analysis.normed.group.quotient ⟷ Mathlib.Analysis.Normed.Group.Quotient

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -530,7 +530,7 @@ noncomputable def lift {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup
       calc
         ‖f m‖ ≤ c * ‖m‖ := hc m
         _ ≤ c * (‖mk' S m‖ + ε / c) := ((mul_lt_mul_left hcpos).mpr hmnorm).le
-        _ = c * ‖mk' S m‖ + ε := by rw [mul_add, mul_div_cancel' _ hcpos.ne.symm] }
+        _ = c * ‖mk' S m‖ + ε := by rw [mul_add, mul_div_cancel₀ _ hcpos.ne.symm] }
 #align normed_add_group_hom.lift NormedAddGroupHom.lift
 -/
 
@@ -615,7 +615,7 @@ theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
       _ ≤ c * (‖S.normed_mk x‖ + ε / c) := ((mul_le_mul_left _).mpr Hx.le)
       _ = c * _ + ε := _
     · exact_mod_cast hc
-    · rw [mul_add, mul_div_cancel']; exact_mod_cast hc.ne'
+    · rw [mul_add, mul_div_cancel₀]; exact_mod_cast hc.ne'
 #align normed_add_group_hom.lift_norm_le NormedAddGroupHom.lift_norm_le
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -229,7 +229,7 @@ theorem quotient_norm_eq_zero_iff (S : AddSubgroup M) (m : M) :
   · calc
       (∀ ε > (0 : ℝ), ∃ r ∈ (fun x => ‖m + x‖) '' (S : Set M), r < ε) ↔
           ∀ ε > 0, ∃ x ∈ S, ‖m + x‖ < ε :=
-        by simp [Set.bex_image_iff]
+        by simp [Set.exists_mem_image]
       _ ↔ ∀ ε > 0, ∃ x ∈ S, ‖m + -x‖ < ε := _
       _ ↔ ∀ ε > 0, ∃ x ∈ S, x ∈ Metric.ball m ε := by
         simp [dist_eq_norm, ← sub_eq_add_neg, norm_sub_rev]
@@ -265,7 +265,7 @@ theorem norm_mk_lt' (S : AddSubgroup M) (m : M) {ε : ℝ} (hε : 0 < ε) :
   by
   obtain ⟨n : M, hn : mk' S n = mk' S m, hn' : ‖n‖ < ‖mk' S m‖ + ε⟩ :=
     norm_mk_lt (QuotientAddGroup.mk' S m) hε
-  erw [eq_comm, QuotientAddGroup.eq] at hn 
+  erw [eq_comm, QuotientAddGroup.eq] at hn
   use-m + n, hn
   rwa [add_neg_cancel_left]
 #align norm_mk_lt' norm_mk_lt'
@@ -300,7 +300,7 @@ theorem norm_mk_zero (S : AddSubgroup M) : ‖(0 : M ⧸ S)‖ = 0 :=
 /-- If `(m : M)` has norm equal to `0` in `M ⧸ S` for a closed subgroup `S` of `M`, then
 `m ∈ S`. -/
 theorem norm_mk_eq_zero (S : AddSubgroup M) (hS : IsClosed (S : Set M)) (m : M)
-    (h : ‖mk' S m‖ = 0) : m ∈ S := by rwa [quotient_norm_eq_zero_iff, hS.closure_eq] at h 
+    (h : ‖mk' S m‖ = 0) : m ∈ S := by rwa [quotient_norm_eq_zero_iff, hS.closure_eq] at h
 #align norm_zero_eq_zero norm_mk_eq_zero
 -/
 
@@ -311,12 +311,12 @@ theorem quotient_nhd_basis (S : AddSubgroup M) :
     intro U
     constructor
     · intro U_in
-      rw [← (mk' S).map_zero] at U_in 
+      rw [← (mk' S).map_zero] at U_in
       have := preimage_nhds_coinduced U_in
       rcases metric.mem_nhds_iff.mp this with ⟨ε, ε_pos, H⟩
       use ε / 2, half_pos ε_pos
       intro x x_in
-      dsimp at x_in 
+      dsimp at x_in
       rcases norm_mk_lt x (half_pos ε_pos) with ⟨y, rfl, ry⟩
       apply H
       rw [ball_zero_eq]
@@ -326,7 +326,7 @@ theorem quotient_nhd_basis (S : AddSubgroup M) :
       have : mk' S '' ball (0 : M) ε ⊆ {x | ‖x‖ < ε} :=
         by
         rintro _ ⟨x, x_in, rfl⟩
-        rw [mem_ball_zero_iff] at x_in 
+        rw [mem_ball_zero_iff] at x_in
         exact lt_of_le_of_lt (quotient_norm_mk_le S x) x_in
       apply Filter.mem_of_superset _ (Set.Subset.trans this h)
       clear h U this
@@ -392,7 +392,7 @@ noncomputable instance AddSubgroup.normedAddCommGroupQuotient (S : AddSubgroup M
     eq_of_dist_eq_zero := by
       rintro ⟨m⟩ ⟨m'⟩ (h : ‖mk' S m - mk' S m'‖ = 0)
       erw [← (mk' S).map_sub, quotient_norm_eq_zero_iff, ‹IsClosed _›.closure_eq, ←
-        QuotientAddGroup.eq_iff_sub_mem] at h 
+        QuotientAddGroup.eq_iff_sub_mem] at h
       exact h }
 #align add_subgroup.normed_add_comm_group_quotient AddSubgroup.normedAddCommGroupQuotient
 -/
@@ -464,20 +464,20 @@ theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) 
     ‖y‖ + min ε (1 / 2) / (1 - min ε (1 / 2)) * ‖y‖ =
       ‖y‖ * (1 + min ε (1 / 2) / (1 - min ε (1 / 2))) :=
     by ring
-  rw [hrw] at hlt 
+  rw [hrw] at hlt
   have hm0 : ‖m‖ ≠ 0 := by
     intro h0
     have hnorm := quotient_norm_mk_le S m
-    rw [h0, hm] at hnorm 
+    rw [h0, hm] at hnorm
     replace hnorm := le_antisymm hnorm (norm_nonneg _)
     simpa [hnorm] using hy
   replace hlt := (div_lt_div_right (lt_of_le_of_ne (norm_nonneg m) hm0.symm)).2 hlt
-  simp only [hm0, div_self, Ne.def, not_false_iff] at hlt 
+  simp only [hm0, div_self, Ne.def, not_false_iff] at hlt
   have hrw₁ :
     ‖y‖ * (1 + min ε (1 / 2) / (1 - min ε (1 / 2))) / ‖m‖ =
       ‖y‖ / ‖m‖ * (1 + min ε (1 / 2) / (1 - min ε (1 / 2))) :=
     by ring
-  rw [hrw₁] at hlt 
+  rw [hrw₁] at hlt
   replace hlt := (inv_pos_lt_iff_one_lt_mul (lt_trans (div_pos hδpos hδ) (lt_one_add _))).2 hlt
   suffices ‖S.normed_mk‖ ≥ 1 - min ε (1 / 2) by exact sub_le_iff_le_add.mp this
   calc
@@ -498,7 +498,7 @@ theorem norm_trivial_quotient_mk (S : AddSubgroup M)
     by
     rw [S.ker_normed_mk]
     exact Set.mem_of_eq_of_mem h trivial
-  rw [ker_normed_mk] at hker 
+  rw [ker_normed_mk] at hker
   simp only [(quotient_norm_eq_zero_iff S x).mpr hker, normed_mk.apply, MulZeroClass.zero_mul]
 #align add_subgroup.norm_trivial_quotient_mk AddSubgroup.norm_trivial_quotient_mk
 -/
@@ -694,7 +694,7 @@ instance Submodule.Quotient.normedSpace (𝕜 : Type _) [NormedField 𝕜] [Norm
         have :=
           (nhds_basis_ball.tendsto_iff nhds_basis_ball).mp
             ((@Real.uniformContinuous_const_mul ‖k‖).Continuous.Tendsto ‖x‖) ε hε
-        simp only [mem_ball, exists_prop, dist, abs_sub_lt_iff] at this 
+        simp only [mem_ball, exists_prop, dist, abs_sub_lt_iff] at this
         rcases this with ⟨δ, hδ, h⟩
         obtain ⟨a, rfl, ha⟩ := Submodule.Quotient.norm_mk_lt x hδ
         specialize h ‖a‖ ⟨by linarith, by linarith [Submodule.Quotient.norm_mk_le S a]⟩
@@ -735,11 +735,11 @@ instance Ideal.Quotient.semiNormedCommRing : SeminormedCommRing (R ⧸ I) :=
         have :=
           ((nhds_basis_ball.prod_nhds nhds_basis_ball).tendsto_iffₓ nhds_basis_ball).mp
             (real.continuous_mul.tendsto (‖x‖, ‖y‖)) ε hε
-        simp only [Set.mem_prod, mem_ball, and_imp, Prod.forall, exists_prop, Prod.exists] at this 
+        simp only [Set.mem_prod, mem_ball, and_imp, Prod.forall, exists_prop, Prod.exists] at this
         rcases this with ⟨ε₁, ε₂, ⟨h₁, h₂⟩, h⟩
         obtain ⟨⟨a, rfl, ha⟩, ⟨b, rfl, hb⟩⟩ := Ideal.Quotient.norm_mk_lt x h₁,
           Ideal.Quotient.norm_mk_lt y h₂
-        simp only [dist, abs_sub_lt_iff] at h 
+        simp only [dist, abs_sub_lt_iff] at h
         specialize
           h ‖a‖ ‖b‖ ⟨by linarith, by linarith [Ideal.Quotient.norm_mk_le I a]⟩
             ⟨by linarith, by linarith [Ideal.Quotient.norm_mk_le I b]⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -122,7 +122,7 @@ theorem image_norm_nonempty {S : AddSubgroup M} :
     ∀ x : M ⧸ S, (norm '' {m | mk' S m = x}).Nonempty :=
   by
   rintro ⟨m⟩
-  rw [Set.nonempty_image_iff]
+  rw [Set.image_nonempty]
   use m
   change mk' S m = _
   rfl
@@ -240,7 +240,7 @@ theorem quotient_norm_eq_zero_iff (S : AddSubgroup M) (m : M) :
   · use 0
     rintro _ ⟨x, x_in, rfl⟩
     apply norm_nonneg
-  rw [Set.nonempty_image_iff]
+  rw [Set.image_nonempty]
   use 0, S.zero_mem
 #align quotient_norm_eq_zero_iff quotient_norm_eq_zero_iff
 -/
@@ -569,7 +569,7 @@ theorem IsQuotient.norm_lift {f : NormedAddGroupHom M N} (hquot : IsQuotient f)
   obtain ⟨m, rfl⟩ := hquot.surjective n
   have nonemp : ((fun m' => ‖m + m'‖) '' f.ker).Nonempty :=
     by
-    rw [Set.nonempty_image_iff]
+    rw [Set.image_nonempty]
     exact ⟨0, f.ker.zero_mem⟩
   rcases Real.lt_sInf_add_pos nonemp hε with
     ⟨_, ⟨⟨x, hx, rfl⟩, H : ‖m + x‖ < Inf ((fun m' : M => ‖m + m'‖) '' f.ker) + ε⟩⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

@@ -3,9 +3,9 @@ Copyright (c) 2021 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Riccardo Brasca
 -/
-import Mathbin.Analysis.NormedSpace.Basic
-import Mathbin.Analysis.Normed.Group.Hom
-import Mathbin.RingTheory.Ideal.QuotientOperations
+import Analysis.NormedSpace.Basic
+import Analysis.Normed.Group.Hom
+import RingTheory.Ideal.QuotientOperations
 
 #align_import analysis.normed.group.quotient from "leanprover-community/mathlib"@"7d34004e19699895c13c86b78ae62bbaea0bc893"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -729,7 +729,7 @@ instance Ideal.Quotient.semiNormedCommRing : SeminormedCommRing (R ⧸ I) :=
     Submodule.Quotient.seminormedAddCommGroup
       I with
     mul_comm := mul_comm
-    norm_mul := fun x y =>
+    norm_hMul := fun x y =>
       le_of_forall_pos_le_add fun ε hε =>
         by
         have :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

@@ -266,7 +266,7 @@ theorem norm_mk_lt' (S : AddSubgroup M) (m : M) {ε : ℝ} (hε : 0 < ε) :
   obtain ⟨n : M, hn : mk' S n = mk' S m, hn' : ‖n‖ < ‖mk' S m‖ + ε⟩ :=
     norm_mk_lt (QuotientAddGroup.mk' S m) hε
   erw [eq_comm, QuotientAddGroup.eq] at hn 
-  use -m + n, hn
+  use-m + n, hn
   rwa [add_neg_cancel_left]
 #align norm_mk_lt' norm_mk_lt'
 -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Riccardo Brasca
-
-! This file was ported from Lean 3 source module analysis.normed.group.quotient
-! leanprover-community/mathlib commit 7d34004e19699895c13c86b78ae62bbaea0bc893
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.NormedSpace.Basic
 import Mathbin.Analysis.Normed.Group.Hom
 import Mathbin.RingTheory.Ideal.QuotientOperations
 
+#align_import analysis.normed.group.quotient from "leanprover-community/mathlib"@"7d34004e19699895c13c86b78ae62bbaea0bc893"
+
 /-!
 # Quotients of seminormed groups
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

@@ -113,11 +113,14 @@ noncomputable instance normOnQuotient (S : AddSubgroup M) : Norm (M ⧸ S)
 #align norm_on_quotient normOnQuotient
 -/
 
+#print AddSubgroup.quotient_norm_eq /-
 theorem AddSubgroup.quotient_norm_eq {S : AddSubgroup M} (x : M ⧸ S) :
     ‖x‖ = sInf (norm '' {m : M | (m : M ⧸ S) = x}) :=
   rfl
 #align add_subgroup.quotient_norm_eq AddSubgroup.quotient_norm_eq
+-/
 
+#print image_norm_nonempty /-
 theorem image_norm_nonempty {S : AddSubgroup M} :
     ∀ x : M ⧸ S, (norm '' {m | mk' S m = x}).Nonempty :=
   by
@@ -127,6 +130,7 @@ theorem image_norm_nonempty {S : AddSubgroup M} :
   change mk' S m = _
   rfl
 #align image_norm_nonempty image_norm_nonempty
+-/
 
 #print bddBelow_image_norm /-
 theorem bddBelow_image_norm (s : Set M) : BddBelow (norm '' s) :=
@@ -137,6 +141,7 @@ theorem bddBelow_image_norm (s : Set M) : BddBelow (norm '' s) :=
 #align bdd_below_image_norm bddBelow_image_norm
 -/
 
+#print quotient_norm_neg /-
 /-- The norm on the quotient satisfies `‖-x‖ = ‖x‖`. -/
 theorem quotient_norm_neg {S : AddSubgroup M} (x : M ⧸ S) : ‖-x‖ = ‖x‖ :=
   by
@@ -149,11 +154,15 @@ theorem quotient_norm_neg {S : AddSubgroup M} (x : M ⧸ S) : ‖-x‖ = ‖x‖
   · rintro ⟨m, hm : mk' S m = -x, rfl⟩
     exact ⟨-m, by simpa using neg_eq_iff_eq_neg.mpr ((mk'_apply _ _).symm.trans hm)⟩
 #align quotient_norm_neg quotient_norm_neg
+-/
 
+#print quotient_norm_sub_rev /-
 theorem quotient_norm_sub_rev {S : AddSubgroup M} (x y : M ⧸ S) : ‖x - y‖ = ‖y - x‖ := by
   rw [show x - y = -(y - x) by abel, quotient_norm_neg]
 #align quotient_norm_sub_rev quotient_norm_sub_rev
+-/
 
+#print quotient_norm_mk_le /-
 /-- The norm of the projection is smaller or equal to the norm of the original element. -/
 theorem quotient_norm_mk_le (S : AddSubgroup M) (m : M) : ‖mk' S m‖ ≤ ‖m‖ :=
   by
@@ -164,12 +173,16 @@ theorem quotient_norm_mk_le (S : AddSubgroup M) (m : M) : ‖mk' S m‖ ≤ ‖m
   · apply Set.mem_image_of_mem
     rw [Set.mem_setOf_eq]
 #align quotient_norm_mk_le quotient_norm_mk_le
+-/
 
+#print quotient_norm_mk_le' /-
 /-- The norm of the projection is smaller or equal to the norm of the original element. -/
 theorem quotient_norm_mk_le' (S : AddSubgroup M) (m : M) : ‖(m : M ⧸ S)‖ ≤ ‖m‖ :=
   quotient_norm_mk_le S m
 #align quotient_norm_mk_le' quotient_norm_mk_le'
+-/
 
+#print quotient_norm_mk_eq /-
 /-- The norm of the image under the natural morphism to the quotient. -/
 theorem quotient_norm_mk_eq (S : AddSubgroup M) (m : M) :
     ‖mk' S m‖ = sInf ((fun x => ‖m + x‖) '' S) :=
@@ -186,7 +199,9 @@ theorem quotient_norm_mk_eq (S : AddSubgroup M) (m : M) :
     use m + y
     simpa using h
 #align quotient_norm_mk_eq quotient_norm_mk_eq
+-/
 
+#print quotient_norm_nonneg /-
 /-- The quotient norm is nonnegative. -/
 theorem quotient_norm_nonneg (S : AddSubgroup M) : ∀ x : M ⧸ S, 0 ≤ ‖x‖ :=
   by
@@ -196,12 +211,16 @@ theorem quotient_norm_nonneg (S : AddSubgroup M) : ∀ x : M ⧸ S, 0 ≤ ‖x
   rintro _ ⟨n, h, rfl⟩
   apply norm_nonneg
 #align quotient_norm_nonneg quotient_norm_nonneg
+-/
 
+#print norm_mk_nonneg /-
 /-- The quotient norm is nonnegative. -/
 theorem norm_mk_nonneg (S : AddSubgroup M) (m : M) : 0 ≤ ‖mk' S m‖ :=
   quotient_norm_nonneg S _
 #align norm_mk_nonneg norm_mk_nonneg
+-/
 
+#print quotient_norm_eq_zero_iff /-
 /-- The norm of the image of `m : M` in the quotient by `S` is zero if and only if `m` belongs
 to the closure of `S`. -/
 theorem quotient_norm_eq_zero_iff (S : AddSubgroup M) (m : M) :
@@ -227,7 +246,9 @@ theorem quotient_norm_eq_zero_iff (S : AddSubgroup M) (m : M) :
   rw [Set.nonempty_image_iff]
   use 0, S.zero_mem
 #align quotient_norm_eq_zero_iff quotient_norm_eq_zero_iff
+-/
 
+#print norm_mk_lt /-
 /-- For any `x : M ⧸ S` and any `0 < ε`, there is `m : M` such that `mk' S m = x`
 and `‖m‖ < ‖x‖ + ε`. -/
 theorem norm_mk_lt {S : AddSubgroup M} (x : M ⧸ S) {ε : ℝ} (hε : 0 < ε) :
@@ -238,7 +259,9 @@ theorem norm_mk_lt {S : AddSubgroup M} (x : M ⧸ S) {ε : ℝ} (hε : 0 < ε) :
   subst H
   exact ⟨m, rfl, hnorm⟩
 #align norm_mk_lt norm_mk_lt
+-/
 
+#print norm_mk_lt' /-
 /-- For any `m : M` and any `0 < ε`, there is `s ∈ S` such that `‖m + s‖ < ‖mk' S m‖ + ε`. -/
 theorem norm_mk_lt' (S : AddSubgroup M) (m : M) {ε : ℝ} (hε : 0 < ε) :
     ∃ s ∈ S, ‖m + s‖ < ‖mk' S m‖ + ε :=
@@ -249,7 +272,9 @@ theorem norm_mk_lt' (S : AddSubgroup M) (m : M) {ε : ℝ} (hε : 0 < ε) :
   use -m + n, hn
   rwa [add_neg_cancel_left]
 #align norm_mk_lt' norm_mk_lt'
+-/
 
+#print quotient_norm_add_le /-
 /-- The quotient norm satisfies the triangle inequality. -/
 theorem quotient_norm_add_le (S : AddSubgroup M) (x y : M ⧸ S) : ‖x + y‖ ≤ ‖x‖ + ‖y‖ :=
   by
@@ -263,20 +288,26 @@ theorem quotient_norm_add_le (S : AddSubgroup M) (x y : M ⧸ S) : ‖x + y‖ 
     _ ≤ ‖m‖ + ‖n‖ := (norm_add_le _ _)
     _ ≤ ‖mk' S m‖ + ‖mk' S n‖ + ε := by linarith
 #align quotient_norm_add_le quotient_norm_add_le
+-/
 
+#print norm_mk_zero /-
 /-- The quotient norm of `0` is `0`. -/
 theorem norm_mk_zero (S : AddSubgroup M) : ‖(0 : M ⧸ S)‖ = 0 :=
   by
   erw [quotient_norm_eq_zero_iff]
   exact subset_closure S.zero_mem
 #align norm_mk_zero norm_mk_zero
+-/
 
+#print norm_mk_eq_zero /-
 /-- If `(m : M)` has norm equal to `0` in `M ⧸ S` for a closed subgroup `S` of `M`, then
 `m ∈ S`. -/
 theorem norm_mk_eq_zero (S : AddSubgroup M) (hS : IsClosed (S : Set M)) (m : M)
     (h : ‖mk' S m‖ = 0) : m ∈ S := by rwa [quotient_norm_eq_zero_iff, hS.closure_eq] at h 
 #align norm_zero_eq_zero norm_mk_eq_zero
+-/
 
+#print quotient_nhd_basis /-
 theorem quotient_nhd_basis (S : AddSubgroup M) :
     (𝓝 (0 : M ⧸ S)).HasBasis (fun ε : ℝ => 0 < ε) fun ε => {x | ‖x‖ < ε} :=
   ⟨by
@@ -310,6 +341,7 @@ theorem quotient_nhd_basis (S : AddSubgroup M) :
         exact (continuous_add_right s).isOpen_preimage _ is_open_ball
       · exact ⟨(0 : M), mem_ball_self ε_pos, (mk' S).map_zero⟩⟩
 #align quotient_nhd_basis quotient_nhd_basis
+-/
 
 #print AddSubgroup.seminormedAddCommGroupQuotient /-
 /-- The seminormed group structure on the quotient by an additive subgroup. -/
@@ -355,6 +387,7 @@ example (S : AddSubgroup M) :
       S.seminormedAddCommGroupQuotient.toUniformSpace.toTopologicalSpace :=
   rfl
 
+#print AddSubgroup.normedAddCommGroupQuotient /-
 /-- The quotient in the category of normed groups. -/
 noncomputable instance AddSubgroup.normedAddCommGroupQuotient (S : AddSubgroup M)
     [IsClosed (S : Set M)] : NormedAddCommGroup (M ⧸ S) :=
@@ -365,6 +398,7 @@ noncomputable instance AddSubgroup.normedAddCommGroupQuotient (S : AddSubgroup M
         QuotientAddGroup.eq_iff_sub_mem] at h 
       exact h }
 #align add_subgroup.normed_add_comm_group_quotient AddSubgroup.normedAddCommGroupQuotient
+-/
 
 -- This is a sanity check left here on purpose to ensure that potential refactors won't destroy
 -- this important property.
@@ -384,11 +418,13 @@ noncomputable def normedMk (S : AddSubgroup M) : NormedAddGroupHom M (M ⧸ S) :
 #align add_subgroup.normed_mk AddSubgroup.normedMk
 -/
 
+#print AddSubgroup.normedMk.apply /-
 /-- `S.normed_mk` agrees with `quotient_add_group.mk' S`. -/
 @[simp]
 theorem normedMk.apply (S : AddSubgroup M) (m : M) : normedMk S m = QuotientAddGroup.mk' S m :=
   rfl
 #align add_subgroup.normed_mk.apply AddSubgroup.normedMk.apply
+-/
 
