤ ‖x‖ₑ + ‖y‖ₑ
 
+/-- An e-seminormed monoid is an additive monoid endowed with a continuous enorm.
+Note that we do not ask for the enorm to be positive definite:
+non-trivial elements may have enorm zero. -/
+@[class_abbrev] structure ESeminormedAddMonoid (E : Type*) [TopologicalSpace E] where
+  [toAddMonoid : AddMonoid E]
+  [toIsESeminormedAddMonoid : IsESeminormedAddMonoid E]
+attribute [instance] ESeminormedAddMonoid.mk
+
 /-- An enormed monoid is an additive monoid endowed with a continuous enorm,
 which is positive definite: in other words, this is an `ESeminormedAddMonoid` with a positive
 definiteness condition added. -/
-class ENormedAddMonoid (E : Type*) [TopologicalSpace E]
-    extends ESeminormedAddMonoid E where
+class IsENormedAddMonoid (E : Type*) [TopologicalSpace E] [AddMonoid E]
+    extends IsESeminormedAddMonoid E where
   enorm_eq_zero : ∀ x : E, ‖x‖ₑ = 0 ↔ x = 0
 
+/-- An enormed monoid is an additive monoid endowed with a continuous enorm,
+which is positive definite: in other words, this is an `ESeminormedAddMonoid` with a positive
+definiteness condition added. -/
+@[class_abbrev] structure ENormedAddMonoid (E : Type*) [TopologicalSpace E] where
+  [toAddMonoid : AddMonoid E]
+  [toIsENormedAddMonoid : IsENormedAddMonoid E]
+attribute [instance] ENormedAddMonoid.mk
+
 /-- An e-seminormed monoid is a monoid endowed with a continuous enorm.
 Note that we only ask for the enorm to be a semi-norm: non-trivial elements may have enorm zero. -/
 @[to_additive]
-class ESeminormedMonoid (E : Type*) [TopologicalSpace E] extends ContinuousENorm E, Monoid E where
+class IsESeminormedMonoid (E : Type*) [TopologicalSpace E] [Monoid E]
+    extends ContinuousENorm E where
   enorm_zero : ‖(1 : E)‖ₑ = 0
   enorm_mul_le : ∀ x y : E, ‖x * y‖ₑ ≤ ‖x‖ₑ + ‖y‖ₑ
 
+/-- An e-seminormed monoid is a monoid endowed with a continuous enorm.
+Note that we only ask for the enorm to be a semi-norm: non-trivial elements may have enorm zero. -/
+@[to_additive, class_abbrev]
+structure ESeminormedMonoid (E : Type*) [TopologicalSpace E] where
+  [toMonoid : Monoid E]
+  [toIsESeminormedMonoid : IsESeminormedMonoid E]
+attribute [instance] ESeminormedMonoid.mk
+
 /-- An enormed monoid is a monoid endowed with a continuous enorm,
 which is positive definite: in other words, this is an `ESeminormedMonoid` with a positive
 definiteness condition added. -/
 @[to_additive]
-class ENormedMonoid (E : Type*) [TopologicalSpace E] extends ESeminormedMonoid E where
+class IsENormedMonoid (E : Type*) [TopologicalSpace E] [Monoid E]
+    extends IsESeminormedMonoid E where
   enorm_eq_zero : ∀ x : E, ‖x‖ₑ = 0 ↔ x = 1
 
+/-- An enormed monoid is a monoid endowed with a continuous enorm,
+which is positive definite: in other words, this is an `ESeminormedMonoid` with a positive
+definiteness condition added. -/
+@[to_additive, class_abbrev] structure ENormedMonoid (E : Type*) [TopologicalSpace E] where
+  [toMonoid : Monoid E]
+  [toIsENormedMonoid : IsENormedMonoid E]
+attribute [instance] ENormedMonoid.mk
+
 /-- An e-seminormed commutative monoid is an additive commutative monoid endowed with a continuous
 enorm.
 
 We don't have `ESeminormedAddCommMonoid` extend `EMetricSpace`, since the canonical instance `ℝ≥0∞`
 is not an `EMetricSpace`. This is because `ℝ≥0∞` carries the order topology, which is distinct from
 the topology coming from `edist`. -/
-class ESeminormedAddCommMonoid (E : Type*) [TopologicalSpace E]
-  extends ESeminormedAddMonoid E, AddCommMonoid E where
+@[class_abbrev] structure ESeminormedAddCommMonoid (E : Type*) [TopologicalSpace E] where
+  [toAddCommMonoid : AddCommMonoid E]
+  [toIsESeminormedAddMonoid : IsESeminormedAddMonoid E]
+attribute [instance] ESeminormedAddCommMonoid.mk
 
 /-- An enormed commutative monoid is an additive commutative monoid
 endowed with a continuous enorm which is positive definite.
@@ -144,19 +180,23 @@ endowed with a continuous enorm which is positive definite.
 We don't have `ENormedAddCommMonoid` extend `EMetricSpace`, since the canonical instance `ℝ≥0∞`
 is not an `EMetricSpace`. This is because `ℝ≥0∞` carries the order topology, which is distinct from
 the topology coming from `edist`. -/
-class ENormedAddCommMonoid (E : Type*) [TopologicalSpace E]
-  extends ESeminormedAddCommMonoid E, ENormedAddMonoid E where
+@[class_abbrev] structure ENormedAddCommMonoid (E : Type*) [TopologicalSpace E] where
+  [toAddCommMonoid : AddCommMonoid E]
+  [toIsEMormedAddMonoid : IsENormedAddMonoid E]
+attribute [instance] ENormedAddCommMonoid.mk
 
