analysis.normed.group.add_circle | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

084f76e2

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

2ed2c631

bump to nightly-2024-04-19-08

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

a9e81450

Diff

@@ -270,13 +270,13 @@ section FiniteOrderPoints
 
 variable {p} [hp : Fact (0 < p)]
 
-#print AddCircle.norm_div_nat_cast /-
-theorem norm_div_nat_cast {m n : ℕ} :
+#print AddCircle.norm_div_natCast /-
+theorem norm_div_natCast {m n : ℕ} :
     ‖(↑(↑m / ↑n * p) : AddCircle p)‖ = p * (↑(min (m % n) (n - m % n)) / n) :=
   by
   have : p⁻¹ * (↑m / ↑n * p) = ↑m / ↑n := by rw [mul_comm _ p, inv_mul_cancel_left₀ hp.out.ne.symm]
   rw [norm_eq' p hp.out, this, abs_sub_round_div_natCast_eq]
-#align add_circle.norm_div_nat_cast AddCircle.norm_div_nat_cast
+#align add_circle.norm_div_nat_cast AddCircle.norm_div_natCast
 -/
 
 #print AddCircle.exists_norm_eq_of_isOfFinAddOrder /-

2ed2c631

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -298,7 +298,7 @@ theorem le_add_order_smul_norm_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFi
   obtain ⟨n, hn⟩ := exists_norm_eq_of_fin_add_order hu
   replace hu : (addOrderOf u : ℝ) ≠ 0; · norm_cast; exact (add_order_of_pos_iff.mpr hu).Ne.symm
   conv_lhs => rw [← mul_one p]
-  rw [hn, nsmul_eq_mul, ← mul_assoc, mul_comm _ p, mul_assoc, mul_div_cancel' _ hu,
+  rw [hn, nsmul_eq_mul, ← mul_assoc, mul_comm _ p, mul_assoc, mul_div_cancel₀ _ hu,
     mul_le_mul_left hp.out, Nat.one_le_cast, Nat.one_le_iff_ne_zero]
   contrapose! hu'
   simpa only [hu', algebraMap.coe_zero, zero_div, MulZeroClass.mul_zero, norm_eq_zero] using hn

2ed2c631

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -102,7 +102,7 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
     rcases eq_or_ne p 0 with (rfl | hp); · simp
     intros
     have hx := norm_coe_mul p x p⁻¹
-    rw [abs_inv, eq_inv_mul_iff_mul_eq₀ ((not_congr abs_eq_zero).mpr hp)] at hx 
+    rw [abs_inv, eq_inv_mul_iff_mul_eq₀ ((not_congr abs_eq_zero).mpr hp)] at hx
     rw [← hx, inv_mul_cancel hp, this, ← abs_mul, mul_sub, mul_inv_cancel_left₀ hp, mul_comm p]
   clear x p
   intros
@@ -126,7 +126,7 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
   · simp only [QuotientAddGroup.mk'_apply, Real.norm_eq_abs, le_csInf_iff h₁ h₂]
     rintro b' ⟨b, hb, rfl⟩
     simp only [mem_set_of_eq, QuotientAddGroup.eq_iff_sub_mem, mem_zmultiples_iff,
-      smul_one_eq_coe] at hb 
+      smul_one_eq_coe] at hb
     obtain ⟨z, hz⟩ := hb
     rw [(by rw [hz]; abel : x = b - z), fract_sub_int, ← abs_sub_round_eq_min]
     convert round_le b 0
@@ -172,11 +172,11 @@ theorem norm_coe_eq_abs_iff {x : ℝ} (hp : p ≠ 0) : ‖(x : AddCircle p)‖ =
   suffices ∀ p : ℝ, 0 < p → |x| ≤ p / 2 → ‖(x : AddCircle p)‖ = |x|
     by
     rcases lt_trichotomy 0 p with (hp | rfl | hp)
-    · rw [abs_eq_self.mpr hp.le] at hx 
+    · rw [abs_eq_self.mpr hp.le] at hx
       exact this p hp hx
     · contradiction
     · rw [← norm_neg_period]
-      rw [abs_eq_neg_self.mpr hp.le] at hx 
+      rw [abs_eq_neg_self.mpr hp.le] at hx
       exact this (-p) (neg_pos.mpr hp) hx
   clear hx
   intro p hp hx
@@ -236,7 +236,7 @@ theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
   by
   cases' le_or_lt (|p| / 2) ε with hε hε
   · rcases eq_or_ne p 0 with (rfl | hp)
-    · simp only [abs_zero, zero_div] at hε 
+    · simp only [abs_zero, zero_div] at hε
       simp only [not_lt.mpr hε, coe_real_preimage_closed_ball_period_zero, abs_zero, zero_div,
         if_false, inter_eq_right_iff_subset]
       exact hs.trans (closed_ball_subset_closed_ball <| by simp [hε])
@@ -256,7 +256,7 @@ theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
         linarith [abs_eq_self.mpr hp.le]
       · have : p ≤ ↑z * p; nlinarith
         linarith [abs_eq_self.mpr hp.le]
-    · simp only [MulZeroClass.mul_zero, add_zero, abs_zero, zero_div] at hy₁ hy₂ hε 
+    · simp only [MulZeroClass.mul_zero, add_zero, abs_zero, zero_div] at hy₁ hy₂ hε
       linarith
     · cases' Int.cast_le_neg_one_or_one_le_cast_of_ne_zero ℝ hz with hz' hz'
       · have : -p ≤ ↑z * p; nlinarith

2ed2c631

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 -/
-import Mathbin.Analysis.Normed.Group.Quotient
-import Mathbin.Topology.Instances.AddCircle
+import Analysis.Normed.Group.Quotient
+import Topology.Instances.AddCircle
 
 #align_import analysis.normed.group.add_circle from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"

2ed2c631

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module analysis.normed.group.add_circle
-! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.Normed.Group.Quotient
 import Mathbin.Topology.Instances.AddCircle
 
+#align_import analysis.normed.group.add_circle from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
+
 /-!
 # The additive circle as a normed group

2ed2c631

bump to nightly-2023-07-02-17

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

9a21e617

Diff

@@ -64,8 +64,7 @@ theorem norm_coe_mul (x : ℝ) (t : ℝ) :
   congr 1
   ext z
   rw [mem_smul_set_iff_inv_smul_mem₀ ht']
-  show
-    (∃ y, y - t * x ∈ zmultiples (t * p) ∧ |y| = z) ↔ ∃ w, w - x ∈ zmultiples p ∧ |w| = (|t|)⁻¹ * z
+  show (∃ y, y - t * x ∈ zmultiples (t * p) ∧ |y| = z) ↔ ∃ w, w - x ∈ zmultiples p ∧ |w| = |t|⁻¹ * z
   constructor
   · rintro ⟨y, hy, rfl⟩
     refine' ⟨t⁻¹ * y, _, by rw [abs_mul, abs_inv]⟩

2ed2c631

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -46,6 +46,7 @@ variable (p : ℝ)
 instance : NormedAddCommGroup (AddCircle p) :=
   AddSubgroup.normedAddCommGroupQuotient _
 
+#print AddCircle.norm_coe_mul /-
 @[simp]
 theorem norm_coe_mul (x : ℝ) (t : ℝ) :
     ‖(↑(t * x) : AddCircle (t * p))‖ = |t| * ‖(x : AddCircle p)‖ :=
@@ -75,14 +76,18 @@ theorem norm_coe_mul (x : ℝ) (t : ℝ) :
     rw [← mul_sub]
     exact aux hw
 #align add_circle.norm_coe_mul AddCircle.norm_coe_mul
+-/
 
+#print AddCircle.norm_neg_period /-
 theorem norm_neg_period (x : ℝ) : ‖(x : AddCircle (-p))‖ = ‖(x : AddCircle p)‖ :=
   by
   suffices ‖(↑(-1 * x) : AddCircle (-1 * p))‖ = ‖(x : AddCircle p)‖ by rw [← this, neg_one_mul];
     simp
   simp only [norm_coe_mul, abs_neg, abs_one, one_mul]
 #align add_circle.norm_neg_period AddCircle.norm_neg_period
+-/
 
+#print AddCircle.norm_eq_of_zero /-
 @[simp]
 theorem norm_eq_of_zero {x : ℝ} : ‖(x : AddCircle (0 : ℝ))‖ = |x| :=
   by
@@ -91,7 +96,9 @@ theorem norm_eq_of_zero {x : ℝ} : ‖(x : AddCircle (0 : ℝ))‖ = |x| :=
   ext y
   simp [QuotientAddGroup.eq_iff_sub_mem, mem_zmultiples_iff, sub_eq_zero]
 #align add_circle.norm_eq_of_zero AddCircle.norm_eq_of_zero
+-/
 
+#print AddCircle.norm_eq /-
 theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) * p| :=
   by
   suffices ∀ x : ℝ, ‖(x : AddCircle (1 : ℝ))‖ = |x - round x|
@@ -129,7 +136,9 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
     convert round_le b 0
     simp
 #align add_circle.norm_eq AddCircle.norm_eq
+-/
 
+#print AddCircle.norm_eq' /-
 theorem norm_eq' (hp : 0 < p) {x : ℝ} : ‖(x : AddCircle p)‖ = p * |p⁻¹ * x - round (p⁻¹ * x)| :=
   by
   conv_rhs =>
@@ -137,7 +146,9 @@ theorem norm_eq' (hp : 0 < p) {x : ℝ} : ‖(x : AddCircle p)‖ = p * |p⁻¹
     rw [← abs_eq_self.mpr hp.le]
   rw [← abs_mul, mul_sub, mul_inv_cancel_left₀ hp.ne.symm, norm_eq, mul_comm p]
 #align add_circle.norm_eq' AddCircle.norm_eq'
+-/
 
+#print AddCircle.norm_le_half_period /-
 theorem norm_le_half_period {x : AddCircle p} (hp : p ≠ 0) : ‖x‖ ≤ |p| / 2 :=
   by
   obtain ⟨x⟩ := x
@@ -146,7 +157,9 @@ theorem norm_le_half_period {x : AddCircle p} (hp : p ≠ 0) : ‖x‖ ≤ |p| /
     ← mul_div_assoc, ← abs_mul, inv_mul_cancel hp, mul_one, abs_one]
   exact abs_sub_round (p⁻¹ * x)
 #align add_circle.norm_le_half_period AddCircle.norm_le_half_period
+-/
 
+#print AddCircle.norm_half_period_eq /-
 @[simp]
 theorem norm_half_period_eq : ‖(↑(p / 2) : AddCircle p)‖ = |p| / 2 :=
   by
@@ -154,7 +167,9 @@ theorem norm_half_period_eq : ‖(↑(p / 2) : AddCircle p)‖ = |p| / 2 :=
   rw [norm_eq, ← mul_div_assoc, inv_mul_cancel hp, one_div, round_two_inv, algebraMap.coe_one,
     one_mul, (by linarith : p / 2 - p = -(p / 2)), abs_neg, abs_div, abs_two]
 #align add_circle.norm_half_period_eq AddCircle.norm_half_period_eq
+-/
 
+#print AddCircle.norm_coe_eq_abs_iff /-
 theorem norm_coe_eq_abs_iff {x : ℝ} (hp : p ≠ 0) : ‖(x : AddCircle p)‖ = |x| ↔ |x| ≤ |p| / 2 :=
   by
   refine' ⟨fun hx => hx ▸ norm_le_half_period p hp, fun hx => _⟩
@@ -182,21 +197,27 @@ theorem norm_coe_eq_abs_iff {x : ℝ} (hp : p ≠ 0) : ‖(x : AddCircle p)‖ =
     rwa [← mul_lt_mul_left hp, ← mul_assoc, mul_inv_cancel hp.ne.symm, one_mul, ← mul_div_assoc,
       mul_one]
 #align add_circle.norm_coe_eq_abs_iff AddCircle.norm_coe_eq_abs_iff
+-/
 
 open Metric
 
+#print AddCircle.closedBall_eq_univ_of_half_period_le /-
 theorem closedBall_eq_univ_of_half_period_le (hp : p ≠ 0) (x : AddCircle p) {ε : ℝ}
     (hε : |p| / 2 ≤ ε) : closedBall x ε = univ :=
   eq_univ_iff_forall.mpr fun x => by
     simpa only [mem_closed_ball, dist_eq_norm] using (norm_le_half_period p hp).trans hε
 #align add_circle.closed_ball_eq_univ_of_half_period_le AddCircle.closedBall_eq_univ_of_half_period_le
+-/
 
