topology.unit_interval
⟷
Mathlib.Topology.UnitInterval
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -5,8 +5,8 @@ Authors: Patrick Massot, Scott Morrison
-/
import Topology.Instances.Real
import Topology.Algebra.Field
-import Data.Set.Intervals.ProjIcc
-import Data.Set.Intervals.Instances
+import Order.Interval.Set.ProjIcc
+import Algebra.Order.Interval.Set.Instances
#align_import topology.unit_interval from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -223,7 +223,7 @@ theorem mul_pos_mem_iff {a t : ℝ} (ha : 0 < a) : a * t ∈ I ↔ t ∈ Set.Icc
· exact nonneg_of_mul_nonneg_right h₁ ha
· rwa [le_div_iff ha, mul_comm]
· exact mul_nonneg ha.le h₁
- · rwa [le_div_iff ha, mul_comm] at h₂
+ · rwa [le_div_iff ha, mul_comm] at h₂
#align unit_interval.mul_pos_mem_iff unitInterval.mul_pos_mem_iff
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -161,7 +161,7 @@ theorem coe_symm_eq (x : I) : (σ x : ℝ) = 1 - x :=
#align unit_interval.coe_symm_eq unitInterval.coe_symm_eq
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:307:22: continuitity! not supported at the moment -/
+/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:303:22: continuitity! not supported at the moment -/
#print unitInterval.continuous_symm /-
@[continuity]
theorem continuous_symm : Continuous σ := by continuity
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,10 +3,10 @@ Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison
-/
-import Mathbin.Topology.Instances.Real
-import Mathbin.Topology.Algebra.Field
-import Mathbin.Data.Set.Intervals.ProjIcc
-import Mathbin.Data.Set.Intervals.Instances
+import Topology.Instances.Real
+import Topology.Algebra.Field
+import Data.Set.Intervals.ProjIcc
+import Data.Set.Intervals.Instances
#align_import topology.unit_interval from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
@@ -161,7 +161,7 @@ theorem coe_symm_eq (x : I) : (σ x : ℝ) = 1 - x :=
#align unit_interval.coe_symm_eq unitInterval.coe_symm_eq
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:305:22: continuitity! not supported at the moment -/
+/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:307:22: continuitity! not supported at the moment -/
#print unitInterval.continuous_symm /-
@[continuity]
theorem continuous_symm : Continuous σ := by continuity
@@ -251,10 +251,10 @@ theorem projIcc_eq_one {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 1 ↔ 1
namespace Tactic.Interactive
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:337:4: warning: unsupported (TODO): `[tacs] -/
/-- A tactic that solves `0 ≤ ↑x`, `0 ≤ 1 - ↑x`, `↑x ≤ 1`, and `1 - ↑x ≤ 1` for `x : I`. -/
unsafe def unit_interval : tactic Unit :=
sorry <|> sorry <|> sorry <|> sorry
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,17 +2,14 @@
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison
-
-! This file was ported from Lean 3 source module topology.unit_interval
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Topology.Instances.Real
import Mathbin.Topology.Algebra.Field
import Mathbin.Data.Set.Intervals.ProjIcc
import Mathbin.Data.Set.Intervals.Instances
+#align_import topology.unit_interval from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
+
/-!
# The unit interval, as a topological space
mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303
@@ -164,7 +164,7 @@ theorem coe_symm_eq (x : I) : (σ x : ℝ) = 1 - x :=
#align unit_interval.coe_symm_eq unitInterval.coe_symm_eq
-/
-/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:304:22: continuitity! not supported at the moment -/
+/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:305:22: continuitity! not supported at the moment -/
#print unitInterval.continuous_symm /-
@[continuity]
theorem continuous_symm : Continuous σ := by continuity
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -43,26 +43,33 @@ abbrev unitInterval : Set ℝ :=
#align unit_interval unitInterval
-/
--- mathport name: unit_interval
scoped[unitInterval] notation "I" => unitInterval
namespace unitInterval
+#print unitInterval.zero_mem /-
theorem zero_mem : (0 : ℝ) ∈ I :=
⟨le_rfl, zero_le_one⟩
#align unit_interval.zero_mem unitInterval.zero_mem
+-/
+#print unitInterval.one_mem /-
theorem one_mem : (1 : ℝ) ∈ I :=
⟨zero_le_one, le_rfl⟩
#align unit_interval.one_mem unitInterval.one_mem
+-/
+#print unitInterval.mul_mem /-
theorem mul_mem {x y : ℝ} (hx : x ∈ I) (hy : y ∈ I) : x * y ∈ I :=
⟨mul_nonneg hx.1 hy.1, (mul_le_mul hx.2 hy.2 hy.1 zero_le_one).trans_eq <| one_mul 1⟩
#align unit_interval.mul_mem unitInterval.mul_mem
+-/
+#print unitInterval.div_mem /-
theorem div_mem {x y : ℝ} (hx : 0 ≤ x) (hy : 0 ≤ y) (hxy : x ≤ y) : x / y ∈ I :=
⟨div_nonneg hx hy, div_le_one_of_le hxy hy⟩
#align unit_interval.div_mem unitInterval.div_mem
+-/
#print unitInterval.fract_mem /-
theorem fract_mem (x : ℝ) : fract x ∈ I :=
@@ -70,11 +77,13 @@ theorem fract_mem (x : ℝ) : fract x ∈ I :=
#align unit_interval.fract_mem unitInterval.fract_mem
-/
+#print unitInterval.mem_iff_one_sub_mem /-
theorem mem_iff_one_sub_mem {t : ℝ} : t ∈ I ↔ 1 - t ∈ I :=
by
rw [mem_Icc, mem_Icc]
constructor <;> intro <;> constructor <;> linarith
#align unit_interval.mem_iff_one_sub_mem unitInterval.mem_iff_one_sub_mem
+-/
#print unitInterval.hasZero /-
instance hasZero : Zero I :=
@@ -88,13 +97,17 @@ instance hasOne : One I :=
#align unit_interval.has_one unitInterval.hasOne
-/
+#print unitInterval.coe_ne_zero /-
theorem coe_ne_zero {x : I} : (x : ℝ) ≠ 0 ↔ x ≠ 0 :=
not_iff_not.mpr coe_eq_zero
#align unit_interval.coe_ne_zero unitInterval.coe_ne_zero
+-/
+#print unitInterval.coe_ne_one /-
theorem coe_ne_one {x : I} : (x : ℝ) ≠ 1 ↔ x ≠ 1 :=
not_iff_not.mpr coe_eq_one
#align unit_interval.coe_ne_one unitInterval.coe_ne_one
+-/
instance : Nonempty I :=
⟨0⟩
@@ -102,14 +115,18 @@ instance : Nonempty I :=
instance : Mul I :=
⟨fun x y => ⟨x * y, mul_mem x.2 y.2⟩⟩
+#print unitInterval.mul_le_left /-
-- todo: we could set up a `linear_ordered_comm_monoid_with_zero I` instance
theorem mul_le_left {x y : I} : x * y ≤ x :=
Subtype.coe_le_coe.mp <| (mul_le_mul_of_nonneg_left y.2.2 x.2.1).trans_eq <| mul_one x
#align unit_interval.mul_le_left unitInterval.mul_le_left
+-/
+#print unitInterval.mul_le_right /-
theorem mul_le_right {x y : I} : x * y ≤ y :=
Subtype.coe_le_coe.mp <| (mul_le_mul_of_nonneg_right x.2.2 y.2.1).trans_eq <| one_mul y
#align unit_interval.mul_le_right unitInterval.mul_le_right
+-/
#print unitInterval.symm /-
/-- Unit interval central symmetry. -/
@@ -117,7 +134,6 @@ def symm : I → I := fun t => ⟨1 - t, mem_iff_one_sub_mem.mp t.Prop⟩
#align unit_interval.symm unitInterval.symm
-/
--- mathport name: unit_interval.symm
scoped notation "σ" => unitInterval.symm
#print unitInterval.symm_zero /-
@@ -141,10 +157,12 @@ theorem symm_symm (x : I) : σ (σ x) = x :=
#align unit_interval.symm_symm unitInterval.symm_symm
-/
+#print unitInterval.coe_symm_eq /-
@[simp]
theorem coe_symm_eq (x : I) : (σ x : ℝ) = 1 - x :=
rfl
#align unit_interval.coe_symm_eq unitInterval.coe_symm_eq
+-/
/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:304:22: continuitity! not supported at the moment -/
#print unitInterval.continuous_symm /-
@@ -159,34 +177,49 @@ instance : ConnectedSpace I :=
/-- Verify there is an instance for `compact_space I`. -/
example : CompactSpace I := by infer_instance
+#print unitInterval.nonneg /-
theorem nonneg (x : I) : 0 ≤ (x : ℝ) :=
x.2.1
#align unit_interval.nonneg unitInterval.nonneg
+-/
+#print unitInterval.one_minus_nonneg /-
theorem one_minus_nonneg (x : I) : 0 ≤ 1 - (x : ℝ) := by simpa using x.2.2
#align unit_interval.one_minus_nonneg unitInterval.one_minus_nonneg
+-/
+#print unitInterval.le_one /-
theorem le_one (x : I) : (x : ℝ) ≤ 1 :=
x.2.2
#align unit_interval.le_one unitInterval.le_one
+-/
+#print unitInterval.one_minus_le_one /-
theorem one_minus_le_one (x : I) : 1 - (x : ℝ) ≤ 1 := by simpa using x.2.1
#align unit_interval.one_minus_le_one unitInterval.one_minus_le_one
+-/
+#print unitInterval.add_pos /-
theorem add_pos {t : I} {x : ℝ} (hx : 0 < x) : 0 < (x + t : ℝ) :=
add_pos_of_pos_of_nonneg hx <| nonneg _
#align unit_interval.add_pos unitInterval.add_pos
+-/
+#print unitInterval.nonneg' /-
/-- like `unit_interval.nonneg`, but with the inequality in `I`. -/
theorem nonneg' {t : I} : 0 ≤ t :=
t.2.1
#align unit_interval.nonneg' unitInterval.nonneg'
+-/
+#print unitInterval.le_one' /-
/-- like `unit_interval.le_one`, but with the inequality in `I`. -/
theorem le_one' {t : I} : t ≤ 1 :=
t.2.2
#align unit_interval.le_one' unitInterval.le_one'
+-/
+#print unitInterval.mul_pos_mem_iff /-
theorem mul_pos_mem_iff {a t : ℝ} (ha : 0 < a) : a * t ∈ I ↔ t ∈ Set.Icc (0 : ℝ) (1 / a) :=
by
constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor
@@ -195,22 +228,29 @@ theorem mul_pos_mem_iff {a t : ℝ} (ha : 0 < a) : a * t ∈ I ↔ t ∈ Set.Icc
· exact mul_nonneg ha.le h₁
· rwa [le_div_iff ha, mul_comm] at h₂
#align unit_interval.mul_pos_mem_iff unitInterval.mul_pos_mem_iff
+-/
+#print unitInterval.two_mul_sub_one_mem_iff /-
theorem two_mul_sub_one_mem_iff {t : ℝ} : 2 * t - 1 ∈ I ↔ t ∈ Set.Icc (1 / 2 : ℝ) 1 := by
constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor <;> linarith
#align unit_interval.two_mul_sub_one_mem_iff unitInterval.two_mul_sub_one_mem_iff
+-/
end unitInterval
+#print projIcc_eq_zero /-
@[simp]
theorem projIcc_eq_zero {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 0 ↔ x ≤ 0 :=
projIcc_eq_left zero_lt_one
#align proj_Icc_eq_zero projIcc_eq_zero
+-/
+#print projIcc_eq_one /-
@[simp]
theorem projIcc_eq_one {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 1 ↔ 1 ≤ x :=
projIcc_eq_right zero_lt_one
#align proj_Icc_eq_one projIcc_eq_one
+-/
namespace Tactic.Interactive
@@ -229,6 +269,7 @@ section
variable {𝕜 : Type _} [LinearOrderedField 𝕜] [TopologicalSpace 𝕜] [TopologicalRing 𝕜]
+#print affineHomeomorph_image_I /-
-- We only need the ordering on `𝕜` here to avoid talking about flipping the interval over.
-- At the end of the day I only care about `ℝ`, so I'm hesitant to put work into generalizing.
/-- The image of `[0,1]` under the homeomorphism `λ x, a * x + b` is `[b, a+b]`.
@@ -236,7 +277,9 @@ variable {𝕜 : Type _} [LinearOrderedField 𝕜] [TopologicalSpace 𝕜] [Topo
theorem affineHomeomorph_image_I (a b : 𝕜) (h : 0 < a) :
affineHomeomorph a b h.Ne.symm '' Set.Icc 0 1 = Set.Icc b (a + b) := by simp [h]
#align affine_homeomorph_image_I affineHomeomorph_image_I
+-/
+#print iccHomeoI /-
/-- The affine homeomorphism from a nontrivial interval `[a,b]` to `[0,1]`.