 #print AddSubgroup.surjective_normedMk /-
 /-- `S.normed_mk` is surjective. -/
@@ -404,11 +440,14 @@ theorem ker_normedMk (S : AddSubgroup M) : S.normedMk.ker = S :=
 #align add_subgroup.ker_normed_mk AddSubgroup.ker_normedMk
 -/
 
+#print AddSubgroup.norm_normedMk_le /-
 /-- The operator norm of the projection is at most `1`. -/
 theorem norm_normedMk_le (S : AddSubgroup M) : ‖S.normedMk‖ ≤ 1 :=
   NormedAddGroupHom.opNorm_le_bound _ zero_le_one fun m => by simp [quotient_norm_mk_le']
 #align add_subgroup.norm_normed_mk_le AddSubgroup.norm_normedMk_le
+-/
 
+#print AddSubgroup.norm_normedMk /-
 /-- The operator norm of the projection is `1` if the subspace is not dense. -/
 theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) ≠ univ) :
     ‖S.normedMk‖ = 1 := by
@@ -450,7 +489,9 @@ theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) 
     _ ≥ (1 + min ε (1 / 2) / (1 - min ε (1 / 2)))⁻¹ := (le_of_lt hlt)
     _ = 1 - min ε (1 / 2) := by field_simp [(ne_of_lt hδ).symm]
 #align add_subgroup.norm_normed_mk AddSubgroup.norm_normedMk
+-/
 
+#print AddSubgroup.norm_trivial_quotient_mk /-
 /-- The operator norm of the projection is `0` if the subspace is dense. -/
 theorem norm_trivial_quotient_mk (S : AddSubgroup M)
     (h : (S.topologicalClosure : Set M) = Set.univ) : ‖S.normedMk‖ = 0 :=
@@ -463,6 +504,7 @@ theorem norm_trivial_quotient_mk (S : AddSubgroup M)
   rw [ker_normed_mk] at hker 
   simp only [(quotient_norm_eq_zero_iff S x).mpr hker, normed_mk.apply, MulZeroClass.zero_mul]
 #align add_subgroup.norm_trivial_quotient_mk AddSubgroup.norm_trivial_quotient_mk
+-/
 
 end AddSubgroup
 
@@ -477,6 +519,7 @@ structure IsQuotient (f : NormedAddGroupHom M N) : Prop where
 #align normed_add_group_hom.is_quotient NormedAddGroupHom.IsQuotient
 -/
 
+#print NormedAddGroupHom.lift /-
 /-- Given  `f : normed_add_group_hom M N` such that `f s = 0` for all `s ∈ S`, where,
 `S : add_subgroup M` is closed, the induced morphism `normed_add_group_hom (M ⧸ S) N`. -/
 noncomputable def lift {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
@@ -492,13 +535,17 @@ noncomputable def lift {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup
         _ ≤ c * (‖mk' S m‖ + ε / c) := ((mul_lt_mul_left hcpos).mpr hmnorm).le
         _ = c * ‖mk' S m‖ + ε := by rw [mul_add, mul_div_cancel' _ hcpos.ne.symm] }
 #align normed_add_group_hom.lift NormedAddGroupHom.lift
+-/
 
+#print NormedAddGroupHom.lift_mk /-
 theorem lift_mk {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (m : M) :
     lift S f hf (S.normedMk m) = f m :=
   rfl
 #align normed_add_group_hom.lift_mk NormedAddGroupHom.lift_mk
+-/
 
+#print NormedAddGroupHom.lift_unique /-
 theorem lift_unique {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (g : NormedAddGroupHom (M ⧸ S) N) :
     g.comp S.normedMk = f → g = lift S f hf :=
@@ -509,6 +556,7 @@ theorem lift_unique {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
   change g.comp S.normed_mk x = _
   simpa only [h]
 #align normed_add_group_hom.lift_unique NormedAddGroupHom.lift_unique
+-/
 
 #print NormedAddGroupHom.isQuotientQuotient /-
 /-- `S.normed_mk` satisfies `is_quotient`. -/
@@ -517,6 +565,7 @@ theorem isQuotientQuotient (S : AddSubgroup M) : IsQuotient S.normedMk :=
 #align normed_add_group_hom.is_quotient_quotient NormedAddGroupHom.isQuotientQuotient
 -/
 
+#print NormedAddGroupHom.IsQuotient.norm_lift /-
 theorem IsQuotient.norm_lift {f : NormedAddGroupHom M N} (hquot : IsQuotient f) {ε : ℝ} (hε : 0 < ε)
     (n : N) : ∃ m : M, f m = n ∧ ‖m‖ < ‖n‖ + ε :=
   by
@@ -530,7 +579,9 @@ theorem IsQuotient.norm_lift {f : NormedAddGroupHom M N} (hquot : IsQuotient f)
   exact
     ⟨m + x, by rw [map_add, (NormedAddGroupHom.mem_ker f x).mp hx, add_zero], by rwa [hquot.norm]⟩
 #align normed_add_group_hom.is_quotient.norm_lift NormedAddGroupHom.IsQuotient.norm_lift
+-/
 
+#print NormedAddGroupHom.IsQuotient.norm_le /-
 theorem IsQuotient.norm_le {f : NormedAddGroupHom M N} (hquot : IsQuotient f) (m : M) :
     ‖f m‖ ≤ ‖m‖ := by
   rw [hquot.norm]
@@ -540,7 +591,9 @@ theorem IsQuotient.norm_le {f : NormedAddGroupHom M N} (hquot : IsQuotient f) (m
     apply norm_nonneg
   · exact ⟨0, f.ker.zero_mem, by simp⟩
 #align normed_add_group_hom.is_quotient.norm_le NormedAddGroupHom.IsQuotient.norm_le
+-/
 
+#print NormedAddGroupHom.lift_norm_le /-
 theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) {c : ℝ≥0} (fb : ‖f‖ ≤ c) :
     ‖lift S f hf‖ ≤ c := by
@@ -567,7 +620,9 @@ theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     · exact_mod_cast hc
     · rw [mul_add, mul_div_cancel']; exact_mod_cast hc.ne'
 #align normed_add_group_hom.lift_norm_le NormedAddGroupHom.lift_norm_le
+-/
 
+#print NormedAddGroupHom.lift_normNoninc /-
 theorem lift_normNoninc {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (fb : f.NormNoninc) :
     (lift S f hf).NormNoninc := fun x =>
@@ -575,6 +630,7 @@ theorem lift_normNoninc {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup
   have fb' : ‖f‖ ≤ (1 : ℝ≥0) := norm_noninc.norm_noninc_iff_norm_le_one.mp fb
   simpa using le_of_op_norm_le _ (f.lift_norm_le _ _ fb') _
 #align normed_add_group_hom.lift_norm_noninc NormedAddGroupHom.lift_normNoninc
+-/
 
 end NormedAddGroupHom
 
@@ -616,16 +672,20 @@ instance Submodule.Quotient.completeSpace [CompleteSpace M] : CompleteSpace (M 
 #align submodule.quotient.complete_space Submodule.Quotient.completeSpace
 -/
 
+#print Submodule.Quotient.norm_mk_lt /-
 /-- For any `x : M ⧸ S` and any `0 < ε`, there is `m : M` such that `submodule.quotient.mk m = x`
 and `‖m‖ < ‖x‖ + ε`. -/
 theorem Submodule.Quotient.norm_mk_lt {S : Submodule R M} (x : M ⧸ S) {ε : ℝ} (hε : 0 < ε) :
     ∃ m : M, Submodule.Quotient.mk m = x ∧ ‖m‖ < ‖x‖ + ε :=
   norm_mk_lt x hε
 #align submodule.quotient.norm_mk_lt Submodule.Quotient.norm_mk_lt
+-/
 
+#print Submodule.Quotient.norm_mk_le /-
 theorem Submodule.Quotient.norm_mk_le (m : M) : ‖(Submodule.Quotient.mk m : M ⧸ S)‖ ≤ ‖m‖ :=
   quotient_norm_mk_le S.toAddSubgroup m
 #align submodule.quotient.norm_mk_le Submodule.Quotient.norm_mk_le
+-/
 
 #print Submodule.Quotient.normedSpace /-
 instance Submodule.Quotient.normedSpace (𝕜 : Type _) [NormedField 𝕜] [NormedSpace 𝕜 M] [SMul 𝕜 R]
@@ -653,14 +713,18 @@ section Ideal
 
 variable {R : Type _} [SeminormedCommRing R] (I : Ideal R)
 
+#print Ideal.Quotient.norm_mk_lt /-
 theorem Ideal.Quotient.norm_mk_lt {I : Ideal R} (x : R ⧸ I) {ε : ℝ} (hε : 0 < ε) :
     ∃ r : R, Ideal.Quotient.mk I r = x ∧ ‖r‖ < ‖x‖ + ε :=
   norm_mk_lt x hε
 #align ideal.quotient.norm_mk_lt Ideal.Quotient.norm_mk_lt
+-/
 
+#print Ideal.Quotient.norm_mk_le /-
 theorem Ideal.Quotient.norm_mk_le (r : R) : ‖Ideal.Quotient.mk I r‖ ≤ ‖r‖ :=
   quotient_norm_mk_le I.toAddSubgroup r
 #align ideal.quotient.norm_mk_le Ideal.Quotient.norm_mk_le
+-/
 
 #print Ideal.Quotient.semiNormedCommRing /-
 instance Ideal.Quotient.semiNormedCommRing : SeminormedCommRing (R ⧸ I) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

@@ -218,7 +218,6 @@ theorem quotient_norm_eq_zero_iff (S : AddSubgroup M) (m : M) :
       _ ↔ ∀ ε > 0, ∃ x ∈ S, x ∈ Metric.ball m ε := by
         simp [dist_eq_norm, ← sub_eq_add_neg, norm_sub_rev]
       _ ↔ m ∈ closure ↑S := by simp [Metric.mem_closure_iff, dist_comm]
-      
     refine' forall₂_congr fun ε ε_pos => _
     rw [← S.exists_neg_mem_iff_exists_mem]
     simp
@@ -263,7 +262,6 @@ theorem quotient_norm_add_le (S : AddSubgroup M) (x y : M ⧸ S) : ‖x + y‖ 
     _ ≤ ‖m + n‖ := (quotient_norm_mk_le S (m + n))
     _ ≤ ‖m‖ + ‖n‖ := (norm_add_le _ _)
     _ ≤ ‖mk' S m‖ + ‖mk' S n‖ + ε := by linarith
-    
 #align quotient_norm_add_le quotient_norm_add_le
 
 /-- The quotient norm of `0` is `0`. -/
@@ -451,7 +449,6 @@ theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) 
     _ = ‖y‖ / ‖m‖ := by rw [normed_mk.apply, hm]
     _ ≥ (1 + min ε (1 / 2) / (1 - min ε (1 / 2)))⁻¹ := (le_of_lt hlt)
     _ = 1 - min ε (1 / 2) := by field_simp [(ne_of_lt hδ).symm]
-    
 #align add_subgroup.norm_normed_mk AddSubgroup.norm_normedMk
 
 /-- The operator norm of the projection is `0` if the subspace is dense. -/
@@ -493,8 +490,7 @@ noncomputable def lift {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup
       calc
         ‖f m‖ ≤ c * ‖m‖ := hc m
         _ ≤ c * (‖mk' S m‖ + ε / c) := ((mul_lt_mul_left hcpos).mpr hmnorm).le
-        _ = c * ‖mk' S m‖ + ε := by rw [mul_add, mul_div_cancel' _ hcpos.ne.symm]
-         }
+        _ = c * ‖mk' S m‖ + ε := by rw [mul_add, mul_div_cancel' _ hcpos.ne.symm] }
 #align normed_add_group_hom.lift NormedAddGroupHom.lift
 
 theorem lift_mk {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
@@ -557,7 +553,6 @@ theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     calc
       ‖f x‖ ≤ 0 * ‖x‖ := f.le_of_op_norm_le fb x
       _ = 0 := MulZeroClass.zero_mul _
-      
   · replace hc : 0 < c := pos_iff_ne_zero.mpr hc
     apply le_of_forall_pos_le_add
     intro ε hε
@@ -569,7 +564,6 @@ theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
       ‖f x‖ ≤ c * ‖x‖ := f.le_of_op_norm_le fb x
       _ ≤ c * (‖S.normed_mk x‖ + ε / c) := ((mul_le_mul_left _).mpr Hx.le)
       _ = c * _ + ε := _
-      
     · exact_mod_cast hc
     · rw [mul_add, mul_div_cancel']; exact_mod_cast hc.ne'
 #align normed_add_group_hom.lift_norm_le NormedAddGroupHom.lift_norm_le
@@ -649,8 +643,7 @@ instance Submodule.Quotient.normedSpace (𝕜 : Type _) [NormedField 𝕜] [Norm
         specialize h ‖a‖ ⟨by linarith, by linarith [Submodule.Quotient.norm_mk_le S a]⟩
         calc
           _ ≤ ‖k‖ * ‖a‖ := (quotient_norm_mk_le S.to_add_subgroup (k • a)).trans_eq (norm_smul k a)
-          _ ≤ _ := (sub_lt_iff_lt_add'.mp h.1).le
-           }
+          _ ≤ _ := (sub_lt_iff_lt_add'.mp h.1).le }
 #align submodule.quotient.normed_space Submodule.Quotient.normedSpace
 -/
 
@@ -691,8 +684,7 @@ instance Ideal.Quotient.semiNormedCommRing : SeminormedCommRing (R ⧸ I) :=
             ⟨by linarith, by linarith [Ideal.Quotient.norm_mk_le I b]⟩
         calc
           _ ≤ ‖a‖ * ‖b‖ := (Ideal.Quotient.norm_mk_le I (a * b)).trans (norm_mul_le a b)
-          _ ≤ _ := (sub_lt_iff_lt_add'.mp h.1).le
-           }
+          _ ≤ _ := (sub_lt_iff_lt_add'.mp h.1).le }
 #align ideal.quotient.semi_normed_comm_ring Ideal.Quotient.semiNormedCommRing
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

@@ -109,17 +109,17 @@ variable {M N : Type _} [SeminormedAddCommGroup M] [SeminormedAddCommGroup N]
 #print normOnQuotient /-
 /-- The definition of the norm on the quotient by an additive subgroup. -/
 noncomputable instance normOnQuotient (S : AddSubgroup M) : Norm (M ⧸ S)
-    where norm x := sInf (norm '' { m | mk' S m = x })
+    where norm x := sInf (norm '' {m | mk' S m = x})
 #align norm_on_quotient normOnQuotient
 -/
 
 theorem AddSubgroup.quotient_norm_eq {S : AddSubgroup M} (x : M ⧸ S) :
-    ‖x‖ = sInf (norm '' { m : M | (m : M ⧸ S) = x }) :=
+    ‖x‖ = sInf (norm '' {m : M | (m : M ⧸ S) = x}) :=
   rfl
 #align add_subgroup.quotient_norm_eq AddSubgroup.quotient_norm_eq
 
 theorem image_norm_nonempty {S : AddSubgroup M} :
-    ∀ x : M ⧸ S, (norm '' { m | mk' S m = x }).Nonempty :=
+    ∀ x : M ⧸ S, (norm '' {m | mk' S m = x}).Nonempty :=
   by
   rintro ⟨m⟩
   rw [Set.nonempty_image_iff]
@@ -140,7 +140,7 @@ theorem bddBelow_image_norm (s : Set M) : BddBelow (norm '' s) :=
 /-- The norm on the quotient satisfies `‖-x‖ = ‖x‖`. -/
 theorem quotient_norm_neg {S : AddSubgroup M} (x : M ⧸ S) : ‖-x‖ = ‖x‖ :=
   by
-  suffices norm '' { m | mk' S m = x } = norm '' { m | mk' S m = -x } by simp only [this, norm]
+  suffices norm '' {m | mk' S m = x} = norm '' {m | mk' S m = -x} by simp only [this, norm]
   ext r
   constructor
   · rintro ⟨m, rfl : mk' S m = x, rfl⟩
@@ -280,7 +280,7 @@ theorem norm_mk_eq_zero (S : AddSubgroup M) (hS : IsClosed (S : Set M)) (m : M)
 #align norm_zero_eq_zero norm_mk_eq_zero
 
 theorem quotient_nhd_basis (S : AddSubgroup M) :
-    (𝓝 (0 : M ⧸ S)).HasBasis (fun ε : ℝ => 0 < ε) fun ε => { x | ‖x‖ < ε } :=
+    (𝓝 (0 : M ⧸ S)).HasBasis (fun ε : ℝ => 0 < ε) fun ε => {x | ‖x‖ < ε} :=
   ⟨by
     intro U
     constructor
@@ -297,7 +297,7 @@ theorem quotient_nhd_basis (S : AddSubgroup M) :
       dsimp
       linarith
     · rintro ⟨ε, ε_pos, h⟩
-      have : mk' S '' ball (0 : M) ε ⊆ { x | ‖x‖ < ε } :=
+      have : mk' S '' ball (0 : M) ε ⊆ {x | ‖x‖ < ε} :=
         by
         rintro _ ⟨x, x_in, rfl⟩
         rw [mem_ball_zero_iff] at x_in 
@@ -333,8 +333,8 @@ noncomputable instance AddSubgroup.seminormedAddCommGroupQuotient (S : AddSubgro
     apply this.eq_of_same_basis
     have :
       ∀ ε : ℝ,
-        (fun p : (M ⧸ S) × M ⧸ S => p.snd - p.fst) ⁻¹' { x | ‖x‖ < ε } =
-          { p : (M ⧸ S) × M ⧸ S | ‖p.fst - p.snd‖ < ε } :=
+        (fun p : (M ⧸ S) × M ⧸ S => p.snd - p.fst) ⁻¹' {x | ‖x‖ < ε} =
+          {p : (M ⧸ S) × M ⧸ S | ‖p.fst - p.snd‖ < ε} :=
       by
       intro ε
       ext x

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

@@ -246,7 +246,7 @@ theorem norm_mk_lt' (S : AddSubgroup M) (m : M) {ε : ℝ} (hε : 0 < ε) :
   by
   obtain ⟨n : M, hn : mk' S n = mk' S m, hn' : ‖n‖ < ‖mk' S m‖ + ε⟩ :=
     norm_mk_lt (QuotientAddGroup.mk' S m) hε
-  erw [eq_comm, QuotientAddGroup.eq] at hn
+  erw [eq_comm, QuotientAddGroup.eq] at hn 
   use -m + n, hn
   rwa [add_neg_cancel_left]
 #align norm_mk_lt' norm_mk_lt'
@@ -276,7 +276,7 @@ theorem norm_mk_zero (S : AddSubgroup M) : ‖(0 : M ⧸ S)‖ = 0 :=
 /-- If `(m : M)` has norm equal to `0` in `M ⧸ S` for a closed subgroup `S` of `M`, then
 `m ∈ S`. -/
 theorem norm_mk_eq_zero (S : AddSubgroup M) (hS : IsClosed (S : Set M)) (m : M)
-    (h : ‖mk' S m‖ = 0) : m ∈ S := by rwa [quotient_norm_eq_zero_iff, hS.closure_eq] at h
+    (h : ‖mk' S m‖ = 0) : m ∈ S := by rwa [quotient_norm_eq_zero_iff, hS.closure_eq] at h 
 #align norm_zero_eq_zero norm_mk_eq_zero
 
 theorem quotient_nhd_basis (S : AddSubgroup M) :
@@ -285,12 +285,12 @@ theorem quotient_nhd_basis (S : AddSubgroup M) :
     intro U
     constructor
     · intro U_in
-      rw [← (mk' S).map_zero] at U_in
+      rw [← (mk' S).map_zero] at U_in 
       have := preimage_nhds_coinduced U_in
       rcases metric.mem_nhds_iff.mp this with ⟨ε, ε_pos, H⟩
       use ε / 2, half_pos ε_pos
       intro x x_in
-      dsimp at x_in
+      dsimp at x_in 
       rcases norm_mk_lt x (half_pos ε_pos) with ⟨y, rfl, ry⟩
       apply H
       rw [ball_zero_eq]
@@ -300,7 +300,7 @@ theorem quotient_nhd_basis (S : AddSubgroup M) :
       have : mk' S '' ball (0 : M) ε ⊆ { x | ‖x‖ < ε } :=
         by
         rintro _ ⟨x, x_in, rfl⟩
-        rw [mem_ball_zero_iff] at x_in
+        rw [mem_ball_zero_iff] at x_in 
         exact lt_of_le_of_lt (quotient_norm_mk_le S x) x_in
       apply Filter.mem_of_superset _ (Set.Subset.trans this h)
       clear h U this
@@ -364,7 +364,7 @@ noncomputable instance AddSubgroup.normedAddCommGroupQuotient (S : AddSubgroup M
     eq_of_dist_eq_zero := by
       rintro ⟨m⟩ ⟨m'⟩ (h : ‖mk' S m - mk' S m'‖ = 0)
       erw [← (mk' S).map_sub, quotient_norm_eq_zero_iff, ‹IsClosed _›.closure_eq, ←
-        QuotientAddGroup.eq_iff_sub_mem] at h
+        QuotientAddGroup.eq_iff_sub_mem] at h 
       exact h }
 #align add_subgroup.normed_add_comm_group_quotient AddSubgroup.normedAddCommGroupQuotient
 
@@ -430,20 +430,20 @@ theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) 
     ‖y‖ + min ε (1 / 2) / (1 - min ε (1 / 2)) * ‖y‖ =
       ‖y‖ * (1 + min ε (1 / 2) / (1 - min ε (1 / 2))) :=
     by ring
-  rw [hrw] at hlt
+  rw [hrw] at hlt 
   have hm0 : ‖m‖ ≠ 0 := by
     intro h0
     have hnorm := quotient_norm_mk_le S m
-    rw [h0, hm] at hnorm
+    rw [h0, hm] at hnorm 
     replace hnorm := le_antisymm hnorm (norm_nonneg _)
     simpa [hnorm] using hy
   replace hlt := (div_lt_div_right (lt_of_le_of_ne (norm_nonneg m) hm0.symm)).2 hlt
-  simp only [hm0, div_self, Ne.def, not_false_iff] at hlt
+  simp only [hm0, div_self, Ne.def, not_false_iff] at hlt 
   have hrw₁ :
     ‖y‖ * (1 + min ε (1 / 2) / (1 - min ε (1 / 2))) / ‖m‖ =
       ‖y‖ / ‖m‖ * (1 + min ε (1 / 2) / (1 - min ε (1 / 2))) :=
     by ring
-  rw [hrw₁] at hlt
+  rw [hrw₁] at hlt 
   replace hlt := (inv_pos_lt_iff_one_lt_mul (lt_trans (div_pos hδpos hδ) (lt_one_add _))).2 hlt
   suffices ‖S.normed_mk‖ ≥ 1 - min ε (1 / 2) by exact sub_le_iff_le_add.mp this
   calc
@@ -463,7 +463,7 @@ theorem norm_trivial_quotient_mk (S : AddSubgroup M)
     by
     rw [S.ker_normed_mk]
     exact Set.mem_of_eq_of_mem h trivial
-  rw [ker_normed_mk] at hker
+  rw [ker_normed_mk] at hker 
   simp only [(quotient_norm_eq_zero_iff S x).mpr hker, normed_mk.apply, MulZeroClass.zero_mul]
 #align add_subgroup.norm_trivial_quotient_mk AddSubgroup.norm_trivial_quotient_mk
 