+#print AddCircle.coe_real_preimage_closedBall_period_zero /-
 @[simp]
 theorem coe_real_preimage_closedBall_period_zero (x ε : ℝ) :
     coe ⁻¹' closedBall (x : AddCircle (0 : ℝ)) ε = closedBall x ε := by
   ext y <;> simp [dist_eq_norm, ← QuotientAddGroup.mk_sub]
 #align add_circle.coe_real_preimage_closed_ball_period_zero AddCircle.coe_real_preimage_closedBall_period_zero
+-/
 
+#print AddCircle.coe_real_preimage_closedBall_eq_iUnion /-
 theorem coe_real_preimage_closedBall_eq_iUnion (x ε : ℝ) :
     coe ⁻¹' closedBall (x : AddCircle p) ε = ⋃ z : ℤ, closedBall (x + z • p) ε :=
   by
@@ -210,7 +231,9 @@ theorem coe_real_preimage_closedBall_eq_iUnion (x ε : ℝ) :
     inv_mul_cancel_left₀ hp] at hn ⊢
   exact (round_le (p⁻¹ * (y - x)) n).trans hn
 #align add_circle.coe_real_preimage_closed_ball_eq_Union AddCircle.coe_real_preimage_closedBall_eq_iUnion
+-/
 
+#print AddCircle.coe_real_preimage_closedBall_inter_eq /-
 theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
     (hs : s ⊆ closedBall x (|p| / 2)) :
     coe ⁻¹' closedBall (x : AddCircle p) ε ∩ s = if ε < |p| / 2 then closedBall x ε ∩ s else s :=
@@ -245,20 +268,22 @@ theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
       · have : ↑z * p ≤ p; nlinarith
         linarith [abs_eq_neg_self.mpr hp.le]
 #align add_circle.coe_real_preimage_closed_ball_inter_eq AddCircle.coe_real_preimage_closedBall_inter_eq
+-/
 
 section FiniteOrderPoints
 
 variable {p} [hp : Fact (0 < p)]
 
-include hp
-
+#print AddCircle.norm_div_nat_cast /-
 theorem norm_div_nat_cast {m n : ℕ} :
     ‖(↑(↑m / ↑n * p) : AddCircle p)‖ = p * (↑(min (m % n) (n - m % n)) / n) :=
   by
   have : p⁻¹ * (↑m / ↑n * p) = ↑m / ↑n := by rw [mul_comm _ p, inv_mul_cancel_left₀ hp.out.ne.symm]
   rw [norm_eq' p hp.out, this, abs_sub_round_div_natCast_eq]
 #align add_circle.norm_div_nat_cast AddCircle.norm_div_nat_cast
+-/
 
+#print AddCircle.exists_norm_eq_of_isOfFinAddOrder /-
 theorem exists_norm_eq_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrder u) :
     ∃ k : ℕ, ‖u‖ = p * (k / addOrderOf u) :=
   by
@@ -268,7 +293,9 @@ theorem exists_norm_eq_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrde
   refine' ⟨min (m % n) (n - m % n), _⟩
   rw [← hm, norm_div_nat_cast]
 #align add_circle.exists_norm_eq_of_fin_add_order AddCircle.exists_norm_eq_of_isOfFinAddOrder
+-/
 
+#print AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder /-
 theorem le_add_order_smul_norm_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrder u)
     (hu' : u ≠ 0) : p ≤ addOrderOf u • ‖u‖ :=
   by
@@ -280,6 +307,7 @@ theorem le_add_order_smul_norm_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFi
   contrapose! hu'
   simpa only [hu', algebraMap.coe_zero, zero_div, MulZeroClass.mul_zero, norm_eq_zero] using hn
 #align add_circle.le_add_order_smul_norm_of_is_of_fin_add_order AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder
+-/
 
 end FiniteOrderPoints
 
@@ -287,8 +315,10 @@ end AddCircle
 
 namespace UnitAddCircle
 
+#print UnitAddCircle.norm_eq /-
 theorem norm_eq {x : ℝ} : ‖(x : UnitAddCircle)‖ = |x - round x| := by simp [AddCircle.norm_eq]
 #align unit_add_circle.norm_eq UnitAddCircle.norm_eq
+-/
 
 end UnitAddCircle

2ed2c631

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -86,7 +86,7 @@ theorem norm_neg_period (x : ℝ) : ‖(x : AddCircle (-p))‖ = ‖(x : AddCirc
 @[simp]
 theorem norm_eq_of_zero {x : ℝ} : ‖(x : AddCircle (0 : ℝ))‖ = |x| :=
   by
-  suffices { y : ℝ | (y : AddCircle (0 : ℝ)) = (x : AddCircle (0 : ℝ)) } = {x} by
+  suffices {y : ℝ | (y : AddCircle (0 : ℝ)) = (x : AddCircle (0 : ℝ))} = {x} by
     rw [quotient_norm_eq, this, image_singleton, Real.norm_eq_abs, csInf_singleton]
   ext y
   simp [QuotientAddGroup.eq_iff_sub_mem, mem_zmultiples_iff, sub_eq_zero]
@@ -104,9 +104,9 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
   clear x p
   intros
   rw [quotient_norm_eq, abs_sub_round_eq_min]
-  have h₁ : BddBelow (abs '' { m : ℝ | (m : AddCircle (1 : ℝ)) = x }) :=
+  have h₁ : BddBelow (abs '' {m : ℝ | (m : AddCircle (1 : ℝ)) = x}) :=
     ⟨0, by simp [mem_lowerBounds]⟩
-  have h₂ : (abs '' { m : ℝ | (m : AddCircle (1 : ℝ)) = x }).Nonempty := ⟨|x|, ⟨x, rfl, rfl⟩⟩
+  have h₂ : (abs '' {m : ℝ | (m : AddCircle (1 : ℝ)) = x}).Nonempty := ⟨|x|, ⟨x, rfl, rfl⟩⟩
   apply le_antisymm
   · simp only [le_min_iff, Real.norm_eq_abs, csInf_le_iff h₁ h₂]
     intro b h

2ed2c631

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -52,7 +52,7 @@ theorem norm_coe_mul (x : ℝ) (t : ℝ) :
   by
   have aux : ∀ {a b c : ℝ}, a ∈ zmultiples b → c * a ∈ zmultiples (c * b) := fun a b c h =>
     by
-    simp only [mem_zmultiples_iff] at h⊢
+    simp only [mem_zmultiples_iff] at h ⊢
     obtain ⟨n, rfl⟩ := h
     exact ⟨n, (mul_smul_comm n c b).symm⟩
   rcases eq_or_ne t 0 with (rfl | ht); · simp
@@ -99,7 +99,7 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
     rcases eq_or_ne p 0 with (rfl | hp); · simp
     intros
     have hx := norm_coe_mul p x p⁻¹
-    rw [abs_inv, eq_inv_mul_iff_mul_eq₀ ((not_congr abs_eq_zero).mpr hp)] at hx
+    rw [abs_inv, eq_inv_mul_iff_mul_eq₀ ((not_congr abs_eq_zero).mpr hp)] at hx 
     rw [← hx, inv_mul_cancel hp, this, ← abs_mul, mul_sub, mul_inv_cancel_left₀ hp, mul_comm p]
   clear x p
   intros
@@ -123,7 +123,7 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
   · simp only [QuotientAddGroup.mk'_apply, Real.norm_eq_abs, le_csInf_iff h₁ h₂]
     rintro b' ⟨b, hb, rfl⟩
     simp only [mem_set_of_eq, QuotientAddGroup.eq_iff_sub_mem, mem_zmultiples_iff,
-      smul_one_eq_coe] at hb
+      smul_one_eq_coe] at hb 
     obtain ⟨z, hz⟩ := hb
     rw [(by rw [hz]; abel : x = b - z), fract_sub_int, ← abs_sub_round_eq_min]
     convert round_le b 0
@@ -161,11 +161,11 @@ theorem norm_coe_eq_abs_iff {x : ℝ} (hp : p ≠ 0) : ‖(x : AddCircle p)‖ =
   suffices ∀ p : ℝ, 0 < p → |x| ≤ p / 2 → ‖(x : AddCircle p)‖ = |x|
     by
     rcases lt_trichotomy 0 p with (hp | rfl | hp)
-    · rw [abs_eq_self.mpr hp.le] at hx
+    · rw [abs_eq_self.mpr hp.le] at hx 
       exact this p hp hx
     · contradiction
     · rw [← norm_neg_period]
-      rw [abs_eq_neg_self.mpr hp.le] at hx
+      rw [abs_eq_neg_self.mpr hp.le] at hx 
       exact this (-p) (neg_pos.mpr hp) hx
   clear hx
   intro p hp hx
@@ -207,7 +207,7 @@ theorem coe_real_preimage_closedBall_eq_iUnion (x ε : ℝ) :
   refine' ⟨fun h => ⟨round (p⁻¹ * (y - x)), h⟩, _⟩
   rintro ⟨n, hn⟩
   rw [← mul_le_mul_left (abs_pos.mpr <| inv_ne_zero hp), ← abs_mul, mul_sub, mul_comm _ p,
-    inv_mul_cancel_left₀ hp] at hn⊢
+    inv_mul_cancel_left₀ hp] at hn ⊢
   exact (round_le (p⁻¹ * (y - x)) n).trans hn
 #align add_circle.coe_real_preimage_closed_ball_eq_Union AddCircle.coe_real_preimage_closedBall_eq_iUnion
 
@@ -217,7 +217,7 @@ theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
   by
   cases' le_or_lt (|p| / 2) ε with hε hε
   · rcases eq_or_ne p 0 with (rfl | hp)
-    · simp only [abs_zero, zero_div] at hε
+    · simp only [abs_zero, zero_div] at hε 
       simp only [not_lt.mpr hε, coe_real_preimage_closed_ball_period_zero, abs_zero, zero_div,
         if_false, inter_eq_right_iff_subset]
       exact hs.trans (closed_ball_subset_closed_ball <| by simp [hε])
@@ -226,7 +226,7 @@ theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
       simp [-zsmul_eq_mul, ← QuotientAddGroup.mk_zero, coe_real_preimage_closed_ball_eq_Union,
         Union_inter, Union_ite, this, hε]
     intro z
-    simp only [Real.closedBall_eq_Icc, zero_sub, zero_add] at hs⊢
+    simp only [Real.closedBall_eq_Icc, zero_sub, zero_add] at hs ⊢
     rcases eq_or_ne z 0 with (rfl | hz); · simp
     simp only [hz, zsmul_eq_mul, if_false, eq_empty_iff_forall_not_mem]
     rintro y ⟨⟨hy₁, hy₂⟩, hy₀⟩
@@ -237,7 +237,7 @@ theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
         linarith [abs_eq_self.mpr hp.le]
       · have : p ≤ ↑z * p; nlinarith
         linarith [abs_eq_self.mpr hp.le]
-    · simp only [MulZeroClass.mul_zero, add_zero, abs_zero, zero_div] at hy₁ hy₂ hε
+    · simp only [MulZeroClass.mul_zero, add_zero, abs_zero, zero_div] at hy₁ hy₂ hε 
       linarith
     · cases' Int.cast_le_neg_one_or_one_le_cast_of_ne_zero ℝ hz with hz' hz'
       · have : -p ≤ ↑z * p; nlinarith

2ed2c631

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -46,12 +46,6 @@ variable (p : ℝ)
 instance : NormedAddCommGroup (AddCircle p) :=
   AddSubgroup.normedAddCommGroupQuotient _
 
-/- warning: add_circle.norm_coe_mul -> AddCircle.norm_coe_mul is a dubious translation:
-lean 3 declaration is
-  forall (p : Real) (x : Real) (t : Real), Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p)) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p)) (AddCircle.normedAddCommGroup (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p)) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p)) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p)) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p)))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t x))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) t) (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x)))
-but is expected to have type
-  forall (p : Real) (x : Real) (t : Real), Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) t p))) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) t p))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) t p)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) t x))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) t) (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x)))
-Case conversion may be inaccurate. Consider using '#align add_circle.norm_coe_mul AddCircle.norm_coe_mulₓ'. -/
 @[simp]
 theorem norm_coe_mul (x : ℝ) (t : ℝ) :
     ‖(↑(t * x) : AddCircle (t * p))‖ = |t| * ‖(x : AddCircle p)‖ :=
@@ -82,12 +76,6 @@ theorem norm_coe_mul (x : ℝ) (t : ℝ) :
     exact aux hw
 #align add_circle.norm_coe_mul AddCircle.norm_coe_mul
 