 /-- An e-seminormed commutative monoid is a commutative monoid endowed with a continuous enorm. -/
-@[to_additive]
-class ESeminormedCommMonoid (E : Type*) [TopologicalSpace E]
-  extends ESeminormedMonoid E, CommMonoid E where
+@[to_additive, class_abbrev] structure ESeminormedCommMonoid (E : Type*) [TopologicalSpace E] where
+  [toCommMonoid : CommMonoid E]
+  [toIsESeminormedMonoid : IsESeminormedMonoid E]
+attribute [instance] ESeminormedCommMonoid.mk
 
 /-- An enormed commutative monoid is a commutative monoid endowed with a continuous enorm
 which is positive definite. -/
-@[to_additive]
-class ENormedCommMonoid (E : Type*) [TopologicalSpace E]
-  extends ESeminormedCommMonoid E, ENormedMonoid E where
+@[to_additive, class_abbrev] structure ENormedCommMonoid (E : Type*) [TopologicalSpace E] where
+  [toCommMonoid : CommMonoid E]
+  [toIsENormedMonoid : IsENormedMonoid E]
+attribute [instance] ENormedCommMonoid.mk
 
 /-- A seminormed group is an additive group endowed with a norm for which `dist x y = ‖x - y‖`
 defines a pseudometric space structure. -/
@@ -903,7 +943,7 @@ section ENorm
 
 @[to_additive (attr := simp) enorm_zero]
 lemma enorm_one' {E : Type*} [TopologicalSpace E] [ESeminormedMonoid E] : ‖(1 : E)‖ₑ = 0 := by
-  rw [ESeminormedMonoid.enorm_zero]
+  rw [IsESeminormedMonoid.enorm_zero]
 
 @[to_additive exists_enorm_lt]
 lemma exists_enorm_lt' (E : Type*) [TopologicalSpace E] [ESeminormedMonoid E]
@@ -968,7 +1008,7 @@ section ESeminormedMonoid
 variable {E : Type*} [TopologicalSpace E] [ESeminormedMonoid E]
 
 @[to_additive enorm_add_le]
-lemma enorm_mul_le' (a b : E) : ‖a * b‖ₑ ≤ ‖a‖ₑ + ‖b‖ₑ := ESeminormedMonoid.enorm_mul_le a b
+lemma enorm_mul_le' (a b : E) : ‖a * b‖ₑ ≤ ‖a‖ₑ + ‖b‖ₑ := IsESeminormedMonoid.enorm_mul_le a b
 
 end ESeminormedMonoid
 
@@ -978,7 +1018,7 @@ variable {E : Type*} [TopologicalSpace E] [ENormedMonoid E]
 
 @[to_additive (attr := simp) enorm_eq_zero]
 lemma enorm_eq_zero' {a : E} : ‖a‖ₑ = 0 ↔ a = 1 := by
-  simp [ENormedMonoid.enorm_eq_zero]
+  simp [IsENormedMonoid.enorm_eq_zero]
 
 @[to_additive enorm_ne_zero]
 lemma enorm_ne_zero' {a : E} : ‖a‖ₑ ≠ 0 ↔ a ≠ 1 :=
@@ -990,7 +1030,7 @@ lemma enorm_pos' {a : E} : 0 < ‖a‖ₑ ↔ a ≠ 1 :=
 
 end ENormedMonoid
 
-instance : ENormedAddCommMonoid ℝ≥0∞ where
+instance : IsENormedAddMonoid ℝ≥0∞ where
   continuous_enorm := continuous_id
   enorm_zero := by simp
   enorm_eq_zero := by simp
diff --git a/Mathlib/Analysis/Normed/Group/Continuity.lean b/Mathlib/Analysis/Normed/Group/Continuity.lean
index 734cf555ca1c6c..609a7e419d9fc3 100644
--- a/Mathlib/Analysis/Normed/Group/Continuity.lean
+++ b/Mathlib/Analysis/Normed/Group/Continuity.lean
@@ -96,16 +96,11 @@ instance SeminormedGroup.toContinuousENorm [SeminormedGroup E] : ContinuousENorm
   continuous_enorm := ENNReal.isOpenEmbedding_coe.continuous.comp continuous_nnnorm'
 
 @[to_additive]
-instance NormedGroup.toENormedMonoid {F : Type*} [NormedGroup F] : ENormedMonoid F where
+instance NormedGroup.toIsENormedMonoid {F : Type*} [NormedGroup F] : IsENormedMonoid F where
   enorm_zero := by simp [enorm_eq_nnnorm]
   enorm_eq_zero := by simp [enorm_eq_nnnorm]
   enorm_mul_le := by simp [enorm_eq_nnnorm, ← coe_add, nnnorm_mul_le']
 
-@[to_additive]
-instance NormedCommGroup.toENormedCommMonoid [NormedCommGroup E] : ENormedCommMonoid E where
-  __ := NormedGroup.toENormedMonoid
-  __ := ‹NormedCommGroup E›
-
 end Instances
 
 section SeminormedGroup