@@ -551,7 +551,7 @@ theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
   apply op_norm_le_bound _ c.coe_nonneg
   intro x
   by_cases hc : c = 0
-  · simp only [hc, NNReal.coe_zero, MulZeroClass.zero_mul] at fb⊢
+  · simp only [hc, NNReal.coe_zero, MulZeroClass.zero_mul] at fb ⊢
     obtain ⟨x, rfl⟩ := surjective_quot_mk _ x
     show ‖f x‖ ≤ 0
     calc
@@ -643,7 +643,7 @@ instance Submodule.Quotient.normedSpace (𝕜 : Type _) [NormedField 𝕜] [Norm
         have :=
           (nhds_basis_ball.tendsto_iff nhds_basis_ball).mp
             ((@Real.uniformContinuous_const_mul ‖k‖).Continuous.Tendsto ‖x‖) ε hε
-        simp only [mem_ball, exists_prop, dist, abs_sub_lt_iff] at this
+        simp only [mem_ball, exists_prop, dist, abs_sub_lt_iff] at this 
         rcases this with ⟨δ, hδ, h⟩
         obtain ⟨a, rfl, ha⟩ := Submodule.Quotient.norm_mk_lt x hδ
         specialize h ‖a‖ ⟨by linarith, by linarith [Submodule.Quotient.norm_mk_le S a]⟩
@@ -681,11 +681,11 @@ instance Ideal.Quotient.semiNormedCommRing : SeminormedCommRing (R ⧸ I) :=
         have :=
           ((nhds_basis_ball.prod_nhds nhds_basis_ball).tendsto_iffₓ nhds_basis_ball).mp
             (real.continuous_mul.tendsto (‖x‖, ‖y‖)) ε hε
-        simp only [Set.mem_prod, mem_ball, and_imp, Prod.forall, exists_prop, Prod.exists] at this
+        simp only [Set.mem_prod, mem_ball, and_imp, Prod.forall, exists_prop, Prod.exists] at this 
         rcases this with ⟨ε₁, ε₂, ⟨h₁, h₂⟩, h⟩
         obtain ⟨⟨a, rfl, ha⟩, ⟨b, rfl, hb⟩⟩ := Ideal.Quotient.norm_mk_lt x h₁,
           Ideal.Quotient.norm_mk_lt y h₂
-        simp only [dist, abs_sub_lt_iff] at h
+        simp only [dist, abs_sub_lt_iff] at h 
         specialize
           h ‖a‖ ‖b‖ ⟨by linarith, by linarith [Ideal.Quotient.norm_mk_le I a]⟩
             ⟨by linarith, by linarith [Ideal.Quotient.norm_mk_le I b]⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -102,7 +102,7 @@ noncomputable section
 
 open quotientAddGroup Metric Set
 
-open Topology NNReal
+open scoped Topology NNReal
 
 variable {M N : Type _} [SeminormedAddCommGroup M] [SeminormedAddCommGroup N]
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -113,20 +113,11 @@ noncomputable instance normOnQuotient (S : AddSubgroup M) : Norm (M ⧸ S)
 #align norm_on_quotient normOnQuotient
 -/
 
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-Case conversion may be inaccurate. Consider using '#align add_subgroup.quotient_norm_eq AddSubgroup.quotient_norm_eqₓ'. -/
 theorem AddSubgroup.quotient_norm_eq {S : AddSubgroup M} (x : M ⧸ S) :
     ‖x‖ = sInf (norm '' { m : M | (m : M ⧸ S) = x }) :=
   rfl
 #align add_subgroup.quotient_norm_eq AddSubgroup.quotient_norm_eq
 
-/- warning: image_norm_nonempty -> image_norm_nonempty is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align image_norm_nonempty image_norm_nonemptyₓ'. -/
 theorem image_norm_nonempty {S : AddSubgroup M} :
     ∀ x : M ⧸ S, (norm '' { m | mk' S m = x }).Nonempty :=
   by
@@ -146,12 +137,6 @@ theorem bddBelow_image_norm (s : Set M) : BddBelow (norm '' s) :=
 #align bdd_below_image_norm bddBelow_image_norm
 -/
 
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-Case conversion may be inaccurate. Consider using '#align quotient_norm_neg quotient_norm_negₓ'. -/
 /-- The norm on the quotient satisfies `‖-x‖ = ‖x‖`. -/
 theorem quotient_norm_neg {S : AddSubgroup M} (x : M ⧸ S) : ‖-x‖ = ‖x‖ :=
   by
@@ -165,16 +150,10 @@ theorem quotient_norm_neg {S : AddSubgroup M} (x : M ⧸ S) : ‖-x‖ = ‖x‖
     exact ⟨-m, by simpa using neg_eq_iff_eq_neg.mpr ((mk'_apply _ _).symm.trans hm)⟩
 #align quotient_norm_neg quotient_norm_neg
 
-/- warning: quotient_norm_sub_rev -> quotient_norm_sub_rev is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quotient_norm_sub_rev quotient_norm_sub_revₓ'. -/
 theorem quotient_norm_sub_rev {S : AddSubgroup M} (x y : M ⧸ S) : ‖x - y‖ = ‖y - x‖ := by
   rw [show x - y = -(y - x) by abel, quotient_norm_neg]
 #align quotient_norm_sub_rev quotient_norm_sub_rev
 
-/- warning: quotient_norm_mk_le -> quotient_norm_mk_le is a dubious translation:
-<too large>
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 /-- The norm of the projection is smaller or equal to the norm of the original element. -/
 theorem quotient_norm_mk_le (S : AddSubgroup M) (m : M) : ‖mk' S m‖ ≤ ‖m‖ :=
   by
@@ -186,20 +165,11 @@ theorem quotient_norm_mk_le (S : AddSubgroup M) (m : M) : ‖mk' S m‖ ≤ ‖m
     rw [Set.mem_setOf_eq]
 #align quotient_norm_mk_le quotient_norm_mk_le
 
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-Case conversion may be inaccurate. Consider using '#align quotient_norm_mk_le' quotient_norm_mk_le'ₓ'. -/
 /-- The norm of the projection is smaller or equal to the norm of the original element. -/
 theorem quotient_norm_mk_le' (S : AddSubgroup M) (m : M) : ‖(m : M ⧸ S)‖ ≤ ‖m‖ :=
   quotient_norm_mk_le S m
 #align quotient_norm_mk_le' quotient_norm_mk_le'
 
-/- warning: quotient_norm_mk_eq -> quotient_norm_mk_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quotient_norm_mk_eq quotient_norm_mk_eqₓ'. -/
 /-- The norm of the image under the natural morphism to the quotient. -/
 theorem quotient_norm_mk_eq (S : AddSubgroup M) (m : M) :
     ‖mk' S m‖ = sInf ((fun x => ‖m + x‖) '' S) :=
@@ -217,12 +187,6 @@ theorem quotient_norm_mk_eq (S : AddSubgroup M) (m : M) :
     simpa using h
 #align quotient_norm_mk_eq quotient_norm_mk_eq
 
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-Case conversion may be inaccurate. Consider using '#align quotient_norm_nonneg quotient_norm_nonnegₓ'. -/
 /-- The quotient norm is nonnegative. -/
 theorem quotient_norm_nonneg (S : AddSubgroup M) : ∀ x : M ⧸ S, 0 ≤ ‖x‖ :=
   by
@@ -233,17 +197,11 @@ theorem quotient_norm_nonneg (S : AddSubgroup M) : ∀ x : M ⧸ S, 0 ≤ ‖x
   apply norm_nonneg
 #align quotient_norm_nonneg quotient_norm_nonneg
 
-/- warning: norm_mk_nonneg -> norm_mk_nonneg is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align norm_mk_nonneg norm_mk_nonnegₓ'. -/
 /-- The quotient norm is nonnegative. -/
 theorem norm_mk_nonneg (S : AddSubgroup M) (m : M) : 0 ≤ ‖mk' S m‖ :=
   quotient_norm_nonneg S _
 #align norm_mk_nonneg norm_mk_nonneg
 
-/- warning: quotient_norm_eq_zero_iff -> quotient_norm_eq_zero_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quotient_norm_eq_zero_iff quotient_norm_eq_zero_iffₓ'. -/
 /-- The norm of the image of `m : M` in the quotient by `S` is zero if and only if `m` belongs
 to the closure of `S`. -/
 theorem quotient_norm_eq_zero_iff (S : AddSubgroup M) (m : M) :
@@ -271,9 +229,6 @@ theorem quotient_norm_eq_zero_iff (S : AddSubgroup M) (m : M) :
   use 0, S.zero_mem
 #align quotient_norm_eq_zero_iff quotient_norm_eq_zero_iff
 
-/- warning: norm_mk_lt -> norm_mk_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align norm_mk_lt norm_mk_ltₓ'. -/
 /-- For any `x : M ⧸ S` and any `0 < ε`, there is `m : M` such that `mk' S m = x`
 and `‖m‖ < ‖x‖ + ε`. -/
 theorem norm_mk_lt {S : AddSubgroup M} (x : M ⧸ S) {ε : ℝ} (hε : 0 < ε) :
@@ -285,9 +240,6 @@ theorem norm_mk_lt {S : AddSubgroup M} (x : M ⧸ S) {ε : ℝ} (hε : 0 < ε) :
   exact ⟨m, rfl, hnorm⟩
 #align norm_mk_lt norm_mk_lt
 
-/- warning: norm_mk_lt' -> norm_mk_lt' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align norm_mk_lt' norm_mk_lt'ₓ'. -/
 /-- For any `m : M` and any `0 < ε`, there is `s ∈ S` such that `‖m + s‖ < ‖mk' S m‖ + ε`. -/
 theorem norm_mk_lt' (S : AddSubgroup M) (m : M) {ε : ℝ} (hε : 0 < ε) :
     ∃ s ∈ S, ‖m + s‖ < ‖mk' S m‖ + ε :=
@@ -299,12 +251,6 @@ theorem norm_mk_lt' (S : AddSubgroup M) (m : M) {ε : ℝ} (hε : 0 < ε) :
   rwa [add_neg_cancel_left]
 #align norm_mk_lt' norm_mk_lt'
 
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-Case conversion may be inaccurate. Consider using '#align quotient_norm_add_le quotient_norm_add_leₓ'. -/
 /-- The quotient norm satisfies the triangle inequality. -/
 theorem quotient_norm_add_le (S : AddSubgroup M) (x y : M ⧸ S) : ‖x + y‖ ≤ ‖x‖ + ‖y‖ :=
   by
@@ -320,12 +266,6 @@ theorem quotient_norm_add_le (S : AddSubgroup M) (x y : M ⧸ S) : ‖x + y‖ 
     
 #align quotient_norm_add_le quotient_norm_add_le
 
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-Case conversion may be inaccurate. Consider using '#align norm_mk_zero norm_mk_zeroₓ'. -/
 /-- The quotient norm of `0` is `0`. -/
 theorem norm_mk_zero (S : AddSubgroup M) : ‖(0 : M ⧸ S)‖ = 0 :=
   by
@@ -333,21 +273,12 @@ theorem norm_mk_zero (S : AddSubgroup M) : ‖(0 : M ⧸ S)‖ = 0 :=
   exact subset_closure S.zero_mem
 #align norm_mk_zero norm_mk_zero
 
-/- warning: norm_zero_eq_zero -> norm_mk_eq_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align norm_zero_eq_zero norm_mk_eq_zeroₓ'. -/
 /-- If `(m : M)` has norm equal to `0` in `M ⧸ S` for a closed subgroup `S` of `M`, then
 `m ∈ S`. -/
 theorem norm_mk_eq_zero (S : AddSubgroup M) (hS : IsClosed (S : Set M)) (m : M)
     (h : ‖mk' S m‖ = 0) : m ∈ S := by rwa [quotient_norm_eq_zero_iff, hS.closure_eq] at h
 #align norm_zero_eq_zero norm_mk_eq_zero
 
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-Case conversion may be inaccurate. Consider using '#align quotient_nhd_basis quotient_nhd_basisₓ'. -/
 theorem quotient_nhd_basis (S : AddSubgroup M) :
     (𝓝 (0 : M ⧸ S)).HasBasis (fun ε : ℝ => 0 < ε) fun ε => { x | ‖x‖ < ε } :=
   ⟨by
@@ -426,12 +357,6 @@ example (S : AddSubgroup M) :
       S.seminormedAddCommGroupQuotient.toUniformSpace.toTopologicalSpace :=
   rfl
 
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 /-- The quotient in the category of normed groups. -/
 noncomputable instance AddSubgroup.normedAddCommGroupQuotient (S : AddSubgroup M)
     [IsClosed (S : Set M)] : NormedAddCommGroup (M ⧸ S) :=
@@ -461,9 +386,6 @@ noncomputable def normedMk (S : AddSubgroup M) : NormedAddGroupHom M (M ⧸ S) :
 #align add_subgroup.normed_mk AddSubgroup.normedMk
 -/
 
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 /-- `S.normed_mk` agrees with `quotient_add_group.mk' S`. -/
 @[simp]
 theorem normedMk.apply (S : AddSubgroup M) (m : M) : normedMk S m = QuotientAddGroup.mk' S m :=
@@ -484,23 +406,11 @@ theorem ker_normedMk (S : AddSubgroup M) : S.normedMk.ker = S :=
 #align add_subgroup.ker_normed_mk AddSubgroup.ker_normedMk
 -/
 
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 /-- The operator norm of the projection is at most `1`. -/
 theorem norm_normedMk_le (S : AddSubgroup M) : ‖S.normedMk‖ ≤ 1 :=
   NormedAddGroupHom.opNorm_le_bound _ zero_le_one fun m => by simp [quotient_norm_mk_le']
 #align add_subgroup.norm_normed_mk_le AddSubgroup.norm_normedMk_le
 
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 /-- The operator norm of the projection is `1` if the subspace is not dense. -/
 theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) ≠ univ) :
     ‖S.normedMk‖ = 1 := by
@@ -544,12 +454,6 @@ theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) 
     
 #align add_subgroup.norm_normed_mk AddSubgroup.norm_normedMk
 
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 /-- The operator norm of the projection is `0` if the subspace is dense. -/
 theorem norm_trivial_quotient_mk (S : AddSubgroup M)
     (h : (S.topologicalClosure : Set M) = Set.univ) : ‖S.normedMk‖ = 0 :=
@@ -576,12 +480,6 @@ structure IsQuotient (f : NormedAddGroupHom M N) : Prop where
 #align normed_add_group_hom.is_quotient NormedAddGroupHom.IsQuotient
 -/
 
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 /-- Given  `f : normed_add_group_hom M N` such that `f s = 0` for all `s ∈ S`, where,
 `S : add_subgroup M` is closed, the induced morphism `normed_add_group_hom (M ⧸ S) N`. -/
 noncomputable def lift {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
@@ -599,21 +497,12 @@ noncomputable def lift {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup
          }
 #align normed_add_group_hom.lift NormedAddGroupHom.lift
 
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 theorem lift_mk {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (m : M) :
     lift S f hf (S.normedMk m) = f m :=
   rfl
 #align normed_add_group_hom.lift_mk NormedAddGroupHom.lift_mk
 
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 theorem lift_unique {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (g : NormedAddGroupHom (M ⧸ S) N) :
     g.comp S.normedMk = f → g = lift S f hf :=
@@ -632,12 +521,6 @@ theorem isQuotientQuotient (S : AddSubgroup M) : IsQuotient S.normedMk :=
 #align normed_add_group_hom.is_quotient_quotient NormedAddGroupHom.isQuotientQuotient
 -/
 
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 theorem IsQuotient.norm_lift {f : NormedAddGroupHom M N} (hquot : IsQuotient f) {ε : ℝ} (hε : 0 < ε)
     (n : N) : ∃ m : M, f m = n ∧ ‖m‖ < ‖n‖ + ε :=
   by
@@ -652,12 +535,6 @@ theorem IsQuotient.norm_lift {f : NormedAddGroupHom M N} (hquot : IsQuotient f)
     ⟨m + x, by rw [map_add, (NormedAddGroupHom.mem_ker f x).mp hx, add_zero], by rwa [hquot.norm]⟩
 #align normed_add_group_hom.is_quotient.norm_lift NormedAddGroupHom.IsQuotient.norm_lift
 
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 theorem IsQuotient.norm_le {f : NormedAddGroupHom M N} (hquot : IsQuotient f) (m : M) :
     ‖f m‖ ≤ ‖m‖ := by
   rw [hquot.norm]
@@ -668,12 +545,6 @@ theorem IsQuotient.norm_le {f : NormedAddGroupHom M N} (hquot : IsQuotient f) (m
   · exact ⟨0, f.ker.zero_mem, by simp⟩
 #align normed_add_group_hom.is_quotient.norm_le NormedAddGroupHom.IsQuotient.norm_le
 
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 theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) {c : ℝ≥0} (fb : ‖f‖ ≤ c) :
     ‖lift S f hf‖ ≤ c := by
@@ -703,12 +574,6 @@ theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     · rw [mul_add, mul_div_cancel']; exact_mod_cast hc.ne'
 #align normed_add_group_hom.lift_norm_le NormedAddGroupHom.lift_norm_le
 
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 theorem lift_normNoninc {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (fb : f.NormNoninc) :
     (lift S f hf).NormNoninc := fun x =>
@@ -757,12 +622,6 @@ instance Submodule.Quotient.completeSpace [CompleteSpace M] : CompleteSpace (M 
 #align submodule.quotient.complete_space Submodule.Quotient.completeSpace
 -/
 
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-Case conversion may be inaccurate. Consider using '#align submodule.quotient.norm_mk_lt Submodule.Quotient.norm_mk_ltₓ'. -/
 /-- For any `x : M ⧸ S` and any `0 < ε`, there is `m : M` such that `submodule.quotient.mk m = x`
 and `‖m‖ < ‖x‖ + ε`. -/
 theorem Submodule.Quotient.norm_mk_lt {S : Submodule R M} (x : M ⧸ S) {ε : ℝ} (hε : 0 < ε) :
@@ -770,12 +629,6 @@ theorem Submodule.Quotient.norm_mk_lt {S : Submodule R M} (x : M ⧸ S) {ε : 
   norm_mk_lt x hε
 #align submodule.quotient.norm_mk_lt Submodule.Quotient.norm_mk_lt
 
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 theorem Submodule.Quotient.norm_mk_le (m : M) : ‖(Submodule.Quotient.mk m : M ⧸ S)‖ ≤ ‖m‖ :=
   quotient_norm_mk_le S.toAddSubgroup m
 #align submodule.quotient.norm_mk_le Submodule.Quotient.norm_mk_le
@@ -807,17 +660,11 @@ section Ideal
 
 variable {R : Type _} [SeminormedCommRing R] (I : Ideal R)
 
-/- warning: ideal.quotient.norm_mk_lt -> Ideal.Quotient.norm_mk_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.quotient.norm_mk_lt Ideal.Quotient.norm_mk_ltₓ'. -/
 theorem Ideal.Quotient.norm_mk_lt {I : Ideal R} (x : R ⧸ I) {ε : ℝ} (hε : 0 < ε) :
     ∃ r : R, Ideal.Quotient.mk I r = x ∧ ‖r‖ < ‖x‖ + ε :=
   norm_mk_lt x hε
 #align ideal.quotient.norm_mk_lt Ideal.Quotient.norm_mk_lt
 
-/- warning: ideal.quotient.norm_mk_le -> Ideal.Quotient.norm_mk_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ideal.quotient.norm_mk_le Ideal.Quotient.norm_mk_leₓ'. -/
 theorem Ideal.Quotient.norm_mk_le (r : R) : ‖Ideal.Quotient.mk I r‖ ≤ ‖r‖ :=
   quotient_norm_mk_le I.toAddSubgroup r
 #align ideal.quotient.norm_mk_le Ideal.Quotient.norm_mk_le

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -700,8 +700,7 @@ theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
       _ = c * _ + ε := _
       
     · exact_mod_cast hc
-    · rw [mul_add, mul_div_cancel']
-      exact_mod_cast hc.ne'
+    · rw [mul_add, mul_div_cancel']; exact_mod_cast hc.ne'
 #align normed_add_group_hom.lift_norm_le NormedAddGroupHom.lift_norm_le
 
 /- warning: normed_add_group_hom.lift_norm_noninc -> NormedAddGroupHom.lift_normNoninc is a dubious translation:

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

@@ -125,10 +125,7 @@ theorem AddSubgroup.quotient_norm_eq {S : AddSubgroup M} (x : M ⧸ S) :
 #align add_subgroup.quotient_norm_eq AddSubgroup.quotient_norm_eq
 
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(SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m) x)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align image_norm_nonempty image_norm_nonemptyₓ'. -/
 theorem image_norm_nonempty {S : AddSubgroup M} :
     ∀ x : M ⧸ S, (norm '' { m | mk' S m = x }).Nonempty :=
@@ -169,20 +166,14 @@ theorem quotient_norm_neg {S : AddSubgroup M} (x : M ⧸ S) : ‖-x‖ = ‖x‖
 #align quotient_norm_neg quotient_norm_neg
 
 /- warning: quotient_norm_sub_rev -> quotient_norm_sub_rev is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quotient_norm_sub_rev quotient_norm_sub_revₓ'. -/
 theorem quotient_norm_sub_rev {S : AddSubgroup M} (x y : M ⧸ S) : ‖x - y‖ = ‖y - x‖ := by
   rw [show x - y = -(y - x) by abel, quotient_norm_neg]
 #align quotient_norm_sub_rev quotient_norm_sub_rev
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quotient_norm_mk_le quotient_norm_mk_leₓ'. -/
 /-- The norm of the projection is smaller or equal to the norm of the original element. -/
 theorem quotient_norm_mk_le (S : AddSubgroup M) (m : M) : ‖mk' S m‖ ≤ ‖m‖ :=
@@ -207,10 +198,7 @@ theorem quotient_norm_mk_le' (S : AddSubgroup M) (m : M) : ‖(m : M ⧸ S)‖ 
 #align quotient_norm_mk_le' quotient_norm_mk_le'
 
 /- warning: quotient_norm_mk_eq -> quotient_norm_mk_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align quotient_norm_mk_eq quotient_norm_mk_eqₓ'. -/
 /-- The norm of the image under the natural morphism to the quotient. -/
 theorem quotient_norm_mk_eq (S : AddSubgroup M) (m : M) :
@@ -246,10 +234,7 @@ theorem quotient_norm_nonneg (S : AddSubgroup M) : ∀ x : M ⧸ S, 0 ≤ ‖x
 #align quotient_norm_nonneg quotient_norm_nonneg
 
 /- warning: norm_mk_nonneg -> norm_mk_nonneg is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align norm_mk_nonneg norm_mk_nonnegₓ'. -/
 /-- The quotient norm is nonnegative. -/
 theorem norm_mk_nonneg (S : AddSubgroup M) (m : M) : 0 ≤ ‖mk' S m‖ :=
@@ -257,10 +242,7 @@ theorem norm_mk_nonneg (S : AddSubgroup M) (m : M) : 0 ≤ ‖mk' S m‖ :=
 #align norm_mk_nonneg norm_mk_nonneg
 
 /- warning: quotient_norm_eq_zero_iff -> quotient_norm_eq_zero_iff is a dubious translation:
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(QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M 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(SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M 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(QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) m (closure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align quotient_norm_eq_zero_iff quotient_norm_eq_zero_iffₓ'. -/
 /-- The norm of the image of `m : M` in the quotient by `S` is zero if and only if `m` belongs
 to the closure of `S`. -/
@@ -290,10 +272,7 @@ theorem quotient_norm_eq_zero_iff (S : AddSubgroup M) (m : M) :
 #align quotient_norm_eq_zero_iff quotient_norm_eq_zero_iff
 
 /- warning: norm_mk_lt -> norm_mk_lt is a dubious translation:
-lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))} (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Exists.{succ u1} M (fun (m : M) => And (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (coeFn.{succ 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(quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) => M -> (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)) (AddMonoidHom.hasCoeToFun.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m) x) (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} M (SeminormedAddCommGroup.toHasNorm.{u1} M _inst_1) m) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x) ε))))
-but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))} (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{succ u1} M (fun (m : M) => And (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) m) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => 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(SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m) x) (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} M (SeminormedAddCommGroup.toNorm.{u1} M _inst_1) m) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x) ε))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align norm_mk_lt norm_mk_ltₓ'. -/
 /-- For any `x : M ⧸ S` and any `0 < ε`, there is `m : M` such that `mk' S m = x`
 and `‖m‖ < ‖x‖ + ε`. -/
@@ -307,10 +286,7 @@ theorem norm_mk_lt {S : AddSubgroup M} (x : M ⧸ S) {ε : ℝ} (hε : 0 < ε) :
 #align norm_mk_lt norm_mk_lt
 