-/- warning: add_circle.norm_neg_period -> AddCircle.norm_neg_period is a dubious translation:
-lean 3 declaration is
-  forall (p : Real) (x : Real), Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (Neg.neg.{0} Real Real.hasNeg p)) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (Neg.neg.{0} Real Real.hasNeg p)) (AddCircle.normedAddCommGroup (Neg.neg.{0} Real Real.hasNeg p))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (Neg.neg.{0} Real Real.hasNeg p)) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (Neg.neg.{0} Real Real.hasNeg p)) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (Neg.neg.{0} Real Real.hasNeg p)) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (Neg.neg.{0} Real Real.hasNeg p)))) x)) (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x))
-but is expected to have type
-  forall (p : Real) (x : Real), Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (Neg.neg.{0} Real Real.instNegReal p))) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (Neg.neg.{0} Real Real.instNegReal p))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (Neg.neg.{0} Real Real.instNegReal p)) x)) (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x))
-Case conversion may be inaccurate. Consider using '#align add_circle.norm_neg_period AddCircle.norm_neg_periodₓ'. -/
 theorem norm_neg_period (x : ℝ) : ‖(x : AddCircle (-p))‖ = ‖(x : AddCircle p)‖ :=
   by
   suffices ‖(↑(-1 * x) : AddCircle (-1 * p))‖ = ‖(x : AddCircle p)‖ by rw [← this, neg_one_mul];
@@ -95,12 +83,6 @@ theorem norm_neg_period (x : ℝ) : ‖(x : AddCircle (-p))‖ = ‖(x : AddCirc
   simp only [norm_coe_mul, abs_neg, abs_one, one_mul]
 #align add_circle.norm_neg_period AddCircle.norm_neg_period
 
-/- warning: add_circle.norm_eq_of_zero -> AddCircle.norm_eq_of_zero is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (AddCircle.normedAddCommGroup (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)
-but is expected to have type
-  forall {x : Real}, Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
-Case conversion may be inaccurate. Consider using '#align add_circle.norm_eq_of_zero AddCircle.norm_eq_of_zeroₓ'. -/
 @[simp]
 theorem norm_eq_of_zero {x : ℝ} : ‖(x : AddCircle (0 : ℝ))‖ = |x| :=
   by
@@ -110,12 +92,6 @@ theorem norm_eq_of_zero {x : ℝ} : ‖(x : AddCircle (0 : ℝ))‖ = |x| :=
   simp [QuotientAddGroup.eq_iff_sub_mem, mem_zmultiples_iff, sub_eq_zero]
 #align add_circle.norm_eq_of_zero AddCircle.norm_eq_of_zero
 
-/- warning: add_circle.norm_eq -> AddCircle.norm_eq is a dubious translation:
-lean 3 declaration is
-  forall (p : Real) {x : Real}, Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) (round.{0} Real Real.linearOrderedRing Real.floorRing (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Inv.inv.{0} Real Real.hasInv p) x))) p)))
-but is expected to have type
-  forall (p : Real) {x : Real}, Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Int.cast.{0} Real Real.intCast (round.{0} Real Real.instLinearOrderedRingReal Real.instFloorRingRealInstLinearOrderedRingReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Inv.inv.{0} Real Real.instInvReal p) x))) p)))
-Case conversion may be inaccurate. Consider using '#align add_circle.norm_eq AddCircle.norm_eqₓ'. -/
 theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) * p| :=
   by
   suffices ∀ x : ℝ, ‖(x : AddCircle (1 : ℝ))‖ = |x - round x|
@@ -154,12 +130,6 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
     simp
 #align add_circle.norm_eq AddCircle.norm_eq
 
-/- warning: add_circle.norm_eq' -> AddCircle.norm_eq' is a dubious translation:
-lean 3 declaration is
-  forall (p : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (forall {x : Real}, Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) p (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Inv.inv.{0} Real Real.hasInv p) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) (round.{0} Real Real.linearOrderedRing Real.floorRing (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Inv.inv.{0} Real Real.hasInv p) x)))))))
-but is expected to have type
-  forall (p : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (forall {x : Real}, Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) p (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Inv.inv.{0} Real Real.instInvReal p) x) (Int.cast.{0} Real Real.intCast (round.{0} Real Real.instLinearOrderedRingReal Real.instFloorRingRealInstLinearOrderedRingReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Inv.inv.{0} Real Real.instInvReal p) x)))))))
-Case conversion may be inaccurate. Consider using '#align add_circle.norm_eq' AddCircle.norm_eq'ₓ'. -/
 theorem norm_eq' (hp : 0 < p) {x : ℝ} : ‖(x : AddCircle p)‖ = p * |p⁻¹ * x - round (p⁻¹ * x)| :=
   by
   conv_rhs =>
@@ -168,12 +138,6 @@ theorem norm_eq' (hp : 0 < p) {x : ℝ} : ‖(x : AddCircle p)‖ = p * |p⁻¹
   rw [← abs_mul, mul_sub, mul_inv_cancel_left₀ hp.ne.symm, norm_eq, mul_comm p]
 #align add_circle.norm_eq' AddCircle.norm_eq'
 
-/- warning: add_circle.norm_le_half_period -> AddCircle.norm_le_half_period is a dubious translation:
-lean 3 declaration is
-  forall (p : Real) {x : AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p}, (Ne.{1} Real p (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) x) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
-but is expected to have type
-  forall (p : Real) {x : AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p}, (Ne.{1} Real p (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNorm.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p)) x) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
-Case conversion may be inaccurate. Consider using '#align add_circle.norm_le_half_period AddCircle.norm_le_half_periodₓ'. -/
 theorem norm_le_half_period {x : AddCircle p} (hp : p ≠ 0) : ‖x‖ ≤ |p| / 2 :=
   by
   obtain ⟨x⟩ := x
@@ -183,12 +147,6 @@ theorem norm_le_half_period {x : AddCircle p} (hp : p ≠ 0) : ‖x‖ ≤ |p| /
   exact abs_sub_round (p⁻¹ * x)
 #align add_circle.norm_le_half_period AddCircle.norm_le_half_period
 
-/- warning: add_circle.norm_half_period_eq -> AddCircle.norm_half_period_eq is a dubious translation:
-lean 3 declaration is
-  forall (p : Real), Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) p (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))
-but is expected to have type
-  forall (p : Real), Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) p (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
-Case conversion may be inaccurate. Consider using '#align add_circle.norm_half_period_eq AddCircle.norm_half_period_eqₓ'. -/
 @[simp]
 theorem norm_half_period_eq : ‖(↑(p / 2) : AddCircle p)‖ = |p| / 2 :=
   by
@@ -197,12 +155,6 @@ theorem norm_half_period_eq : ‖(↑(p / 2) : AddCircle p)‖ = |p| / 2 :=
     one_mul, (by linarith : p / 2 - p = -(p / 2)), abs_neg, abs_div, abs_two]
 #align add_circle.norm_half_period_eq AddCircle.norm_half_period_eq
 
-/- warning: add_circle.norm_coe_eq_abs_iff -> AddCircle.norm_coe_eq_abs_iff is a dubious translation:
-lean 3 declaration is
-  forall (p : Real) {x : Real}, (Ne.{1} Real p (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Iff (Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)) (LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))))
-but is expected to have type
-  forall (p : Real) {x : Real}, (Ne.{1} Real p (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Iff (Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)) (LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))
-Case conversion may be inaccurate. Consider using '#align add_circle.norm_coe_eq_abs_iff AddCircle.norm_coe_eq_abs_iffₓ'. -/
 theorem norm_coe_eq_abs_iff {x : ℝ} (hp : p ≠ 0) : ‖(x : AddCircle p)‖ = |x| ↔ |x| ≤ |p| / 2 :=
   by
   refine' ⟨fun hx => hx ▸ norm_le_half_period p hp, fun hx => _⟩
@@ -233,36 +185,18 @@ theorem norm_coe_eq_abs_iff {x : ℝ} (hp : p ≠ 0) : ‖(x : AddCircle p)‖ =
 
 open Metric
 
-/- warning: add_circle.closed_ball_eq_univ_of_half_period_le -> AddCircle.closedBall_eq_univ_of_half_period_le is a dubious translation:
-lean 3 declaration is
-  forall (p : Real), (Ne.{1} Real p (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (x : AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) {ε : Real}, (LE.le.{0} Real Real.hasLe (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) ε) -> (Eq.{1} (Set.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p)) (Metric.closedBall.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toSeminormedAddCommGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))) x ε) (Set.univ.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))))
-but is expected to have type
-  forall (p : Real), (Ne.{1} Real p (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (x : AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) {ε : Real}, (LE.le.{0} Real Real.instLEReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) ε) -> (Eq.{1} (Set.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p)) (Metric.closedBall.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toSeminormedAddCommGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))) x ε) (Set.univ.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))))
-Case conversion may be inaccurate. Consider using '#align add_circle.closed_ball_eq_univ_of_half_period_le AddCircle.closedBall_eq_univ_of_half_period_leₓ'. -/
 theorem closedBall_eq_univ_of_half_period_le (hp : p ≠ 0) (x : AddCircle p) {ε : ℝ}
     (hε : |p| / 2 ≤ ε) : closedBall x ε = univ :=
   eq_univ_iff_forall.mpr fun x => by
     simpa only [mem_closed_ball, dist_eq_norm] using (norm_le_half_period p hp).trans hε
 #align add_circle.closed_ball_eq_univ_of_half_period_le AddCircle.closedBall_eq_univ_of_half_period_le
 
-/- warning: add_circle.coe_real_preimage_closed_ball_period_zero -> AddCircle.coe_real_preimage_closedBall_period_zero is a dubious translation:
-lean 3 declaration is
-  forall (x : Real) (ε : Real), Eq.{1} (Set.{0} Real) (Set.preimage.{0, 0} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))))) (Metric.closedBall.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (AddCircle.normedAddCommGroup (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) x) ε)) (Metric.closedBall.{0} Real Real.pseudoMetricSpace x ε)
-but is expected to have type
-  forall (x : Real) (ε : Real), Eq.{1} (Set.{0} Real) (Set.preimage.{0, 0} Real (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Metric.closedBall.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (AddSubgroup.seminormedAddCommGroupQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) x) ε)) (Metric.closedBall.{0} Real Real.pseudoMetricSpace x ε)
-Case conversion may be inaccurate. Consider using '#align add_circle.coe_real_preimage_closed_ball_period_zero AddCircle.coe_real_preimage_closedBall_period_zeroₓ'. -/
 @[simp]
 theorem coe_real_preimage_closedBall_period_zero (x ε : ℝ) :
     coe ⁻¹' closedBall (x : AddCircle (0 : ℝ)) ε = closedBall x ε := by
   ext y <;> simp [dist_eq_norm, ← QuotientAddGroup.mk_sub]
 #align add_circle.coe_real_preimage_closed_ball_period_zero AddCircle.coe_real_preimage_closedBall_period_zero
 
-/- warning: add_circle.coe_real_preimage_closed_ball_eq_Union -> AddCircle.coe_real_preimage_closedBall_eq_iUnion is a dubious translation:
-lean 3 declaration is
-  forall (p : Real) (x : Real) (ε : Real), Eq.{1} (Set.{0} Real) (Set.preimage.{0, 0} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p)))) (Metric.closedBall.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toSeminormedAddCommGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x) ε)) (Set.iUnion.{0, 1} Real Int (fun (z : Int) => Metric.closedBall.{0} Real Real.pseudoMetricSpace (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) x (SMul.smul.{0, 0} Int Real (SubNegMonoid.SMulInt.{0} Real (AddGroup.toSubNegMonoid.{0} Real Real.addGroup)) z p)) ε))
-but is expected to have type
-  forall (p : Real) (x : Real) (ε : Real), Eq.{1} (Set.{0} Real) (Set.preimage.{0, 0} Real (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (Metric.closedBall.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (AddSubgroup.seminormedAddCommGroupQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x) ε)) (Set.iUnion.{0, 1} Real Int (fun (z : Int) => Metric.closedBall.{0} Real Real.pseudoMetricSpace (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) x (HSMul.hSMul.{0, 0, 0} Int Real Real (instHSMul.{0, 0} Int Real (SubNegMonoid.SMulInt.{0} Real (AddGroup.toSubNegMonoid.{0} Real Real.instAddGroupReal))) z p)) ε))
-Case conversion may be inaccurate. Consider using '#align add_circle.coe_real_preimage_closed_ball_eq_Union AddCircle.coe_real_preimage_closedBall_eq_iUnionₓ'. -/
 theorem coe_real_preimage_closedBall_eq_iUnion (x ε : ℝ) :
     coe ⁻¹' closedBall (x : AddCircle p) ε = ⋃ z : ℤ, closedBall (x + z • p) ε :=
   by
@@ -277,12 +211,6 @@ theorem coe_real_preimage_closedBall_eq_iUnion (x ε : ℝ) :
   exact (round_le (p⁻¹ * (y - x)) n).trans hn
 #align add_circle.coe_real_preimage_closed_ball_eq_Union AddCircle.coe_real_preimage_closedBall_eq_iUnion
 