-/
def iccHomeoI (a b : 𝕜) (h : a < b) : Set.Icc a b ≃ₜ Set.Icc (0 : 𝕜) (1 : 𝕜) :=
@@ -246,18 +289,23 @@ def iccHomeoI (a b : 𝕜) (h : a < b) : Set.Icc a b ≃ₜ Set.Icc (0 : 𝕜) (
apply Homeomorph.setCongr
simp [sub_pos.mpr h]
#align Icc_homeo_I iccHomeoI
+-/
+#print iccHomeoI_apply_coe /-
@[simp]
theorem iccHomeoI_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc a b) :
((iccHomeoI a b h) x : 𝕜) = (x - a) / (b - a) :=
rfl
#align Icc_homeo_I_apply_coe iccHomeoI_apply_coe
+-/
+#print iccHomeoI_symm_apply_coe /-
@[simp]
theorem iccHomeoI_symm_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc (0 : 𝕜) (1 : 𝕜)) :
((iccHomeoI a b h).symm x : 𝕜) = (b - a) * x + a :=
rfl
#align Icc_homeo_I_symm_apply_coe iccHomeoI_symm_apply_coe
+-/
end
mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0
@@ -214,10 +214,10 @@ theorem projIcc_eq_one {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 1 ↔ 1
namespace Tactic.Interactive
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:336:4: warning: unsupported (TODO): `[tacs] -/
/-- A tactic that solves `0 ≤ ↑x`, `0 ≤ 1 - ↑x`, `↑x ≤ 1`, and `1 - ↑x ≤ 1` for `x : I`. -/
unsafe def unit_interval : tactic Unit :=
sorry <|> sorry <|> sorry <|> sorry
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -193,7 +193,7 @@ theorem mul_pos_mem_iff {a t : ℝ} (ha : 0 < a) : a * t ∈ I ↔ t ∈ Set.Icc
· exact nonneg_of_mul_nonneg_right h₁ ha
· rwa [le_div_iff ha, mul_comm]
· exact mul_nonneg ha.le h₁
- · rwa [le_div_iff ha, mul_comm] at h₂
+ · rwa [le_div_iff ha, mul_comm] at h₂
#align unit_interval.mul_pos_mem_iff unitInterval.mul_pos_mem_iff
theorem two_mul_sub_one_mem_iff {t : ℝ} : 2 * t - 1 ∈ I ↔ t ∈ Set.Icc (1 / 2 : ℝ) 1 := by
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -214,18 +214,14 @@ theorem projIcc_eq_one {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 1 ↔ 1
namespace Tactic.Interactive
-/- warning: tactic.interactive.unit_interval clashes with [anonymous] -> [anonymous]
-Case conversion may be inaccurate. Consider using '#align tactic.interactive.unit_interval [anonymous]ₓ'. -/
/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
-#print [anonymous] /-
/-- A tactic that solves `0 ≤ ↑x`, `0 ≤ 1 - ↑x`, `↑x ≤ 1`, and `1 - ↑x ≤ 1` for `x : I`. -/
-unsafe def [anonymous] : tactic Unit :=
+unsafe def unit_interval : tactic Unit :=
sorry <|> sorry <|> sorry <|> sorry
-#align tactic.interactive.unit_interval [anonymous]
--/
+#align tactic.interactive.unit_interval tactic.interactive.unit_interval
end Tactic.Interactive
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -29,7 +29,7 @@ We provide basic instances, as well as a custom tactic for discharging
noncomputable section
-open Classical Topology Filter
+open scoped Classical Topology Filter
open Set Int Set.Icc
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -48,42 +48,18 @@ scoped[unitInterval] notation "I" => unitInterval
namespace unitInterval
-/- warning: unit_interval.zero_mem -> unitInterval.zero_mem is a dubious translation:
-lean 3 declaration is
- Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) unitInterval
-but is expected to have type
- Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) unitInterval
-Case conversion may be inaccurate. Consider using '#align unit_interval.zero_mem unitInterval.zero_memₓ'. -/
theorem zero_mem : (0 : ℝ) ∈ I :=
⟨le_rfl, zero_le_one⟩
#align unit_interval.zero_mem unitInterval.zero_mem
-/- warning: unit_interval.one_mem -> unitInterval.one_mem is a dubious translation:
-lean 3 declaration is
- Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) unitInterval
-but is expected to have type
- Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) unitInterval
-Case conversion may be inaccurate. Consider using '#align unit_interval.one_mem unitInterval.one_memₓ'. -/
theorem one_mem : (1 : ℝ) ∈ I :=
⟨zero_le_one, le_rfl⟩
#align unit_interval.one_mem unitInterval.one_mem
-/- warning: unit_interval.mul_mem -> unitInterval.mul_mem is a dubious translation:
-lean 3 declaration is
- forall {x : Real} {y : Real}, (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) -> (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) y unitInterval) -> (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) x y) unitInterval)
-but is expected to have type
- forall {x : Real} {y : Real}, (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) -> (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) y unitInterval) -> (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x y) unitInterval)
-Case conversion may be inaccurate. Consider using '#align unit_interval.mul_mem unitInterval.mul_memₓ'. -/
theorem mul_mem {x y : ℝ} (hx : x ∈ I) (hy : y ∈ I) : x * y ∈ I :=
⟨mul_nonneg hx.1 hy.1, (mul_le_mul hx.2 hy.2 hy.1 zero_le_one).trans_eq <| one_mul 1⟩
#align unit_interval.mul_mem unitInterval.mul_mem
-/- warning: unit_interval.div_mem -> unitInterval.div_mem is a dubious translation:
-lean 3 declaration is
- forall {x : Real} {y : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y) -> (LE.le.{0} Real Real.hasLe x y) -> (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) x y) unitInterval)
-but is expected to have type
- forall {x : Real} {y : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y) -> (LE.le.{0} Real Real.instLEReal x y) -> (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) x y) unitInterval)
-Case conversion may be inaccurate. Consider using '#align unit_interval.div_mem unitInterval.div_memₓ'. -/
theorem div_mem {x y : ℝ} (hx : 0 ≤ x) (hy : 0 ≤ y) (hxy : x ≤ y) : x / y ∈ I :=
⟨div_nonneg hx hy, div_le_one_of_le hxy hy⟩
#align unit_interval.div_mem unitInterval.div_mem
@@ -94,12 +70,6 @@ theorem fract_mem (x : ℝ) : fract x ∈ I :=
#align unit_interval.fract_mem unitInterval.fract_mem
-/
-/- warning: unit_interval.mem_iff_one_sub_mem -> unitInterval.mem_iff_one_sub_mem is a dubious translation:
-lean 3 declaration is
- forall {t : Real}, Iff (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) t unitInterval) (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) t) unitInterval)
-but is expected to have type
- forall {t : Real}, Iff (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) t unitInterval) (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) t) unitInterval)
-Case conversion may be inaccurate. Consider using '#align unit_interval.mem_iff_one_sub_mem unitInterval.mem_iff_one_sub_memₓ'. -/
theorem mem_iff_one_sub_mem {t : ℝ} : t ∈ I ↔ 1 - t ∈ I :=
by
rw [mem_Icc, mem_Icc]
@@ -118,22 +88,10 @@ instance hasOne : One I :=
#align unit_interval.has_one unitInterval.hasOne
-/
-/- warning: unit_interval.coe_ne_zero -> unitInterval.coe_ne_zero is a dubious translation:
-lean 3 declaration is
- forall {x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval}, Iff (Ne.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Ne.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) x (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (Zero.zero.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasZero))))
-but is expected to have type
- forall {x : Set.Elem.{0} Real unitInterval}, Iff (Ne.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Ne.{1} (Set.Elem.{0} Real unitInterval) x (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)))
-Case conversion may be inaccurate. Consider using '#align unit_interval.coe_ne_zero unitInterval.coe_ne_zeroₓ'. -/
theorem coe_ne_zero {x : I} : (x : ℝ) ≠ 0 ↔ x ≠ 0 :=
not_iff_not.mpr coe_eq_zero
#align unit_interval.coe_ne_zero unitInterval.coe_ne_zero
-/- warning: unit_interval.coe_ne_one -> unitInterval.coe_ne_one is a dubious translation:
-lean 3 declaration is
- forall {x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval}, Iff (Ne.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Ne.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) x (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (One.one.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasOne))))
-but is expected to have type
- forall {x : Set.Elem.{0} Real unitInterval}, Iff (Ne.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Ne.{1} (Set.Elem.{0} Real unitInterval) x (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne)))
-Case conversion may be inaccurate. Consider using '#align unit_interval.coe_ne_one unitInterval.coe_ne_oneₓ'. -/
theorem coe_ne_one {x : I} : (x : ℝ) ≠ 1 ↔ x ≠ 1 :=
not_iff_not.mpr coe_eq_one
#align unit_interval.coe_ne_one unitInterval.coe_ne_one
@@ -144,23 +102,11 @@ instance : Nonempty I :=
instance : Mul I :=
⟨fun x y => ⟨x * y, mul_mem x.2 y.2⟩⟩
-/- warning: unit_interval.mul_le_left -> unitInterval.mul_le_left is a dubious translation:
-lean 3 declaration is
- forall {x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval} {y : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval}, LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval)) (HMul.hMul.{0, 0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (instHMul.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasMul) x y) x
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-Case conversion may be inaccurate. Consider using '#align unit_interval.mul_le_left unitInterval.mul_le_leftₓ'. -/
-- todo: we could set up a `linear_ordered_comm_monoid_with_zero I` instance
theorem mul_le_left {x y : I} : x * y ≤ x :=
Subtype.coe_le_coe.mp <| (mul_le_mul_of_nonneg_left y.2.2 x.2.1).trans_eq <| mul_one x
#align unit_interval.mul_le_left unitInterval.mul_le_left
-/- warning: unit_interval.mul_le_right -> unitInterval.mul_le_right is a dubious translation:
-lean 3 declaration is
- forall {x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval} {y : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval}, LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval)) (HMul.hMul.{0, 0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (instHMul.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasMul) x y) y
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-Case conversion may be inaccurate. Consider using '#align unit_interval.mul_le_right unitInterval.mul_le_rightₓ'. -/
theorem mul_le_right {x y : I} : x * y ≤ y :=
Subtype.coe_le_coe.mp <| (mul_le_mul_of_nonneg_right x.2.2 y.2.1).trans_eq <| one_mul y
#align unit_interval.mul_le_right unitInterval.mul_le_right
@@ -195,12 +141,6 @@ theorem symm_symm (x : I) : σ (σ x) = x :=
#align unit_interval.symm_symm unitInterval.symm_symm
-/
-/- warning: unit_interval.coe_symm_eq -> unitInterval.coe_symm_eq is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align unit_interval.coe_symm_eq unitInterval.coe_symm_eqₓ'. -/
@[simp]
theorem coe_symm_eq (x : I) : (σ x : ℝ) = 1 - x :=
rfl
@@ -219,82 +159,34 @@ instance : ConnectedSpace I :=
/-- Verify there is an instance for `compact_space I`. -/
example : CompactSpace I := by infer_instance
-/- warning: unit_interval.nonneg -> unitInterval.nonneg is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align unit_interval.nonneg unitInterval.nonnegₓ'. -/
theorem nonneg (x : I) : 0 ≤ (x : ℝ) :=
x.2.1
#align unit_interval.nonneg unitInterval.nonneg
-/- warning: unit_interval.one_minus_nonneg -> unitInterval.one_minus_nonneg is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align unit_interval.one_minus_nonneg unitInterval.one_minus_nonnegₓ'. -/
theorem one_minus_nonneg (x : I) : 0 ≤ 1 - (x : ℝ) := by simpa using x.2.2
#align unit_interval.one_minus_nonneg unitInterval.one_minus_nonneg
-/- warning: unit_interval.le_one -> unitInterval.le_one is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align unit_interval.le_one unitInterval.le_oneₓ'. -/
theorem le_one (x : I) : (x : ℝ) ≤ 1 :=
x.2.2
#align unit_interval.le_one unitInterval.le_one
-/- warning: unit_interval.one_minus_le_one -> unitInterval.one_minus_le_one is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align unit_interval.one_minus_le_one unitInterval.one_minus_le_oneₓ'. -/
theorem one_minus_le_one (x : I) : 1 - (x : ℝ) ≤ 1 := by simpa using x.2.1
#align unit_interval.one_minus_le_one unitInterval.one_minus_le_one
-/- warning: unit_interval.add_pos -> unitInterval.add_pos is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align unit_interval.add_pos unitInterval.add_posₓ'. -/
theorem add_pos {t : I} {x : ℝ} (hx : 0 < x) : 0 < (x + t : ℝ) :=
add_pos_of_pos_of_nonneg hx <| nonneg _
#align unit_interval.add_pos unitInterval.add_pos
-/- warning: unit_interval.nonneg' -> unitInterval.nonneg' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align unit_interval.nonneg' unitInterval.nonneg'ₓ'. -/
/-- like `unit_interval.nonneg`, but with the inequality in `I`. -/
theorem nonneg' {t : I} : 0 ≤ t :=
t.2.1
#align unit_interval.nonneg' unitInterval.nonneg'
-/- warning: unit_interval.le_one' -> unitInterval.le_one' is a dubious translation:
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- forall {t : Set.Elem.{0} Real unitInterval}, LE.le.{0} (Set.Elem.{0} Real unitInterval) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval)) t (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne))
-Case conversion may be inaccurate. Consider using '#align unit_interval.le_one' unitInterval.le_one'ₓ'. -/
/-- like `unit_interval.le_one`, but with the inequality in `I`. -/
theorem le_one' {t : I} : t ≤ 1 :=
t.2.2
#align unit_interval.le_one' unitInterval.le_one'
-/- warning: unit_interval.mul_pos_mem_iff -> unitInterval.mul_pos_mem_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align unit_interval.mul_pos_mem_iff unitInterval.mul_pos_mem_iffₓ'. -/
theorem mul_pos_mem_iff {a t : ℝ} (ha : 0 < a) : a * t ∈ I ↔ t ∈ Set.Icc (0 : ℝ) (1 / a) :=
by
constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor
@@ -304,35 +196,17 @@ theorem mul_pos_mem_iff {a t : ℝ} (ha : 0 < a) : a * t ∈ I ↔ t ∈ Set.Icc
· rwa [le_div_iff ha, mul_comm] at h₂
#align unit_interval.mul_pos_mem_iff unitInterval.mul_pos_mem_iff
-/- warning: unit_interval.two_mul_sub_one_mem_iff -> unitInterval.two_mul_sub_one_mem_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align unit_interval.two_mul_sub_one_mem_iff unitInterval.two_mul_sub_one_mem_iffₓ'. -/
theorem two_mul_sub_one_mem_iff {t : ℝ} : 2 * t - 1 ∈ I ↔ t ∈ Set.Icc (1 / 2 : ℝ) 1 := by
constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor <;> linarith
#align unit_interval.two_mul_sub_one_mem_iff unitInterval.two_mul_sub_one_mem_iff
end unitInterval
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-Case conversion may be inaccurate. Consider using '#align proj_Icc_eq_zero projIcc_eq_zeroₓ'. -/
@[simp]
theorem projIcc_eq_zero {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 0 ↔ x ≤ 0 :=
projIcc_eq_left zero_lt_one
#align proj_Icc_eq_zero projIcc_eq_zero
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-Case conversion may be inaccurate. Consider using '#align proj_Icc_eq_one projIcc_eq_oneₓ'. -/
@[simp]
theorem projIcc_eq_one {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 1 ↔ 1 ≤ x :=
projIcc_eq_right zero_lt_one
@@ -359,12 +233,6 @@ section
variable {𝕜 : Type _} [LinearOrderedField 𝕜] [TopologicalSpace 𝕜] [TopologicalRing 𝕜]
-/- warning: affine_homeomorph_image_I -> affineHomeomorph_image_I is a dubious translation:
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- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (coeFn.{succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (fun (_x : Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) => 𝕜 -> 𝕜) (Homeomorph.hasCoeToFun.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b))
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- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 (fun (_x : 𝕜) => 𝕜) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (Homeomorph.instEquivLikeHomeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2))) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) a b))
-Case conversion may be inaccurate. Consider using '#align affine_homeomorph_image_I affineHomeomorph_image_Iₓ'. -/
-- We only need the ordering on `𝕜` here to avoid talking about flipping the interval over.