 /- warning: norm_mk_lt' -> norm_mk_lt' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align norm_mk_lt' norm_mk_lt'ₓ'. -/
 /-- For any `m : M` and any `0 < ε`, there is `s ∈ S` such that `‖m + s‖ < ‖mk' S m‖ + ε`. -/
 theorem norm_mk_lt' (S : AddSubgroup M) (m : M) {ε : ℝ} (hε : 0 < ε) :
@@ -358,10 +334,7 @@ theorem norm_mk_zero (S : AddSubgroup M) : ‖(0 : M ⧸ S)‖ = 0 :=
 #align norm_mk_zero norm_mk_zero
 
 /- warning: norm_zero_eq_zero -> norm_mk_eq_zero is a dubious translation:
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(SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Membership.mem.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))) m S))
+<too large>
 Case conversion may be inaccurate. Consider using '#align norm_zero_eq_zero norm_mk_eq_zeroₓ'. -/
 /-- If `(m : M)` has norm equal to `0` in `M ⧸ S` for a closed subgroup `S` of `M`, then
 `m ∈ S`. -/
@@ -489,10 +462,7 @@ noncomputable def normedMk (S : AddSubgroup M) : NormedAddGroupHom M (M ⧸ S) :
 -/
 
 /- warning: add_subgroup.normed_mk.apply -> AddSubgroup.normedMk.apply is a dubious translation:
-lean 3 declaration is
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(HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) => M -> (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)) (NormedAddGroupHom.hasCoeToFun.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S) m) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M 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(QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)
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(SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SeminormedAddGroup.toAddGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M 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(AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M 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(QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M 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+<too large>
 Case conversion may be inaccurate. Consider using '#align add_subgroup.normed_mk.apply AddSubgroup.normedMk.applyₓ'. -/
 /-- `S.normed_mk` agrees with `quotient_add_group.mk' S`. -/
 @[simp]
@@ -630,10 +600,7 @@ noncomputable def lift {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup
 #align normed_add_group_hom.lift NormedAddGroupHom.lift
 
 /- warning: normed_add_group_hom.lift_mk -> NormedAddGroupHom.lift_mk is a dubious translation:
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N _inst_1 _inst_3) M N (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (SeminormedAddGroup.toAddGroup.{u2} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} N _inst_3)))))) (AddMonoidHomClass.toAddHomClass.{max u1 u2, u1, u2} (NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) M N (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (SeminormedAddGroup.toAddGroup.{u2} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} N _inst_3))))) (NormedAddGroupHom.toAddMonoidHomClass.{u1, u2} M N _inst_1 _inst_3))) f s) (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)))))))))) (m : M), Eq.{succ u2} N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (NormedAddGroupHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) N (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S) _inst_3) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (fun (_x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) => N) (AddHomClass.toFunLike.{max u1 u2, u1, u2} (NormedAddGroupHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) N (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S) _inst_3) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) N (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SeminormedAddGroup.toAddGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S))))))) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (SeminormedAddGroup.toAddGroup.{u2} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} N _inst_3)))))) (AddMonoidHomClass.toAddHomClass.{max u1 u2, u1, u2} (NormedAddGroupHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) N (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S) _inst_3) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) N (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SeminormedAddGroup.toAddGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)))))) (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (SeminormedAddGroup.toAddGroup.{u2} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} N _inst_3))))) (NormedAddGroupHom.toAddMonoidHomClass.{u1, u2} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) N (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S) _inst_3))) (NormedAddGroupHom.lift.{u1, u2} M _inst_1 N _inst_3 S f hf) (FunLike.coe.{succ u1, succ u1, succ u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) M (fun (_x : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddHomClass.toFunLike.{u1, u1, u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SeminormedAddGroup.toAddGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M 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(SeminormedAddCommGroup.toSeminormedAddGroup.{u2} N _inst_3)))))) (AddMonoidHomClass.toAddHomClass.{max u1 u2, u1, u2} (NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) M N (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (SeminormedAddGroup.toAddGroup.{u2} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} N _inst_3))))) (NormedAddGroupHom.toAddMonoidHomClass.{u1, u2} M N _inst_1 _inst_3))) f m)
+<too large>
 Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.lift_mk NormedAddGroupHom.lift_mkₓ'. -/
 theorem lift_mk {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (m : M) :
@@ -842,10 +809,7 @@ section Ideal
 variable {R : Type _} [SeminormedCommRing R] (I : Ideal R)
 
 /- warning: ideal.quotient.norm_mk_lt -> Ideal.Quotient.norm_mk_lt is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.quotient.norm_mk_lt Ideal.Quotient.norm_mk_ltₓ'. -/
 theorem Ideal.Quotient.norm_mk_lt {I : Ideal R} (x : R ⧸ I) {ε : ℝ} (hε : 0 < ε) :
     ∃ r : R, Ideal.Quotient.mk I r = x ∧ ‖r‖ < ‖x‖ + ε :=
@@ -853,10 +817,7 @@ theorem Ideal.Quotient.norm_mk_lt {I : Ideal R} (x : R ⧸ I) {ε : ℝ} (hε :
 #align ideal.quotient.norm_mk_lt Ideal.Quotient.norm_mk_lt
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ideal.quotient.norm_mk_le Ideal.Quotient.norm_mk_leₓ'. -/
 theorem Ideal.Quotient.norm_mk_le (r : R) : ‖Ideal.Quotient.mk I r‖ ≤ ‖r‖ :=
   quotient_norm_mk_le I.toAddSubgroup r

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -527,9 +527,9 @@ theorem norm_normedMk_le (S : AddSubgroup M) : ‖S.normedMk‖ ≤ 1 :=
 
 /- warning: add_subgroup.norm_normed_mk -> AddSubgroup.norm_normedMk is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (Ne.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddSubgroup.topologicalClosure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_1) S)) (Set.univ.{u1} M)) -> (Eq.{1} Real (Norm.norm.{u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (NormedAddGroupHom.hasOpNorm.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (Ne.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddSubgroup.topologicalClosure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} M _inst_1) S)) (Set.univ.{u1} M)) -> (Eq.{1} Real (Norm.norm.{u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (NormedAddGroupHom.hasOpNorm.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (Ne.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (AddSubgroup.topologicalClosure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_1) S)) (Set.univ.{u1} M)) -> (Eq.{1} Real (Norm.norm.{u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (NormedAddGroupHom.hasOpNorm.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (Ne.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (AddSubgroup.topologicalClosure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} M _inst_1) S)) (Set.univ.{u1} M)) -> (Eq.{1} Real (Norm.norm.{u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (NormedAddGroupHom.hasOpNorm.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.norm_normed_mk AddSubgroup.norm_normedMkₓ'. -/
 /-- The operator norm of the projection is `1` if the subspace is not dense. -/
 theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) ≠ univ) :
@@ -576,9 +576,9 @@ theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) 
 
 /- warning: add_subgroup.norm_trivial_quotient_mk -> AddSubgroup.norm_trivial_quotient_mk is a dubious translation:
 lean 3 declaration is
-  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddSubgroup.topologicalClosure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_1) S)) (Set.univ.{u1} M)) -> (Eq.{1} Real (Norm.norm.{u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (NormedAddGroupHom.hasOpNorm.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddSubgroup.topologicalClosure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} M _inst_1) S)) (Set.univ.{u1} M)) -> (Eq.{1} Real (Norm.norm.{u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (NormedAddGroupHom.hasOpNorm.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (AddSubgroup.topologicalClosure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_1) S)) (Set.univ.{u1} M)) -> (Eq.{1} Real (Norm.norm.{u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (NormedAddGroupHom.hasOpNorm.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (AddSubgroup.topologicalClosure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (SeminormedAddCommGroup.toTopologicalAddGroup.{u1} M _inst_1) S)) (Set.univ.{u1} M)) -> (Eq.{1} Real (Norm.norm.{u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (NormedAddGroupHom.hasOpNorm.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.norm_trivial_quotient_mk AddSubgroup.norm_trivial_quotient_mkₓ'. -/
 /-- The operator norm of the projection is `0` if the subspace is dense. -/
 theorem norm_trivial_quotient_mk (S : AddSubgroup M)

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

@@ -845,7 +845,7 @@ variable {R : Type _} [SeminormedCommRing R] (I : Ideal R)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))} (x : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Exists.{succ u1} R (fun (r : R) => And (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (fun (_x : RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) => R -> (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I)) (RingHom.hasCoeToFun.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (Ideal.Quotient.mk.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I) r) x) (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (SeminormedRing.toHasNorm.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)) r) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (SeminormedAddCommGroup.toHasNorm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} R (SeminormedRing.toNonUnitalSeminormedRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3))) R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) I)) x) ε))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))} (x : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{succ u1} R (fun (r : R) => And (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))))) (Ideal.Quotient.mk.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I) r) x) (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (SeminormedRing.toNorm.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) r) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (SeminormedAddCommGroup.toNorm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} R (SeminormedRing.toNonUnitalSeminormedRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3))) R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) I)) x) ε))))
+  forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))} (x : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{succ u1} R (fun (r : R) => And (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))))) (Ideal.Quotient.mk.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I) r) x) (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (SeminormedRing.toNorm.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) r) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (SeminormedAddCommGroup.toNorm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} R (SeminormedRing.toNonUnitalSeminormedRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3))) R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) I)) x) ε))))
 Case conversion may be inaccurate. Consider using '#align ideal.quotient.norm_mk_lt Ideal.Quotient.norm_mk_ltₓ'. -/
 theorem Ideal.Quotient.norm_mk_lt {I : Ideal R} (x : R ⧸ I) {ε : ℝ} (hε : 0 < ε) :
     ∃ r : R, Ideal.Quotient.mk I r = x ∧ ‖r‖ < ‖x‖ + ε :=
@@ -856,7 +856,7 @@ theorem Ideal.Quotient.norm_mk_lt {I : Ideal R} (x : R ⧸ I) {ε : ℝ} (hε :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) (r : R), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (SeminormedAddCommGroup.toHasNorm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} R (SeminormedRing.toNonUnitalSeminormedRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3))) R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) I)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (fun (_x : RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) => R -> (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I)) (RingHom.hasCoeToFun.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (Ideal.Quotient.mk.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I) r)) (Norm.norm.{u1} R (SeminormedRing.toHasNorm.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)) r)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (r : R), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (SeminormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} R (SeminormedRing.toNonUnitalSeminormedRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3))) R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) I)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R 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(CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R 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(Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))))) (Ideal.Quotient.mk.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I) r)) (Norm.norm.{u1} R (SeminormedRing.toNorm.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) r)
+  forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (r : R), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (SeminormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} R (SeminormedRing.toNonUnitalSeminormedRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3))) R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) I)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2397 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R 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 Case conversion may be inaccurate. Consider using '#align ideal.quotient.norm_mk_le Ideal.Quotient.norm_mk_leₓ'. -/
 theorem Ideal.Quotient.norm_mk_le (r : R) : ‖Ideal.Quotient.mk I r‖ ≤ ‖r‖ :=
   quotient_norm_mk_le I.toAddSubgroup r

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -109,18 +109,18 @@ variable {M N : Type _} [SeminormedAddCommGroup M] [SeminormedAddCommGroup N]
 #print normOnQuotient /-
 /-- The definition of the norm on the quotient by an additive subgroup. -/
 noncomputable instance normOnQuotient (S : AddSubgroup M) : Norm (M ⧸ S)
-    where norm x := infₛ (norm '' { m | mk' S m = x })
+    where norm x := sInf (norm '' { m | mk' S m = x })
 #align norm_on_quotient normOnQuotient
 -/
 
 /- warning: add_subgroup.quotient_norm_eq -> AddSubgroup.quotient_norm_eq is a dubious translation:
 lean 3 declaration is
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+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))} (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S), Eq.{1} Real (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x) (InfSet.sInf.{0} Real Real.hasInf (Set.image.{u1, 0} M Real (Norm.norm.{u1} M (SeminormedAddCommGroup.toHasNorm.{u1} M _inst_1)) (setOf.{u1} M (fun (m : M) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (HasLiftT.mk.{succ u1, succ u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (CoeTCₓ.coe.{succ u1, succ u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (quotientAddGroup.HasQuotient.Quotient.hasCoeT.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S))) m) x))))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))} (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S), Eq.{1} Real (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x) (InfSet.infₛ.{0} Real Real.instInfSetReal (Set.image.{u1, 0} M Real (Norm.norm.{u1} M (SeminormedAddCommGroup.toNorm.{u1} M _inst_1)) (setOf.{u1} M (fun (m : M) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.mk.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S m) x))))
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))} (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S), Eq.{1} Real (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x) (InfSet.sInf.{0} Real Real.instInfSetReal (Set.image.{u1, 0} M Real (Norm.norm.{u1} M (SeminormedAddCommGroup.toNorm.{u1} M _inst_1)) (setOf.{u1} M (fun (m : M) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.mk.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S m) x))))
 Case conversion may be inaccurate. Consider using '#align add_subgroup.quotient_norm_eq AddSubgroup.quotient_norm_eqₓ'. -/
 theorem AddSubgroup.quotient_norm_eq {S : AddSubgroup M} (x : M ⧸ S) :
-    ‖x‖ = infₛ (norm '' { m : M | (m : M ⧸ S) = x }) :=
+    ‖x‖ = sInf (norm '' { m : M | (m : M ⧸ S) = x }) :=
   rfl
 #align add_subgroup.quotient_norm_eq AddSubgroup.quotient_norm_eq
 
@@ -187,7 +187,7 @@ Case conversion may be inaccurate. Consider using '#align quotient_norm_mk_le qu
 /-- The norm of the projection is smaller or equal to the norm of the original element. -/
 theorem quotient_norm_mk_le (S : AddSubgroup M) (m : M) : ‖mk' S m‖ ≤ ‖m‖ :=
   by
-  apply cinfₛ_le
+  apply csInf_le
   use 0
   · rintro _ ⟨n, h, rfl⟩
     apply norm_nonneg
@@ -208,13 +208,13 @@ theorem quotient_norm_mk_le' (S : AddSubgroup M) (m : M) : ‖(m : M ⧸ S)‖ 
 
 /- warning: quotient_norm_mk_eq -> quotient_norm_mk_eq is a dubious translation:
 lean 3 declaration is
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(quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (fun (_x : AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) => M -> (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)) (AddMonoidHom.hasCoeToFun.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) (InfSet.infₛ.{0} Real Real.hasInf (Set.image.{u1, 0} M Real (fun (x : M) => Norm.norm.{u1} M (SeminormedAddCommGroup.toHasNorm.{u1} M _inst_1) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))))) m x)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) S)))
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (m : M), Eq.{1} Real (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (fun (_x : AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) => M -> (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)) (AddMonoidHom.hasCoeToFun.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) (InfSet.sInf.{0} Real Real.hasInf (Set.image.{u1, 0} M Real (fun (x : M) => Norm.norm.{u1} M (SeminormedAddCommGroup.toHasNorm.{u1} M _inst_1) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))))) m x)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) S)))
 but is expected to have type
-  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (m : M), Eq.{1} Real (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) m) (normOnQuotient.{u1} M _inst_1 S) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) (InfSet.infₛ.{0} Real Real.instInfSetReal (Set.image.{u1, 0} M Real (fun (x : M) => Norm.norm.{u1} M (SeminormedAddCommGroup.toNorm.{u1} M _inst_1) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))))) m x)) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)))
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (m : M), Eq.{1} Real (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) m) (normOnQuotient.{u1} M _inst_1 S) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) (InfSet.sInf.{0} Real Real.instInfSetReal (Set.image.{u1, 0} M Real (fun (x : M) => Norm.norm.{u1} M (SeminormedAddCommGroup.toNorm.{u1} M _inst_1) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))))) m x)) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)))
 Case conversion may be inaccurate. Consider using '#align quotient_norm_mk_eq quotient_norm_mk_eqₓ'. -/
 /-- The norm of the image under the natural morphism to the quotient. -/
 theorem quotient_norm_mk_eq (S : AddSubgroup M) (m : M) :
-    ‖mk' S m‖ = infₛ ((fun x => ‖m + x‖) '' S) :=
+    ‖mk' S m‖ = sInf ((fun x => ‖m + x‖) '' S) :=
   by
   change Inf _ = _
   congr 1
@@ -240,7 +240,7 @@ theorem quotient_norm_nonneg (S : AddSubgroup M) : ∀ x : M ⧸ S, 0 ≤ ‖x
   by
   rintro ⟨m⟩
   change 0 ≤ ‖mk' S m‖
-  apply le_cinfₛ (image_norm_nonempty _)
+  apply le_csInf (image_norm_nonempty _)
   rintro _ ⟨n, h, rfl⟩
   apply norm_nonneg
 #align quotient_norm_nonneg quotient_norm_nonneg
@@ -268,7 +268,7 @@ theorem quotient_norm_eq_zero_iff (S : AddSubgroup M) (m : M) :
     ‖mk' S m‖ = 0 ↔ m ∈ closure (S : Set M) :=
   by
   have : 0 ≤ ‖mk' S m‖ := norm_mk_nonneg S m
-  rw [← this.le_iff_eq, quotient_norm_mk_eq, Real.infₛ_le_iff]
+  rw [← this.le_iff_eq, quotient_norm_mk_eq, Real.sInf_le_iff]
   simp_rw [zero_add]
   · calc
       (∀ ε > (0 : ℝ), ∃ r ∈ (fun x => ‖m + x‖) '' (S : Set M), r < ε) ↔
@@ -301,7 +301,7 @@ theorem norm_mk_lt {S : AddSubgroup M} (x : M ⧸ S) {ε : ℝ} (hε : 0 < ε) :
     ∃ m : M, mk' S m = x ∧ ‖m‖ < ‖x‖ + ε :=
   by
   obtain ⟨_, ⟨m : M, H : mk' S m = x, rfl⟩, hnorm : ‖m‖ < ‖x‖ + ε⟩ :=
-    Real.lt_infₛ_add_pos (image_norm_nonempty x) hε
+    Real.lt_sInf_add_pos (image_norm_nonempty x) hε
   subst H
   exact ⟨m, rfl, hnorm⟩
 #align norm_mk_lt norm_mk_lt
@@ -403,7 +403,7 @@ theorem quotient_nhd_basis (S : AddSubgroup M) :
       apply IsOpen.mem_nhds
       · change IsOpen (mk' S ⁻¹' _)
         erw [QuotientAddGroup.preimage_image_mk]
-        apply isOpen_unionᵢ
+        apply isOpen_iUnion
         rintro ⟨s, s_in⟩
         exact (continuous_add_right s).isOpen_preimage _ is_open_ball
       · exact ⟨(0 : M), mem_ball_self ε_pos, (mk' S).map_zero⟩⟩
@@ -437,7 +437,7 @@ noncomputable instance AddSubgroup.seminormedAddCommGroupQuotient (S : AddSubgro
       dsimp
       rw [quotient_norm_sub_rev]
     rw [funext this]
-    refine' Filter.hasBasis_binfᵢ_principal _ Set.nonempty_Ioi
+    refine' Filter.hasBasis_biInf_principal _ Set.nonempty_Ioi
     rintro ε (ε_pos : 0 < ε) η (η_pos : 0 < η)
     refine' ⟨min ε η, lt_min ε_pos η_pos, _, _⟩
     · suffices ∀ a b : M ⧸ S, ‖a - b‖ < ε → ‖a - b‖ < η → ‖a - b‖ < ε by simpa
@@ -602,7 +602,7 @@ namespace NormedAddGroupHom
 by the kernel of `f`. -/
 structure IsQuotient (f : NormedAddGroupHom M N) : Prop where
   Surjective : Function.Surjective f
-  norm : ∀ x, ‖f x‖ = infₛ ((fun m => ‖x + m‖) '' f.ker)
+  norm : ∀ x, ‖f x‖ = sInf ((fun m => ‖x + m‖) '' f.ker)
 #align normed_add_group_hom.is_quotient NormedAddGroupHom.IsQuotient
 -/
 
@@ -679,7 +679,7 @@ theorem IsQuotient.norm_lift {f : NormedAddGroupHom M N} (hquot : IsQuotient f)
     by
     rw [Set.nonempty_image_iff]
     exact ⟨0, f.ker.zero_mem⟩
-  rcases Real.lt_infₛ_add_pos nonemp hε with
+  rcases Real.lt_sInf_add_pos nonemp hε with
     ⟨_, ⟨⟨x, hx, rfl⟩, H : ‖m + x‖ < Inf ((fun m' : M => ‖m + m'‖) '' f.ker) + ε⟩⟩
   exact
     ⟨m + x, by rw [map_add, (NormedAddGroupHom.mem_ker f x).mp hx, add_zero], by rwa [hquot.norm]⟩
@@ -694,7 +694,7 @@ Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.i
 theorem IsQuotient.norm_le {f : NormedAddGroupHom M N} (hquot : IsQuotient f) (m : M) :
     ‖f m‖ ≤ ‖m‖ := by
   rw [hquot.norm]
-  apply cinfₛ_le
+  apply csInf_le
   · use 0
     rintro _ ⟨m', hm', rfl⟩
     apply norm_nonneg

mathlib commit https://github.com/leanprover-community/mathlib/commit/cc5dd6244981976cc9da7afc4eee5682b037a013

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Riccardo Brasca
 
 ! This file was ported from Lean 3 source module analysis.normed.group.quotient
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
+! leanprover-community/mathlib commit 7d34004e19699895c13c86b78ae62bbaea0bc893
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.RingTheory.Ideal.QuotientOperations
 /-!
 # Quotients of seminormed groups
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 For any `seminormed_add_comm_group M` and any `S : add_subgroup M`, we provide a
 `seminormed_add_comm_group`, the group quotient `M ⧸ S`.
 If `S` is closed, we provide `normed_add_comm_group (M ⧸ S)` (regardless of whether `M` itself is

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -842,7 +842,7 @@ variable {R : Type _} [SeminormedCommRing R] (I : Ideal R)
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))} (x : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Exists.{succ u1} R (fun (r : R) => And (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (fun (_x : RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) => R -> (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I)) (RingHom.hasCoeToFun.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (Ideal.Quotient.mk.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I) r) x) (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (SeminormedRing.toHasNorm.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)) r) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (SeminormedAddCommGroup.toHasNorm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} R (SeminormedRing.toNonUnitalSeminormedRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3))) R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) I)) x) ε))))
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)))} (x : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{succ u1} R (fun (r : R) => And (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))))) (Ideal.Quotient.mk.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I) r) x) (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (SeminormedRing.toNorm.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) r) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (SeminormedAddCommGroup.toNorm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} R (SeminormedRing.toNonUnitalSeminormedRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3))) R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)))) I)) x) ε))))
+  forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] {I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))} (x : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{succ u1} R (fun (r : R) => And (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Semiring.toNonAssocSemiring.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Semiring.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommSemiring.toSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toCommSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))))) (Ideal.Quotient.mk.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I) r) x) (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} R (SeminormedRing.toNorm.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) r) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (SeminormedAddCommGroup.toNorm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} R (SeminormedRing.toNonUnitalSeminormedRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3))) R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) (Semiring.toModule.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) I)) x) ε))))
 Case conversion may be inaccurate. Consider using '#align ideal.quotient.norm_mk_lt Ideal.Quotient.norm_mk_ltₓ'. -/
 theorem Ideal.Quotient.norm_mk_lt {I : Ideal R} (x : R ⧸ I) {ε : ℝ} (hε : 0 < ε) :
     ∃ r : R, Ideal.Quotient.mk I r = x ∧ ‖r‖ < ‖x‖ + ε :=
@@ -853,7 +853,7 @@ theorem Ideal.Quotient.norm_mk_lt {I : Ideal R} (x : R ⧸ I) {ε : ℝ} (hε :
 lean 3 declaration is
   forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) (r : R), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (SeminormedAddCommGroup.toHasNorm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} R (SeminormedRing.toNonUnitalSeminormedRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3))) R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) I)) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (fun (_x : RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) => R -> (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I)) (RingHom.hasCoeToFun.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (Ideal.Quotient.mk.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I) r)) (Norm.norm.{u1} R (SeminormedRing.toHasNorm.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)) r)
 but is expected to have type
-  forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] (I : Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)))) (r : R), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (SeminormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} R (SeminormedRing.toNonUnitalSeminormedRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3))) R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)))) I)) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))))) (Ideal.Quotient.mk.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I) r)) (Norm.norm.{u1} R (SeminormedRing.toNorm.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) r)
+  forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] (I : Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (r : R), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (SeminormedAddCommGroup.toNorm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (CommSemiring.toSemiring.{u1} R (CommRing.toCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToCommSemiring.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R 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 Case conversion may be inaccurate. Consider using '#align ideal.quotient.norm_mk_le Ideal.Quotient.norm_mk_leₓ'. -/
 theorem Ideal.Quotient.norm_mk_le (r : R) : ‖Ideal.Quotient.mk I r‖ ≤ ‖r‖ :=
   quotient_norm_mk_le I.toAddSubgroup r

mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1

@@ -103,16 +103,30 @@ open Topology NNReal
 
 variable {M N : Type _} [SeminormedAddCommGroup M] [SeminormedAddCommGroup N]
 