-/- warning: add_circle.coe_real_preimage_closed_ball_inter_eq -> AddCircle.coe_real_preimage_closedBall_inter_eq is a dubious translation:
-lean 3 declaration is
-  forall (p : Real) {x : Real} {ε : Real} (s : Set.{0} Real), (HasSubset.Subset.{0} (Set.{0} Real) (Set.hasSubset.{0} Real) s (Metric.closedBall.{0} Real Real.pseudoMetricSpace x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) -> (Eq.{1} (Set.{0} Real) (Inter.inter.{0} (Set.{0} Real) (Set.hasInter.{0} Real) (Set.preimage.{0, 0} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p)))) (Metric.closedBall.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toSeminormedAddCommGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x) ε)) s) (ite.{1} (Set.{0} Real) (LT.lt.{0} Real Real.hasLt ε (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Real.decidableLT ε (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Inter.inter.{0} (Set.{0} Real) (Set.hasInter.{0} Real) (Metric.closedBall.{0} Real Real.pseudoMetricSpace x ε) s) s))
-but is expected to have type
-  forall (p : Real) {x : Real} {ε : Real} (s : Set.{0} Real), (HasSubset.Subset.{0} (Set.{0} Real) (Set.instHasSubsetSet.{0} Real) s (Metric.closedBall.{0} Real Real.pseudoMetricSpace x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) -> (Eq.{1} (Set.{0} Real) (Inter.inter.{0} (Set.{0} Real) (Set.instInterSet.{0} Real) (Set.preimage.{0, 0} Real (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (Metric.closedBall.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (AddSubgroup.seminormedAddCommGroupQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x) ε)) s) (ite.{1} (Set.{0} Real) (LT.lt.{0} Real Real.instLTReal ε (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Real.decidableLT ε (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Inter.inter.{0} (Set.{0} Real) (Set.instInterSet.{0} Real) (Metric.closedBall.{0} Real Real.pseudoMetricSpace x ε) s) s))
-Case conversion may be inaccurate. Consider using '#align add_circle.coe_real_preimage_closed_ball_inter_eq AddCircle.coe_real_preimage_closedBall_inter_eqₓ'. -/
 theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
     (hs : s ⊆ closedBall x (|p| / 2)) :
     coe ⁻¹' closedBall (x : AddCircle p) ε ∩ s = if ε < |p| / 2 then closedBall x ε ∩ s else s :=
@@ -324,12 +252,6 @@ variable {p} [hp : Fact (0 < p)]
 
 include hp
 
-/- warning: add_circle.norm_div_nat_cast -> AddCircle.norm_div_nat_cast is a dubious translation:
-lean 3 declaration is
-  forall {p : Real} [hp : Fact (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)] {m : Nat} {n : Nat}, Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) m) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)) p))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) p (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) (LinearOrder.min.{0} Nat Nat.linearOrder (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) m n) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) m n)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)))
-but is expected to have type
-  forall {p : Real} [hp : Fact (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)] {m : Nat} {n : Nat}, Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Nat.cast.{0} Real Real.natCast m) (Nat.cast.{0} Real Real.natCast n)) p))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) p (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Nat.cast.{0} Real Real.natCast (Min.min.{0} Nat instMinNat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) m n) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) m n)))) (Nat.cast.{0} Real Real.natCast n)))
-Case conversion may be inaccurate. Consider using '#align add_circle.norm_div_nat_cast AddCircle.norm_div_nat_castₓ'. -/
 theorem norm_div_nat_cast {m n : ℕ} :
     ‖(↑(↑m / ↑n * p) : AddCircle p)‖ = p * (↑(min (m % n) (n - m % n)) / n) :=
   by
@@ -337,12 +259,6 @@ theorem norm_div_nat_cast {m n : ℕ} :
   rw [norm_eq' p hp.out, this, abs_sub_round_div_natCast_eq]
 #align add_circle.norm_div_nat_cast AddCircle.norm_div_nat_cast
 
-/- warning: add_circle.exists_norm_eq_of_fin_add_order -> AddCircle.exists_norm_eq_of_isOfFinAddOrder is a dubious translation:
-lean 3 declaration is
-  forall {p : Real} [hp : Fact (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)] {u : AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p}, (IsOfFinAddOrder.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))))) u) -> (Exists.{1} Nat (fun (k : Nat) => Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) u) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) p (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) k) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) (addOrderOf.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))))) u))))))
-but is expected to have type
-  forall {p : Real} [hp : Fact (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)] {u : AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p}, (IsOfFinAddOrder.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))))) u) -> (Exists.{1} Nat (fun (k : Nat) => Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNorm.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p)) u) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) p (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Nat.cast.{0} Real Real.natCast k) (Nat.cast.{0} Real Real.natCast (addOrderOf.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))))) u))))))
-Case conversion may be inaccurate. Consider using '#align add_circle.exists_norm_eq_of_fin_add_order AddCircle.exists_norm_eq_of_isOfFinAddOrderₓ'. -/
 theorem exists_norm_eq_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrder u) :
     ∃ k : ℕ, ‖u‖ = p * (k / addOrderOf u) :=
   by
@@ -353,9 +269,6 @@ theorem exists_norm_eq_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrde
   rw [← hm, norm_div_nat_cast]
 #align add_circle.exists_norm_eq_of_fin_add_order AddCircle.exists_norm_eq_of_isOfFinAddOrder
 
-/- warning: add_circle.le_add_order_smul_norm_of_is_of_fin_add_order -> AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align add_circle.le_add_order_smul_norm_of_is_of_fin_add_order AddCircle.le_add_order_smul_norm_of_isOfFinAddOrderₓ'. -/
 theorem le_add_order_smul_norm_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrder u)
     (hu' : u ≠ 0) : p ≤ addOrderOf u • ‖u‖ :=
   by
@@ -374,12 +287,6 @@ end AddCircle
 
 namespace UnitAddCircle
 
-/- warning: unit_add_circle.norm_eq -> UnitAddCircle.norm_eq is a dubious translation:
-lean 3 declaration is
-  forall {x : Real}, Eq.{1} Real (Norm.norm.{0} UnitAddCircle (NormedAddCommGroup.toHasNorm.{0} UnitAddCircle (AddCircle.normedAddCommGroup (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real UnitAddCircle (HasLiftT.mk.{1, 1} Real UnitAddCircle (CoeTCₓ.coe.{1, 1} Real UnitAddCircle (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) (round.{0} Real Real.linearOrderedRing Real.floorRing x))))
-but is expected to have type
-  forall {x : Real}, Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) x (Int.cast.{0} Real Real.intCast (round.{0} Real Real.instLinearOrderedRingReal Real.instFloorRingRealInstLinearOrderedRingReal x))))
-Case conversion may be inaccurate. Consider using '#align unit_add_circle.norm_eq UnitAddCircle.norm_eqₓ'. -/
 theorem norm_eq {x : ℝ} : ‖(x : UnitAddCircle)‖ = |x - round x| := by simp [AddCircle.norm_eq]
 #align unit_add_circle.norm_eq UnitAddCircle.norm_eq

2ed2c631

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -90,9 +90,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align add_circle.norm_neg_period AddCircle.norm_neg_periodₓ'. -/
 theorem norm_neg_period (x : ℝ) : ‖(x : AddCircle (-p))‖ = ‖(x : AddCircle p)‖ :=
   by
-  suffices ‖(↑(-1 * x) : AddCircle (-1 * p))‖ = ‖(x : AddCircle p)‖
-    by
-    rw [← this, neg_one_mul]
+  suffices ‖(↑(-1 * x) : AddCircle (-1 * p))‖ = ‖(x : AddCircle p)‖ by rw [← this, neg_one_mul];
     simp
   simp only [norm_coe_mul, abs_neg, abs_one, one_mul]
 #align add_circle.norm_neg_period AddCircle.norm_neg_period
@@ -122,8 +120,7 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
   by
   suffices ∀ x : ℝ, ‖(x : AddCircle (1 : ℝ))‖ = |x - round x|
     by
-    rcases eq_or_ne p 0 with (rfl | hp)
-    · simp
+    rcases eq_or_ne p 0 with (rfl | hp); · simp
     intros
     have hx := norm_coe_mul p x p⁻¹
     rw [abs_inv, eq_inv_mul_iff_mul_eq₀ ((not_congr abs_eq_zero).mpr hp)] at hx
@@ -152,10 +149,7 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
     simp only [mem_set_of_eq, QuotientAddGroup.eq_iff_sub_mem, mem_zmultiples_iff,
       smul_one_eq_coe] at hb
     obtain ⟨z, hz⟩ := hb
-    rw [(by
-        rw [hz]
-        abel : x = b - z),
-      fract_sub_int, ← abs_sub_round_eq_min]
+    rw [(by rw [hz]; abel : x = b - z), fract_sub_int, ← abs_sub_round_eq_min]
     convert round_le b 0
     simp
 #align add_circle.norm_eq AddCircle.norm_eq
@@ -223,8 +217,7 @@ theorem norm_coe_eq_abs_iff {x : ℝ} (hp : p ≠ 0) : ‖(x : AddCircle p)‖ =
       exact this (-p) (neg_pos.mpr hp) hx
   clear hx
   intro p hp hx
-  rcases eq_or_ne x (p / 2) with (rfl | hx')
-  · simp [abs_div, abs_two]
+  rcases eq_or_ne x (p / 2) with (rfl | hx'); · simp [abs_div, abs_two]
   suffices round (p⁻¹ * x) = 0 by simp [norm_eq, this]
   rw [round_eq_zero_iff]
   obtain ⟨hx₁, hx₂⟩ := abs_le.mp hx
@@ -306,27 +299,22 @@ theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
         Union_inter, Union_ite, this, hε]
     intro z
     simp only [Real.closedBall_eq_Icc, zero_sub, zero_add] at hs⊢
-    rcases eq_or_ne z 0 with (rfl | hz)
-    · simp
+    rcases eq_or_ne z 0 with (rfl | hz); · simp
     simp only [hz, zsmul_eq_mul, if_false, eq_empty_iff_forall_not_mem]
     rintro y ⟨⟨hy₁, hy₂⟩, hy₀⟩
     obtain ⟨hy₃, hy₄⟩ := hs hy₀
     rcases lt_trichotomy 0 p with (hp | rfl | hp)
     · cases' Int.cast_le_neg_one_or_one_le_cast_of_ne_zero ℝ hz with hz' hz'
-      · have : ↑z * p ≤ -p
-        nlinarith
+      · have : ↑z * p ≤ -p; nlinarith
         linarith [abs_eq_self.mpr hp.le]
-      · have : p ≤ ↑z * p
-        nlinarith
+      · have : p ≤ ↑z * p; nlinarith
         linarith [abs_eq_self.mpr hp.le]
     · simp only [MulZeroClass.mul_zero, add_zero, abs_zero, zero_div] at hy₁ hy₂ hε
       linarith
     · cases' Int.cast_le_neg_one_or_one_le_cast_of_ne_zero ℝ hz with hz' hz'
-      · have : -p ≤ ↑z * p
-        nlinarith
+      · have : -p ≤ ↑z * p; nlinarith
         linarith [abs_eq_neg_self.mpr hp.le]
-      · have : ↑z * p ≤ p
-        nlinarith
+      · have : ↑z * p ≤ p; nlinarith
         linarith [abs_eq_neg_self.mpr hp.le]
 #align add_circle.coe_real_preimage_closed_ball_inter_eq AddCircle.coe_real_preimage_closedBall_inter_eq
 
@@ -372,9 +360,7 @@ theorem le_add_order_smul_norm_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFi
     (hu' : u ≠ 0) : p ≤ addOrderOf u • ‖u‖ :=
   by
   obtain ⟨n, hn⟩ := exists_norm_eq_of_fin_add_order hu
-  replace hu : (addOrderOf u : ℝ) ≠ 0;
-  · norm_cast
-    exact (add_order_of_pos_iff.mpr hu).Ne.symm
+  replace hu : (addOrderOf u : ℝ) ≠ 0; · norm_cast; exact (add_order_of_pos_iff.mpr hu).Ne.symm
   conv_lhs => rw [← mul_one p]
   rw [hn, nsmul_eq_mul, ← mul_assoc, mul_comm _ p, mul_assoc, mul_div_cancel' _ hu,
     mul_le_mul_left hp.out, Nat.one_le_cast, Nat.one_le_iff_ne_zero]