-- At the end of the day I only care about `ℝ`, so I'm hesitant to put work into generalizing.
/-- The image of `[0,1]` under the homeomorphism `λ x, a * x + b` is `[b, a+b]`.
@@ -373,12 +241,6 @@ theorem affineHomeomorph_image_I (a b : 𝕜) (h : 0 < a) :
affineHomeomorph a b h.Ne.symm '' Set.Icc 0 1 = Set.Icc b (a + b) := by simp [h]
#align affine_homeomorph_image_I affineHomeomorph_image_I
-/- warning: Icc_homeo_I -> iccHomeoI is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align Icc_homeo_I iccHomeoIₓ'. -/
/-- The affine homeomorphism from a nontrivial interval `[a,b]` to `[0,1]`.
-/
def iccHomeoI (a b : 𝕜) (h : a < b) : Set.Icc a b ≃ₜ Set.Icc (0 : 𝕜) (1 : 𝕜) :=
@@ -389,18 +251,12 @@ def iccHomeoI (a b : 𝕜) (h : a < b) : Set.Icc a b ≃ₜ Set.Icc (0 : 𝕜) (
simp [sub_pos.mpr h]
#align Icc_homeo_I iccHomeoI
-/- warning: Icc_homeo_I_apply_coe -> iccHomeoI_apply_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_apply_coe iccHomeoI_apply_coeₓ'. -/
@[simp]
theorem iccHomeoI_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc a b) :
((iccHomeoI a b h) x : 𝕜) = (x - a) / (b - a) :=
rfl
#align Icc_homeo_I_apply_coe iccHomeoI_apply_coe
-/- warning: Icc_homeo_I_symm_apply_coe -> iccHomeoI_symm_apply_coe is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_symm_apply_coe iccHomeoI_symm_apply_coeₓ'. -/
@[simp]
theorem iccHomeoI_symm_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc (0 : 𝕜) (1 : 𝕜)) :
((iccHomeoI a b h).symm x : 𝕜) = (b - a) * x + a :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -390,10 +390,7 @@ def iccHomeoI (a b : 𝕜) (h : a < b) : Set.Icc a b ≃ₜ Set.Icc (0 : 𝕜) (
#align Icc_homeo_I iccHomeoI
/- warning: Icc_homeo_I_apply_coe -> iccHomeoI_apply_coe is a dubious translation:
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+<too large>
Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_apply_coe iccHomeoI_apply_coeₓ'. -/
@[simp]
theorem iccHomeoI_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc a b) :
@@ -402,10 +399,7 @@ theorem iccHomeoI_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc a b) :
#align Icc_homeo_I_apply_coe iccHomeoI_apply_coe
/- warning: Icc_homeo_I_symm_apply_coe -> iccHomeoI_symm_apply_coe is a dubious translation:
-lean 3 declaration is
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: 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)))) (Homeomorph.symm.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h)) x)) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x)) a)
+<too large>
Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_symm_apply_coe iccHomeoI_symm_apply_coeₓ'. -/
@[simp]
theorem iccHomeoI_symm_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc (0 : 𝕜) (1 : 𝕜)) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -206,7 +206,7 @@ theorem coe_symm_eq (x : I) : (σ x : ℝ) = 1 - x :=
rfl
#align unit_interval.coe_symm_eq unitInterval.coe_symm_eq
-/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:301:22: continuitity! not supported at the moment -/
+/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:304:22: continuitity! not supported at the moment -/
#print unitInterval.continuous_symm /-
@[continuity]
theorem continuous_symm : Continuous σ := by continuity
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -318,7 +318,7 @@ end unitInterval
/- warning: proj_Icc_eq_zero -> projIcc_eq_zero is a dubious translation:
lean 3 declaration is
- forall {x : Real}, Iff (Eq.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (zero_le_one.{0} Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) x) (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) 0 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) 0 (Zero.zero.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) unitInterval.hasZero)))) (LE.le.{0} Real Real.hasLe x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+ forall {x : Real}, Iff (Eq.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (zero_le_one.{0} Real Real.hasZero Real.hasOne (Preorder.toHasLe.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) x) (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) 0 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) 0 (Zero.zero.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) unitInterval.hasZero)))) (LE.le.{0} Real Real.hasLe x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
but is expected to have type
forall {x : Real}, Iff (Eq.{1} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (zero_le_one.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder)))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) x) (OfNat.ofNat.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) unitInterval.hasZero))) (LE.le.{0} Real Real.instLEReal x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
Case conversion may be inaccurate. Consider using '#align proj_Icc_eq_zero projIcc_eq_zeroₓ'. -/
@@ -329,7 +329,7 @@ theorem projIcc_eq_zero {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 0 ↔ x
/- warning: proj_Icc_eq_one -> projIcc_eq_one is a dubious translation:
lean 3 declaration is
- forall {x : Real}, Iff (Eq.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (zero_le_one.{0} Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) x) (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) 1 (One.one.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) unitInterval.hasOne)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) x)
+ forall {x : Real}, Iff (Eq.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (zero_le_one.{0} Real Real.hasZero Real.hasOne (Preorder.toHasLe.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) x) (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) 1 (One.one.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) unitInterval.hasOne)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) x)
but is expected to have type
forall {x : Real}, Iff (Eq.{1} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (zero_le_one.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder)))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) x) (OfNat.ofNat.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) unitInterval.hasOne))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) x)
Case conversion may be inaccurate. Consider using '#align proj_Icc_eq_one projIcc_eq_oneₓ'. -/
@@ -361,7 +361,7 @@ variable {𝕜 : Type _} [LinearOrderedField 𝕜] [TopologicalSpace 𝕜] [Topo
/- warning: affine_homeomorph_image_I -> affineHomeomorph_image_I is a dubious translation:
lean 3 declaration is
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (coeFn.{succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (fun (_x : Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) => 𝕜 -> 𝕜) (Homeomorph.hasCoeToFun.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b))
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (coeFn.{succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (fun (_x : Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) => 𝕜 -> 𝕜) (Homeomorph.hasCoeToFun.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b))
but is expected to have type
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 (fun (_x : 𝕜) => 𝕜) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (Homeomorph.instEquivLikeHomeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2))) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) a b))
Case conversion may be inaccurate. Consider using '#align affine_homeomorph_image_I affineHomeomorph_image_Iₓ'. -/
@@ -375,7 +375,7 @@ theorem affineHomeomorph_image_I (a b : 𝕜) (h : 0 < a) :
/- warning: Icc_homeo_I -> iccHomeoI is a dubious translation:
lean 3 declaration is
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) -> (Homeomorph.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) _inst_2) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) _inst_2))
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toHasLt.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) -> (Homeomorph.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) _inst_2) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) _inst_2))
but is expected to have type
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) -> (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2))
Case conversion may be inaccurate. Consider using '#align Icc_homeo_I iccHomeoIₓ'. -/
@@ -391,7 +391,7 @@ def iccHomeoI (a b : 𝕜) (h : a < b) : Set.Icc a b ≃ₜ Set.Icc (0 : 𝕜) (
/- warning: Icc_homeo_I_apply_coe -> iccHomeoI_apply_coe is a dubious translation:
lean 3 declaration is
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 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(LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) _inst_2)) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h) x)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (coeSubtype.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)))))) x) a) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))) b a))
but is expected to have type
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 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𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 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(LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 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(Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2)))) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h) x)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedField.toDiv.{u1} 𝕜 _inst_1)) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) x) a) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 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Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_apply_coe iccHomeoI_apply_coeₓ'. -/
@@ -403,7 +403,7 @@ theorem iccHomeoI_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc a b) :
/- warning: Icc_homeo_I_symm_apply_coe -> iccHomeoI_symm_apply_coe is a dubious translation:
lean 3 declaration is
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 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𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))))))) x)) a)
but is expected to have type
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)))) (Homeomorph.symm.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h)) x)) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x)) a)
Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_symm_apply_coe iccHomeoI_symm_apply_coeₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1
@@ -363,7 +363,7 @@ variable {𝕜 : Type _} [LinearOrderedField 𝕜] [TopologicalSpace 𝕜] [Topo
lean 3 declaration is
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (coeFn.{succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (fun (_x : Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) => 𝕜 -> 𝕜) (Homeomorph.hasCoeToFun.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b))
but is expected to have type
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 (fun (_x : 𝕜) => 𝕜) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (Homeomorph.instEquivLikeHomeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2))) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) a b))
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 (fun (_x : 𝕜) => 𝕜) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (Homeomorph.instEquivLikeHomeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2))) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) a b))
Case conversion may be inaccurate. Consider using '#align affine_homeomorph_image_I affineHomeomorph_image_Iₓ'. -/
-- We only need the ordering on `𝕜` here to avoid talking about flipping the interval over.
-- At the end of the day I only care about `ℝ`, so I'm hesitant to put work into generalizing.
@@ -377,7 +377,7 @@ theorem affineHomeomorph_image_I (a b : 𝕜) (h : 0 < a) :
lean 3 declaration is
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) -> (Homeomorph.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) _inst_2) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) _inst_2))
but is expected to have type
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) -> (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2))
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) -> (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2))
Case conversion may be inaccurate. Consider using '#align Icc_homeo_I iccHomeoIₓ'. -/
/-- The affine homeomorphism from a nontrivial interval `[a,b]` to `[0,1]`.