+#print normOnQuotient /-
 /-- The definition of the norm on the quotient by an additive subgroup. -/
 noncomputable instance normOnQuotient (S : AddSubgroup M) : Norm (M ⧸ S)
     where norm x := infₛ (norm '' { m | mk' S m = x })
 #align norm_on_quotient normOnQuotient
+-/
 
+/- warning: add_subgroup.quotient_norm_eq -> AddSubgroup.quotient_norm_eq is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))} (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S), Eq.{1} Real (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x) (InfSet.infₛ.{0} Real Real.hasInf (Set.image.{u1, 0} M Real (Norm.norm.{u1} M (SeminormedAddCommGroup.toHasNorm.{u1} M _inst_1)) (setOf.{u1} M (fun (m : M) => Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (HasLiftT.mk.{succ u1, succ u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (CoeTCₓ.coe.{succ u1, succ u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (quotientAddGroup.HasQuotient.Quotient.hasCoeT.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S))) m) x))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align add_subgroup.quotient_norm_eq AddSubgroup.quotient_norm_eqₓ'. -/
 theorem AddSubgroup.quotient_norm_eq {S : AddSubgroup M} (x : M ⧸ S) :
     ‖x‖ = infₛ (norm '' { m : M | (m : M ⧸ S) = x }) :=
   rfl
 #align add_subgroup.quotient_norm_eq AddSubgroup.quotient_norm_eq
 
+/- warning: image_norm_nonempty -> image_norm_nonempty is a dubious translation:
+lean 3 declaration is
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M _inst_1) S)) m) x)))
+but is expected to have type
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(SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m) x)))
+Case conversion may be inaccurate. Consider using '#align image_norm_nonempty image_norm_nonemptyₓ'. -/
 theorem image_norm_nonempty {S : AddSubgroup M} :
     ∀ x : M ⧸ S, (norm '' { m | mk' S m = x }).Nonempty :=
   by
@@ -123,13 +137,21 @@ theorem image_norm_nonempty {S : AddSubgroup M} :
   rfl
 #align image_norm_nonempty image_norm_nonempty
 
+#print bddBelow_image_norm /-
 theorem bddBelow_image_norm (s : Set M) : BddBelow (norm '' s) :=
   by
   use 0
   rintro _ ⟨x, hx, rfl⟩
   apply norm_nonneg
 #align bdd_below_image_norm bddBelow_image_norm
+-/
 
+/- warning: quotient_norm_neg -> quotient_norm_neg is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))} (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S), Eq.{1} Real (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (Neg.neg.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toHasNeg.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))) x)) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x)
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))} (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S), Eq.{1} Real (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (Neg.neg.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (NegZeroClass.toNeg.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegZeroMonoid.toNegZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubtractionMonoid.toSubNegZeroMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubtractionCommMonoid.toSubtractionMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddCommGroup.toDivisionAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addCommGroup.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) x)) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x)
+Case conversion may be inaccurate. Consider using '#align quotient_norm_neg quotient_norm_negₓ'. -/
 /-- The norm on the quotient satisfies `‖-x‖ = ‖x‖`. -/
 theorem quotient_norm_neg {S : AddSubgroup M} (x : M ⧸ S) : ‖-x‖ = ‖x‖ :=
   by
@@ -143,10 +165,22 @@ theorem quotient_norm_neg {S : AddSubgroup M} (x : M ⧸ S) : ‖-x‖ = ‖x‖
     exact ⟨-m, by simpa using neg_eq_iff_eq_neg.mpr ((mk'_apply _ _).symm.trans hm)⟩
 #align quotient_norm_neg quotient_norm_neg
 
+/- warning: quotient_norm_sub_rev -> quotient_norm_sub_rev is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))} (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (y : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S), Eq.{1} Real (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (HSub.hSub.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (instHSub.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toHasSub.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) x y)) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (HSub.hSub.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (instHSub.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toHasSub.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) y x))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))} (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (y : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S), Eq.{1} Real (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (HSub.hSub.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (instHSub.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toSub.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) x y)) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (HSub.hSub.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (instHSub.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toSub.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) y x))
+Case conversion may be inaccurate. Consider using '#align quotient_norm_sub_rev quotient_norm_sub_revₓ'. -/
 theorem quotient_norm_sub_rev {S : AddSubgroup M} (x y : M ⧸ S) : ‖x - y‖ = ‖y - x‖ := by
   rw [show x - y = -(y - x) by abel, quotient_norm_neg]
 #align quotient_norm_sub_rev quotient_norm_sub_rev
 
+/- warning: quotient_norm_mk_le -> quotient_norm_mk_le is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (m : M), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (fun (_x : AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) => M -> (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)) (AddMonoidHom.hasCoeToFun.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) (Norm.norm.{u1} M (SeminormedAddCommGroup.toHasNorm.{u1} M _inst_1) m)
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (m : M), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) m) (normOnQuotient.{u1} M _inst_1 S) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) (Norm.norm.{u1} M (SeminormedAddCommGroup.toNorm.{u1} M _inst_1) m)
+Case conversion may be inaccurate. Consider using '#align quotient_norm_mk_le quotient_norm_mk_leₓ'. -/
 /-- The norm of the projection is smaller or equal to the norm of the original element. -/
 theorem quotient_norm_mk_le (S : AddSubgroup M) (m : M) : ‖mk' S m‖ ≤ ‖m‖ :=
   by
@@ -158,11 +192,23 @@ theorem quotient_norm_mk_le (S : AddSubgroup M) (m : M) : ‖mk' S m‖ ≤ ‖m
     rw [Set.mem_setOf_eq]
 #align quotient_norm_mk_le quotient_norm_mk_le
 
+/- warning: quotient_norm_mk_le' -> quotient_norm_mk_le' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quotient_norm_mk_le' quotient_norm_mk_le'ₓ'. -/
 /-- The norm of the projection is smaller or equal to the norm of the original element. -/
 theorem quotient_norm_mk_le' (S : AddSubgroup M) (m : M) : ‖(m : M ⧸ S)‖ ≤ ‖m‖ :=
   quotient_norm_mk_le S m
 #align quotient_norm_mk_le' quotient_norm_mk_le'
 
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+Case conversion may be inaccurate. Consider using '#align quotient_norm_mk_eq quotient_norm_mk_eqₓ'. -/
 /-- The norm of the image under the natural morphism to the quotient. -/
 theorem quotient_norm_mk_eq (S : AddSubgroup M) (m : M) :
     ‖mk' S m‖ = infₛ ((fun x => ‖m + x‖) '' S) :=
@@ -180,6 +226,12 @@ theorem quotient_norm_mk_eq (S : AddSubgroup M) (m : M) :
     simpa using h
 #align quotient_norm_mk_eq quotient_norm_mk_eq
 
+/- warning: quotient_norm_nonneg -> quotient_norm_nonneg is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x)
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x)
+Case conversion may be inaccurate. Consider using '#align quotient_norm_nonneg quotient_norm_nonnegₓ'. -/
 /-- The quotient norm is nonnegative. -/
 theorem quotient_norm_nonneg (S : AddSubgroup M) : ∀ x : M ⧸ S, 0 ≤ ‖x‖ :=
   by
@@ -190,11 +242,23 @@ theorem quotient_norm_nonneg (S : AddSubgroup M) : ∀ x : M ⧸ S, 0 ≤ ‖x
   apply norm_nonneg
 #align quotient_norm_nonneg quotient_norm_nonneg
 
+/- warning: norm_mk_nonneg -> norm_mk_nonneg is a dubious translation:
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(SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (m : M), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) m) (normOnQuotient.{u1} M _inst_1 S) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _x) (AddHomClass.toFunLike.{u1, u1, 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(QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M 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(AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M 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(SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m))
+Case conversion may be inaccurate. Consider using '#align norm_mk_nonneg norm_mk_nonnegₓ'. -/
 /-- The quotient norm is nonnegative. -/
 theorem norm_mk_nonneg (S : AddSubgroup M) (m : M) : 0 ≤ ‖mk' S m‖ :=
   quotient_norm_nonneg S _
 #align norm_mk_nonneg norm_mk_nonneg
 
+/- warning: quotient_norm_eq_zero_iff -> quotient_norm_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (m : M), Iff (Eq.{1} Real (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (fun (_x : AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) => M -> (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)) (AddMonoidHom.hasCoeToFun.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Membership.Mem.{u1, u1} M (Set.{u1} M) (Set.hasMem.{u1} M) m (closure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) S)))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (m : M), Iff (Eq.{1} Real (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) m) (normOnQuotient.{u1} M _inst_1 S) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Membership.mem.{u1, u1} M (Set.{u1} M) (Set.instMembershipSet.{u1} M) m (closure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)))
+Case conversion may be inaccurate. Consider using '#align quotient_norm_eq_zero_iff quotient_norm_eq_zero_iffₓ'. -/
 /-- The norm of the image of `m : M` in the quotient by `S` is zero if and only if `m` belongs
 to the closure of `S`. -/
 theorem quotient_norm_eq_zero_iff (S : AddSubgroup M) (m : M) :
@@ -222,6 +286,12 @@ theorem quotient_norm_eq_zero_iff (S : AddSubgroup M) (m : M) :
   use 0, S.zero_mem
 #align quotient_norm_eq_zero_iff quotient_norm_eq_zero_iff
 
+/- warning: norm_mk_lt -> norm_mk_lt is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))} (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Exists.{succ u1} M (fun (m : M) => And (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M 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(quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M 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M _inst_1) S)) m) x) (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} M (SeminormedAddCommGroup.toHasNorm.{u1} M _inst_1) m) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x) ε))))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))} (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{succ u1} M (fun (m : M) => And (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M 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(SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m) x) (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} M (SeminormedAddCommGroup.toNorm.{u1} M _inst_1) m) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x) ε))))
+Case conversion may be inaccurate. Consider using '#align norm_mk_lt norm_mk_ltₓ'. -/
 /-- For any `x : M ⧸ S` and any `0 < ε`, there is `m : M` such that `mk' S m = x`
 and `‖m‖ < ‖x‖ + ε`. -/
 theorem norm_mk_lt {S : AddSubgroup M} (x : M ⧸ S) {ε : ℝ} (hε : 0 < ε) :
@@ -233,6 +303,12 @@ theorem norm_mk_lt {S : AddSubgroup M} (x : M ⧸ S) {ε : ℝ} (hε : 0 < ε) :
   exact ⟨m, rfl, hnorm⟩
 #align norm_mk_lt norm_mk_lt
 
+/- warning: norm_mk_lt' -> norm_mk_lt' is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (m : M) {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Exists.{succ u1} M (fun (s : M) => Exists.{0} (Membership.Mem.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))) s S) (fun (H : Membership.Mem.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))) s S) => LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} M (SeminormedAddCommGroup.toHasNorm.{u1} M _inst_1) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toHasAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))))) m s)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (fun (_x : AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) => M -> (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)) (AddMonoidHom.hasCoeToFun.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) ε))))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (m : M) {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{succ u1} M (fun (s : M) => And (Membership.mem.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))) s S) (LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} M (SeminormedAddCommGroup.toNorm.{u1} M _inst_1) (HAdd.hAdd.{u1, u1, u1} M M M (instHAdd.{u1} M (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))))) m s)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) m) (normOnQuotient.{u1} M _inst_1 S) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (fun (a : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) a) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) ε))))
+Case conversion may be inaccurate. Consider using '#align norm_mk_lt' norm_mk_lt'ₓ'. -/
 /-- For any `m : M` and any `0 < ε`, there is `s ∈ S` such that `‖m + s‖ < ‖mk' S m‖ + ε`. -/
 theorem norm_mk_lt' (S : AddSubgroup M) (m : M) {ε : ℝ} (hε : 0 < ε) :
     ∃ s ∈ S, ‖m + s‖ < ‖mk' S m‖ + ε :=
@@ -244,6 +320,12 @@ theorem norm_mk_lt' (S : AddSubgroup M) (m : M) {ε : ℝ} (hε : 0 < ε) :
   rwa [add_neg_cancel_left]
 #align norm_mk_lt' norm_mk_lt'
 
+/- warning: quotient_norm_add_le -> quotient_norm_add_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (y : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S), LE.le.{0} Real Real.instLEReal (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (HAdd.hAdd.{u1, u1, u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (instHAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))))) x y)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) y))
+Case conversion may be inaccurate. Consider using '#align quotient_norm_add_le quotient_norm_add_leₓ'. -/
 /-- The quotient norm satisfies the triangle inequality. -/
 theorem quotient_norm_add_le (S : AddSubgroup M) (x y : M ⧸ S) : ‖x + y‖ ≤ ‖x‖ + ‖y‖ :=
   by
@@ -259,6 +341,12 @@ theorem quotient_norm_add_le (S : AddSubgroup M) (x y : M ⧸ S) : ‖x + y‖ 
     
 #align quotient_norm_add_le quotient_norm_add_le
 
+/- warning: norm_mk_zero -> norm_mk_zero is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), Eq.{1} Real (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (OfNat.ofNat.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) 0 (OfNat.mk.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) 0 (Zero.zero.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toHasZero.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align norm_mk_zero norm_mk_zeroₓ'. -/
 /-- The quotient norm of `0` is `0`. -/
 theorem norm_mk_zero (S : AddSubgroup M) : ‖(0 : M ⧸ S)‖ = 0 :=
   by
@@ -266,12 +354,24 @@ theorem norm_mk_zero (S : AddSubgroup M) : ‖(0 : M ⧸ S)‖ = 0 :=
   exact subset_closure S.zero_mem
 #align norm_mk_zero norm_mk_zero
 
+/- warning: norm_zero_eq_zero -> norm_mk_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (IsClosed.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) S)) -> (forall (m : M), (Eq.{1} Real (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) (coeFn.{succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (fun (_x : AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) => M -> (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)) (AddMonoidHom.hasCoeToFun.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Membership.Mem.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))) m S))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (IsClosed.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)) -> (forall (m : M), (Eq.{1} Real (Norm.norm.{u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) m) (normOnQuotient.{u1} M _inst_1 S) (FunLike.coe.{succ u1, succ u1, succ u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (fun (_x : M) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : M) => HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _x) (AddHomClass.toFunLike.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (AddMonoidHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))) (AddMonoidHom.addMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))) (QuotientAddGroup.mk'.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)) m)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Membership.mem.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))) m S))
+Case conversion may be inaccurate. Consider using '#align norm_zero_eq_zero norm_mk_eq_zeroₓ'. -/
 /-- If `(m : M)` has norm equal to `0` in `M ⧸ S` for a closed subgroup `S` of `M`, then
 `m ∈ S`. -/
-theorem norm_zero_eq_zero (S : AddSubgroup M) (hS : IsClosed (S : Set M)) (m : M)
+theorem norm_mk_eq_zero (S : AddSubgroup M) (hS : IsClosed (S : Set M)) (m : M)
     (h : ‖mk' S m‖ = 0) : m ∈ S := by rwa [quotient_norm_eq_zero_iff, hS.closure_eq] at h
-#align norm_zero_eq_zero norm_zero_eq_zero
-
+#align norm_zero_eq_zero norm_mk_eq_zero
+
+/- warning: quotient_nhd_basis -> quotient_nhd_basis is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), Filter.HasBasis.{u1, 1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) Real (nhds.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.topologicalSpace.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) S) (OfNat.ofNat.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) 0 (OfNat.mk.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) 0 (Zero.zero.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddZeroClass.toHasZero.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addGroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) S (AddSubgroup.normal_of_comm.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S)))))))))) (fun (ε : Real) => LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) (fun (ε : Real) => setOf.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (fun (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) => LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x) ε))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), Filter.HasBasis.{u1, 1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) Real (nhds.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.topologicalSpace.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) S) (OfNat.ofNat.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) 0 (Zero.toOfNat0.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (NegZeroClass.toZero.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegZeroMonoid.toNegZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubtractionMonoid.toSubNegZeroMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubtractionCommMonoid.toSubtractionMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddCommGroup.toDivisionAddCommMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (QuotientAddGroup.Quotient.addCommGroup.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) S))))))))) (fun (ε : Real) => LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) (fun (ε : Real) => setOf.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (fun (x : HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) => LT.lt.{0} Real Real.instLTReal (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (normOnQuotient.{u1} M _inst_1 S) x) ε))
+Case conversion may be inaccurate. Consider using '#align quotient_nhd_basis quotient_nhd_basisₓ'. -/
 theorem quotient_nhd_basis (S : AddSubgroup M) :
     (𝓝 (0 : M ⧸ S)).HasBasis (fun ε : ℝ => 0 < ε) fun ε => { x | ‖x‖ < ε } :=
   ⟨by
@@ -306,6 +406,7 @@ theorem quotient_nhd_basis (S : AddSubgroup M) :
       · exact ⟨(0 : M), mem_ball_self ε_pos, (mk' S).map_zero⟩⟩
 #align quotient_nhd_basis quotient_nhd_basis
 
+#print AddSubgroup.seminormedAddCommGroupQuotient /-
 /-- The seminormed group structure on the quotient by an additive subgroup. -/
 noncomputable instance AddSubgroup.seminormedAddCommGroupQuotient (S : AddSubgroup M) :
     SeminormedAddCommGroup (M ⧸ S) where
@@ -340,6 +441,7 @@ noncomputable instance AddSubgroup.seminormedAddCommGroupQuotient (S : AddSubgro
       exact fun a b h h' => h
     · simp
 #align add_subgroup.seminormed_add_comm_group_quotient AddSubgroup.seminormedAddCommGroupQuotient
+-/
 
 -- This is a sanity check left here on purpose to ensure that potential refactors won't destroy
 -- this important property.
@@ -348,6 +450,12 @@ example (S : AddSubgroup M) :
       S.seminormedAddCommGroupQuotient.toUniformSpace.toTopologicalSpace :=
   rfl
 
+/- warning: add_subgroup.normed_add_comm_group_quotient -> AddSubgroup.normedAddCommGroupQuotient is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) [_inst_3 : IsClosed.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) S)], NormedAddCommGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) [_inst_3 : IsClosed.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)], NormedAddCommGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)
+Case conversion may be inaccurate. Consider using '#align add_subgroup.normed_add_comm_group_quotient AddSubgroup.normedAddCommGroupQuotientₓ'. -/
 /-- The quotient in the category of normed groups. -/
 noncomputable instance AddSubgroup.normedAddCommGroupQuotient (S : AddSubgroup M)
     [IsClosed (S : Set M)] : NormedAddCommGroup (M ⧸ S) :=
@@ -369,33 +477,57 @@ namespace AddSubgroup
 
 open NormedAddGroupHom
 
+#print AddSubgroup.normedMk /-
 /-- The morphism from a seminormed group to the quotient by a subgroup. -/
 noncomputable def normedMk (S : AddSubgroup M) : NormedAddGroupHom M (M ⧸ S) :=
   { QuotientAddGroup.mk' S with
     bound' := ⟨1, fun m => by simpa [one_mul] using quotient_norm_mk_le _ m⟩ }
 #align add_subgroup.normed_mk AddSubgroup.normedMk
+-/
 
+/- warning: add_subgroup.normed_mk.apply -> AddSubgroup.normedMk.apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (m : M), Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (FunLike.coe.{succ u1, succ u1, succ u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) M (fun (_x : M) => 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+Case conversion may be inaccurate. Consider using '#align add_subgroup.normed_mk.apply AddSubgroup.normedMk.applyₓ'. -/
 /-- `S.normed_mk` agrees with `quotient_add_group.mk' S`. -/
 @[simp]
 theorem normedMk.apply (S : AddSubgroup M) (m : M) : normedMk S m = QuotientAddGroup.mk' S m :=
   rfl
 #align add_subgroup.normed_mk.apply AddSubgroup.normedMk.apply
 
+#print AddSubgroup.surjective_normedMk /-
 /-- `S.normed_mk` is surjective. -/
 theorem surjective_normedMk (S : AddSubgroup M) : Function.Surjective (normedMk S) :=
   surjective_quot_mk _
 #align add_subgroup.surjective_normed_mk AddSubgroup.surjective_normedMk
+-/
 
+#print AddSubgroup.ker_normedMk /-
 /-- The kernel of `S.normed_mk` is `S`. -/
 theorem ker_normedMk (S : AddSubgroup M) : S.normedMk.ker = S :=
   QuotientAddGroup.ker_mk' _
 #align add_subgroup.ker_normed_mk AddSubgroup.ker_normedMk
+-/
 
+/- warning: add_subgroup.norm_normed_mk_le -> AddSubgroup.norm_normedMk_le is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (NormedAddGroupHom.hasOpNorm.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align add_subgroup.norm_normed_mk_le AddSubgroup.norm_normedMk_leₓ'. -/
 /-- The operator norm of the projection is at most `1`. -/
 theorem norm_normedMk_le (S : AddSubgroup M) : ‖S.normedMk‖ ≤ 1 :=
   NormedAddGroupHom.opNorm_le_bound _ zero_le_one fun m => by simp [quotient_norm_mk_le']
 #align add_subgroup.norm_normed_mk_le AddSubgroup.norm_normedMk_le
 
+/- warning: add_subgroup.norm_normed_mk -> AddSubgroup.norm_normedMk is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (Ne.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddSubgroup.topologicalClosure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_1) S)) (Set.univ.{u1} M)) -> (Eq.{1} Real (Norm.norm.{u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (NormedAddGroupHom.hasOpNorm.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))
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+Case conversion may be inaccurate. Consider using '#align add_subgroup.norm_normed_mk AddSubgroup.norm_normedMkₓ'. -/
 /-- The operator norm of the projection is `1` if the subspace is not dense. -/
 theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) ≠ univ) :
     ‖S.normedMk‖ = 1 := by
@@ -439,6 +571,12 @@ theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) 
     