2ed2c631

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -366,10 +366,7 @@ theorem exists_norm_eq_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrde
 #align add_circle.exists_norm_eq_of_fin_add_order AddCircle.exists_norm_eq_of_isOfFinAddOrder
 
 /- warning: add_circle.le_add_order_smul_norm_of_is_of_fin_add_order -> AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder is a dubious translation:
-lean 3 declaration is
-  forall {p : Real} [hp : Fact (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)] {u : AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p}, (IsOfFinAddOrder.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))))) u) -> (Ne.{1} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) u (OfNat.ofNat.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) 0 (OfNat.mk.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) 0 (Zero.zero.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddZeroClass.toHasZero.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddMonoid.toAddZeroClass.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))))))))))) -> (LE.le.{0} Real Real.hasLe p (SMul.smul.{0, 0} Nat Real (AddMonoid.SMul.{0} Real Real.addMonoid) (addOrderOf.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))))) u) (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) u)))
-but is expected to have type
-  forall {p : Real} [hp : Fact (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)] {u : AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p}, (IsOfFinAddOrder.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))))) u) -> (Ne.{1} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) u (OfNat.ofNat.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) 0 (Zero.toOfNat0.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NegZeroClass.toZero.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubNegZeroMonoid.toNegZeroClass.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubtractionMonoid.toSubNegZeroMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubtractionCommMonoid.toSubtractionMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCommGroup.toDivisionAddCommMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (instAddCommGroupAddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))))))))) -> (LE.le.{0} Real Real.instLEReal p (HSMul.hSMul.{0, 0, 0} Nat Real Real (instHSMul.{0, 0} Nat Real (AddMonoid.SMul.{0} Real Real.instAddMonoidReal)) (addOrderOf.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))))) u) (Norm.norm.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNorm.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p)) u)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align add_circle.le_add_order_smul_norm_of_is_of_fin_add_order AddCircle.le_add_order_smul_norm_of_isOfFinAddOrderₓ'. -/
 theorem le_add_order_smul_norm_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrder u)
     (hu' : u ≠ 0) : p ≤ addOrderOf u • ‖u‖ :=

2ed2c631

bump to nightly-2023-05-18-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

b46e9d53

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 
 ! This file was ported from Lean 3 source module analysis.normed.group.add_circle
-! leanprover-community/mathlib commit 084f76e20c88eae536222583331abd9468b08e1c
+! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Topology.Instances.AddCircle
 /-!
 # The additive circle as a normed group
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define the normed group structure on `add_circle p`, for `p : ℝ`. For example if `p = 1` then:
 `‖(x : add_circle 1)‖ = |x - round x|` for any `x : ℝ` (see `unit_add_circle.norm_eq`).

084f76e2

bump to nightly-2023-05-16-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

b550b1b3

Diff

@@ -43,6 +43,12 @@ variable (p : ℝ)
 instance : NormedAddCommGroup (AddCircle p) :=
   AddSubgroup.normedAddCommGroupQuotient _
 
+/- warning: add_circle.norm_coe_mul -> AddCircle.norm_coe_mul is a dubious translation:
+lean 3 declaration is
+  forall (p : Real) (x : Real) (t : Real), Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p)) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p)) (AddCircle.normedAddCommGroup (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p)) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p)) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p)) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t p)))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) t x))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) t) (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x)))
+but is expected to have type
+  forall (p : Real) (x : Real) (t : Real), Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) t p))) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) t p))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) t p)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) t x))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) t) (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x)))
+Case conversion may be inaccurate. Consider using '#align add_circle.norm_coe_mul AddCircle.norm_coe_mulₓ'. -/
 @[simp]
 theorem norm_coe_mul (x : ℝ) (t : ℝ) :
     ‖(↑(t * x) : AddCircle (t * p))‖ = |t| * ‖(x : AddCircle p)‖ :=
@@ -73,6 +79,12 @@ theorem norm_coe_mul (x : ℝ) (t : ℝ) :
     exact aux hw
 #align add_circle.norm_coe_mul AddCircle.norm_coe_mul
 
+/- warning: add_circle.norm_neg_period -> AddCircle.norm_neg_period is a dubious translation:
+lean 3 declaration is
+  forall (p : Real) (x : Real), Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (Neg.neg.{0} Real Real.hasNeg p)) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (Neg.neg.{0} Real Real.hasNeg p)) (AddCircle.normedAddCommGroup (Neg.neg.{0} Real Real.hasNeg p))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (Neg.neg.{0} Real Real.hasNeg p)) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (Neg.neg.{0} Real Real.hasNeg p)) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (Neg.neg.{0} Real Real.hasNeg p)) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (Neg.neg.{0} Real Real.hasNeg p)))) x)) (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x))
+but is expected to have type
+  forall (p : Real) (x : Real), Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (Neg.neg.{0} Real Real.instNegReal p))) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (Neg.neg.{0} Real Real.instNegReal p))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (Neg.neg.{0} Real Real.instNegReal p)) x)) (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x))
+Case conversion may be inaccurate. Consider using '#align add_circle.norm_neg_period AddCircle.norm_neg_periodₓ'. -/
 theorem norm_neg_period (x : ℝ) : ‖(x : AddCircle (-p))‖ = ‖(x : AddCircle p)‖ :=
   by
   suffices ‖(↑(-1 * x) : AddCircle (-1 * p))‖ = ‖(x : AddCircle p)‖
@@ -82,6 +94,12 @@ theorem norm_neg_period (x : ℝ) : ‖(x : AddCircle (-p))‖ = ‖(x : AddCirc
   simp only [norm_coe_mul, abs_neg, abs_one, one_mul]
 #align add_circle.norm_neg_period AddCircle.norm_neg_period
 
+/- warning: add_circle.norm_eq_of_zero -> AddCircle.norm_eq_of_zero is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (AddCircle.normedAddCommGroup (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)
+but is expected to have type
+  forall {x : Real}, Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)
+Case conversion may be inaccurate. Consider using '#align add_circle.norm_eq_of_zero AddCircle.norm_eq_of_zeroₓ'. -/
 @[simp]
 theorem norm_eq_of_zero {x : ℝ} : ‖(x : AddCircle (0 : ℝ))‖ = |x| :=
   by
@@ -91,6 +109,12 @@ theorem norm_eq_of_zero {x : ℝ} : ‖(x : AddCircle (0 : ℝ))‖ = |x| :=
   simp [QuotientAddGroup.eq_iff_sub_mem, mem_zmultiples_iff, sub_eq_zero]
 #align add_circle.norm_eq_of_zero AddCircle.norm_eq_of_zero
 
+/- warning: add_circle.norm_eq -> AddCircle.norm_eq is a dubious translation:
+lean 3 declaration is
+  forall (p : Real) {x : Real}, Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) (round.{0} Real Real.linearOrderedRing Real.floorRing (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Inv.inv.{0} Real Real.hasInv p) x))) p)))
+but is expected to have type
+  forall (p : Real) {x : Real}, Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Int.cast.{0} Real Real.intCast (round.{0} Real Real.instLinearOrderedRingReal Real.instFloorRingRealInstLinearOrderedRingReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Inv.inv.{0} Real Real.instInvReal p) x))) p)))
+Case conversion may be inaccurate. Consider using '#align add_circle.norm_eq AddCircle.norm_eqₓ'. -/
 theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) * p| :=
   by
   suffices ∀ x : ℝ, ‖(x : AddCircle (1 : ℝ))‖ = |x - round x|
@@ -133,6 +157,12 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
     simp
 #align add_circle.norm_eq AddCircle.norm_eq
 
+/- warning: add_circle.norm_eq' -> AddCircle.norm_eq' is a dubious translation:
+lean 3 declaration is
+  forall (p : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p) -> (forall {x : Real}, Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) p (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Inv.inv.{0} Real Real.hasInv p) x) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) (round.{0} Real Real.linearOrderedRing Real.floorRing (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (Inv.inv.{0} Real Real.hasInv p) x)))))))
+but is expected to have type
+  forall (p : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p) -> (forall {x : Real}, Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) p (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Inv.inv.{0} Real Real.instInvReal p) x) (Int.cast.{0} Real Real.intCast (round.{0} Real Real.instLinearOrderedRingReal Real.instFloorRingRealInstLinearOrderedRingReal (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (Inv.inv.{0} Real Real.instInvReal p) x)))))))
+Case conversion may be inaccurate. Consider using '#align add_circle.norm_eq' AddCircle.norm_eq'ₓ'. -/
 theorem norm_eq' (hp : 0 < p) {x : ℝ} : ‖(x : AddCircle p)‖ = p * |p⁻¹ * x - round (p⁻¹ * x)| :=
   by
   conv_rhs =>
@@ -141,6 +171,12 @@ theorem norm_eq' (hp : 0 < p) {x : ℝ} : ‖(x : AddCircle p)‖ = p * |p⁻¹
   rw [← abs_mul, mul_sub, mul_inv_cancel_left₀ hp.ne.symm, norm_eq, mul_comm p]
 #align add_circle.norm_eq' AddCircle.norm_eq'
 
+/- warning: add_circle.norm_le_half_period -> AddCircle.norm_le_half_period is a dubious translation:
+lean 3 declaration is
+  forall (p : Real) {x : AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p}, (Ne.{1} Real p (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (LE.le.{0} Real Real.hasLe (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) x) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
+but is expected to have type
+  forall (p : Real) {x : AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p}, (Ne.{1} Real p (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (LE.le.{0} Real Real.instLEReal (Norm.norm.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNorm.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p)) x) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+Case conversion may be inaccurate. Consider using '#align add_circle.norm_le_half_period AddCircle.norm_le_half_periodₓ'. -/
 theorem norm_le_half_period {x : AddCircle p} (hp : p ≠ 0) : ‖x‖ ≤ |p| / 2 :=
   by
   obtain ⟨x⟩ := x
@@ -150,6 +186,12 @@ theorem norm_le_half_period {x : AddCircle p} (hp : p ≠ 0) : ‖x‖ ≤ |p| /
   exact abs_sub_round (p⁻¹ * x)
 #align add_circle.norm_le_half_period AddCircle.norm_le_half_period
 
+/- warning: add_circle.norm_half_period_eq -> AddCircle.norm_half_period_eq is a dubious translation:
+lean 3 declaration is
+  forall (p : Real), Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) p (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+  forall (p : Real), Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) p (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+Case conversion may be inaccurate. Consider using '#align add_circle.norm_half_period_eq AddCircle.norm_half_period_eqₓ'. -/
 @[simp]
 theorem norm_half_period_eq : ‖(↑(p / 2) : AddCircle p)‖ = |p| / 2 :=
   by
@@ -158,6 +200,12 @@ theorem norm_half_period_eq : ‖(↑(p / 2) : AddCircle p)‖ = |p| / 2 :=
     one_mul, (by linarith : p / 2 - p = -(p / 2)), abs_neg, abs_div, abs_two]
 #align add_circle.norm_half_period_eq AddCircle.norm_half_period_eq
 
+/- warning: add_circle.norm_coe_eq_abs_iff -> AddCircle.norm_coe_eq_abs_iff is a dubious translation:
+lean 3 declaration is
+  forall (p : Real) {x : Real}, (Ne.{1} Real p (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Iff (Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x)) (LE.le.{0} Real Real.hasLe (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) x) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))))
+but is expected to have type
+  forall (p : Real) {x : Real}, (Ne.{1} Real p (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Iff (Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x)) (LE.le.{0} Real Real.instLEReal (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) x) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))))
+Case conversion may be inaccurate. Consider using '#align add_circle.norm_coe_eq_abs_iff AddCircle.norm_coe_eq_abs_iffₓ'. -/
 theorem norm_coe_eq_abs_iff {x : ℝ} (hp : p ≠ 0) : ‖(x : AddCircle p)‖ = |x| ↔ |x| ≤ |p| / 2 :=
   by
   refine' ⟨fun hx => hx ▸ norm_le_half_period p hp, fun hx => _⟩
@@ -189,18 +237,36 @@ theorem norm_coe_eq_abs_iff {x : ℝ} (hp : p ≠ 0) : ‖(x : AddCircle p)‖ =
 
 open Metric
 
+/- warning: add_circle.closed_ball_eq_univ_of_half_period_le -> AddCircle.closedBall_eq_univ_of_half_period_le is a dubious translation:
+lean 3 declaration is
+  forall (p : Real), (Ne.{1} Real p (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (forall (x : AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) {ε : Real}, (LE.le.{0} Real Real.hasLe (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) ε) -> (Eq.{1} (Set.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p)) (Metric.closedBall.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toSeminormedAddCommGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))) x ε) (Set.univ.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))))
+but is expected to have type
+  forall (p : Real), (Ne.{1} Real p (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (forall (x : AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) {ε : Real}, (LE.le.{0} Real Real.instLEReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) ε) -> (Eq.{1} (Set.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p)) (Metric.closedBall.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toSeminormedAddCommGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))) x ε) (Set.univ.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))))
+Case conversion may be inaccurate. Consider using '#align add_circle.closed_ball_eq_univ_of_half_period_le AddCircle.closedBall_eq_univ_of_half_period_leₓ'. -/
 theorem closedBall_eq_univ_of_half_period_le (hp : p ≠ 0) (x : AddCircle p) {ε : ℝ}
     (hε : |p| / 2 ≤ ε) : closedBall x ε = univ :=
   eq_univ_iff_forall.mpr fun x => by
     simpa only [mem_closed_ball, dist_eq_norm] using (norm_le_half_period p hp).trans hε
 #align add_circle.closed_ball_eq_univ_of_half_period_le AddCircle.closedBall_eq_univ_of_half_period_le
 