-/
@@ -393,7 +393,7 @@ def iccHomeoI (a b : 𝕜) (h : a < b) : Set.Icc a b ≃ₜ Set.Icc (0 : 𝕜) (
lean 3 declaration is
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)), Eq.{succ u1} 𝕜 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) 𝕜 (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) 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a b h) x)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (coeSubtype.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)))))) x) a) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 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but is expected to have type
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) 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(Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)))) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h) x)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedField.toDiv.{u1} 𝕜 _inst_1)) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) x) a) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a))
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2)))) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h) x)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedField.toDiv.{u1} 𝕜 _inst_1)) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) x) a) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a))
Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_apply_coe iccHomeoI_apply_coeₓ'. -/
@[simp]
theorem iccHomeoI_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc a b) :
@@ -405,7 +405,7 @@ theorem iccHomeoI_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc a b) :
lean 3 declaration is
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 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𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))))))) x)) a)
but is expected to have type
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)))) (Homeomorph.symm.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h)) x)) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) x)) a)
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)))) (Homeomorph.symm.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) _inst_2) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h)) x)) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (Semiring.toOne.{u1} 𝕜 (DivisionSemiring.toSemiring.{u1} 𝕜 (Semifield.toDivisionSemiring.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))))) x)) a)
Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_symm_apply_coe iccHomeoI_symm_apply_coeₓ'. -/
@[simp]
theorem iccHomeoI_symm_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc (0 : 𝕜) (1 : 𝕜)) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1
@@ -361,7 +361,7 @@ variable {𝕜 : Type _} [LinearOrderedField 𝕜] [TopologicalSpace 𝕜] [Topo
/- warning: affine_homeomorph_image_I -> affineHomeomorph_image_I is a dubious translation:
lean 3 declaration is
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (coeFn.{succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (fun (_x : Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) => 𝕜 -> 𝕜) (Homeomorph.hasCoeToFun.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b))
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (coeFn.{succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (fun (_x : Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) => 𝕜 -> 𝕜) (Homeomorph.hasCoeToFun.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b))
but is expected to have type
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 (fun (_x : 𝕜) => 𝕜) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (Homeomorph.instEquivLikeHomeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2))) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) a b))
Case conversion may be inaccurate. Consider using '#align affine_homeomorph_image_I affineHomeomorph_image_Iₓ'. -/
@@ -375,7 +375,7 @@ theorem affineHomeomorph_image_I (a b : 𝕜) (h : 0 < a) :
/- warning: Icc_homeo_I -> iccHomeoI is a dubious translation:
lean 3 declaration is
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) -> (Homeomorph.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) _inst_2) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) _inst_2))
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) -> (Homeomorph.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) _inst_2) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) _inst_2))
but is expected to have type
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) -> (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2))
Case conversion may be inaccurate. Consider using '#align Icc_homeo_I iccHomeoIₓ'. -/
@@ -391,7 +391,7 @@ def iccHomeoI (a b : 𝕜) (h : a < b) : Set.Icc a b ≃ₜ Set.Icc (0 : 𝕜) (
/- warning: Icc_homeo_I_apply_coe -> iccHomeoI_apply_coe is a dubious translation:
lean 3 declaration is
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 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(LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) _inst_2)) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h) x)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (DivInvMonoid.toHasDiv.{u1} 𝕜 (DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (coeBase.{succ u1, succ u1} 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(Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))) b a))
but is expected to have type
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)))) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h) x)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedField.toDiv.{u1} 𝕜 _inst_1)) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) x) a) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a))
Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_apply_coe iccHomeoI_apply_coeₓ'. -/
@@ -403,7 +403,7 @@ theorem iccHomeoI_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc a b) :
/- warning: Icc_homeo_I_symm_apply_coe -> iccHomeoI_symm_apply_coe is a dubious translation:
lean 3 declaration is
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 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(LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) 𝕜 (coeSubtype.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))))))) x)) a)
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 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𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (AddCommGroupWithOne.toAddGroupWithOne.{u1} 𝕜 (Ring.toAddCommGroupWithOne.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))))))) x)) a)
but is expected to have type
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)))) (Homeomorph.symm.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h)) x)) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) x)) a)
Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_symm_apply_coe iccHomeoI_symm_apply_coeₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d
@@ -363,7 +363,7 @@ variable {𝕜 : Type _} [LinearOrderedField 𝕜] [TopologicalSpace 𝕜] [Topo
lean 3 declaration is
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (coeFn.{succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (fun (_x : Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) => 𝕜 -> 𝕜) (Homeomorph.hasCoeToFun.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b))
but is expected to have type
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : 𝕜) => 𝕜) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (Homeomorph.instEquivLikeHomeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2))) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) a b))
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 (fun (_x : 𝕜) => 𝕜) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (Homeomorph.instEquivLikeHomeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2))) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) a b))
Case conversion may be inaccurate. Consider using '#align affine_homeomorph_image_I affineHomeomorph_image_Iₓ'. -/
-- We only need the ordering on `𝕜` here to avoid talking about flipping the interval over.
-- At the end of the day I only care about `ℝ`, so I'm hesitant to put work into generalizing.
@@ -393,7 +393,7 @@ def iccHomeoI (a b : 𝕜) (h : a < b) : Set.Icc a b ≃ₜ Set.Icc (0 : 𝕜) (
lean 3 declaration is
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)), Eq.{succ u1} 𝕜 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) 𝕜 (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) 𝕜 (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 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(LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) _inst_2) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 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(DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (coeSubtype.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)))))) x) a) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))) b a))
but is expected to have type
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)))) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h) x)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedField.toDiv.{u1} 𝕜 _inst_1)) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) x) a) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a))
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)))) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h) x)) (HDiv.hDiv.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHDiv.{u1} 𝕜 (LinearOrderedField.toDiv.{u1} 𝕜 _inst_1)) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) x) a) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a))
Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_apply_coe iccHomeoI_apply_coeₓ'. -/
@[simp]
theorem iccHomeoI_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc a b) :
@@ -405,7 +405,7 @@ theorem iccHomeoI_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc a b) :
lean 3 declaration is
forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 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(LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) 𝕜 (coeSubtype.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))))))) x)) a)
but is expected to have type
- forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)))) (Homeomorph.symm.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h)) x)) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) x)) a)
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)))) (Homeomorph.symm.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h)) x)) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) x)) a)
Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_symm_apply_coe iccHomeoI_symm_apply_coeₓ'. -/
@[simp]
theorem iccHomeoI_symm_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc (0 : 𝕜) (1 : 𝕜)) :
mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison
! This file was ported from Lean 3 source module topology.unit_interval
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -16,6 +16,9 @@ import Mathbin.Data.Set.Intervals.Instances
/-!
# The unit interval, as a topological space
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
Use `open_locale unit_interval` to turn on the notation `I := set.Icc (0 : ℝ) (1 : ℝ)`.
We provide basic instances, as well as a custom tactic for discharging
mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5
@@ -33,54 +33,104 @@ open Set Int Set.Icc
/-! ### The unit interval -/
+#print unitInterval /-
/-- The unit interval `[0,1]` in ℝ. -/
abbrev unitInterval : Set ℝ :=
Set.Icc 0 1
#align unit_interval unitInterval
+-/
-- mathport name: unit_interval
scoped[unitInterval] notation "I" => unitInterval
namespace unitInterval
+/- warning: unit_interval.zero_mem -> unitInterval.zero_mem is a dubious translation:
+lean 3 declaration is
+ Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) unitInterval
+but is expected to have type
+ Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) unitInterval
+Case conversion may be inaccurate. Consider using '#align unit_interval.zero_mem unitInterval.zero_memₓ'. -/
theorem zero_mem : (0 : ℝ) ∈ I :=
⟨le_rfl, zero_le_one⟩
#align unit_interval.zero_mem unitInterval.zero_mem
+/- warning: unit_interval.one_mem -> unitInterval.one_mem is a dubious translation:
+lean 3 declaration is
+ Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) unitInterval
+but is expected to have type
+ Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) unitInterval
+Case conversion may be inaccurate. Consider using '#align unit_interval.one_mem unitInterval.one_memₓ'. -/
theorem one_mem : (1 : ℝ) ∈ I :=
⟨zero_le_one, le_rfl⟩
#align unit_interval.one_mem unitInterval.one_mem
+/- warning: unit_interval.mul_mem -> unitInterval.mul_mem is a dubious translation:
+lean 3 declaration is
+ forall {x : Real} {y : Real}, (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval) -> (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) y unitInterval) -> (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) x y) unitInterval)
+but is expected to have type
+ forall {x : Real} {y : Real}, (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) -> (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) y unitInterval) -> (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) x y) unitInterval)
+Case conversion may be inaccurate. Consider using '#align unit_interval.mul_mem unitInterval.mul_memₓ'. -/
theorem mul_mem {x y : ℝ} (hx : x ∈ I) (hy : y ∈ I) : x * y ∈ I :=
⟨mul_nonneg hx.1 hy.1, (mul_le_mul hx.2 hy.2 hy.1 zero_le_one).trans_eq <| one_mul 1⟩
#align unit_interval.mul_mem unitInterval.mul_mem
+/- warning: unit_interval.div_mem -> unitInterval.div_mem is a dubious translation:
+lean 3 declaration is
+ forall {x : Real} {y : Real}, (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) y) -> (LE.le.{0} Real Real.hasLe x y) -> (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) x y) unitInterval)
+but is expected to have type
+ forall {x : Real} {y : Real}, (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) y) -> (LE.le.{0} Real Real.instLEReal x y) -> (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) x y) unitInterval)
+Case conversion may be inaccurate. Consider using '#align unit_interval.div_mem unitInterval.div_memₓ'. -/
theorem div_mem {x y : ℝ} (hx : 0 ≤ x) (hy : 0 ≤ y) (hxy : x ≤ y) : x / y ∈ I :=
⟨div_nonneg hx hy, div_le_one_of_le hxy hy⟩
#align unit_interval.div_mem unitInterval.div_mem
+#print unitInterval.fract_mem /-
theorem fract_mem (x : ℝ) : fract x ∈ I :=
⟨fract_nonneg _, (fract_lt_one _).le⟩
#align unit_interval.fract_mem unitInterval.fract_mem
+-/
+/- warning: unit_interval.mem_iff_one_sub_mem -> unitInterval.mem_iff_one_sub_mem is a dubious translation:
+lean 3 declaration is
+ forall {t : Real}, Iff (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) t unitInterval) (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) t) unitInterval)
+but is expected to have type
+ forall {t : Real}, Iff (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) t unitInterval) (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) t) unitInterval)
+Case conversion may be inaccurate. Consider using '#align unit_interval.mem_iff_one_sub_mem unitInterval.mem_iff_one_sub_memₓ'. -/
theorem mem_iff_one_sub_mem {t : ℝ} : t ∈ I ↔ 1 - t ∈ I :=
by
rw [mem_Icc, mem_Icc]
constructor <;> intro <;> constructor <;> linarith
#align unit_interval.mem_iff_one_sub_mem unitInterval.mem_iff_one_sub_mem
+#print unitInterval.hasZero /-
instance hasZero : Zero I :=
⟨⟨0, zero_mem⟩⟩
#align unit_interval.has_zero unitInterval.hasZero
+-/
+#print unitInterval.hasOne /-
instance hasOne : One I :=
⟨⟨1, by constructor <;> norm_num⟩⟩
#align unit_interval.has_one unitInterval.hasOne
+-/
+/- warning: unit_interval.coe_ne_zero -> unitInterval.coe_ne_zero is a dubious translation:
+lean 3 declaration is
+ forall {x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval}, Iff (Ne.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) x) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) (Ne.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) x (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (Zero.zero.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasZero))))
+but is expected to have type
+ forall {x : Set.Elem.{0} Real unitInterval}, Iff (Ne.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) x) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) (Ne.{1} (Set.Elem.{0} Real unitInterval) x (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)))
+Case conversion may be inaccurate. Consider using '#align unit_interval.coe_ne_zero unitInterval.coe_ne_zeroₓ'. -/
theorem coe_ne_zero {x : I} : (x : ℝ) ≠ 0 ↔ x ≠ 0 :=
not_iff_not.mpr coe_eq_zero
#align unit_interval.coe_ne_zero unitInterval.coe_ne_zero
+/- warning: unit_interval.coe_ne_one -> unitInterval.coe_ne_one is a dubious translation:
+lean 3 declaration is
+ forall {x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval}, Iff (Ne.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) (Ne.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) x (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (One.one.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasOne))))
+but is expected to have type
+ forall {x : Set.Elem.{0} Real unitInterval}, Iff (Ne.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) (Ne.{1} (Set.Elem.{0} Real unitInterval) x (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne)))
+Case conversion may be inaccurate. Consider using '#align unit_interval.coe_ne_one unitInterval.coe_ne_oneₓ'. -/
theorem coe_ne_one {x : I} : (x : ℝ) ≠ 1 ↔ x ≠ 1 :=
not_iff_not.mpr coe_eq_one
#align unit_interval.coe_ne_one unitInterval.coe_ne_one
@@ -91,46 +141,74 @@ instance : Nonempty I :=
instance : Mul I :=
⟨fun x y => ⟨x * y, mul_mem x.2 y.2⟩⟩
+/- warning: unit_interval.mul_le_left -> unitInterval.mul_le_left is a dubious translation:
+lean 3 declaration is
+ forall {x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval} {y : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval}, LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval)) (HMul.hMul.{0, 0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (instHMul.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasMul) x y) x
+but is expected to have type
+ forall {x : Set.Elem.{0} Real unitInterval} {y : Set.Elem.{0} Real unitInterval}, LE.le.{0} (Set.Elem.{0} Real unitInterval) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval)) (HMul.hMul.{0, 0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) (instHMul.{0} (Set.Elem.{0} Real unitInterval) unitInterval.instMulElemRealUnitInterval) x y) x
+Case conversion may be inaccurate. Consider using '#align unit_interval.mul_le_left unitInterval.mul_le_leftₓ'. -/
-- todo: we could set up a `linear_ordered_comm_monoid_with_zero I` instance
theorem mul_le_left {x y : I} : x * y ≤ x :=
Subtype.coe_le_coe.mp <| (mul_le_mul_of_nonneg_left y.2.2 x.2.1).trans_eq <| mul_one x
#align unit_interval.mul_le_left unitInterval.mul_le_left
+/- warning: unit_interval.mul_le_right -> unitInterval.mul_le_right is a dubious translation:
+lean 3 declaration is
+ forall {x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval} {y : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval}, LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval)) (HMul.hMul.{0, 0, 0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (instHMul.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasMul) x y) y
+but is expected to have type
+ forall {x : Set.Elem.{0} Real unitInterval} {y : Set.Elem.{0} Real unitInterval}, LE.le.{0} (Set.Elem.{0} Real unitInterval) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval)) (HMul.hMul.{0, 0, 0} (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) (Set.Elem.{0} Real unitInterval) (instHMul.{0} (Set.Elem.{0} Real unitInterval) unitInterval.instMulElemRealUnitInterval) x y) y
+Case conversion may be inaccurate. Consider using '#align unit_interval.mul_le_right unitInterval.mul_le_rightₓ'. -/
theorem mul_le_right {x y : I} : x * y ≤ y :=
Subtype.coe_le_coe.mp <| (mul_le_mul_of_nonneg_right x.2.2 y.2.1).trans_eq <| one_mul y
#align unit_interval.mul_le_right unitInterval.mul_le_right
+#print unitInterval.symm /-
/-- Unit interval central symmetry. -/
def symm : I → I := fun t => ⟨1 - t, mem_iff_one_sub_mem.mp t.Prop⟩
#align unit_interval.symm unitInterval.symm
+-/
-- mathport name: unit_interval.symm
scoped notation "σ" => unitInterval.symm
+#print unitInterval.symm_zero /-
@[simp]
theorem symm_zero : σ 0 = 1 :=
Subtype.ext <| by simp [symm]
#align unit_interval.symm_zero unitInterval.symm_zero
+-/
+#print unitInterval.symm_one /-
@[simp]
theorem symm_one : σ 1 = 0 :=
Subtype.ext <| by simp [symm]
#align unit_interval.symm_one unitInterval.symm_one
+-/
+#print unitInterval.symm_symm /-
@[simp]
theorem symm_symm (x : I) : σ (σ x) = x :=
Subtype.ext <| by simp [symm]
#align unit_interval.symm_symm unitInterval.symm_symm
+-/
+/- warning: unit_interval.coe_symm_eq -> unitInterval.coe_symm_eq is a dubious translation:
+lean 3 declaration is
+ forall (x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), Eq.{1} Real ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) (unitInterval.symm x)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (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) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) x))
+but is expected to have type
+ forall (x : Set.Elem.{0} Real unitInterval), Eq.{1} Real (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) (unitInterval.symm x)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) x))
+Case conversion may be inaccurate. Consider using '#align unit_interval.coe_symm_eq unitInterval.coe_symm_eqₓ'. -/
@[simp]
theorem coe_symm_eq (x : I) : (σ x : ℝ) = 1 - x :=
rfl
#align unit_interval.coe_symm_eq unitInterval.coe_symm_eq
/- ./././Mathport/Syntax/Translate/Tactic/Mathlib/Misc2.lean:301:22: continuitity! not supported at the moment -/
+#print unitInterval.continuous_symm /-
@[continuity]
theorem continuous_symm : Continuous σ := by continuity
#align unit_interval.continuous_symm unitInterval.continuous_symm
+-/
instance : ConnectedSpace I :=
Subtype.connectedSpace ⟨nonempty_Icc.mpr zero_le_one, isPreconnected_Icc⟩
@@ -138,34 +216,82 @@ instance : ConnectedSpace I :=
/-- Verify there is an instance for `compact_space I`. -/
example : CompactSpace I := by infer_instance
+/- warning: unit_interval.nonneg -> unitInterval.nonneg is a dubious translation:
+lean 3 declaration is
+ forall (x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), LE.le.{0} Real Real.hasLe (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) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) x)
+but is expected to have type
+ forall (x : Set.Elem.{0} Real unitInterval), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) x)
+Case conversion may be inaccurate. Consider using '#align unit_interval.nonneg unitInterval.nonnegₓ'. -/
theorem nonneg (x : I) : 0 ≤ (x : ℝ) :=
x.2.1
#align unit_interval.nonneg unitInterval.nonneg
+/- warning: unit_interval.one_minus_nonneg -> unitInterval.one_minus_nonneg is a dubious translation:
+lean 3 declaration is
+ forall (x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (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) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) x))
+but is expected to have type
+ forall (x : Set.Elem.{0} Real unitInterval), LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) x))
+Case conversion may be inaccurate. Consider using '#align unit_interval.one_minus_nonneg unitInterval.one_minus_nonnegₓ'. -/
theorem one_minus_nonneg (x : I) : 0 ≤ 1 - (x : ℝ) := by simpa using x.2.2
#align unit_interval.one_minus_nonneg unitInterval.one_minus_nonneg
+/- warning: unit_interval.le_one -> unitInterval.le_one is a dubious translation:
+lean 3 declaration is
+ forall (x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), LE.le.{0} Real Real.hasLe ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) x) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+ forall (x : Set.Elem.{0} Real unitInterval), LE.le.{0} Real Real.instLEReal (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) x) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align unit_interval.le_one unitInterval.le_oneₓ'. -/
theorem le_one (x : I) : (x : ℝ) ≤ 1 :=
x.2.2
#align unit_interval.le_one unitInterval.le_one
+/- warning: unit_interval.one_minus_le_one -> unitInterval.one_minus_le_one is a dubious translation:
+lean 3 declaration is
+ forall (x : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval), LE.le.{0} Real Real.hasLe (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (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) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) x)) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))
+but is expected to have type
+ forall (x : Set.Elem.{0} Real unitInterval), LE.le.{0} Real Real.instLEReal (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) x)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))
+Case conversion may be inaccurate. Consider using '#align unit_interval.one_minus_le_one unitInterval.one_minus_le_oneₓ'. -/
theorem one_minus_le_one (x : I) : 1 - (x : ℝ) ≤ 1 := by simpa using x.2.1
#align unit_interval.one_minus_le_one unitInterval.one_minus_le_one
+/- warning: unit_interval.add_pos -> unitInterval.add_pos is a dubious translation:
+lean 3 declaration is
+ forall {t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval} {x : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) x) -> (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.hasAdd) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval))))) t)))
+but is expected to have type
+ forall {t : Set.Elem.{0} Real unitInterval} {x : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) x) -> (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HAdd.hAdd.{0, 0, 0} Real Real Real (instHAdd.{0} Real Real.instAddReal) x (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval) t)))
+Case conversion may be inaccurate. Consider using '#align unit_interval.add_pos unitInterval.add_posₓ'. -/
theorem add_pos {t : I} {x : ℝ} (hx : 0 < x) : 0 < (x + t : ℝ) :=
add_pos_of_pos_of_nonneg hx <| nonneg _
#align unit_interval.add_pos unitInterval.add_pos
+/- warning: unit_interval.nonneg' -> unitInterval.nonneg' is a dubious translation:
+lean 3 declaration is
+ forall {t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval}, LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval)) (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 0 (Zero.zero.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasZero))) t
+but is expected to have type
+ forall {t : Set.Elem.{0} Real unitInterval}, LE.le.{0} (Set.Elem.{0} Real unitInterval) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval)) (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasZero)) t
+Case conversion may be inaccurate. Consider using '#align unit_interval.nonneg' unitInterval.nonneg'ₓ'. -/
/-- like `unit_interval.nonneg`, but with the inequality in `I`. -/
theorem nonneg' {t : I} : 0 ≤ t :=
t.2.1
#align unit_interval.nonneg' unitInterval.nonneg'
+/- warning: unit_interval.le_one' -> unitInterval.le_one' is a dubious translation:
+lean 3 declaration is
+ forall {t : coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval}, LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x unitInterval)) t (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) 1 (One.one.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) unitInterval) unitInterval.hasOne)))
+but is expected to have type
+ forall {t : Set.Elem.{0} Real unitInterval}, LE.le.{0} (Set.Elem.{0} Real unitInterval) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x unitInterval)) t (OfNat.ofNat.{0} (Set.Elem.{0} Real unitInterval) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real unitInterval) unitInterval.hasOne))
+Case conversion may be inaccurate. Consider using '#align unit_interval.le_one' unitInterval.le_one'ₓ'. -/
/-- like `unit_interval.le_one`, but with the inequality in `I`. -/
theorem le_one' {t : I} : t ≤ 1 :=
t.2.2
#align unit_interval.le_one' unitInterval.le_one'
+/- warning: unit_interval.mul_pos_mem_iff -> unitInterval.mul_pos_mem_iff is a dubious translation:
+lean 3 declaration is
+ forall {a : Real} {t : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) a) -> (Iff (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) a t) unitInterval) (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) t (Set.Icc.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) a))))
+but is expected to have type
+ forall {a : Real} {t : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) a) -> (Iff (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) a t) unitInterval) (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) t (Set.Icc.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) a))))
+Case conversion may be inaccurate. Consider using '#align unit_interval.mul_pos_mem_iff unitInterval.mul_pos_mem_iffₓ'. -/
theorem mul_pos_mem_iff {a t : ℝ} (ha : 0 < a) : a * t ∈ I ↔ t ∈ Set.Icc (0 : ℝ) (1 / a) :=
by
constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor
@@ -175,17 +301,35 @@ theorem mul_pos_mem_iff {a t : ℝ} (ha : 0 < a) : a * t ∈ I ↔ t ∈ Set.Icc
· rwa [le_div_iff ha, mul_comm] at h₂
#align unit_interval.mul_pos_mem_iff unitInterval.mul_pos_mem_iff