 #align add_subgroup.norm_normed_mk AddSubgroup.norm_normedMk
 
+/- warning: add_subgroup.norm_trivial_quotient_mk -> AddSubgroup.norm_trivial_quotient_mk is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (Eq.{succ u1} (Set.{u1} M) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (HasLiftT.mk.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (CoeTCₓ.coe.{succ u1, succ u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (Set.{u1} M) (SetLike.Set.hasCoeT.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddSubgroup.topologicalClosure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_1) S)) (Set.univ.{u1} M)) -> (Eq.{1} Real (Norm.norm.{u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (NormedAddGroupHom.hasOpNorm.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))), (Eq.{succ u1} (Set.{u1} M) (SetLike.coe.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (AddSubgroup.topologicalClosure.{u1} M (UniformSpace.toTopologicalSpace.{u1} M (PseudoMetricSpace.toUniformSpace.{u1} M (SeminormedAddCommGroup.toPseudoMetricSpace.{u1} M _inst_1))) (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)) (SeminormedAddCommGroup.to_topologicalAddGroup.{u1} M _inst_1) S)) (Set.univ.{u1} M)) -> (Eq.{1} Real (Norm.norm.{u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (NormedAddGroupHom.hasOpNorm.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align add_subgroup.norm_trivial_quotient_mk AddSubgroup.norm_trivial_quotient_mkₓ'. -/
 /-- The operator norm of the projection is `0` if the subspace is dense. -/
 theorem norm_trivial_quotient_mk (S : AddSubgroup M)
     (h : (S.topologicalClosure : Set M) = Set.univ) : ‖S.normedMk‖ = 0 :=
@@ -456,13 +594,21 @@ end AddSubgroup
 
 namespace NormedAddGroupHom
 
+#print NormedAddGroupHom.IsQuotient /-
 /-- `is_quotient f`, for `f : M ⟶ N` means that `N` is isomorphic to the quotient of `M`
 by the kernel of `f`. -/
 structure IsQuotient (f : NormedAddGroupHom M N) : Prop where
   Surjective : Function.Surjective f
   norm : ∀ x, ‖f x‖ = infₛ ((fun m => ‖x + m‖) '' f.ker)
 #align normed_add_group_hom.is_quotient NormedAddGroupHom.IsQuotient
+-/
 
+/- warning: normed_add_group_hom.lift -> NormedAddGroupHom.lift is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {N : Type.{u2}} [_inst_3 : SeminormedAddCommGroup.{u2} N] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (f : NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3), (forall (s : M), (Membership.Mem.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))) s S) -> (Eq.{succ u2} N (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) (fun (_x : NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) => M -> N) (NormedAddGroupHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_3) f s) (OfNat.ofNat.{u2} N 0 (OfNat.mk.{u2} N 0 (Zero.zero.{u2} N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (SeminormedAddGroup.toAddGroup.{u2} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} N _inst_3))))))))))) -> (NormedAddGroupHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) N (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S) _inst_3)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.lift NormedAddGroupHom.liftₓ'. -/
 /-- Given  `f : normed_add_group_hom M N` such that `f s = 0` for all `s ∈ S`, where,
 `S : add_subgroup M` is closed, the induced morphism `normed_add_group_hom (M ⧸ S) N`. -/
 noncomputable def lift {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
@@ -480,12 +626,24 @@ noncomputable def lift {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup
          }
 #align normed_add_group_hom.lift NormedAddGroupHom.lift
 
+/- warning: normed_add_group_hom.lift_mk -> NormedAddGroupHom.lift_mk is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {N : Type.{u2}} [_inst_3 : SeminormedAddCommGroup.{u2} N] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (f : NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) (hf : forall (s : M), (Membership.Mem.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (SetLike.hasMem.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.setLike.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))) s S) -> (Eq.{succ u2} N (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) (fun (_x : NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) => M -> N) (NormedAddGroupHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_3) f s) (OfNat.ofNat.{u2} N 0 (OfNat.mk.{u2} N 0 (Zero.zero.{u2} N (AddZeroClass.toHasZero.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (SeminormedAddGroup.toAddGroup.{u2} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} N _inst_3))))))))))) (m : M), Eq.{succ u2} N (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) N (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S) _inst_3) (fun (_x : NormedAddGroupHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) N (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S) _inst_3) => (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) -> N) (NormedAddGroupHom.hasCoeToFun.{u1, u2} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) N (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S) _inst_3) (NormedAddGroupHom.lift.{u1, u2} M _inst_1 N _inst_3 S f hf) (coeFn.{succ u1, succ u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (fun (_x : NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) => M -> (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S)) (NormedAddGroupHom.hasCoeToFun.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (quotientAddGroup.Subgroup.hasQuotient.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) (AddSubgroup.normedMk.{u1} M _inst_1 S) m)) (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) (fun (_x : NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) => M -> N) (NormedAddGroupHom.hasCoeToFun.{u1, u2} M N _inst_1 _inst_3) f m)
+but is expected to have type
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {N : Type.{u2}} [_inst_3 : SeminormedAddCommGroup.{u2} N] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (f : NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) (hf : forall (s : M), (Membership.mem.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))) s S) -> (Eq.{succ u2} N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) M (fun (_x : M) => N) (AddHomClass.toFunLike.{max u1 u2, u1, u2} (NormedAddGroupHom.{u1, u2} M 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(NormedAddGroupHom.toAddMonoidHomClass.{u1, u2} M N _inst_1 _inst_3))) f s) (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)))))))))) (m : M), Eq.{succ u2} N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (NormedAddGroupHom.{u1, u2} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) N (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S) _inst_3) (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M 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(SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SeminormedAddGroup.toAddGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S))))))) (AddMonoidHomClass.toAddHomClass.{u1, u1, u1} (NormedAddGroupHom.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)) M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SubNegMonoid.toAddMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddGroup.toSubNegMonoid.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SeminormedAddGroup.toAddGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)))))) (NormedAddGroupHom.toAddMonoidHomClass.{u1, u1} M (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) _inst_1 (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S)))) (AddSubgroup.normedMk.{u1} M _inst_1 S) m)) (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) M (fun (_x : M) => N) (AddHomClass.toFunLike.{max u1 u2, u1, u2} (NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) M N (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (SeminormedAddGroup.toAddGroup.{u2} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} N _inst_3)))))) (AddMonoidHomClass.toAddHomClass.{max u1 u2, u1, u2} (NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) M N (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (SeminormedAddGroup.toAddGroup.{u2} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} N _inst_3))))) (NormedAddGroupHom.toAddMonoidHomClass.{u1, u2} M N _inst_1 _inst_3))) f m)
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.lift_mk NormedAddGroupHom.lift_mkₓ'. -/
 theorem lift_mk {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (m : M) :
     lift S f hf (S.normedMk m) = f m :=
   rfl
 #align normed_add_group_hom.lift_mk NormedAddGroupHom.lift_mk
 
+/- warning: normed_add_group_hom.lift_unique -> NormedAddGroupHom.lift_unique is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.lift_unique NormedAddGroupHom.lift_uniqueₓ'. -/
 theorem lift_unique {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (g : NormedAddGroupHom (M ⧸ S) N) :
     g.comp S.normedMk = f → g = lift S f hf :=
@@ -497,11 +655,19 @@ theorem lift_unique {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
   simpa only [h]
 #align normed_add_group_hom.lift_unique NormedAddGroupHom.lift_unique
 
+#print NormedAddGroupHom.isQuotientQuotient /-
 /-- `S.normed_mk` satisfies `is_quotient`. -/
 theorem isQuotientQuotient (S : AddSubgroup M) : IsQuotient S.normedMk :=
   ⟨S.surjective_normedMk, fun m => by simpa [S.ker_normed_mk] using quotient_norm_mk_eq _ m⟩
 #align normed_add_group_hom.is_quotient_quotient NormedAddGroupHom.isQuotientQuotient
+-/
 
+/- warning: normed_add_group_hom.is_quotient.norm_lift -> NormedAddGroupHom.IsQuotient.norm_lift is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.is_quotient.norm_lift NormedAddGroupHom.IsQuotient.norm_liftₓ'. -/
 theorem IsQuotient.norm_lift {f : NormedAddGroupHom M N} (hquot : IsQuotient f) {ε : ℝ} (hε : 0 < ε)
     (n : N) : ∃ m : M, f m = n ∧ ‖m‖ < ‖n‖ + ε :=
   by
@@ -516,6 +682,12 @@ theorem IsQuotient.norm_lift {f : NormedAddGroupHom M N} (hquot : IsQuotient f)
     ⟨m + x, by rw [map_add, (NormedAddGroupHom.mem_ker f x).mp hx, add_zero], by rwa [hquot.norm]⟩
 #align normed_add_group_hom.is_quotient.norm_lift NormedAddGroupHom.IsQuotient.norm_lift
 
+/- warning: normed_add_group_hom.is_quotient.norm_le -> NormedAddGroupHom.IsQuotient.norm_le is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.is_quotient.norm_le NormedAddGroupHom.IsQuotient.norm_leₓ'. -/
 theorem IsQuotient.norm_le {f : NormedAddGroupHom M N} (hquot : IsQuotient f) (m : M) :
     ‖f m‖ ≤ ‖m‖ := by
   rw [hquot.norm]
@@ -526,6 +698,12 @@ theorem IsQuotient.norm_le {f : NormedAddGroupHom M N} (hquot : IsQuotient f) (m
   · exact ⟨0, f.ker.zero_mem, by simp⟩
 #align normed_add_group_hom.is_quotient.norm_le NormedAddGroupHom.IsQuotient.norm_le
 
+/- warning: normed_add_group_hom.lift_norm_le -> NormedAddGroupHom.lift_norm_le is a dubious translation:
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+but is expected to have type
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 theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) {c : ℝ≥0} (fb : ‖f‖ ≤ c) :
     ‖lift S f hf‖ ≤ c := by
@@ -556,6 +734,12 @@ theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
       exact_mod_cast hc.ne'
 #align normed_add_group_hom.lift_norm_le NormedAddGroupHom.lift_norm_le
 
+/- warning: normed_add_group_hom.lift_norm_noninc -> NormedAddGroupHom.lift_normNoninc is a dubious translation:
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+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {N : Type.{u2}} [_inst_3 : SeminormedAddCommGroup.{u2} N] (S : AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (f : NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) (hf : forall (s : M), (Membership.mem.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (SetLike.instMembership.{u1, u1} (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) M (AddSubgroup.instSetLikeAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))) s S) -> (Eq.{succ u2} N (FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) M (fun (_x : M) => N) (AddHomClass.toFunLike.{max u1 u2, u1, u2} (NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) M N (AddZeroClass.toAdd.{u1} M (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1)))))) (AddZeroClass.toAdd.{u2} N (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (SeminormedAddGroup.toAddGroup.{u2} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} N _inst_3)))))) (AddMonoidHomClass.toAddHomClass.{max u1 u2, u1, u2} (NormedAddGroupHom.{u1, u2} M N _inst_1 _inst_3) M N (AddMonoid.toAddZeroClass.{u1} M (SubNegMonoid.toAddMonoid.{u1} M (AddGroup.toSubNegMonoid.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))))) (AddMonoid.toAddZeroClass.{u2} N (SubNegMonoid.toAddMonoid.{u2} N (AddGroup.toSubNegMonoid.{u2} N (SeminormedAddGroup.toAddGroup.{u2} N (SeminormedAddCommGroup.toSeminormedAddGroup.{u2} N _inst_3))))) (NormedAddGroupHom.toAddMonoidHomClass.{u1, u2} M N _inst_1 _inst_3))) f s) (OfNat.ofNat.{u2} N 0 (Zero.toOfNat0.{u2} N (NegZeroClass.toZero.{u2} N (SubNegZeroMonoid.toNegZeroClass.{u2} N (SubtractionMonoid.toSubNegZeroMonoid.{u2} N (SubtractionCommMonoid.toSubtractionMonoid.{u2} N (AddCommGroup.toDivisionAddCommMonoid.{u2} N (SeminormedAddCommGroup.toAddCommGroup.{u2} N _inst_3)))))))))), (NormedAddGroupHom.NormNoninc.{u1, u2} M N _inst_1 _inst_3 f) -> (NormedAddGroupHom.NormNoninc.{u1, u2} (HasQuotient.Quotient.{u1, u1} M (AddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) (QuotientAddGroup.instHasQuotientAddSubgroup.{u1} M (SeminormedAddGroup.toAddGroup.{u1} M (SeminormedAddCommGroup.toSeminormedAddGroup.{u1} M _inst_1))) S) N (AddSubgroup.seminormedAddCommGroupQuotient.{u1} M _inst_1 S) _inst_3 (NormedAddGroupHom.lift.{u1, u2} M _inst_1 N _inst_3 S f hf))
+Case conversion may be inaccurate. Consider using '#align normed_add_group_hom.lift_norm_noninc NormedAddGroupHom.lift_normNonincₓ'. -/
 theorem lift_normNoninc {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (fb : f.NormNoninc) :
     (lift S f hf).NormNoninc := fun x =>
@@ -585,19 +769,31 @@ section Submodule
 
 variable {R : Type _} [Ring R] [Module R M] (S : Submodule R M)
 
+#print Submodule.Quotient.seminormedAddCommGroup /-
 instance Submodule.Quotient.seminormedAddCommGroup : SeminormedAddCommGroup (M ⧸ S) :=
   AddSubgroup.seminormedAddCommGroupQuotient S.toAddSubgroup
 #align submodule.quotient.seminormed_add_comm_group Submodule.Quotient.seminormedAddCommGroup
+-/
 
+#print Submodule.Quotient.normedAddCommGroup /-
 instance Submodule.Quotient.normedAddCommGroup [hS : IsClosed (S : Set M)] :
     NormedAddCommGroup (M ⧸ S) :=
   @AddSubgroup.normedAddCommGroupQuotient _ _ S.toAddSubgroup hS
 #align submodule.quotient.normed_add_comm_group Submodule.Quotient.normedAddCommGroup
+-/
 
+#print Submodule.Quotient.completeSpace /-
 instance Submodule.Quotient.completeSpace [CompleteSpace M] : CompleteSpace (M ⧸ S) :=
   QuotientAddGroup.completeSpace M S.toAddSubgroup
 #align submodule.quotient.complete_space Submodule.Quotient.completeSpace
+-/
 
+/- warning: submodule.quotient.norm_mk_lt -> Submodule.Quotient.norm_mk_lt is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align submodule.quotient.norm_mk_lt Submodule.Quotient.norm_mk_ltₓ'. -/
 /-- For any `x : M ⧸ S` and any `0 < ε`, there is `m : M` such that `submodule.quotient.mk m = x`
 and `‖m‖ < ‖x‖ + ε`. -/
 theorem Submodule.Quotient.norm_mk_lt {S : Submodule R M} (x : M ⧸ S) {ε : ℝ} (hε : 0 < ε) :
@@ -605,10 +801,17 @@ theorem Submodule.Quotient.norm_mk_lt {S : Submodule R M} (x : M ⧸ S) {ε : 
   norm_mk_lt x hε
 #align submodule.quotient.norm_mk_lt Submodule.Quotient.norm_mk_lt
 
+/- warning: submodule.quotient.norm_mk_le -> Submodule.Quotient.norm_mk_le is a dubious translation:
+lean 3 declaration is
+  forall {M : Type.{u1}} [_inst_1 : SeminormedAddCommGroup.{u1} M] {R : Type.{u2}} [_inst_3 : Ring.{u2} R] [_inst_4 : Module.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1))] (S : Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1)) _inst_4) (m : M), LE.le.{0} Real Real.hasLe (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1)) _inst_4) (Submodule.hasQuotient.{u2, u1} R M _inst_3 (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) _inst_4) S) (SeminormedAddCommGroup.toHasNorm.{u1} (HasQuotient.Quotient.{u1, u1} M (Submodule.{u2, u1} R M (Ring.toSemiring.{u2} R _inst_3) (AddCommGroup.toAddCommMonoid.{u1} M (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1)) _inst_4) (Submodule.hasQuotient.{u2, u1} R M _inst_3 (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) _inst_4) S) (Submodule.Quotient.seminormedAddCommGroup.{u1, u2} M _inst_1 R _inst_3 _inst_4 S)) (Submodule.Quotient.mk.{u2, u1} R M _inst_3 (SeminormedAddCommGroup.toAddCommGroup.{u1} M _inst_1) _inst_4 S m)) (Norm.norm.{u1} M (SeminormedAddCommGroup.toHasNorm.{u1} M _inst_1) m)
+but is expected to have type
+  forall {M : Type.{u2}} [_inst_1 : SeminormedAddCommGroup.{u2} M] {R : Type.{u1}} [_inst_3 : Ring.{u1} R] [_inst_4 : Module.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_1))] (S : Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_1)) _inst_4) (m : M), LE.le.{0} Real Real.instLEReal (Norm.norm.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_1)) _inst_4) (Submodule.hasQuotient.{u1, u2} R M _inst_3 (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_1) _inst_4) S) (SeminormedAddCommGroup.toNorm.{u2} (HasQuotient.Quotient.{u2, u2} M (Submodule.{u1, u2} R M (Ring.toSemiring.{u1} R _inst_3) (AddCommGroup.toAddCommMonoid.{u2} M (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_1)) _inst_4) (Submodule.hasQuotient.{u1, u2} R M _inst_3 (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_1) _inst_4) S) (Submodule.Quotient.seminormedAddCommGroup.{u2, u1} M _inst_1 R _inst_3 _inst_4 S)) (Submodule.Quotient.mk.{u1, u2} R M _inst_3 (SeminormedAddCommGroup.toAddCommGroup.{u2} M _inst_1) _inst_4 S m)) (Norm.norm.{u2} M (SeminormedAddCommGroup.toNorm.{u2} M _inst_1) m)
+Case conversion may be inaccurate. Consider using '#align submodule.quotient.norm_mk_le Submodule.Quotient.norm_mk_leₓ'. -/
 theorem Submodule.Quotient.norm_mk_le (m : M) : ‖(Submodule.Quotient.mk m : M ⧸ S)‖ ≤ ‖m‖ :=
   quotient_norm_mk_le S.toAddSubgroup m
 #align submodule.quotient.norm_mk_le Submodule.Quotient.norm_mk_le
 
+#print Submodule.Quotient.normedSpace /-
 instance Submodule.Quotient.normedSpace (𝕜 : Type _) [NormedField 𝕜] [NormedSpace 𝕜 M] [SMul 𝕜 R]
     [IsScalarTower 𝕜 R M] : NormedSpace 𝕜 (M ⧸ S) :=
   { Submodule.Quotient.module' S with
@@ -627,6 +830,7 @@ instance Submodule.Quotient.normedSpace (𝕜 : Type _) [NormedField 𝕜] [Norm
           _ ≤ _ := (sub_lt_iff_lt_add'.mp h.1).le
            }
 #align submodule.quotient.normed_space Submodule.Quotient.normedSpace
+-/
 
 end Submodule
 
@@ -634,15 +838,28 @@ section Ideal
 
 variable {R : Type _} [SeminormedCommRing R] (I : Ideal R)
 
+/- warning: ideal.quotient.norm_mk_lt -> Ideal.Quotient.norm_mk_lt is a dubious translation:
+lean 3 declaration is
+  forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))} (x : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) {ε : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) ε) -> (Exists.{succ u1} R (fun (r : R) => And (Eq.{succ u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (coeFn.{succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R 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(SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (fun (_x : RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) => R -> (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I)) (RingHom.hasCoeToFun.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (Ideal.Quotient.mk.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I) r) x) (LT.lt.{0} Real Real.hasLt (Norm.norm.{u1} R (SeminormedRing.toHasNorm.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)) r) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) (Norm.norm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (SeminormedAddCommGroup.toHasNorm.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) (Ideal.hasQuotient.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Submodule.Quotient.seminormedAddCommGroup.{u1, u1} R (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{u1} R (SeminormedRing.toNonUnitalSeminormedRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3))) R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)) (Semiring.toModule.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSemiNormedRing.{u1} R _inst_3)))) I)) x) ε))))
+but is expected to have type
+  forall {R : Type.{u1}} [_inst_3 : SeminormedCommRing.{u1} R] {I : Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)))} (x : HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (SeminormedRing.toRing.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) {ε : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) ε) -> (Exists.{succ u1} R (fun (r : R) => And (Eq.{succ u1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) r) (FunLike.coe.{succ u1, succ u1, succ u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (fun (_x : R) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.2391 : R) => HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) _x) (MulHomClass.toFunLike.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R 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+Case conversion may be inaccurate. Consider using '#align ideal.quotient.norm_mk_lt Ideal.Quotient.norm_mk_ltₓ'. -/
 theorem Ideal.Quotient.norm_mk_lt {I : Ideal R} (x : R ⧸ I) {ε : ℝ} (hε : 0 < ε) :
     ∃ r : R, Ideal.Quotient.mk I r = x ∧ ‖r‖ < ‖x‖ + ε :=
   norm_mk_lt x hε
 #align ideal.quotient.norm_mk_lt Ideal.Quotient.norm_mk_lt
 
+/- warning: ideal.quotient.norm_mk_le -> Ideal.Quotient.norm_mk_le is a dubious translation:
+lean 3 declaration is
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_inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonUnitalNonAssocSemiring.toMul.{u1} R (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))))) (NonUnitalNonAssocSemiring.toMul.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))) (NonUnitalRingHomClass.toMulHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} R (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3))))) (NonAssocSemiring.toNonUnitalNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) (RingHomClass.toNonUnitalRingHomClass.{u1, u1, u1} (RingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I))))) R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))) (RingHom.instRingHomClassRingHom.{u1, u1} R (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (NonAssocRing.toNonAssocSemiring.{u1} R (Ring.toNonAssocRing.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (NonAssocRing.toNonAssocSemiring.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ring.toNonAssocRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (CommRing.toRing.{u1} (HasQuotient.Quotient.{u1, u1} R (Ideal.{u1} R (Ring.toSemiring.{u1} R (CommRing.toRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)))) (Ideal.instHasQuotientIdealToSemiringToRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3)) I) (Ideal.Quotient.commRing.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I)))))))) (Ideal.Quotient.mk.{u1} R (SeminormedCommRing.toCommRing.{u1} R _inst_3) I) r)) (Norm.norm.{u1} R (SeminormedRing.toNorm.{u1} R (SeminormedCommRing.toSeminormedRing.{u1} R _inst_3)) r)
+Case conversion may be inaccurate. Consider using '#align ideal.quotient.norm_mk_le Ideal.Quotient.norm_mk_leₓ'. -/
 theorem Ideal.Quotient.norm_mk_le (r : R) : ‖Ideal.Quotient.mk I r‖ ≤ ‖r‖ :=
   quotient_norm_mk_le I.toAddSubgroup r
 #align ideal.quotient.norm_mk_le Ideal.Quotient.norm_mk_le
 
+#print Ideal.Quotient.semiNormedCommRing /-
 instance Ideal.Quotient.semiNormedCommRing : SeminormedCommRing (R ⧸ I) :=
   {
     Submodule.Quotient.seminormedAddCommGroup
@@ -667,16 +884,21 @@ instance Ideal.Quotient.semiNormedCommRing : SeminormedCommRing (R ⧸ I) :=
           _ ≤ _ := (sub_lt_iff_lt_add'.mp h.1).le
            }
 #align ideal.quotient.semi_normed_comm_ring Ideal.Quotient.semiNormedCommRing
+-/
 
+#print Ideal.Quotient.normedCommRing /-
 instance Ideal.Quotient.normedCommRing [IsClosed (I : Set R)] : NormedCommRing (R ⧸ I) :=
   { Ideal.Quotient.semiNormedCommRing I, Submodule.Quotient.normedAddCommGroup I with }
 #align ideal.quotient.normed_comm_ring Ideal.Quotient.normedCommRing
+-/
 
 variable (𝕜 : Type _) [NormedField 𝕜]
 
+#print Ideal.Quotient.normedAlgebra /-
 instance Ideal.Quotient.normedAlgebra [NormedAlgebra 𝕜 R] : NormedAlgebra 𝕜 (R ⧸ I) :=
   { Submodule.Quotient.normedSpace I 𝕜, Ideal.Quotient.algebra 𝕜 with }
 #align ideal.quotient.normed_algebra Ideal.Quotient.normedAlgebra
+-/
 
 end Ideal
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Riccardo Brasca
 
 ! This file was ported from Lean 3 source module analysis.normed.group.quotient
-! leanprover-community/mathlib commit e7f0ddbf65bd7181a85edb74b64bdc35ba4bdc74
+! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -140,7 +140,7 @@ theorem quotient_norm_neg {S : AddSubgroup M} (x : M ⧸ S) : ‖-x‖ = ‖x‖
     rw [← norm_neg]
     exact ⟨-m, by simp only [(mk' S).map_neg, Set.mem_setOf_eq], rfl⟩
   · rintro ⟨m, hm : mk' S m = -x, rfl⟩
-    exact ⟨-m, by simpa [eq_comm] using eq_neg_iff_eq_neg.mp ((mk'_apply _ _).symm.trans hm)⟩
+    exact ⟨-m, by simpa using neg_eq_iff_eq_neg.mpr ((mk'_apply _ _).symm.trans hm)⟩
 #align quotient_norm_neg quotient_norm_neg
 
 theorem quotient_norm_sub_rev {S : AddSubgroup M} (x y : M ⧸ S) : ‖x - y‖ = ‖y - x‖ := by