+/- warning: add_circle.coe_real_preimage_closed_ball_period_zero -> AddCircle.coe_real_preimage_closedBall_period_zero is a dubious translation:
+lean 3 declaration is
+  forall (x : Real) (ε : Real), Eq.{1} (Set.{0} Real) (Set.preimage.{0, 0} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))))) (Metric.closedBall.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (NormedAddCommGroup.toSeminormedAddCommGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (AddCircle.normedAddCommGroup (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) x) ε)) (Metric.closedBall.{0} Real Real.pseudoMetricSpace x ε)
+but is expected to have type
+  forall (x : Real) (ε : Real), Eq.{1} (Set.{0} Real) (Set.preimage.{0, 0} Real (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Metric.closedBall.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (AddSubgroup.seminormedAddCommGroupQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) x) ε)) (Metric.closedBall.{0} Real Real.pseudoMetricSpace x ε)
+Case conversion may be inaccurate. Consider using '#align add_circle.coe_real_preimage_closed_ball_period_zero AddCircle.coe_real_preimage_closedBall_period_zeroₓ'. -/
 @[simp]
 theorem coe_real_preimage_closedBall_period_zero (x ε : ℝ) :
     coe ⁻¹' closedBall (x : AddCircle (0 : ℝ)) ε = closedBall x ε := by
   ext y <;> simp [dist_eq_norm, ← QuotientAddGroup.mk_sub]
 #align add_circle.coe_real_preimage_closed_ball_period_zero AddCircle.coe_real_preimage_closedBall_period_zero
 
+/- warning: add_circle.coe_real_preimage_closed_ball_eq_Union -> AddCircle.coe_real_preimage_closedBall_eq_iUnion is a dubious translation:
+lean 3 declaration is
+  forall (p : Real) (x : Real) (ε : Real), Eq.{1} (Set.{0} Real) (Set.preimage.{0, 0} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p)))) (Metric.closedBall.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toSeminormedAddCommGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x) ε)) (Set.iUnion.{0, 1} Real Int (fun (z : Int) => Metric.closedBall.{0} Real Real.pseudoMetricSpace (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) x (SMul.smul.{0, 0} Int Real (SubNegMonoid.SMulInt.{0} Real (AddGroup.toSubNegMonoid.{0} Real Real.addGroup)) z p)) ε))
+but is expected to have type
+  forall (p : Real) (x : Real) (ε : Real), Eq.{1} (Set.{0} Real) (Set.preimage.{0, 0} Real (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (Metric.closedBall.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (AddSubgroup.seminormedAddCommGroupQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x) ε)) (Set.iUnion.{0, 1} Real Int (fun (z : Int) => Metric.closedBall.{0} Real Real.pseudoMetricSpace (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) x (HSMul.hSMul.{0, 0, 0} Int Real Real (instHSMul.{0, 0} Int Real (SubNegMonoid.SMulInt.{0} Real (AddGroup.toSubNegMonoid.{0} Real Real.instAddGroupReal))) z p)) ε))
+Case conversion may be inaccurate. Consider using '#align add_circle.coe_real_preimage_closed_ball_eq_Union AddCircle.coe_real_preimage_closedBall_eq_iUnionₓ'. -/
 theorem coe_real_preimage_closedBall_eq_iUnion (x ε : ℝ) :
     coe ⁻¹' closedBall (x : AddCircle p) ε = ⋃ z : ℤ, closedBall (x + z • p) ε :=
   by
@@ -215,6 +281,12 @@ theorem coe_real_preimage_closedBall_eq_iUnion (x ε : ℝ) :
   exact (round_le (p⁻¹ * (y - x)) n).trans hn
 #align add_circle.coe_real_preimage_closed_ball_eq_Union AddCircle.coe_real_preimage_closedBall_eq_iUnion
 
+/- warning: add_circle.coe_real_preimage_closed_ball_inter_eq -> AddCircle.coe_real_preimage_closedBall_inter_eq is a dubious translation:
+lean 3 declaration is
+  forall (p : Real) {x : Real} {ε : Real} (s : Set.{0} Real), (HasSubset.Subset.{0} (Set.{0} Real) (Set.hasSubset.{0} Real) s (Metric.closedBall.{0} Real Real.pseudoMetricSpace x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))) -> (Eq.{1} (Set.{0} Real) (Inter.inter.{0} (Set.{0} Real) (Set.hasInter.{0} Real) (Set.preimage.{0, 0} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p)))) (Metric.closedBall.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toSeminormedAddCommGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) x) ε)) s) (ite.{1} (Set.{0} Real) (LT.lt.{0} Real Real.hasLt ε (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Real.decidableLT ε (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) p) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))))) (Inter.inter.{0} (Set.{0} Real) (Set.hasInter.{0} Real) (Metric.closedBall.{0} Real Real.pseudoMetricSpace x ε) s) s))
+but is expected to have type
+  forall (p : Real) {x : Real} {ε : Real} (s : Set.{0} Real), (HasSubset.Subset.{0} (Set.{0} Real) (Set.instHasSubsetSet.{0} Real) s (Metric.closedBall.{0} Real Real.pseudoMetricSpace x (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) -> (Eq.{1} (Set.{0} Real) (Inter.inter.{0} (Set.{0} Real) (Set.instInterSet.{0} Real) (Set.preimage.{0, 0} Real (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (Metric.closedBall.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (SeminormedAddCommGroup.toPseudoMetricSpace.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (AddSubgroup.seminormedAddCommGroupQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) x) ε)) s) (ite.{1} (Set.{0} Real) (LT.lt.{0} Real Real.instLTReal ε (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Real.decidableLT ε (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) p) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (Inter.inter.{0} (Set.{0} Real) (Set.instInterSet.{0} Real) (Metric.closedBall.{0} Real Real.pseudoMetricSpace x ε) s) s))
+Case conversion may be inaccurate. Consider using '#align add_circle.coe_real_preimage_closed_ball_inter_eq AddCircle.coe_real_preimage_closedBall_inter_eqₓ'. -/
 theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
     (hs : s ⊆ closedBall x (|p| / 2)) :
     coe ⁻¹' closedBall (x : AddCircle p) ε ∩ s = if ε < |p| / 2 then closedBall x ε ∩ s else s :=
@@ -261,6 +333,12 @@ variable {p} [hp : Fact (0 < p)]
 
 include hp
 
+/- warning: add_circle.norm_div_nat_cast -> AddCircle.norm_div_nat_cast is a dubious translation:
+lean 3 declaration is
+  forall {p : Real} [hp : Fact (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)] {m : Nat} {n : Nat}, Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (HasLiftT.mk.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (CoeTCₓ.coe.{1, 1} Real (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) m) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)) p))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) p (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) (LinearOrder.min.{0} Nat Nat.linearOrder (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) m n) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat Nat.hasSub) n (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.hasMod) m n)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) n)))
+but is expected to have type
+  forall {p : Real} [hp : Fact (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)] {m : Nat} {n : Nat}, Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p)) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) p) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Nat.cast.{0} Real Real.natCast m) (Nat.cast.{0} Real Real.natCast n)) p))) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) p (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Nat.cast.{0} Real Real.natCast (Min.min.{0} Nat instMinNat (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) m n) (HSub.hSub.{0, 0, 0} Nat Nat Nat (instHSub.{0} Nat instSubNat) n (HMod.hMod.{0, 0, 0} Nat Nat Nat (instHMod.{0} Nat Nat.instModNat) m n)))) (Nat.cast.{0} Real Real.natCast n)))
+Case conversion may be inaccurate. Consider using '#align add_circle.norm_div_nat_cast AddCircle.norm_div_nat_castₓ'. -/
 theorem norm_div_nat_cast {m n : ℕ} :
     ‖(↑(↑m / ↑n * p) : AddCircle p)‖ = p * (↑(min (m % n) (n - m % n)) / n) :=
   by
@@ -268,7 +346,13 @@ theorem norm_div_nat_cast {m n : ℕ} :
   rw [norm_eq' p hp.out, this, abs_sub_round_div_natCast_eq]
 #align add_circle.norm_div_nat_cast AddCircle.norm_div_nat_cast
 
-theorem exists_norm_eq_of_fin_add_order {u : AddCircle p} (hu : IsOfFinAddOrder u) :
+/- warning: add_circle.exists_norm_eq_of_fin_add_order -> AddCircle.exists_norm_eq_of_isOfFinAddOrder is a dubious translation:
+lean 3 declaration is
+  forall {p : Real} [hp : Fact (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)] {u : AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p}, (IsOfFinAddOrder.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))))) u) -> (Exists.{1} Nat (fun (k : Nat) => Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) u) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) p (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) k) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat Real (HasLiftT.mk.{1, 1} Nat Real (CoeTCₓ.coe.{1, 1} Nat Real (Nat.castCoe.{0} Real Real.hasNatCast))) (addOrderOf.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))))) u))))))
+but is expected to have type
+  forall {p : Real} [hp : Fact (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)] {u : AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p}, (IsOfFinAddOrder.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))))) u) -> (Exists.{1} Nat (fun (k : Nat) => Eq.{1} Real (Norm.norm.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNorm.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p)) u) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) p (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (Nat.cast.{0} Real Real.natCast k) (Nat.cast.{0} Real Real.natCast (addOrderOf.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))))) u))))))
+Case conversion may be inaccurate. Consider using '#align add_circle.exists_norm_eq_of_fin_add_order AddCircle.exists_norm_eq_of_isOfFinAddOrderₓ'. -/
+theorem exists_norm_eq_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrder u) :
     ∃ k : ℕ, ‖u‖ = p * (k / addOrderOf u) :=
   by
   let n := addOrderOf u
@@ -276,8 +360,14 @@ theorem exists_norm_eq_of_fin_add_order {u : AddCircle p} (hu : IsOfFinAddOrder
   obtain ⟨m, -, -, hm⟩ := exists_gcd_eq_one_of_is_of_fin_add_order hu
   refine' ⟨min (m % n) (n - m % n), _⟩
   rw [← hm, norm_div_nat_cast]
-#align add_circle.exists_norm_eq_of_fin_add_order AddCircle.exists_norm_eq_of_fin_add_order
-
+#align add_circle.exists_norm_eq_of_fin_add_order AddCircle.exists_norm_eq_of_isOfFinAddOrder
+
+/- warning: add_circle.le_add_order_smul_norm_of_is_of_fin_add_order -> AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder is a dubious translation:
+lean 3 declaration is
+  forall {p : Real} [hp : Fact (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) p)] {u : AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p}, (IsOfFinAddOrder.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))))) u) -> (Ne.{1} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) u (OfNat.ofNat.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) 0 (OfNat.mk.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) 0 (Zero.zero.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddZeroClass.toHasZero.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddMonoid.toAddZeroClass.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))))))))))) -> (LE.le.{0} Real Real.hasLe p (SMul.smul.{0, 0} Nat Real (AddMonoid.SMul.{0} Real Real.addMonoid) (addOrderOf.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p))))) u) (Norm.norm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (NormedAddCommGroup.toHasNorm.{0} (AddCircle.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology p) (AddCircle.normedAddCommGroup p)) u)))
+but is expected to have type
+  forall {p : Real} [hp : Fact (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) p)] {u : AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p}, (IsOfFinAddOrder.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))))) u) -> (Ne.{1} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) u (OfNat.ofNat.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) 0 (Zero.toOfNat0.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NegZeroClass.toZero.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubNegZeroMonoid.toNegZeroClass.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubtractionMonoid.toSubNegZeroMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubtractionCommMonoid.toSubtractionMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCommGroup.toDivisionAddCommMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (instAddCommGroupAddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))))))))) -> (LE.le.{0} Real Real.instLEReal p (HSMul.hSMul.{0, 0, 0} Nat Real Real (instHSMul.{0, 0} Nat Real (AddMonoid.SMul.{0} Real Real.instAddMonoidReal)) (addOrderOf.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (SubNegMonoid.toAddMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddGroup.toSubNegMonoid.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddGroup.toAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNormedAddGroup.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p))))) u) (Norm.norm.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (NormedAddCommGroup.toNorm.{0} (AddCircle.{0} Real Real.instLinearOrderedAddCommGroupReal (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) instOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p) (AddCircle.instNormedAddCommGroupAddCircleRealInstLinearOrderedAddCommGroupRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstOrderTopologyRealToTopologicalSpaceToUniformSpacePseudoMetricSpaceInstPreorderReal p)) u)))
+Case conversion may be inaccurate. Consider using '#align add_circle.le_add_order_smul_norm_of_is_of_fin_add_order AddCircle.le_add_order_smul_norm_of_isOfFinAddOrderₓ'. -/
 theorem le_add_order_smul_norm_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrder u)
     (hu' : u ≠ 0) : p ≤ addOrderOf u • ‖u‖ :=
   by
@@ -298,6 +388,12 @@ end AddCircle
 