+/- warning: unit_interval.two_mul_sub_one_mem_iff -> unitInterval.two_mul_sub_one_mem_iff is a dubious translation:
+lean 3 declaration is
+ forall {t : Real}, Iff (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) (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) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) t) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))) unitInterval) (Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) t (Set.Icc.{0} Real Real.preorder (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne)))))
+but is expected to have type
+ forall {t : Real}, Iff (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) (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) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) t) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))) unitInterval) (Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) t (Set.Icc.{0} Real Real.instPreorderReal (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal))))
+Case conversion may be inaccurate. Consider using '#align unit_interval.two_mul_sub_one_mem_iff unitInterval.two_mul_sub_one_mem_iffₓ'. -/
theorem two_mul_sub_one_mem_iff {t : ℝ} : 2 * t - 1 ∈ I ↔ t ∈ Set.Icc (1 / 2 : ℝ) 1 := by
constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor <;> linarith
#align unit_interval.two_mul_sub_one_mem_iff unitInterval.two_mul_sub_one_mem_iff
end unitInterval
+/- warning: proj_Icc_eq_zero -> projIcc_eq_zero is a dubious translation:
+lean 3 declaration is
+ forall {x : Real}, Iff (Eq.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (zero_le_one.{0} Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) x) (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) 0 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) 0 (Zero.zero.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) unitInterval.hasZero)))) (LE.le.{0} Real Real.hasLe x (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))
+but is expected to have type
+ forall {x : Real}, Iff (Eq.{1} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (zero_le_one.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder)))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) x) (OfNat.ofNat.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) 0 (Zero.toOfNat0.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) unitInterval.hasZero))) (LE.le.{0} Real Real.instLEReal x (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))
+Case conversion may be inaccurate. Consider using '#align proj_Icc_eq_zero projIcc_eq_zeroₓ'. -/
@[simp]
theorem projIcc_eq_zero {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 0 ↔ x ≤ 0 :=
projIcc_eq_left zero_lt_one
#align proj_Icc_eq_zero projIcc_eq_zero
+/- warning: proj_Icc_eq_one -> projIcc_eq_one is a dubious translation:
+lean 3 declaration is
+ forall {x : Real}, Iff (Eq.{1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) (zero_le_one.{0} Real Real.hasZero Real.hasOne (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) x) (OfNat.ofNat.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) 1 (OfNat.mk.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) 1 (One.one.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (LinearOrder.toLattice.{0} Real Real.linearOrder)))) (Zero.zero.{0} Real Real.hasZero) (One.one.{0} Real Real.hasOne))) unitInterval.hasOne)))) (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) x)
+but is expected to have type
+ forall {x : Real}, Iff (Eq.{1} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) (Set.projIcc.{0} Real Real.linearOrder (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) (zero_le_one.{0} Real Real.instZeroReal Real.instOneReal (Preorder.toLE.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder)))))) (OrderedSemiring.zeroLEOneClass.{0} Real Real.orderedSemiring)) x) (OfNat.ofNat.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) 1 (One.toOfNat1.{0} (Set.Elem.{0} Real (Set.Icc.{0} Real (PartialOrder.toPreorder.{0} Real (SemilatticeInf.toPartialOrder.{0} Real (Lattice.toSemilatticeInf.{0} Real (DistribLattice.toLattice.{0} Real (instDistribLattice.{0} Real Real.linearOrder))))) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)))) unitInterval.hasOne))) (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) x)
+Case conversion may be inaccurate. Consider using '#align proj_Icc_eq_one projIcc_eq_oneₓ'. -/
@[simp]
theorem projIcc_eq_one {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 1 ↔ 1 ≤ x :=
projIcc_eq_right zero_lt_one
@@ -193,14 +337,18 @@ theorem projIcc_eq_one {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 1 ↔ 1
namespace Tactic.Interactive
+/- warning: tactic.interactive.unit_interval clashes with [anonymous] -> [anonymous]
+Case conversion may be inaccurate. Consider using '#align tactic.interactive.unit_interval [anonymous]ₓ'. -/
/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+#print [anonymous] /-
/-- A tactic that solves `0 ≤ ↑x`, `0 ≤ 1 - ↑x`, `↑x ≤ 1`, and `1 - ↑x ≤ 1` for `x : I`. -/
-unsafe def unit_interval : tactic Unit :=
+unsafe def [anonymous] : tactic Unit :=
sorry <|> sorry <|> sorry <|> sorry
-#align tactic.interactive.unit_interval tactic.interactive.unit_interval
+#align tactic.interactive.unit_interval [anonymous]
+-/
end Tactic.Interactive
@@ -208,6 +356,12 @@ section
variable {𝕜 : Type _} [LinearOrderedField 𝕜] [TopologicalSpace 𝕜] [TopologicalRing 𝕜]
+/- warning: affine_homeomorph_image_I -> affineHomeomorph_image_I is a dubious translation:
+lean 3 declaration is
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (coeFn.{succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (fun (_x : Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) => 𝕜 -> 𝕜) (Homeomorph.hasCoeToFun.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toHasAdd.{u1} 𝕜 (Ring.toDistrib.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b))
+but is expected to have type
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a), Eq.{succ u1} (Set.{u1} 𝕜) (Set.image.{u1, u1} 𝕜 𝕜 (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 (fun (_x : 𝕜) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : 𝕜) => 𝕜) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2) 𝕜 𝕜 (Homeomorph.instEquivLikeHomeomorph.{u1, u1} 𝕜 𝕜 _inst_2 _inst_2))) (affineHomeomorph.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1) _inst_2 _inst_3 a b (Ne.symm.{succ u1} 𝕜 (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a (LT.lt.ne.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) a h)))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) b (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) a b))
+Case conversion may be inaccurate. Consider using '#align affine_homeomorph_image_I affineHomeomorph_image_Iₓ'. -/
-- We only need the ordering on `𝕜` here to avoid talking about flipping the interval over.
-- At the end of the day I only care about `ℝ`, so I'm hesitant to put work into generalizing.
/-- The image of `[0,1]` under the homeomorphism `λ x, a * x + b` is `[b, a+b]`.
@@ -216,6 +370,12 @@ theorem affineHomeomorph_image_I (a b : 𝕜) (h : 0 < a) :
affineHomeomorph a b h.Ne.symm '' Set.Icc 0 1 = Set.Icc b (a + b) := by simp [h]
#align affine_homeomorph_image_I affineHomeomorph_image_I
+/- warning: Icc_homeo_I -> iccHomeoI is a dubious translation:
+lean 3 declaration is
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) -> (Homeomorph.{u1, u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) _inst_2) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) _inst_2))
+but is expected to have type
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜), (LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) -> (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2))
+Case conversion may be inaccurate. Consider using '#align Icc_homeo_I iccHomeoIₓ'. -/
/-- The affine homeomorphism from a nontrivial interval `[a,b]` to `[0,1]`.
-/
def iccHomeoI (a b : 𝕜) (h : a < b) : Set.Icc a b ≃ₜ Set.Icc (0 : 𝕜) (1 : 𝕜) :=
@@ -226,12 +386,24 @@ def iccHomeoI (a b : 𝕜) (h : a < b) : Set.Icc a b ≃ₜ Set.Icc (0 : 𝕜) (
simp [sub_pos.mpr h]
#align Icc_homeo_I iccHomeoI
+/- warning: Icc_homeo_I_apply_coe -> iccHomeoI_apply_coe is a dubious translation:
+lean 3 declaration is
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))) a b) (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 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(LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) _inst_2) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 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(DivisionRing.toDivInvMonoid.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} 𝕜) Type.{u1} (Set.hasCoeToSort.{u1} 𝕜) (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)) 𝕜 (coeSubtype.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b)))))) x) a) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (SubNegMonoid.toHasSub.{u1} 𝕜 (AddGroup.toSubNegMonoid.{u1} 𝕜 (AddGroupWithOne.toAddGroup.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))) b a))
+but is expected to have type
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 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(OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 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+Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_apply_coe iccHomeoI_apply_coeₓ'. -/
@[simp]
theorem iccHomeoI_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc a b) :
((iccHomeoI a b h) x : 𝕜) = (x - a) / (b - a) :=
rfl
#align Icc_homeo_I_apply_coe iccHomeoI_apply_coe
+/- warning: Icc_homeo_I_symm_apply_coe -> iccHomeoI_symm_apply_coe is a dubious translation:
+lean 3 declaration is
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𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) (Subtype.topologicalSpace.{u1} 𝕜 (fun (x : 𝕜) => 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(LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))) 𝕜 (coeSubtype.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.Mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.hasMem.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (OrderedAddCommGroup.toPartialOrder.{u1} 𝕜 (StrictOrderedRing.toOrderedAddCommGroup.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) (OfNat.ofNat.{u1} 𝕜 0 (OfNat.mk.{u1} 𝕜 0 (Zero.zero.{u1} 𝕜 (MulZeroClass.toHasZero.{u1} 𝕜 (NonUnitalNonAssocSemiring.toMulZeroClass.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))))))))) (OfNat.ofNat.{u1} 𝕜 1 (OfNat.mk.{u1} 𝕜 1 (One.one.{u1} 𝕜 (AddMonoidWithOne.toOne.{u1} 𝕜 (AddGroupWithOne.toAddMonoidWithOne.{u1} 𝕜 (NonAssocRing.toAddGroupWithOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (StrictOrderedRing.toRing.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))))))))))))))) x)) a)
+but is expected to have type
+ forall {𝕜 : Type.{u1}} [_inst_1 : LinearOrderedField.{u1} 𝕜] [_inst_2 : TopologicalSpace.{u1} 𝕜] [_inst_3 : TopologicalRing.{u1} 𝕜 _inst_2 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1)))))] (a : 𝕜) (b : 𝕜) (h : LT.lt.{u1} 𝕜 (Preorder.toLT.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1)))))) a b) (x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))), Eq.{succ u1} 𝕜 (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (FunLike.coe.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (fun (_x : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) => Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (EquivLike.toEmbeddingLike.{succ u1, succ u1, succ u1} (Homeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Homeomorph.instEquivLikeHomeomorph.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2)))) (Homeomorph.symm.{u1, u1} (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) (Set.Elem.{u1} 𝕜 (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) a b)) _inst_2) (instTopologicalSpaceSubtype.{u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) _inst_2) (iccHomeoI.{u1} 𝕜 _inst_1 _inst_2 _inst_3 a b h)) x)) (HAdd.hAdd.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHAdd.{u1} 𝕜 (Distrib.toAdd.{u1} 𝕜 (NonUnitalNonAssocSemiring.toDistrib.{u1} 𝕜 (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) (HMul.hMul.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHMul.{u1} 𝕜 (NonUnitalNonAssocRing.toMul.{u1} 𝕜 (NonAssocRing.toNonUnitalNonAssocRing.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))) (HSub.hSub.{u1, u1, u1} 𝕜 𝕜 𝕜 (instHSub.{u1} 𝕜 (Ring.toSub.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))) b a) (Subtype.val.{succ u1} 𝕜 (fun (x : 𝕜) => Membership.mem.{u1, u1} 𝕜 (Set.{u1} 𝕜) (Set.instMembershipSet.{u1} 𝕜) x (Set.Icc.{u1} 𝕜 (PartialOrder.toPreorder.{u1} 𝕜 (StrictOrderedRing.toPartialOrder.{u1} 𝕜 (LinearOrderedRing.toStrictOrderedRing.{u1} 𝕜 (LinearOrderedCommRing.toLinearOrderedRing.{u1} 𝕜 (LinearOrderedField.toLinearOrderedCommRing.{u1} 𝕜 _inst_1))))) (OfNat.ofNat.{u1} 𝕜 0 (Zero.toOfNat0.{u1} 𝕜 (CommMonoidWithZero.toZero.{u1} 𝕜 (CommGroupWithZero.toCommMonoidWithZero.{u1} 𝕜 (Semifield.toCommGroupWithZero.{u1} 𝕜 (LinearOrderedSemifield.toSemifield.{u1} 𝕜 (LinearOrderedField.toLinearOrderedSemifield.{u1} 𝕜 _inst_1))))))) (OfNat.ofNat.{u1} 𝕜 1 (One.toOfNat1.{u1} 𝕜 (NonAssocRing.toOne.{u1} 𝕜 (Ring.toNonAssocRing.{u1} 𝕜 (DivisionRing.toRing.{u1} 𝕜 (Field.toDivisionRing.{u1} 𝕜 (LinearOrderedField.toField.{u1} 𝕜 _inst_1))))))))) x)) a)
+Case conversion may be inaccurate. Consider using '#align Icc_homeo_I_symm_apply_coe iccHomeoI_symm_apply_coeₓ'. -/
@[simp]
theorem iccHomeoI_symm_apply_coe (a b : 𝕜) (h : a < b) (x : Set.Icc (0 : 𝕜) (1 : 𝕜)) :
((iccHomeoI a b h).symm x : 𝕜) = (b - a) * x + a :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442
@@ -193,10 +193,10 @@ theorem projIcc_eq_one {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 1 ↔ 1
namespace Tactic.Interactive
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
-/- ./././Mathport/Syntax/Translate/Expr.lean:334:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
+/- ./././Mathport/Syntax/Translate/Expr.lean:330:4: warning: unsupported (TODO): `[tacs] -/
/-- A tactic that solves `0 ≤ ↑x`, `0 ≤ 1 - ↑x`, `↑x ≤ 1`, and `1 - ↑x ≤ 1` for `x : I`. -/
unsafe def unit_interval : tactic Unit :=
sorry <|> sorry <|> sorry <|> sorry
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Move Set.Ixx
, Finset.Ixx
, Multiset.Ixx
together under two different folders:
Order.Interval
for their definition and basic propertiesAlgebra.Order.Interval
for their algebraic propertiesMove the definitions of Multiset.Ixx
to what is now Order.Interval.Multiset
. I believe we could just delete this file in a later PR as nothing uses it (and I already had doubts when defining Multiset.Ixx
three years ago).
Move the algebraic results out of what is now Order.Interval.Finset.Basic
to a new file Algebra.Order.Interval.Finset.Basic
.