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

@@ -632,7 +632,7 @@ end Submodule
 
 section Ideal
 
-variable {R : Type _} [SemiNormedCommRing R] (I : Ideal R)
+variable {R : Type _} [SeminormedCommRing R] (I : Ideal R)
 
 theorem Ideal.Quotient.norm_mk_lt {I : Ideal R} (x : R ⧸ I) {ε : ℝ} (hε : 0 < ε) :
     ∃ r : R, Ideal.Quotient.mk I r = x ∧ ‖r‖ < ‖x‖ + ε :=
@@ -643,7 +643,7 @@ theorem Ideal.Quotient.norm_mk_le (r : R) : ‖Ideal.Quotient.mk I r‖ ≤ ‖r
   quotient_norm_mk_le I.toAddSubgroup r
 #align ideal.quotient.norm_mk_le Ideal.Quotient.norm_mk_le
 
-instance Ideal.Quotient.semiNormedCommRing : SemiNormedCommRing (R ⧸ I) :=
+instance Ideal.Quotient.semiNormedCommRing : SeminormedCommRing (R ⧸ I) :=
   {
     Submodule.Quotient.seminormedAddCommGroup
       I with

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -449,7 +449,7 @@ theorem norm_trivial_quotient_mk (S : AddSubgroup M)
     rw [S.ker_normed_mk]
     exact Set.mem_of_eq_of_mem h trivial
   rw [ker_normed_mk] at hker
-  simp only [(quotient_norm_eq_zero_iff S x).mpr hker, normed_mk.apply, zero_mul]
+  simp only [(quotient_norm_eq_zero_iff S x).mpr hker, normed_mk.apply, MulZeroClass.zero_mul]
 #align add_subgroup.norm_trivial_quotient_mk AddSubgroup.norm_trivial_quotient_mk
 
 end AddSubgroup
@@ -532,12 +532,12 @@ theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
   apply op_norm_le_bound _ c.coe_nonneg
   intro x
   by_cases hc : c = 0
-  · simp only [hc, NNReal.coe_zero, zero_mul] at fb⊢
+  · simp only [hc, NNReal.coe_zero, MulZeroClass.zero_mul] at fb⊢
     obtain ⟨x, rfl⟩ := surjective_quot_mk _ x
     show ‖f x‖ ≤ 0
     calc
       ‖f x‖ ≤ 0 * ‖x‖ := f.le_of_op_norm_le fb x
-      _ = 0 := zero_mul _
+      _ = 0 := MulZeroClass.zero_mul _
       
   · replace hc : 0 < c := pos_iff_ne_zero.mpr hc
     apply le_of_forall_pos_le_add

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

@@ -393,7 +393,7 @@ theorem ker_normedMk (S : AddSubgroup M) : S.normedMk.ker = S :=
 
 /-- The operator norm of the projection is at most `1`. -/
 theorem norm_normedMk_le (S : AddSubgroup M) : ‖S.normedMk‖ ≤ 1 :=
-  NormedAddGroupHom.op_norm_le_bound _ zero_le_one fun m => by simp [quotient_norm_mk_le']
+  NormedAddGroupHom.opNorm_le_bound _ zero_le_one fun m => by simp [quotient_norm_mk_le']
 #align add_subgroup.norm_normed_mk_le AddSubgroup.norm_normedMk_le
 
 /-- The operator norm of the projection is `1` if the subspace is not dense. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

@@ -104,7 +104,7 @@ open Topology NNReal
 variable {M N : Type _} [SeminormedAddCommGroup M] [SeminormedAddCommGroup N]
 
 /-- The definition of the norm on the quotient by an additive subgroup. -/
-noncomputable instance normOnQuotient (S : AddSubgroup M) : HasNorm (M ⧸ S)
+noncomputable instance normOnQuotient (S : AddSubgroup M) : Norm (M ⧸ S)
     where norm x := infₛ (norm '' { m | mk' S m = x })
 #align norm_on_quotient normOnQuotient
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

@@ -4,12 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Riccardo Brasca
 
 ! This file was ported from Lean 3 source module analysis.normed.group.quotient
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit e7f0ddbf65bd7181a85edb74b64bdc35ba4bdc74
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.NormedSpace.Basic
 import Mathbin.Analysis.Normed.Group.Hom
+import Mathbin.RingTheory.Ideal.QuotientOperations
 
 /-!
 # Quotients of seminormed groups

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -252,8 +252,8 @@ theorem quotient_norm_add_le (S : AddSubgroup M) (x y : M ⧸ S) : ‖x + y‖ 
   obtain ⟨n, rfl, hn : ‖n‖ < ‖mk' S n‖ + ε / 2⟩ := norm_mk_lt y hε
   calc
     ‖mk' S m + mk' S n‖ = ‖mk' S (m + n)‖ := by rw [(mk' S).map_add]
-    _ ≤ ‖m + n‖ := quotient_norm_mk_le S (m + n)
-    _ ≤ ‖m‖ + ‖n‖ := norm_add_le _ _
+    _ ≤ ‖m + n‖ := (quotient_norm_mk_le S (m + n))
+    _ ≤ ‖m‖ + ‖n‖ := (norm_add_le _ _)
     _ ≤ ‖mk' S m‖ + ‖mk' S n‖ + ε := by linarith
     
 #align quotient_norm_add_le quotient_norm_add_le
@@ -433,7 +433,7 @@ theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) 
   calc
     ‖S.normed_mk‖ ≥ ‖S.normed_mk m‖ / ‖m‖ := ratio_le_op_norm S.normed_mk m
     _ = ‖y‖ / ‖m‖ := by rw [normed_mk.apply, hm]
-    _ ≥ (1 + min ε (1 / 2) / (1 - min ε (1 / 2)))⁻¹ := le_of_lt hlt
+    _ ≥ (1 + min ε (1 / 2) / (1 - min ε (1 / 2)))⁻¹ := (le_of_lt hlt)
     _ = 1 - min ε (1 / 2) := by field_simp [(ne_of_lt hδ).symm]
     
 #align add_subgroup.norm_normed_mk AddSubgroup.norm_normedMk
@@ -547,7 +547,7 @@ theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     rw [lift_mk]
     calc
       ‖f x‖ ≤ c * ‖x‖ := f.le_of_op_norm_le fb x
-      _ ≤ c * (‖S.normed_mk x‖ + ε / c) := (mul_le_mul_left _).mpr Hx.le
+      _ ≤ c * (‖S.normed_mk x‖ + ε / c) := ((mul_le_mul_left _).mpr Hx.le)
       _ = c * _ + ε := _
       
     · exact_mod_cast hc

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -594,7 +594,7 @@ instance Submodule.Quotient.normedAddCommGroup [hS : IsClosed (S : Set M)] :
 #align submodule.quotient.normed_add_comm_group Submodule.Quotient.normedAddCommGroup
 
 instance Submodule.Quotient.completeSpace [CompleteSpace M] : CompleteSpace (M ⧸ S) :=
-  quotientAddGroup.completeSpace M S.toAddSubgroup
+  QuotientAddGroup.completeSpace M S.toAddSubgroup
 #align submodule.quotient.complete_space Submodule.Quotient.completeSpace
 
 /-- For any `x : M ⧸ S` and any `0 < ε`, there is `m : M` such that `submodule.quotient.mk m = x`

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

Classifies by adding issue number #10756 to porting notes claiming anything semantically equivalent to:

• "new lemma"
• "added lemma"

@@ -398,7 +398,7 @@ theorem IsQuotient.norm_le {f : NormedAddGroupHom M N} (hquot : IsQuotient f) (m
   · exact ⟨0, f.ker.zero_mem, by simp⟩
 #align normed_add_group_hom.is_quotient.norm_le NormedAddGroupHom.IsQuotient.norm_le
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem norm_lift_le {N : Type*} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) :
     ‖lift S f hf‖ ≤ ‖f‖ :=

Classifies by adding issue number #11215 to porting notes claiming "TODO".

@@ -404,7 +404,7 @@ theorem norm_lift_le {N : Type*} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     ‖lift S f hf‖ ≤ ‖f‖ :=
   opNorm_le_bound _ (norm_nonneg f) (norm_lift_apply_le f hf)
 
--- Porting note: todo: deprecate?
+-- Porting note (#11215): TODO: deprecate?
 theorem lift_norm_le {N : Type*} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) {c : ℝ≥0} (fb : ‖f‖ ≤ c) :
     ‖lift S f hf‖ ≤ c :=

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

@@ -130,7 +130,7 @@ theorem image_norm_nonempty {S : AddSubgroup M} (x : M ⧸ S) :
 #align image_norm_nonempty image_norm_nonempty
 
 theorem bddBelow_image_norm (s : Set M) : BddBelow (norm '' s) :=
-  ⟨0, ball_image_iff.2 fun _ _ ↦ norm_nonneg _⟩
+  ⟨0, forall_mem_image.2 fun _ _ ↦ norm_nonneg _⟩
 #align bdd_below_image_norm bddBelow_image_norm
 
 theorem isGLB_quotient_norm {S : AddSubgroup M} (x : M ⧸ S) :
@@ -168,7 +168,7 @@ theorem quotient_norm_mk_eq (S : AddSubgroup M) (m : M) :
 
 /-- The quotient norm is nonnegative. -/
 theorem quotient_norm_nonneg (S : AddSubgroup M) (x : M ⧸ S) : 0 ≤ ‖x‖ :=
-  Real.sInf_nonneg _ <| ball_image_iff.2 fun _ _ ↦ norm_nonneg _
+  Real.sInf_nonneg _ <| forall_mem_image.2 fun _ _ ↦ norm_nonneg _
 #align quotient_norm_nonneg quotient_norm_nonneg
 
 /-- The quotient norm is nonnegative. -/
@@ -186,7 +186,7 @@ theorem quotient_norm_eq_zero_iff (S : AddSubgroup M) (m : M) :
 
 theorem QuotientAddGroup.norm_lt_iff {S : AddSubgroup M} {x : M ⧸ S} {r : ℝ} :
     ‖x‖ < r ↔ ∃ m : M, ↑m = x ∧ ‖m‖ < r := by
-  rw [isGLB_lt_iff (isGLB_quotient_norm _), bex_image_iff]
+  rw [isGLB_lt_iff (isGLB_quotient_norm _), exists_mem_image]
   rfl
 
 /-- For any `x : M ⧸ S` and any `0 < ε`, there is `m : M` such that `mk' S m = x`
@@ -211,7 +211,7 @@ theorem quotient_norm_add_le (S : AddSubgroup M) (x y : M ⧸ S) : ‖x + y‖ 
   rcases And.intro (mk_surjective x) (mk_surjective y) with ⟨⟨x, rfl⟩, ⟨y, rfl⟩⟩
   simp only [← mk'_apply, ← map_add, quotient_norm_mk_eq, sInf_image']
   refine le_ciInf_add_ciInf fun a b ↦ ?_
-  refine ciInf_le_of_le ⟨0, forall_range_iff.2 fun _ ↦ norm_nonneg _⟩ (a + b) ?_
+  refine ciInf_le_of_le ⟨0, forall_mem_range.2 fun _ ↦ norm_nonneg _⟩ (a + b) ?_
   exact (congr_arg norm (add_add_add_comm _ _ _ _)).trans_le (norm_add_le _ _)
 #align quotient_norm_add_le quotient_norm_add_le
 

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -398,13 +398,13 @@ theorem IsQuotient.norm_le {f : NormedAddGroupHom M N} (hquot : IsQuotient f) (m
   · exact ⟨0, f.ker.zero_mem, by simp⟩
 #align normed_add_group_hom.is_quotient.norm_le NormedAddGroupHom.IsQuotient.norm_le
 
--- porting note: new lemma
+-- Porting note: new lemma
 theorem norm_lift_le {N : Type*} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) :
     ‖lift S f hf‖ ≤ ‖f‖ :=
   opNorm_le_bound _ (norm_nonneg f) (norm_lift_apply_le f hf)
 
--- porting note: todo: deprecate?
+-- Porting note: todo: deprecate?
 theorem lift_norm_le {N : Type*} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) {c : ℝ≥0} (fb : ‖f‖ ≤ c) :
     ‖lift S f hf‖ ≤ c :=
@@ -466,7 +466,7 @@ instance Submodule.Quotient.instBoundedSMul (𝕜 : Type*)
     [SeminormedCommRing 𝕜] [Module 𝕜 M] [BoundedSMul 𝕜 M] [SMul 𝕜 R] [IsScalarTower 𝕜 R M] :
     BoundedSMul 𝕜 (M ⧸ S) :=
   .of_norm_smul_le fun k x =>
-    -- porting note: this is `QuotientAddGroup.norm_lift_apply_le` for `f : M → M ⧸ S` given by
+    -- Porting note: this is `QuotientAddGroup.norm_lift_apply_le` for `f : M → M ⧸ S` given by
     -- `x ↦ mk (k • x)`; todo: add scalar multiplication as `NormedAddGroupHom`, use it here
     _root_.le_of_forall_pos_le_add fun ε hε => by
       have := (nhds_basis_ball.tendsto_iff nhds_basis_ball).mp

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

@@ -318,8 +318,8 @@ theorem _root_.QuotientAddGroup.norm_lift_apply_le {S : AddSubgroup M} (f : Norm
 theorem norm_normedMk (S : AddSubgroup M) (h : (S.topologicalClosure : Set M) ≠ univ) :
     ‖S.normedMk‖ = 1 := by
   refine le_antisymm (norm_normedMk_le S) ?_
-  obtain ⟨x, hx⟩ : ∃ x : M, 0 < ‖(x : M ⧸ S)‖
-  · refine (Set.nonempty_compl.2 h).imp fun x hx ↦ ?_
+  obtain ⟨x, hx⟩ : ∃ x : M, 0 < ‖(x : M ⧸ S)‖ := by
+    refine (Set.nonempty_compl.2 h).imp fun x hx ↦ ?_
     exact (norm_nonneg _).lt_of_ne' <| mt (quotient_norm_eq_zero_iff S x).1 hx
   refine (le_mul_iff_one_le_left hx).1 ?_
   exact norm_lift_apply_le S.normedMk (fun x ↦ (eq_zero_iff x).2) x

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -229,8 +229,8 @@ theorem norm_mk_eq_zero (S : AddSubgroup M) (hS : IsClosed (S : Set M)) (m : M)
 
 theorem quotient_nhd_basis (S : AddSubgroup M) :
     (𝓝 (0 : M ⧸ S)).HasBasis (fun ε ↦ 0 < ε) fun ε ↦ { x | ‖x‖ < ε } := by
-  have : ∀ ε : ℝ, mk '' ball (0 : M) ε = { x : M ⧸ S | ‖x‖ < ε }
-  · refine fun ε ↦ Set.ext <| forall_mk.2 fun x ↦ ?_
+  have : ∀ ε : ℝ, mk '' ball (0 : M) ε = { x : M ⧸ S | ‖x‖ < ε } := by
+    refine fun ε ↦ Set.ext <| forall_mk.2 fun x ↦ ?_
     rw [ball_zero_eq, mem_setOf_eq, norm_lt_iff, mem_image]
     exact exists_congr fun _ ↦ and_comm
   rw [← mk_zero, nhds_eq, ← funext this]

The proof needs minimal modifications to go through for the inequality case.

@@ -462,22 +462,26 @@ theorem Submodule.Quotient.norm_mk_le (m : M) : ‖(Submodule.Quotient.mk m : M
   quotient_norm_mk_le S.toAddSubgroup m
 #align submodule.quotient.norm_mk_le Submodule.Quotient.norm_mk_le
 
+instance Submodule.Quotient.instBoundedSMul (𝕜 : Type*)
+    [SeminormedCommRing 𝕜] [Module 𝕜 M] [BoundedSMul 𝕜 M] [SMul 𝕜 R] [IsScalarTower 𝕜 R M] :
+    BoundedSMul 𝕜 (M ⧸ S) :=
+  .of_norm_smul_le fun k x =>
+    -- porting note: this is `QuotientAddGroup.norm_lift_apply_le` for `f : M → M ⧸ S` given by
+    -- `x ↦ mk (k • x)`; todo: add scalar multiplication as `NormedAddGroupHom`, use it here
+    _root_.le_of_forall_pos_le_add fun ε hε => by
+      have := (nhds_basis_ball.tendsto_iff nhds_basis_ball).mp
+        ((@Real.uniformContinuous_const_mul ‖k‖).continuous.tendsto ‖x‖) ε hε
+      simp only [mem_ball, exists_prop, dist, abs_sub_lt_iff] at this
+      rcases this with ⟨δ, hδ, h⟩
+      obtain ⟨a, rfl, ha⟩ := Submodule.Quotient.norm_mk_lt x hδ
+      specialize h ‖a‖ ⟨by linarith, by linarith [Submodule.Quotient.norm_mk_le S a]⟩
+      calc
+        _ ≤ ‖k‖ * ‖a‖ := (quotient_norm_mk_le S.toAddSubgroup (k • a)).trans (norm_smul_le k a)
+        _ ≤ _ := (sub_lt_iff_lt_add'.mp h.1).le
+
 instance Submodule.Quotient.normedSpace (𝕜 : Type*) [NormedField 𝕜] [NormedSpace 𝕜 M] [SMul 𝕜 R]
-    [IsScalarTower 𝕜 R M] : NormedSpace 𝕜 (M ⧸ S) :=
-  { Submodule.Quotient.module' S with
-    norm_smul_le := fun k x =>
-      -- porting note: this is `QuotientAddGroup.norm_lift_apply_le` for `f : M → M ⧸ S` given by
-      -- `x ↦ mk (k • x)`; todo: add scalar multiplication as `NormedAddGroupHom`, use it here
-      le_of_forall_pos_le_add fun ε hε => by
-        have := (nhds_basis_ball.tendsto_iff nhds_basis_ball).mp
-          ((@Real.uniformContinuous_const_mul ‖k‖).continuous.tendsto ‖x‖) ε hε
-        simp only [mem_ball, exists_prop, dist, abs_sub_lt_iff] at this
-        rcases this with ⟨δ, hδ, h⟩
-        obtain ⟨a, rfl, ha⟩ := Submodule.Quotient.norm_mk_lt x hδ
-        specialize h ‖a‖ ⟨by linarith, by linarith [Submodule.Quotient.norm_mk_le S a]⟩
-        calc
-          _ ≤ ‖k‖ * ‖a‖ := (quotient_norm_mk_le S.toAddSubgroup (k • a)).trans_eq (norm_smul k a)
-          _ ≤ _ := (sub_lt_iff_lt_add'.mp h.1).le }
+    [IsScalarTower 𝕜 R M] : NormedSpace 𝕜 (M ⧸ S) where
+  norm_smul_le := norm_smul_le
 #align submodule.quotient.normed_space Submodule.Quotient.normedSpace
 
 end Submodule

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -5,6 +5,7 @@ Authors: Patrick Massot, Riccardo Brasca
 -/
 import Mathlib.Analysis.NormedSpace.Basic
 import Mathlib.Analysis.Normed.Group.Hom
+import Mathlib.Data.Real.Sqrt
 import Mathlib.RingTheory.Ideal.QuotientOperations
 import Mathlib.Topology.MetricSpace.HausdorffDistance
 

• rename Finset.Nonempty.image_iff to Finset.image_nonempty, deprecate the old version;
• rename Set.nonempty_image_iff to Set.image_nonempty, deprecate the old version;
• drop unneeded Finset.Nonempty arguments here and there;
• add versions of some lemmas that assume Nonempty s instead of Nonempty (s.image f) or Nonempty (s.map f).

@@ -379,7 +379,7 @@ theorem IsQuotient.norm_lift {f : NormedAddGroupHom M N} (hquot : IsQuotient f)
     (n : N) : ∃ m : M, f m = n ∧ ‖m‖ < ‖n‖ + ε := by
   obtain ⟨m, rfl⟩ := hquot.surjective n
   have nonemp : ((fun m' => ‖m + m'‖) '' f.ker).Nonempty := by
-    rw [Set.nonempty_image_iff]
+    rw [Set.image_nonempty]
     exact ⟨0, f.ker.zero_mem⟩
   rcases Real.lt_sInf_add_pos nonemp hε
     with ⟨_, ⟨⟨x, hx, rfl⟩, H : ‖m + x‖ < sInf ((fun m' : M => ‖m + m'‖) '' f.ker) + ε⟩⟩

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -97,7 +97,7 @@ noncomputable section
 
 open QuotientAddGroup Metric Set Topology NNReal
 
-variable {M N : Type _} [SeminormedAddCommGroup M] [SeminormedAddCommGroup N]
+variable {M N : Type*} [SeminormedAddCommGroup M] [SeminormedAddCommGroup N]
 
 /-- The definition of the norm on the quotient by an additive subgroup. -/
 noncomputable instance normOnQuotient (S : AddSubgroup M) : Norm (M ⧸ S) where
@@ -348,19 +348,19 @@ structure IsQuotient (f : NormedAddGroupHom M N) : Prop where
 
 /-- Given `f : NormedAddGroupHom M N` such that `f s = 0` for all `s ∈ S`, where,
 `S : AddSubgroup M` is closed, the induced morphism `NormedAddGroupHom (M ⧸ S) N`. -/
-noncomputable def lift {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
+noncomputable def lift {N : Type*} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) : NormedAddGroupHom (M ⧸ S) N :=
   { QuotientAddGroup.lift S f.toAddMonoidHom hf with
     bound' := ⟨‖f‖, norm_lift_apply_le f hf⟩ }
 #align normed_add_group_hom.lift NormedAddGroupHom.lift
 
-theorem lift_mk {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
+theorem lift_mk {N : Type*} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (m : M) :
     lift S f hf (S.normedMk m) = f m :=
   rfl
 #align normed_add_group_hom.lift_mk NormedAddGroupHom.lift_mk
 
-theorem lift_unique {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
+theorem lift_unique {N : Type*} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (g : NormedAddGroupHom (M ⧸ S) N)
     (h : g.comp S.normedMk = f) : g = lift S f hf := by
   ext x
@@ -398,19 +398,19 @@ theorem IsQuotient.norm_le {f : NormedAddGroupHom M N} (hquot : IsQuotient f) (m
 #align normed_add_group_hom.is_quotient.norm_le NormedAddGroupHom.IsQuotient.norm_le
 
 -- porting note: new lemma
-theorem norm_lift_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
+theorem norm_lift_le {N : Type*} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) :
     ‖lift S f hf‖ ≤ ‖f‖ :=
   opNorm_le_bound _ (norm_nonneg f) (norm_lift_apply_le f hf)
 
 -- porting note: todo: deprecate?
-theorem lift_norm_le {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
+theorem lift_norm_le {N : Type*} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) {c : ℝ≥0} (fb : ‖f‖ ≤ c) :
     ‖lift S f hf‖ ≤ c :=
   (norm_lift_le S f hf).trans fb
 #align normed_add_group_hom.lift_norm_le NormedAddGroupHom.lift_norm_le
 
-theorem lift_normNoninc {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
+theorem lift_normNoninc {N : Type*} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) (fb : f.NormNoninc) :
     (lift S f hf).NormNoninc := fun x => by
   have fb' : ‖f‖ ≤ (1 : ℝ≥0) := NormNoninc.normNoninc_iff_norm_le_one.mp fb
@@ -435,7 +435,7 @@ have quotients of rings by two-sided ideals, hence the commutativity hypotheses
 
 section Submodule
 
-variable {R : Type _} [Ring R] [Module R M] (S : Submodule R M)
+variable {R : Type*} [Ring R] [Module R M] (S : Submodule R M)
 
 instance Submodule.Quotient.seminormedAddCommGroup : SeminormedAddCommGroup (M ⧸ S) :=
   AddSubgroup.seminormedAddCommGroupQuotient S.toAddSubgroup
@@ -461,7 +461,7 @@ theorem Submodule.Quotient.norm_mk_le (m : M) : ‖(Submodule.Quotient.mk m : M
   quotient_norm_mk_le S.toAddSubgroup m
 #align submodule.quotient.norm_mk_le Submodule.Quotient.norm_mk_le
 
-instance Submodule.Quotient.normedSpace (𝕜 : Type _) [NormedField 𝕜] [NormedSpace 𝕜 M] [SMul 𝕜 R]
+instance Submodule.Quotient.normedSpace (𝕜 : Type*) [NormedField 𝕜] [NormedSpace 𝕜 M] [SMul 𝕜 R]
     [IsScalarTower 𝕜 R M] : NormedSpace 𝕜 (M ⧸ S) :=
   { Submodule.Quotient.module' S with
     norm_smul_le := fun k x =>
@@ -483,7 +483,7 @@ end Submodule
 
 section Ideal
 
-variable {R : Type _} [SeminormedCommRing R] (I : Ideal R)
+variable {R : Type*} [SeminormedCommRing R] (I : Ideal R)
 
 nonrec theorem Ideal.Quotient.norm_mk_lt {I : Ideal R} (x : R ⧸ I) {ε : ℝ} (hε : 0 < ε) :
     ∃ r : R, Ideal.Quotient.mk I r = x ∧ ‖r‖ < ‖x‖ + ε :=
@@ -516,7 +516,7 @@ instance Ideal.Quotient.normedCommRing [IsClosed (I : Set R)] : NormedCommRing (
   { Ideal.Quotient.semiNormedCommRing I, Submodule.Quotient.normedAddCommGroup I with }
 #align ideal.quotient.normed_comm_ring Ideal.Quotient.normedCommRing
 
-variable (𝕜 : Type _) [NormedField 𝕜]
+variable (𝕜 : Type*) [NormedField 𝕜]
 
 instance Ideal.Quotient.normedAlgebra [NormedAlgebra 𝕜 R] : NormedAlgebra 𝕜 (R ⧸ I) :=
   { Submodule.Quotient.normedSpace I 𝕜, Ideal.Quotient.algebra 𝕜 with }

@@ -77,7 +77,7 @@ Mathematically there is something to prove. The main point is proved in the auxi
 `quotient_nhd_basis` that has no use beyond this verification and states that zero in the quotient
 admits as basis of neighborhoods in the quotient topology the sets `{x | ‖x‖ < ε}` for positive `ε`.
 