 namespace UnitAddCircle
 
+/- warning: unit_add_circle.norm_eq -> UnitAddCircle.norm_eq is a dubious translation:
+lean 3 declaration is
+  forall {x : Real}, Eq.{1} Real (Norm.norm.{0} UnitAddCircle (NormedAddCommGroup.toHasNorm.{0} UnitAddCircle (AddCircle.normedAddCommGroup (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Real UnitAddCircle (HasLiftT.mk.{1, 1} Real UnitAddCircle (CoeTCₓ.coe.{1, 1} Real UnitAddCircle (AddCircle.hasCoeT.{0} Real Real.linearOrderedAddCommGroup (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) Real.orderTopology (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.hasNeg Real.hasSup) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Int Real (HasLiftT.mk.{1, 1} Int Real (CoeTCₓ.coe.{1, 1} Int Real (Int.castCoe.{0} Real Real.hasIntCast))) (round.{0} Real Real.linearOrderedRing Real.floorRing x))))
+but is expected to have type
+  forall {x : Real}, Eq.{1} Real (Norm.norm.{0} (HasQuotient.Quotient.{0, 0} Real (AddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (QuotientAddGroup.instHasQuotientAddSubgroup.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (normOnQuotient.{0} Real (NonUnitalSeminormedRing.toSeminormedAddCommGroup.{0} Real (NonUnitalNormedRing.toNonUnitalSeminormedRing.{0} Real (NormedRing.toNonUnitalNormedRing.{0} Real (NormedCommRing.toNormedRing.{0} Real Real.normedCommRing)))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (QuotientAddGroup.mk.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (AddSubgroup.zmultiples.{0} Real (AddCommGroup.toAddGroup.{0} Real (OrderedAddCommGroup.toAddCommGroup.{0} Real (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{0} Real Real.instLinearOrderedAddCommGroupReal))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) x)) (Abs.abs.{0} Real (Neg.toHasAbs.{0} Real Real.instNegReal Real.instSupReal) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) x (Int.cast.{0} Real Real.intCast (round.{0} Real Real.instLinearOrderedRingReal Real.instFloorRingRealInstLinearOrderedRingReal x))))
+Case conversion may be inaccurate. Consider using '#align unit_add_circle.norm_eq UnitAddCircle.norm_eqₓ'. -/
 theorem norm_eq {x : ℝ} : ‖(x : UnitAddCircle)‖ = |x - round x| := by simp [AddCircle.norm_eq]
 #align unit_add_circle.norm_eq UnitAddCircle.norm_eq

084f76e2

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -55,7 +55,7 @@ theorem norm_coe_mul (x : ℝ) (t : ℝ) :
   rcases eq_or_ne t 0 with (rfl | ht); · simp
   have ht' : |t| ≠ 0 := (not_congr abs_eq_zero).mpr ht
   simp only [quotient_norm_eq, Real.norm_eq_abs]
-  conv_rhs => rw [← smul_eq_mul, ← Real.infₛ_smul_of_nonneg (abs_nonneg t)]
+  conv_rhs => rw [← smul_eq_mul, ← Real.sInf_smul_of_nonneg (abs_nonneg t)]
   simp only [QuotientAddGroup.mk'_apply, QuotientAddGroup.eq_iff_sub_mem]
   congr 1
   ext z
@@ -86,7 +86,7 @@ theorem norm_neg_period (x : ℝ) : ‖(x : AddCircle (-p))‖ = ‖(x : AddCirc
 theorem norm_eq_of_zero {x : ℝ} : ‖(x : AddCircle (0 : ℝ))‖ = |x| :=
   by
   suffices { y : ℝ | (y : AddCircle (0 : ℝ)) = (x : AddCircle (0 : ℝ)) } = {x} by
-    rw [quotient_norm_eq, this, image_singleton, Real.norm_eq_abs, cinfₛ_singleton]
+    rw [quotient_norm_eq, this, image_singleton, Real.norm_eq_abs, csInf_singleton]
   ext y
   simp [QuotientAddGroup.eq_iff_sub_mem, mem_zmultiples_iff, sub_eq_zero]
 #align add_circle.norm_eq_of_zero AddCircle.norm_eq_of_zero
@@ -108,7 +108,7 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
     ⟨0, by simp [mem_lowerBounds]⟩
   have h₂ : (abs '' { m : ℝ | (m : AddCircle (1 : ℝ)) = x }).Nonempty := ⟨|x|, ⟨x, rfl, rfl⟩⟩
   apply le_antisymm
-  · simp only [le_min_iff, Real.norm_eq_abs, cinfₛ_le_iff h₁ h₂]
+  · simp only [le_min_iff, Real.norm_eq_abs, csInf_le_iff h₁ h₂]
     intro b h
     refine'
       ⟨mem_lowerBounds.1 h _ ⟨fract x, _, abs_fract⟩,
@@ -120,7 +120,7 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
       simp only [mem_set_of_eq, fract, sub_eq_self, QuotientAddGroup.mk_sub,
         QuotientAddGroup.eq_zero_iff, int_cast_mem_zmultiples_one, sub_sub,
         (by norm_cast : (⌊x⌋ : ℝ) + 1 = (↑(⌊x⌋ + 1) : ℝ))]
-  · simp only [QuotientAddGroup.mk'_apply, Real.norm_eq_abs, le_cinfₛ_iff h₁ h₂]
+  · simp only [QuotientAddGroup.mk'_apply, Real.norm_eq_abs, le_csInf_iff h₁ h₂]
     rintro b' ⟨b, hb, rfl⟩
     simp only [mem_set_of_eq, QuotientAddGroup.eq_iff_sub_mem, mem_zmultiples_iff,
       smul_one_eq_coe] at hb
@@ -201,7 +201,7 @@ theorem coe_real_preimage_closedBall_period_zero (x ε : ℝ) :
   ext y <;> simp [dist_eq_norm, ← QuotientAddGroup.mk_sub]
 #align add_circle.coe_real_preimage_closed_ball_period_zero AddCircle.coe_real_preimage_closedBall_period_zero
 
-theorem coe_real_preimage_closedBall_eq_unionᵢ (x ε : ℝ) :
+theorem coe_real_preimage_closedBall_eq_iUnion (x ε : ℝ) :
     coe ⁻¹' closedBall (x : AddCircle p) ε = ⋃ z : ℤ, closedBall (x + z • p) ε :=
   by
   rcases eq_or_ne p 0 with (rfl | hp); · simp [Union_const]
@@ -213,7 +213,7 @@ theorem coe_real_preimage_closedBall_eq_unionᵢ (x ε : ℝ) :
   rw [← mul_le_mul_left (abs_pos.mpr <| inv_ne_zero hp), ← abs_mul, mul_sub, mul_comm _ p,
     inv_mul_cancel_left₀ hp] at hn⊢
   exact (round_le (p⁻¹ * (y - x)) n).trans hn
-#align add_circle.coe_real_preimage_closed_ball_eq_Union AddCircle.coe_real_preimage_closedBall_eq_unionᵢ
+#align add_circle.coe_real_preimage_closed_ball_eq_Union AddCircle.coe_real_preimage_closedBall_eq_iUnion
 
 theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
     (hs : s ⊆ closedBall x (|p| / 2)) :

084f76e2

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -244,7 +244,7 @@ theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
       · have : p ≤ ↑z * p
         nlinarith
         linarith [abs_eq_self.mpr hp.le]
-    · simp only [mul_zero, add_zero, abs_zero, zero_div] at hy₁ hy₂ hε
+    · simp only [MulZeroClass.mul_zero, add_zero, abs_zero, zero_div] at hy₁ hy₂ hε
       linarith
     · cases' Int.cast_le_neg_one_or_one_le_cast_of_ne_zero ℝ hz with hz' hz'
       · have : -p ≤ ↑z * p
@@ -289,7 +289,7 @@ theorem le_add_order_smul_norm_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFi
   rw [hn, nsmul_eq_mul, ← mul_assoc, mul_comm _ p, mul_assoc, mul_div_cancel' _ hu,
     mul_le_mul_left hp.out, Nat.one_le_cast, Nat.one_le_iff_ne_zero]
   contrapose! hu'
-  simpa only [hu', algebraMap.coe_zero, zero_div, mul_zero, norm_eq_zero] using hn
+  simpa only [hu', algebraMap.coe_zero, zero_div, MulZeroClass.mul_zero, norm_eq_zero] using hn
 #align add_circle.le_add_order_smul_norm_of_is_of_fin_add_order AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder
 
 end FiniteOrderPoints

084f76e2

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

084f76e2

chore: Rename nat_cast/int_cast/rat_cast to natCast/intCast/ratCast (#11486)

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

145460b9

Diff

@@ -103,9 +103,9 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
       ⟨mem_lowerBounds.1 h _ ⟨fract x, _, abs_fract⟩,
         mem_lowerBounds.1 h _ ⟨fract x - 1, _, by rw [abs_sub_comm, abs_one_sub_fract]⟩⟩
     · simp only [mem_setOf, fract, sub_eq_self, QuotientAddGroup.mk_sub,
-        QuotientAddGroup.eq_zero_iff, int_cast_mem_zmultiples_one]
+        QuotientAddGroup.eq_zero_iff, intCast_mem_zmultiples_one]
     · simp only [mem_setOf, fract, sub_eq_self, QuotientAddGroup.mk_sub,
-        QuotientAddGroup.eq_zero_iff, int_cast_mem_zmultiples_one, sub_sub,
+        QuotientAddGroup.eq_zero_iff, intCast_mem_zmultiples_one, sub_sub,
         (by norm_cast : (⌊x⌋ : ℝ) + 1 = (↑(⌊x⌋ + 1) : ℝ))]
   · simp only [QuotientAddGroup.mk'_apply, Real.norm_eq_abs, le_csInf_iff h₁ h₂]
     rintro b' ⟨b, hb, rfl⟩
@@ -238,11 +238,11 @@ section FiniteOrderPoints
 
 variable {p} [hp : Fact (0 < p)]
 
-theorem norm_div_nat_cast {m n : ℕ} :
+theorem norm_div_natCast {m n : ℕ} :
     ‖(↑(↑m / ↑n * p) : AddCircle p)‖ = p * (↑(min (m % n) (n - m % n)) / n) := by
   have : p⁻¹ * (↑m / ↑n * p) = ↑m / ↑n := by rw [mul_comm _ p, inv_mul_cancel_left₀ hp.out.ne.symm]
   rw [norm_eq' p hp.out, this, abs_sub_round_div_natCast_eq]
-#align add_circle.norm_div_nat_cast AddCircle.norm_div_nat_cast
+#align add_circle.norm_div_nat_cast AddCircle.norm_div_natCast
 
 theorem exists_norm_eq_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrder u) :
     ∃ k : ℕ, ‖u‖ = p * (k / addOrderOf u) := by
@@ -250,7 +250,7 @@ theorem exists_norm_eq_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrde
   change ∃ k : ℕ, ‖u‖ = p * (k / n)
   obtain ⟨m, -, -, hm⟩ := exists_gcd_eq_one_of_isOfFinAddOrder hu
   refine' ⟨min (m % n) (n - m % n), _⟩
-  rw [← hm, norm_div_nat_cast]
+  rw [← hm, norm_div_natCast]
 #align add_circle.exists_norm_eq_of_fin_add_order AddCircle.exists_norm_eq_of_isOfFinAddOrder
 
 theorem le_add_order_smul_norm_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrder u)

084f76e2

chore: Rename mul-div cancellation lemmas (#11530)

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

4ea4a86a

Diff

@@ -260,7 +260,7 @@ theorem le_add_order_smul_norm_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFi
     norm_cast
     exact (addOrderOf_pos_iff.mpr hu).ne'
   conv_lhs => rw [← mul_one p]
-  rw [hn, nsmul_eq_mul, ← mul_assoc, mul_comm _ p, mul_assoc, mul_div_cancel' _ hu,
+  rw [hn, nsmul_eq_mul, ← mul_assoc, mul_comm _ p, mul_assoc, mul_div_cancel₀ _ hu,
     mul_le_mul_left hp.out, Nat.one_le_cast, Nat.one_le_iff_ne_zero]
   contrapose! hu'
   simpa only [hu', Nat.cast_zero, zero_div, mul_zero, norm_eq_zero] using hn

084f76e2

chore: remove unused tactics (#11351)

I removed some of the tactics that were not used and are hopefully uncontroversial arising from the linter at #11308.