@@ -5,8 +5,8 @@ Authors: Patrick Massot, Scott Morrison
-/
import Mathlib.Topology.Instances.Real
import Mathlib.Topology.Algebra.Field
-import Mathlib.Data.Set.Intervals.ProjIcc
-import Mathlib.Data.Set.Intervals.Instances
+import Mathlib.Order.Interval.Set.ProjIcc
+import Mathlib.Algebra.Order.Interval.Set.Instances
#align_import topology.unit_interval from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
We change the following field in the definition of an additive commutative monoid:
nsmul_succ : ∀ (n : ℕ) (x : G),
- AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+ AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x
where the latter is more natural
We adjust the definitions of ^
in monoids, groups, etc.
Originally there was a warning comment about why this natural order was preferred
use
x * npowRec n x
and notnpowRec n x * x
in the definition to make sure that definitional unfolding ofnpowRec
is blocked, to avoid deep recursion issues.
but it seems to no longer apply.
Remarks on the PR :
pow_succ
and pow_succ'
have switched their meanings.Ideal.IsPrime.mul_mem_pow
which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul
.@@ -248,7 +248,7 @@ lemma abs_sub_addNSMul_le (hδ : 0 ≤ δ) {t : Icc a b} (n : ℕ)
(|t - addNSMul h δ n| : α) ≤ δ :=
(abs_eq_self.2 <| sub_nonneg.2 ht.1).trans_le <| (sub_le_sub_right (by exact ht.2) _).trans <|
(le_abs_self _).trans <| (abs_projIcc_sub_projIcc h).trans <| by
- rw [add_sub_add_comm, sub_self, zero_add, succ_nsmul, add_sub_cancel_right]
+ rw [add_sub_add_comm, sub_self, zero_add, succ_nsmul', add_sub_cancel_right]
exact (abs_eq_self.mpr hδ).le
end Set.Icc
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).
| Statement | New name | Old name | |
@@ -248,7 +248,7 @@ lemma abs_sub_addNSMul_le (hδ : 0 ≤ δ) {t : Icc a b} (n : ℕ)
(|t - addNSMul h δ n| : α) ≤ δ :=
(abs_eq_self.2 <| sub_nonneg.2 ht.1).trans_le <| (sub_le_sub_right (by exact ht.2) _).trans <|
(le_abs_self _).trans <| (abs_projIcc_sub_projIcc h).trans <| by
- rw [add_sub_add_comm, sub_self, zero_add, succ_nsmul, add_sub_cancel]
+ rw [add_sub_add_comm, sub_self, zero_add, succ_nsmul, add_sub_cancel_right]
exact (abs_eq_self.mpr hδ).le
end Set.Icc
open Classical
(#11199)
We remove all but one open Classical
s, instead preferring to use open scoped Classical
. The only real side-effect this led to is moving a couple declarations to use Exists.choose
instead of Classical.choose
.
The first few commits are explicitly labelled regex replaces for ease of review.
@@ -22,7 +22,8 @@ We provide basic instances, as well as a custom tactic for discharging
noncomputable section
-open Classical Topology Filter
+open scoped Classical
+open Topology Filter
open Set Int Set.Icc
@@ -123,8 +123,9 @@ theorem symm_symm (x : I) : σ (σ x) = x :=
Subtype.ext <| by simp [symm]
#align unit_interval.symm_symm unitInterval.symm_symm
-theorem symm_bijective : Function.Bijective (symm : I → I) :=
- Function.bijective_iff_has_inverse.mpr ⟨_, symm_symm, symm_symm⟩
+theorem symm_involutive : Function.Involutive (symm : I → I) := symm_symm
+
+theorem symm_bijective : Function.Bijective (symm : I → I) := symm_involutive.bijective
@[simp]
theorem coe_symm_eq (x : I) : (σ x : ℝ) = 1 - x :=
@@ -137,11 +138,21 @@ theorem continuous_symm : Continuous σ :=
(continuous_const.add continuous_induced_dom.neg).subtype_mk _
#align unit_interval.continuous_symm unitInterval.continuous_symm
+/-- `unitInterval.symm` as a `Homeomorph`. -/
+@[simps]
+def symmHomeomorph : I ≃ₜ I where
+ toFun := symm
+ invFun := symm
+ left_inv := symm_symm
+ right_inv := symm_symm
+
theorem strictAnti_symm : StrictAnti σ := fun _ _ h ↦ sub_lt_sub_left (α := ℝ) h _
-theorem involutive_symm : Function.Involutive σ := symm_symm
+-- 2024-02-27
+@[deprecated] alias involutive_symm := symm_involutive
-theorem bijective_symm : Function.Bijective σ := involutive_symm.bijective
+-- 2024-02-27
+@[deprecated] alias bijective_symm := symm_bijective
theorem half_le_symm_iff (t : I) : 1 / 2 ≤ (σ t : ℝ) ↔ (t : ℝ) ≤ 1 / 2 := by
rw [coe_symm_eq, le_sub_iff_add_le, add_comm, ← le_sub_iff_add_le, sub_half]
@@ -48,7 +48,7 @@ theorem one_mem : (1 : ℝ) ∈ I :=
#align unit_interval.one_mem unitInterval.one_mem
theorem mul_mem {x y : ℝ} (hx : x ∈ I) (hy : y ∈ I) : x * y ∈ I :=
- ⟨mul_nonneg hx.1 hy.1, (mul_le_mul hx.2 hy.2 hy.1 zero_le_one).trans_eq <| one_mul 1⟩
+ ⟨mul_nonneg hx.1 hy.1, mul_le_one hx.2 hy.1 hy.2⟩
#align unit_interval.mul_mem unitInterval.mul_mem
theorem div_mem {x y : ℝ} (hx : 0 ≤ x) (hy : 0 ≤ y) (hxy : x ≤ y) : x / y ∈ I :=
@@ -94,11 +94,11 @@ instance : Mul I :=
-- todo: we could set up a `LinearOrderedCommMonoidWithZero I` instance
theorem mul_le_left {x y : I} : x * y ≤ x :=
- Subtype.coe_le_coe.mp <| (mul_le_mul_of_nonneg_left y.2.2 x.2.1).trans_eq <| mul_one x.1
+ Subtype.coe_le_coe.mp <| mul_le_of_le_one_right x.2.1 y.2.2
#align unit_interval.mul_le_left unitInterval.mul_le_left
theorem mul_le_right {x y : I} : x * y ≤ y :=
- Subtype.coe_le_coe.mp <| (mul_le_mul_of_nonneg_right x.2.2 y.2.1).trans_eq <| one_mul y.1
+ Subtype.coe_le_coe.mp <| mul_le_of_le_one_left y.2.1 x.2.2
#align unit_interval.mul_le_right unitInterval.mul_le_right
/-- Unit interval central symmetry. -/
The names for lemmas about monotonicity of (a ^ ·)
and (· ^ n)
were a mess. This PR tidies up everything related by following the naming convention for (a * ·)
and (· * b)
. Namely, (a ^ ·)
is pow_right
and (· ^ n)
is pow_left
in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.
Algebra.GroupPower.Order
pow_mono
→ pow_right_mono
pow_le_pow
→ pow_le_pow_right
pow_le_pow_of_le_left
→ pow_le_pow_left
pow_lt_pow_of_lt_left
→ pow_lt_pow_left
strictMonoOn_pow
→ pow_left_strictMonoOn
pow_strictMono_right
→ pow_right_strictMono
pow_lt_pow
→ pow_lt_pow_right
pow_lt_pow_iff
→ pow_lt_pow_iff_right
pow_le_pow_iff
→ pow_le_pow_iff_right
self_lt_pow
→ lt_self_pow
strictAnti_pow
→ pow_right_strictAnti
pow_lt_pow_iff_of_lt_one
→ pow_lt_pow_iff_right_of_lt_one
pow_lt_pow_of_lt_one
→ pow_lt_pow_right_of_lt_one
lt_of_pow_lt_pow
→ lt_of_pow_lt_pow_left
le_of_pow_le_pow
→ le_of_pow_le_pow_left
pow_lt_pow₀
→ pow_lt_pow_right₀
Algebra.GroupPower.CovariantClass
pow_le_pow_of_le_left'
→ pow_le_pow_left'
nsmul_le_nsmul_of_le_right
→ nsmul_le_nsmul_right
pow_lt_pow'
→ pow_lt_pow_right'
nsmul_lt_nsmul
→ nsmul_lt_nsmul_left
pow_strictMono_left
→ pow_right_strictMono'
nsmul_strictMono_right
→ nsmul_left_strictMono
StrictMono.pow_right'
→ StrictMono.pow_const
StrictMono.nsmul_left
→ StrictMono.const_nsmul
pow_strictMono_right'
→ pow_left_strictMono
nsmul_strictMono_left
→ nsmul_right_strictMono
Monotone.pow_right
→ Monotone.pow_const
Monotone.nsmul_left
→ Monotone.const_nsmul
lt_of_pow_lt_pow'
→ lt_of_pow_lt_pow_left'
lt_of_nsmul_lt_nsmul
→ lt_of_nsmul_lt_nsmul_right
pow_le_pow'
→ pow_le_pow_right'
nsmul_le_nsmul
→ nsmul_le_nsmul_left
pow_le_pow_of_le_one'
→ pow_le_pow_right_of_le_one'
nsmul_le_nsmul_of_nonpos
→ nsmul_le_nsmul_left_of_nonpos
le_of_pow_le_pow'
→ le_of_pow_le_pow_left'
le_of_nsmul_le_nsmul'
→ le_of_nsmul_le_nsmul_right'
pow_le_pow_iff'
→ pow_le_pow_iff_right'
nsmul_le_nsmul_iff
→ nsmul_le_nsmul_iff_left
pow_lt_pow_iff'
→ pow_lt_pow_iff_right'
nsmul_lt_nsmul_iff
→ nsmul_lt_nsmul_iff_left
Data.Nat.Pow
Nat.pow_lt_pow_of_lt_left
→ Nat.pow_lt_pow_left
Nat.pow_le_iff_le_left
→ Nat.pow_le_pow_iff_left
Nat.pow_lt_iff_lt_left
→ Nat.pow_lt_pow_iff_left
pow_le_pow_iff_left
pow_lt_pow_iff_left
pow_right_injective
pow_right_inj
Nat.pow_le_pow_left
to have the correct name since Nat.pow_le_pow_of_le_left
is in Std.Nat.pow_le_pow_right
to have the correct name since Nat.pow_le_pow_of_le_right
is in Std.self_le_pow
was a duplicate of le_self_pow
.Nat.pow_lt_pow_of_lt_right
is defeq to pow_lt_pow_right
.Nat.pow_right_strictMono
is defeq to pow_right_strictMono
.Nat.pow_le_iff_le_right
is defeq to pow_le_pow_iff_right
.Nat.pow_lt_iff_lt_right
is defeq to pow_lt_pow_iff_right
.0 < n
or 1 ≤ n
to n ≠ 0
.Nat
lemmas have been protected
.@@ -226,10 +226,10 @@ lemma addNSMul_eq_right [Archimedean α] (hδ : 0 < δ) :
obtain ⟨m, hm⟩ := Archimedean.arch (b - a) hδ
refine ⟨m, fun n hn ↦ ?_⟩
rw [addNSMul, coe_projIcc, add_comm, min_eq_left_iff.mpr, max_eq_right h]
- exact sub_le_iff_le_add.mp (hm.trans <| nsmul_le_nsmul hδ.le hn)
+ exact sub_le_iff_le_add.mp (hm.trans <| nsmul_le_nsmul_left hδ.le hn)
lemma monotone_addNSMul (hδ : 0 ≤ δ) : Monotone (addNSMul h δ) :=
- fun _ _ hnm ↦ monotone_projIcc h <| (add_le_add_iff_left _).mpr (nsmul_le_nsmul hδ hnm)
+ fun _ _ hnm ↦ monotone_projIcc h <| (add_le_add_iff_left _).mpr (nsmul_le_nsmul_left hδ hnm)
lemma abs_sub_addNSMul_le (hδ : 0 ≤ δ) {t : Icc a b} (n : ℕ)
(ht : t ∈ Icc (addNSMul h δ n) (addNSMul h δ (n+1))) :
Nsmul
-> NSMul
, Zpow
-> ZPow
, etc (#9067)
Normalising to naming convention rule number 6.