-Once this mathematical point it settled, we have two topologies that are propositionally equal. This
+Once this mathematical point is settled, we have two topologies that are propositionally equal. This
 is not good enough for the type class system. As usual we ensure *definitional* equality
 using forgetful inheritance, see Note [forgetful inheritance]. A (semi)-normed group structure
 includes a uniform space structure which includes a topological space structure, together

• depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Riccardo Brasca
-
-! This file was ported from Lean 3 source module analysis.normed.group.quotient
-! leanprover-community/mathlib commit 2196ab363eb097c008d4497125e0dde23fb36db2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.NormedSpace.Basic
 import Mathlib.Analysis.Normed.Group.Hom
 import Mathlib.RingTheory.Ideal.QuotientOperations
 import Mathlib.Topology.MetricSpace.HausdorffDistance
 
+#align_import analysis.normed.group.quotient from "leanprover-community/mathlib"@"2196ab363eb097c008d4497125e0dde23fb36db2"
+
 /-!
 # Quotients of seminormed groups
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -349,7 +349,7 @@ structure IsQuotient (f : NormedAddGroupHom M N) : Prop where
   protected norm : ∀ x, ‖f x‖ = sInf ((fun m => ‖x + m‖) '' f.ker)
 #align normed_add_group_hom.is_quotient NormedAddGroupHom.IsQuotient
 
-/-- Given  `f : NormedAddGroupHom M N` such that `f s = 0` for all `s ∈ S`, where,
+/-- Given `f : NormedAddGroupHom M N` such that `f s = 0` for all `s ∈ S`, where,
 `S : AddSubgroup M` is closed, the induced morphism `NormedAddGroupHom (M ⧸ S) N`. -/
 noncomputable def lift {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
     (f : NormedAddGroupHom M N) (hf : ∀ s ∈ S, f s = 0) : NormedAddGroupHom (M ⧸ S) N :=

These are all doc fixes

@@ -80,7 +80,7 @@ Mathematically there is something to prove. The main point is proved in the auxi
 `quotient_nhd_basis` that has no use beyond this verification and states that zero in the quotient
 admits as basis of neighborhoods in the quotient topology the sets `{x | ‖x‖ < ε}` for positive `ε`.
 
-Once this mathematical point it settled, we have two topologies that are propositionaly equal. This
+Once this mathematical point it settled, we have two topologies that are propositionally equal. This
 is not good enough for the type class system. As usual we ensure *definitional* equality
 using forgetful inheritance, see Note [forgetful inheritance]. A (semi)-normed group structure
 includes a uniform space structure which includes a topological space structure, together

I ran codespell Mathlib and got tired halfway through the suggestions.

@@ -44,10 +44,10 @@ All the following definitions are in the `AddSubgroup` namespace. Hence we can a
 `AddSubgroup.normedMk S` as `S.normedMk`.
 
 * `seminormedAddCommGroupQuotient` : The seminormed group structure on the quotient by
-    an additive subgroup. This is an instance so there is no need to explictly use it.
+    an additive subgroup. This is an instance so there is no need to explicitly use it.
 
 * `normedAddCommGroupQuotient` : The normed group structure on the quotient by
-    a closed additive subgroup. This is an instance so there is no need to explictly use it.
+    a closed additive subgroup. This is an instance so there is no need to explicitly use it.
 
 * `normedMk S` : the normed group hom from `M` to `M ⧸ S`.
 

@@ -25,7 +25,7 @@ topology and the projection is a normed group homomorphism which is norm non-inc
 universal property is that every normed group hom defined on `M` which vanishes on `S` descends
 to a normed group hom defined on `M ⧸ S`.
 
-This file also introduces a predicate `is_quotient` characterizing normed group homs that
+This file also introduces a predicate `IsQuotient` characterizing normed group homs that
 are isomorphic to the canonical projection onto a normed group quotient.
 
 In addition, this file also provides normed structures for quotients of modules by submodules, and
@@ -41,36 +41,36 @@ this instance in `Submodule.Quotient.completeSpace` so that it applies to these
 
 We use `M` and `N` to denote seminormed groups and `S : AddSubgroup M`.
 All the following definitions are in the `AddSubgroup` namespace. Hence we can access
-`AddSubgroup.normedMk S` as `S.normed_mk`.
+`AddSubgroup.normedMk S` as `S.normedMk`.
 
-* `seminormed_add_comm_group_quotient` : The seminormed group structure on the quotient by
+* `seminormedAddCommGroupQuotient` : The seminormed group structure on the quotient by
     an additive subgroup. This is an instance so there is no need to explictly use it.
 
-* `normed_add_comm_group_quotient` : The normed group structure on the quotient by
+* `normedAddCommGroupQuotient` : The normed group structure on the quotient by
     a closed additive subgroup. This is an instance so there is no need to explictly use it.
 
-* `normed_mk S` : the normed group hom from `M` to `M ⧸ S`.
+* `normedMk S` : the normed group hom from `M` to `M ⧸ S`.
 
 * `lift S f hf`: implements the universal property of `M ⧸ S`. Here
     `(f : NormedAddGroupHom M N)`, `(hf : ∀ s ∈ S, f s = 0)` and
     `lift S f hf : NormedAddGroupHom (M ⧸ S) N`.
 
-* `is_quotient`: given `f : NormedAddGroupHom M N`, `is_quotient f` means `N` is isomorphic
+* `IsQuotient`: given `f : NormedAddGroupHom M N`, `IsQuotient f` means `N` is isomorphic
     to a quotient of `M` by a subgroup, with projection `f`. Technically it asserts `f` is
     surjective and the norm of `f x` is the infimum of the norms of `x + m` for `m` in `f.ker`.
 
 ## Main results
 
-* `norm_normed_mk` : the operator norm of the projection is `1` if the subspace is not dense.
+* `norm_normedMk` : the operator norm of the projection is `1` if the subspace is not dense.
 
-* `is_quotient.norm_lift`: Provided `f : normed_hom M N` satisfies `is_quotient f`, for every
+* `IsQuotient.norm_lift`: Provided `f : normed_hom M N` satisfies `IsQuotient f`, for every
      `n : N` and positive `ε`, there exists `m` such that `f m = n ∧ ‖m‖ < ‖n‖ + ε`.
 
 
 ## Implementation details
 
 For any `SeminormedAddCommGroup M` and any `S : AddSubgroup M` we define a norm on `M ⧸ S` by
-`‖x‖ = Inf (norm '' {m | mk' S m = x})`. This formula is really an implementation detail, it
+`‖x‖ = sInf (norm '' {m | mk' S m = x})`. This formula is really an implementation detail, it
 shouldn't be needed outside of this file setting up the theory.
 
 Since `M ⧸ S` is automatically a topological space (as any quotient of a topological space),
@@ -252,8 +252,7 @@ noncomputable instance AddSubgroup.seminormedAddCommGroupQuotient (S : AddSubgro
   toUniformSpace := TopologicalAddGroup.toUniformSpace (M ⧸ S)
   uniformity_dist := by
     rw [uniformity_eq_comap_nhds_zero', ((quotient_nhd_basis S).comap _).eq_biInf]
-    simp only [dist, quotient_norm_sub_rev (Prod.fst _)]
-    rfl
+    simp only [dist, quotient_norm_sub_rev (Prod.fst _), preimage_setOf_eq]
 #align add_subgroup.seminormed_add_comm_group_quotient AddSubgroup.seminormedAddCommGroupQuotient
 
 -- This is a sanity check left here on purpose to ensure that potential refactors won't destroy
@@ -285,18 +284,18 @@ noncomputable def normedMk (S : AddSubgroup M) : NormedAddGroupHom M (M ⧸ S) :
     bound' := ⟨1, fun m => by simpa [one_mul] using quotient_norm_mk_le _ m⟩ }
 #align add_subgroup.normed_mk AddSubgroup.normedMk
 
-/-- `S.normed_mk` agrees with `QuotientAddGroup.mk' S`. -/
+/-- `S.normedMk` agrees with `QuotientAddGroup.mk' S`. -/
 @[simp]
 theorem normedMk.apply (S : AddSubgroup M) (m : M) : normedMk S m = QuotientAddGroup.mk' S m :=
   rfl
 #align add_subgroup.normed_mk.apply AddSubgroup.normedMk.apply
 
-/-- `S.normed_mk` is surjective. -/
+/-- `S.normedMk` is surjective. -/
 theorem surjective_normedMk (S : AddSubgroup M) : Function.Surjective (normedMk S) :=
   surjective_quot_mk _
 #align add_subgroup.surjective_normed_mk AddSubgroup.surjective_normedMk
 
-/-- The kernel of `S.normed_mk` is `S`. -/
+/-- The kernel of `S.normedMk` is `S`. -/
 theorem ker_normedMk (S : AddSubgroup M) : S.normedMk.ker = S :=
   QuotientAddGroup.ker_mk' _
 #align add_subgroup.ker_normed_mk AddSubgroup.ker_normedMk
@@ -343,7 +342,7 @@ end AddSubgroup
 
 namespace NormedAddGroupHom
 
-/-- `is_quotient f`, for `f : M ⟶ N` means that `N` is isomorphic to the quotient of `M`
+/-- `IsQuotient f`, for `f : M ⟶ N` means that `N` is isomorphic to the quotient of `M`
 by the kernel of `f`. -/
 structure IsQuotient (f : NormedAddGroupHom M N) : Prop where
   protected surjective : Function.Surjective f
@@ -374,7 +373,7 @@ theorem lift_unique {N : Type _} [SeminormedAddCommGroup N] (S : AddSubgroup M)
   rfl
 #align normed_add_group_hom.lift_unique NormedAddGroupHom.lift_unique
 
-/-- `S.normed_mk` satisfies `is_quotient`. -/
+/-- `S.normedMk` satisfies `IsQuotient`. -/
 theorem isQuotientQuotient (S : AddSubgroup M) : IsQuotient S.normedMk :=
   ⟨S.surjective_normedMk, fun m => by simpa [S.ker_normedMk] using quotient_norm_mk_eq _ m⟩
 #align normed_add_group_hom.is_quotient_quotient NormedAddGroupHom.isQuotientQuotient

Now that leanprover/lean4#2210 has been merged, this PR:

• removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
• removes many but not quite all set_option maxHeartbeats commands
• makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -489,19 +489,15 @@ section Ideal
 
 variable {R : Type _} [SeminormedCommRing R] (I : Ideal R)
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 nonrec theorem Ideal.Quotient.norm_mk_lt {I : Ideal R} (x : R ⧸ I) {ε : ℝ} (hε : 0 < ε) :
     ∃ r : R, Ideal.Quotient.mk I r = x ∧ ‖r‖ < ‖x‖ + ε :=
   norm_mk_lt x hε
 #align ideal.quotient.norm_mk_lt Ideal.Quotient.norm_mk_lt
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 theorem Ideal.Quotient.norm_mk_le (r : R) : ‖Ideal.Quotient.mk I r‖ ≤ ‖r‖ :=
   quotient_norm_mk_le I.toAddSubgroup r
 #align ideal.quotient.norm_mk_le Ideal.Quotient.norm_mk_le
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
-set_option maxHeartbeats 400000 in
 instance Ideal.Quotient.semiNormedCommRing : SeminormedCommRing (R ⧸ I) where
   dist_eq := dist_eq_norm
   mul_comm := _root_.mul_comm
@@ -520,15 +516,12 @@ instance Ideal.Quotient.semiNormedCommRing : SeminormedCommRing (R ⧸ I) where
       _ ≤ _ := (sub_lt_iff_lt_add'.mp h.1).le
 #align ideal.quotient.semi_normed_comm_ring Ideal.Quotient.semiNormedCommRing
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
 instance Ideal.Quotient.normedCommRing [IsClosed (I : Set R)] : NormedCommRing (R ⧸ I) :=
   { Ideal.Quotient.semiNormedCommRing I, Submodule.Quotient.normedAddCommGroup I with }
 #align ideal.quotient.normed_comm_ring Ideal.Quotient.normedCommRing
 
 variable (𝕜 : Type _) [NormedField 𝕜]
 
-set_option synthInstance.etaExperiment true in -- Porting note: gets around lean4#2074
-set_option maxHeartbeats 700000 in
 instance Ideal.Quotient.normedAlgebra [NormedAlgebra 𝕜 R] : NormedAlgebra 𝕜 (R ⧸ I) :=
   { Submodule.Quotient.normedSpace I 𝕜, Ideal.Quotient.algebra 𝕜 with }
 #align ideal.quotient.normed_algebra Ideal.Quotient.normedAlgebra

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -104,17 +104,17 @@ variable {M N : Type _} [SeminormedAddCommGroup M] [SeminormedAddCommGroup N]
 
 /-- The definition of the norm on the quotient by an additive subgroup. -/
 noncomputable instance normOnQuotient (S : AddSubgroup M) : Norm (M ⧸ S) where
-  norm x := infₛ (norm '' { m | mk' S m = x })
+  norm x := sInf (norm '' { m | mk' S m = x })
 #align norm_on_quotient normOnQuotient
 
 theorem AddSubgroup.quotient_norm_eq {S : AddSubgroup M} (x : M ⧸ S) :
-    ‖x‖ = infₛ (norm '' { m : M | (m : M ⧸ S) = x }) :=
+    ‖x‖ = sInf (norm '' { m : M | (m : M ⧸ S) = x }) :=
   rfl
 #align add_subgroup.quotient_norm_eq AddSubgroup.quotient_norm_eq
 
 theorem QuotientAddGroup.norm_eq_infDist {S : AddSubgroup M} (x : M ⧸ S) :
     ‖x‖ = infDist 0 { m : M | (m : M ⧸ S) = x } := by
-  simp only [AddSubgroup.quotient_norm_eq, infDist_eq_infᵢ, infₛ_image', dist_zero_left]
+  simp only [AddSubgroup.quotient_norm_eq, infDist_eq_iInf, sInf_image', dist_zero_left]
 
 /-- An alternative definition of the norm on the quotient group: the norm of `((x : M) : M ⧸ S)` is
 equal to the distance from `x` to `S`. -/
@@ -137,7 +137,7 @@ theorem bddBelow_image_norm (s : Set M) : BddBelow (norm '' s) :=
 
 theorem isGLB_quotient_norm {S : AddSubgroup M} (x : M ⧸ S) :
     IsGLB (norm '' { m | mk' S m = x }) (‖x‖) :=
-  isGLB_cinfₛ (image_norm_nonempty x) (bddBelow_image_norm _)
+  isGLB_csInf (image_norm_nonempty x) (bddBelow_image_norm _)
 
 /-- The norm on the quotient satisfies `‖-x‖ = ‖x‖`. -/
 theorem quotient_norm_neg {S : AddSubgroup M} (x : M ⧸ S) : ‖-x‖ = ‖x‖ := by
@@ -152,7 +152,7 @@ theorem quotient_norm_sub_rev {S : AddSubgroup M} (x y : M ⧸ S) : ‖x - y‖
 
 /-- The norm of the projection is smaller or equal to the norm of the original element. -/
 theorem quotient_norm_mk_le (S : AddSubgroup M) (m : M) : ‖mk' S m‖ ≤ ‖m‖ :=
-  cinfₛ_le (bddBelow_image_norm _) <| Set.mem_image_of_mem _ rfl
+  csInf_le (bddBelow_image_norm _) <| Set.mem_image_of_mem _ rfl
 #align quotient_norm_mk_le quotient_norm_mk_le
 
 /-- The norm of the projection is smaller or equal to the norm of the original element. -/
@@ -162,15 +162,15 @@ theorem quotient_norm_mk_le' (S : AddSubgroup M) (m : M) : ‖(m : M ⧸ S)‖ 
 
 /-- The norm of the image under the natural morphism to the quotient. -/
 theorem quotient_norm_mk_eq (S : AddSubgroup M) (m : M) :
-    ‖mk' S m‖ = infₛ ((‖m + ·‖) '' S) := by
-  rw [mk'_apply, norm_mk, infₛ_image', ← infDist_image isometry_neg, image_neg,
-    neg_coe_set (H := S), infDist_eq_infᵢ]
+    ‖mk' S m‖ = sInf ((‖m + ·‖) '' S) := by
+  rw [mk'_apply, norm_mk, sInf_image', ← infDist_image isometry_neg, image_neg,
+    neg_coe_set (H := S), infDist_eq_iInf]
   simp only [dist_eq_norm', sub_neg_eq_add, add_comm]
 #align quotient_norm_mk_eq quotient_norm_mk_eq
 
 /-- The quotient norm is nonnegative. -/
 theorem quotient_norm_nonneg (S : AddSubgroup M) (x : M ⧸ S) : 0 ≤ ‖x‖ :=
-  Real.infₛ_nonneg _ <| ball_image_iff.2 fun _ _ ↦ norm_nonneg _
+  Real.sInf_nonneg _ <| ball_image_iff.2 fun _ _ ↦ norm_nonneg _
 #align quotient_norm_nonneg quotient_norm_nonneg
 
 /-- The quotient norm is nonnegative. -/
@@ -211,9 +211,9 @@ theorem norm_mk_lt' (S : AddSubgroup M) (m : M) {ε : ℝ} (hε : 0 < ε) :
 /-- The quotient norm satisfies the triangle inequality. -/
 theorem quotient_norm_add_le (S : AddSubgroup M) (x y : M ⧸ S) : ‖x + y‖ ≤ ‖x‖ + ‖y‖ := by
   rcases And.intro (mk_surjective x) (mk_surjective y) with ⟨⟨x, rfl⟩, ⟨y, rfl⟩⟩
-  simp only [← mk'_apply, ← map_add, quotient_norm_mk_eq, infₛ_image']
-  refine le_cinfᵢ_add_cinfᵢ fun a b ↦ ?_
-  refine cinfᵢ_le_of_le ⟨0, forall_range_iff.2 fun _ ↦ norm_nonneg _⟩ (a + b) ?_
+  simp only [← mk'_apply, ← map_add, quotient_norm_mk_eq, sInf_image']
+  refine le_ciInf_add_ciInf fun a b ↦ ?_
+  refine ciInf_le_of_le ⟨0, forall_range_iff.2 fun _ ↦ norm_nonneg _⟩ (a + b) ?_
   exact (congr_arg norm (add_add_add_comm _ _ _ _)).trans_le (norm_add_le _ _)
 #align quotient_norm_add_le quotient_norm_add_le
 
@@ -251,7 +251,7 @@ noncomputable instance AddSubgroup.seminormedAddCommGroupQuotient (S : AddSubgro
   edist_dist x y := by exact ENNReal.coe_nnreal_eq _
   toUniformSpace := TopologicalAddGroup.toUniformSpace (M ⧸ S)
   uniformity_dist := by
-    rw [uniformity_eq_comap_nhds_zero', ((quotient_nhd_basis S).comap _).eq_binfᵢ]
+    rw [uniformity_eq_comap_nhds_zero', ((quotient_nhd_basis S).comap _).eq_biInf]
     simp only [dist, quotient_norm_sub_rev (Prod.fst _)]
     rfl
 #align add_subgroup.seminormed_add_comm_group_quotient AddSubgroup.seminormedAddCommGroupQuotient
@@ -347,7 +347,7 @@ namespace NormedAddGroupHom
 by the kernel of `f`. -/
 structure IsQuotient (f : NormedAddGroupHom M N) : Prop where
   protected surjective : Function.Surjective f
-  protected norm : ∀ x, ‖f x‖ = infₛ ((fun m => ‖x + m‖) '' f.ker)
+  protected norm : ∀ x, ‖f x‖ = sInf ((fun m => ‖x + m‖) '' f.ker)
 #align normed_add_group_hom.is_quotient NormedAddGroupHom.IsQuotient
 
 /-- Given  `f : NormedAddGroupHom M N` such that `f s = 0` for all `s ∈ S`, where,
@@ -385,8 +385,8 @@ theorem IsQuotient.norm_lift {f : NormedAddGroupHom M N} (hquot : IsQuotient f)
   have nonemp : ((fun m' => ‖m + m'‖) '' f.ker).Nonempty := by
     rw [Set.nonempty_image_iff]
     exact ⟨0, f.ker.zero_mem⟩
-  rcases Real.lt_infₛ_add_pos nonemp hε
-    with ⟨_, ⟨⟨x, hx, rfl⟩, H : ‖m + x‖ < infₛ ((fun m' : M => ‖m + m'‖) '' f.ker) + ε⟩⟩
+  rcases Real.lt_sInf_add_pos nonemp hε
+    with ⟨_, ⟨⟨x, hx, rfl⟩, H : ‖m + x‖ < sInf ((fun m' : M => ‖m + m'‖) '' f.ker) + ε⟩⟩
   exact ⟨m + x, by rw [map_add, (NormedAddGroupHom.mem_ker f x).mp hx, add_zero], by
     rwa [hquot.norm]⟩
 #align normed_add_group_hom.is_quotient.norm_lift NormedAddGroupHom.IsQuotient.norm_lift
@@ -394,7 +394,7 @@ theorem IsQuotient.norm_lift {f : NormedAddGroupHom M N} (hquot : IsQuotient f)
 theorem IsQuotient.norm_le {f : NormedAddGroupHom M N} (hquot : IsQuotient f) (m : M) :
     ‖f m‖ ≤ ‖m‖ := by
   rw [hquot.norm]
-  apply cinfₛ_le
+  apply csInf_le
   · use 0
     rintro _ ⟨m', -, rfl⟩
     apply norm_nonneg

Co-authored-by: Mauricio Collares <mauricio@collares.org>