As the commit messages should convey, the removed tactics are, essentially,

push_cast
norm_cast
congr
norm_num
dsimp
funext
intro
infer_instance

b99084a9

Diff

@@ -87,7 +87,6 @@ theorem norm_eq {x : ℝ} : ‖(x : AddCircle p)‖ = |x - round (p⁻¹ * x) *
   suffices ∀ x : ℝ, ‖(x : AddCircle (1 : ℝ))‖ = |x - round x| by
     rcases eq_or_ne p 0 with (rfl | hp)
     · simp
-    intros
     have hx := norm_coe_mul p x p⁻¹
     rw [abs_inv, eq_inv_mul_iff_mul_eq₀ ((not_congr abs_eq_zero).mpr hp)] at hx
     rw [← hx, inv_mul_cancel hp, this, ← abs_mul, mul_sub, mul_inv_cancel_left₀ hp, mul_comm p]

084f76e2

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

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>

a13e8040

Diff

@@ -222,20 +222,16 @@ theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
     obtain ⟨hy₃, hy₄⟩ := hs hy₀
     rcases lt_trichotomy 0 p with (hp | (rfl : 0 = p) | hp)
     · cases' Int.cast_le_neg_one_or_one_le_cast_of_ne_zero ℝ hz with hz' hz'
-      · have : ↑z * p ≤ -p
-        nlinarith
+      · have : ↑z * p ≤ -p := by nlinarith
         linarith [abs_eq_self.mpr hp.le]
-      · have : p ≤ ↑z * p
-        nlinarith
+      · have : p ≤ ↑z * p := by nlinarith
         linarith [abs_eq_self.mpr hp.le]
     · simp only [mul_zero, add_zero, abs_zero, zero_div] at hy₁ hy₂ hε
       linarith
     · cases' Int.cast_le_neg_one_or_one_le_cast_of_ne_zero ℝ hz with hz' hz'
-      · have : -p ≤ ↑z * p
-        nlinarith
+      · have : -p ≤ ↑z * p := by nlinarith
         linarith [abs_eq_neg_self.mpr hp.le]
-      · have : ↑z * p ≤ p
-        nlinarith
+      · have : ↑z * p ≤ p := by nlinarith
         linarith [abs_eq_neg_self.mpr hp.le]
 #align add_circle.coe_real_preimage_closed_ball_inter_eq AddCircle.coe_real_preimage_closedBall_inter_eq
 
@@ -261,8 +257,8 @@ theorem exists_norm_eq_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrde
 theorem le_add_order_smul_norm_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFinAddOrder u)
     (hu' : u ≠ 0) : p ≤ addOrderOf u • ‖u‖ := by
   obtain ⟨n, hn⟩ := exists_norm_eq_of_isOfFinAddOrder hu
-  replace hu : (addOrderOf u : ℝ) ≠ 0
-  · norm_cast
+  replace hu : (addOrderOf u : ℝ) ≠ 0 := by
+    norm_cast
     exact (addOrderOf_pos_iff.mpr hu).ne'
   conv_lhs => rw [← mul_one p]
   rw [hn, nsmul_eq_mul, ← mul_assoc, mul_comm _ p, mul_assoc, mul_div_cancel' _ hu,

084f76e2

chore: remove uses of cases' (#9171)

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

3fca282c

Diff

@@ -199,7 +199,7 @@ theorem coe_real_preimage_closedBall_eq_iUnion (x ε : ℝ) :
 theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
     (hs : s ⊆ closedBall x (|p| / 2)) :
     (↑) ⁻¹' closedBall (x : AddCircle p) ε ∩ s = if ε < |p| / 2 then closedBall x ε ∩ s else s := by
-  cases' le_or_lt (|p| / 2) ε with hε hε
+  rcases le_or_lt (|p| / 2) ε with hε | hε
   · rcases eq_or_ne p 0 with (rfl | hp)
     · simp only [abs_zero, zero_div] at hε
       simp only [not_lt.mpr hε, coe_real_preimage_closedBall_period_zero, abs_zero, zero_div,

084f76e2

chore: fix some cases in names (#7469)

And fix some names in comments where this revealed issues

be0d066c

Diff

@@ -20,7 +20,7 @@ We define the normed group structure on `AddCircle p`, for `p : ℝ`. For exampl
 
 ## TODO
 
- * The fact `inner_product_geometry.angle (Real.cos θ) (Real.sin θ) = ‖(θ : Real.Angle)‖`
+ * The fact `InnerProductGeometry.angle (Real.cos θ) (Real.sin θ) = ‖(θ : Real.Angle)‖`
 
 -/

084f76e2

chore: Make Set/Finset lemmas match lattice lemma names (#7378)

Rename union_eq_left_iff_subset to union_eq_left to match sup_eq_left. Similarly for the right and inter versions.

aef04106

Diff

@@ -203,11 +203,11 @@ theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
   · rcases eq_or_ne p 0 with (rfl | hp)
     · simp only [abs_zero, zero_div] at hε
       simp only [not_lt.mpr hε, coe_real_preimage_closedBall_period_zero, abs_zero, zero_div,
-        if_false, inter_eq_right_iff_subset]
+        if_false, inter_eq_right]
       exact hs.trans (closedBall_subset_closedBall <| by simp [hε])
     -- Porting note: was
     -- simp [closedBall_eq_univ_of_half_period_le p hp (↑x) hε, not_lt.mpr hε]
-    simp only [not_lt.mpr hε, ite_false, inter_eq_right_iff_subset]
+    simp only [not_lt.mpr hε, ite_false, inter_eq_right]
     rw [closedBall_eq_univ_of_half_period_le p hp (↑x : ℝ ⧸ zmultiples p) hε, preimage_univ]
     apply subset_univ
   · suffices ∀ z : ℤ, closedBall (x + z • p) ε ∩ s = if z = 0 then closedBall x ε ∩ s else ∅ by

084f76e2

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

277dea95

Diff

@@ -228,7 +228,7 @@ theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
       · have : p ≤ ↑z * p
         nlinarith
         linarith [abs_eq_self.mpr hp.le]
-    · simp only [MulZeroClass.mul_zero, add_zero, abs_zero, zero_div] at hy₁ hy₂ hε
+    · simp only [mul_zero, add_zero, abs_zero, zero_div] at hy₁ hy₂ hε
       linarith
     · cases' Int.cast_le_neg_one_or_one_le_cast_of_ne_zero ℝ hz with hz' hz'
       · have : -p ≤ ↑z * p
@@ -268,7 +268,7 @@ theorem le_add_order_smul_norm_of_isOfFinAddOrder {u : AddCircle p} (hu : IsOfFi
   rw [hn, nsmul_eq_mul, ← mul_assoc, mul_comm _ p, mul_assoc, mul_div_cancel' _ hu,
     mul_le_mul_left hp.out, Nat.one_le_cast, Nat.one_le_iff_ne_zero]
   contrapose! hu'
-  simpa only [hu', Nat.cast_zero, zero_div, MulZeroClass.mul_zero, norm_eq_zero] using hn
+  simpa only [hu', Nat.cast_zero, zero_div, mul_zero, norm_eq_zero] using hn
 #align add_circle.le_add_order_smul_norm_of_is_of_fin_add_order AddCircle.le_add_order_smul_norm_of_isOfFinAddOrder
 
 end FiniteOrderPoints

084f76e2

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module analysis.normed.group.add_circle
-! leanprover-community/mathlib commit 084f76e20c88eae536222583331abd9468b08e1c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.Normed.Group.Quotient
 import Mathlib.Topology.Instances.AddCircle
 
+#align_import analysis.normed.group.add_circle from "leanprover-community/mathlib"@"084f76e20c88eae536222583331abd9468b08e1c"
+
 /-!
 # The additive circle as a normed group

084f76e2

fix: precedence of ⁺, ⁻ and abs (#5619)

6c1021b5

Diff

@@ -59,7 +59,7 @@ theorem norm_coe_mul (x : ℝ) (t : ℝ) :
   ext z
   rw [mem_smul_set_iff_inv_smul_mem₀ ht']
   show
-    (∃ y, y - t * x ∈ zmultiples (t * p) ∧ |y| = z) ↔ ∃ w, w - x ∈ zmultiples p ∧ |w| = (|t|)⁻¹ * z
+    (∃ y, y - t * x ∈ zmultiples (t * p) ∧ |y| = z) ↔ ∃ w, w - x ∈ zmultiples p ∧ |w| = |t|⁻¹ * z
   constructor
   · rintro ⟨y, hy, rfl⟩
     refine' ⟨t⁻¹ * y, _, by rw [abs_mul, abs_inv]⟩

084f76e2

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -47,7 +47,7 @@ instance : NormedAddCommGroup (AddCircle p) :=
 theorem norm_coe_mul (x : ℝ) (t : ℝ) :
     ‖(↑(t * x) : AddCircle (t * p))‖ = |t| * ‖(x : AddCircle p)‖ := by
   have aux : ∀ {a b c : ℝ}, a ∈ zmultiples b → c * a ∈ zmultiples (c * b) := fun {a b c} h => by
-    simp only [mem_zmultiples_iff] at h⊢
+    simp only [mem_zmultiples_iff] at h ⊢
     obtain ⟨n, rfl⟩ := h
     exact ⟨n, (mul_smul_comm n c b).symm⟩
   rcases eq_or_ne t 0 with (rfl | ht); · simp
@@ -195,7 +195,7 @@ theorem coe_real_preimage_closedBall_eq_iUnion (x ε : ℝ) :
   refine' ⟨fun h => ⟨round (p⁻¹ * (y - x)), h⟩, _⟩
   rintro ⟨n, hn⟩
   rw [← mul_le_mul_left (abs_pos.mpr <| inv_ne_zero hp), ← abs_mul, mul_sub, mul_comm _ p,
-    inv_mul_cancel_left₀ hp] at hn⊢
+    inv_mul_cancel_left₀ hp] at hn ⊢
   exact (round_le (p⁻¹ * (y - x)) n).trans hn
 #align add_circle.coe_real_preimage_closed_ball_eq_Union AddCircle.coe_real_preimage_closedBall_eq_iUnion
 
@@ -217,7 +217,7 @@ theorem coe_real_preimage_closedBall_inter_eq {x ε : ℝ} (s : Set ℝ)
       simp [-zsmul_eq_mul, ← QuotientAddGroup.mk_zero, coe_real_preimage_closedBall_eq_iUnion,
         iUnion_inter, iUnion_ite, this, hε]
     intro z
-    simp only [Real.closedBall_eq_Icc, zero_sub, zero_add] at hs⊢
+    simp only [Real.closedBall_eq_Icc, zero_sub, zero_add] at hs ⊢
     rcases eq_or_ne z 0 with (rfl | hz)
     · simp
     simp only [hz, zsmul_eq_mul, if_false, eq_empty_iff_forall_not_mem]

084f76e2

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -23,7 +23,7 @@ We define the normed group structure on `AddCircle p`, for `p : ℝ`. For exampl
 
 ## TODO
 
- * The fact `inner_product_geometry.angle (Real.cos θ) (Real.sin θ) = ‖(θ : real.angle)‖`
+ * The fact `inner_product_geometry.angle (Real.cos θ) (Real.sin θ) = ‖(θ : Real.Angle)‖`
 
 -/

084f76e2

feat: port Analysis.Normed.Group.AddCircle (#4023)

Co-authored-by: Chris Hughes <33847686+ChrisHughes24@users.noreply.github.com>

95a9188d

`analysis.normed.group.add_circle` ⟷ `Mathlib.Analysis.Normed.Group.AddCircle`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 662

analysis.normed.group.add_circle ⟷ Mathlib.Analysis.Normed.Group.AddCircle

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 662

`analysis.normed.group.add_circle` ⟷ `Mathlib.Analysis.Normed.Group.AddCircle`