@@ -214,26 +214,26 @@ lemma _root_.Set.abs_projIcc_sub_projIcc : (|projIcc a b h c - projIcc a b h d|
· rwa [sub_self, abs_zero]
· exact (abs_eq_self.mpr hdc).le
-/-- When `h : a ≤ b` and `δ > 0`, `addNsmul h δ` is a sequence of points in the closed interval
+/-- When `h : a ≤ b` and `δ > 0`, `addNSMul h δ` is a sequence of points in the closed interval
`[a,b]`, which is initially equally spaced but eventually stays at the right endpoint `b`. -/
-def addNsmul (δ : α) (n : ℕ) : Icc a b := projIcc a b h (a + n • δ)
+def addNSMul (δ : α) (n : ℕ) : Icc a b := projIcc a b h (a + n • δ)
-lemma addNsmul_zero : addNsmul h δ 0 = a := by
- rw [addNsmul, zero_smul, add_zero, projIcc_left]
+lemma addNSMul_zero : addNSMul h δ 0 = a := by
+ rw [addNSMul, zero_smul, add_zero, projIcc_left]
-lemma addNsmul_eq_right [Archimedean α] (hδ : 0 < δ) :
- ∃ m, ∀ n ≥ m, addNsmul h δ n = b := by
+lemma addNSMul_eq_right [Archimedean α] (hδ : 0 < δ) :
+ ∃ m, ∀ n ≥ m, addNSMul h δ n = b := by
obtain ⟨m, hm⟩ := Archimedean.arch (b - a) hδ
refine ⟨m, fun n hn ↦ ?_⟩
- rw [addNsmul, coe_projIcc, add_comm, min_eq_left_iff.mpr, max_eq_right h]
+ rw [addNSMul, coe_projIcc, add_comm, min_eq_left_iff.mpr, max_eq_right h]
exact sub_le_iff_le_add.mp (hm.trans <| nsmul_le_nsmul hδ.le hn)
-lemma monotone_addNsmul (hδ : 0 ≤ δ) : Monotone (addNsmul h δ) :=
+lemma monotone_addNSMul (hδ : 0 ≤ δ) : Monotone (addNSMul h δ) :=
fun _ _ hnm ↦ monotone_projIcc h <| (add_le_add_iff_left _).mpr (nsmul_le_nsmul hδ hnm)
-lemma abs_sub_addNsmul_le (hδ : 0 ≤ δ) {t : Icc a b} (n : ℕ)
- (ht : t ∈ Icc (addNsmul h δ n) (addNsmul h δ (n+1))) :
- (|t - addNsmul h δ n| : α) ≤ δ :=
+lemma abs_sub_addNSMul_le (hδ : 0 ≤ δ) {t : Icc a b} (n : ℕ)
+ (ht : t ∈ Icc (addNSMul h δ n) (addNSMul h δ (n+1))) :
+ (|t - addNSMul h δ n| : α) ≤ δ :=
(abs_eq_self.2 <| sub_nonneg.2 ht.1).trans_le <| (sub_le_sub_right (by exact ht.2) _).trans <|
(le_abs_self _).trans <| (abs_projIcc_sub_projIcc h).trans <| by
rw [add_sub_add_comm, sub_self, zero_add, succ_nsmul, add_sub_cancel]
@@ -250,10 +250,10 @@ lemma exists_monotone_Icc_subset_open_cover_Icc {ι} {a b : ℝ} (h : a ≤ b) {
Monotone t ∧ (∃ m, ∀ n ≥ m, t n = b) ∧ ∀ n, ∃ i, Icc (t n) (t (n + 1)) ⊆ c i := by
obtain ⟨δ, δ_pos, ball_subset⟩ := lebesgue_number_lemma_of_metric isCompact_univ hc₁ hc₂
have hδ := half_pos δ_pos
- refine ⟨addNsmul h (δ/2), addNsmul_zero h,
- monotone_addNsmul h hδ.le, addNsmul_eq_right h hδ, fun n ↦ ?_⟩
- obtain ⟨i, hsub⟩ := ball_subset (addNsmul h (δ/2) n) trivial
- exact ⟨i, fun t ht ↦ hsub ((abs_sub_addNsmul_le h hδ.le n ht).trans_lt <| half_lt_self δ_pos)⟩
+ refine ⟨addNSMul h (δ/2), addNSMul_zero h,
+ monotone_addNSMul h hδ.le, addNSMul_eq_right h hδ, fun n ↦ ?_⟩
+ obtain ⟨i, hsub⟩ := ball_subset (addNSMul h (δ/2) n) trivial
+ exact ⟨i, fun t ht ↦ hsub ((abs_sub_addNSMul_le h hδ.le n ht).trans_lt <| half_lt_self δ_pos)⟩
/-- Any open cover of the unit interval can be refined to a finite partition into subintervals. -/
lemma exists_monotone_Icc_subset_open_cover_unitInterval {ι} {c : ι → Set I}
@@ -270,11 +270,11 @@ lemma exists_monotone_Icc_subset_open_cover_unitInterval_prod_self {ι} {c : ι
have hδ := half_pos δ_pos
simp_rw [Subtype.ext_iff]
have h : (0 : ℝ) ≤ 1 := zero_le_one
- refine ⟨addNsmul h (δ/2), addNsmul_zero h,
- monotone_addNsmul h hδ.le, addNsmul_eq_right h hδ, fun n m ↦ ?_⟩
- obtain ⟨i, hsub⟩ := ball_subset (addNsmul h (δ/2) n, addNsmul h (δ/2) m) trivial
- exact ⟨i, fun t ht ↦ hsub (Metric.mem_ball.mpr <| (max_le (abs_sub_addNsmul_le h hδ.le n ht.1) <|
- abs_sub_addNsmul_le h hδ.le m ht.2).trans_lt <| half_lt_self δ_pos)⟩
+ refine ⟨addNSMul h (δ/2), addNSMul_zero h,
+ monotone_addNSMul h hδ.le, addNSMul_eq_right h hδ, fun n m ↦ ?_⟩
+ obtain ⟨i, hsub⟩ := ball_subset (addNSMul h (δ/2) n, addNSMul h (δ/2) m) trivial
+ exact ⟨i, fun t ht ↦ hsub (Metric.mem_ball.mpr <| (max_le (abs_sub_addNSMul_le h hδ.le n ht.1) <|
+ abs_sub_addNSMul_le h hδ.le m ht.2).trans_lt <| half_lt_self δ_pos)⟩
end partition
[@foo](https://github.com/foo) _ _ _ _ _ ...
by named arguments (#8702)
Using Lean4's named arguments, we manage to remove a few hard-to-read explicit function calls [@foo](https://github.com/foo) _ _ _ _ _ ...
which used to be necessary in Lean3.
Occasionally, this results in slightly longer code. The benefit of named arguments is readability, as well as to reduce the brittleness of the code when the argument order is changed.
Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>
@@ -72,7 +72,7 @@ instance hasOne : One I :=
⟨⟨1, by constructor <;> norm_num⟩⟩
#align unit_interval.has_one unitInterval.hasOne
-instance : ZeroLEOneClass I := ⟨@zero_le_one ℝ _ _ _ _⟩
+instance : ZeroLEOneClass I := ⟨zero_le_one (α := ℝ)⟩
instance : BoundedOrder I := Set.Icc.boundedOrder zero_le_one
@@ -180,7 +180,7 @@ theorem le_one' {t : I} : t ≤ 1 :=
t.2.2
#align unit_interval.le_one' unitInterval.le_one'
-instance : NeZero (1 : I) := ⟨fun h ↦ one_ne_zero <| congrArg Subtype.val h⟩
+instance : Nontrivial I := ⟨⟨1, 0, (one_ne_zero <| congrArg Subtype.val ·)⟩⟩
theorem mul_pos_mem_iff {a t : ℝ} (ha : 0 < a) : a * t ∈ I ↔ t ∈ Set.Icc (0 : ℝ) (1 / a) := by
constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor
@@ -144,7 +144,7 @@ theorem involutive_symm : Function.Involutive σ := symm_symm
theorem bijective_symm : Function.Bijective σ := involutive_symm.bijective
theorem half_le_symm_iff (t : I) : 1 / 2 ≤ (σ t : ℝ) ↔ (t : ℝ) ≤ 1 / 2 := by
- rw [coe_symm_eq, le_sub_iff_add_le, add_comm, ←le_sub_iff_add_le, sub_half]
+ rw [coe_symm_eq, le_sub_iff_add_le, add_comm, ← le_sub_iff_add_le, sub_half]
instance : ConnectedSpace I :=
Subtype.connectedSpace ⟨nonempty_Icc.mpr zero_le_one, isPreconnected_Icc⟩
@@ -123,6 +123,9 @@ theorem symm_symm (x : I) : σ (σ x) = x :=
Subtype.ext <| by simp [symm]
#align unit_interval.symm_symm unitInterval.symm_symm
+theorem symm_bijective : Function.Bijective (symm : I → I) :=
+ Function.bijective_iff_has_inverse.mpr ⟨_, symm_symm, symm_symm⟩
+
@[simp]
theorem coe_symm_eq (x : I) : (σ x : ℝ) = 1 - x :=
rfl
@@ -20,7 +20,6 @@ We provide basic instances, as well as a custom tactic for discharging
-/
-
noncomputable section
open Classical Topology Filter
@@ -73,6 +72,12 @@ instance hasOne : One I :=
⟨⟨1, by constructor <;> norm_num⟩⟩
#align unit_interval.has_one unitInterval.hasOne
+instance : ZeroLEOneClass I := ⟨@zero_le_one ℝ _ _ _ _⟩
+
+instance : BoundedOrder I := Set.Icc.boundedOrder zero_le_one
+
+lemma univ_eq_Icc : (univ : Set I) = Icc (0 : I) (1 : I) := Icc_bot_top.symm
+
theorem coe_ne_zero {x : I} : (x : ℝ) ≠ 0 ↔ x ≠ 0 :=
not_iff_not.mpr coe_eq_zero
#align unit_interval.coe_ne_zero unitInterval.coe_ne_zero
@@ -129,6 +134,15 @@ theorem continuous_symm : Continuous σ :=
(continuous_const.add continuous_induced_dom.neg).subtype_mk _
#align unit_interval.continuous_symm unitInterval.continuous_symm
+theorem strictAnti_symm : StrictAnti σ := fun _ _ h ↦ sub_lt_sub_left (α := ℝ) h _
+
+theorem involutive_symm : Function.Involutive σ := symm_symm
+
+theorem bijective_symm : Function.Bijective σ := involutive_symm.bijective
+
+theorem half_le_symm_iff (t : I) : 1 / 2 ≤ (σ t : ℝ) ↔ (t : ℝ) ≤ 1 / 2 := by
+ rw [coe_symm_eq, le_sub_iff_add_le, add_comm, ←le_sub_iff_add_le, sub_half]
+
instance : ConnectedSpace I :=
Subtype.connectedSpace ⟨nonempty_Icc.mpr zero_le_one, isPreconnected_Icc⟩
@@ -179,6 +193,88 @@ theorem two_mul_sub_one_mem_iff {t : ℝ} : 2 * t - 1 ∈ I ↔ t ∈ Set.Icc (1
end unitInterval
+section partition
+
+namespace Set.Icc
+
+variable {α} [LinearOrderedAddCommGroup α] {a b c d : α} (h : a ≤ b) {δ : α}
+
+-- TODO: Set.projIci, Set.projIic
+/-- `Set.projIcc` is a contraction. -/
+lemma _root_.Set.abs_projIcc_sub_projIcc : (|projIcc a b h c - projIcc a b h d| : α) ≤ |c - d| := by
+ wlog hdc : d ≤ c generalizing c d
+ · rw [abs_sub_comm, abs_sub_comm c]; exact this (le_of_not_le hdc)
+ rw [abs_eq_self.2 (sub_nonneg.2 hdc), abs_eq_self.2 (sub_nonneg.2 <| monotone_projIcc h hdc)]
+ rw [← sub_nonneg] at hdc
+ refine (max_sub_max_le_max _ _ _ _).trans (max_le (by rwa [sub_self]) ?_)
+ refine ((le_abs_self _).trans <| abs_min_sub_min_le_max _ _ _ _).trans (max_le ?_ ?_)
+ · rwa [sub_self, abs_zero]
+ · exact (abs_eq_self.mpr hdc).le
+
+/-- When `h : a ≤ b` and `δ > 0`, `addNsmul h δ` is a sequence of points in the closed interval
+ `[a,b]`, which is initially equally spaced but eventually stays at the right endpoint `b`. -/
+def addNsmul (δ : α) (n : ℕ) : Icc a b := projIcc a b h (a + n • δ)
+
+lemma addNsmul_zero : addNsmul h δ 0 = a := by
+ rw [addNsmul, zero_smul, add_zero, projIcc_left]
+
+lemma addNsmul_eq_right [Archimedean α] (hδ : 0 < δ) :
+ ∃ m, ∀ n ≥ m, addNsmul h δ n = b := by
+ obtain ⟨m, hm⟩ := Archimedean.arch (b - a) hδ
+ refine ⟨m, fun n hn ↦ ?_⟩
+ rw [addNsmul, coe_projIcc, add_comm, min_eq_left_iff.mpr, max_eq_right h]
+ exact sub_le_iff_le_add.mp (hm.trans <| nsmul_le_nsmul hδ.le hn)
+
+lemma monotone_addNsmul (hδ : 0 ≤ δ) : Monotone (addNsmul h δ) :=
+ fun _ _ hnm ↦ monotone_projIcc h <| (add_le_add_iff_left _).mpr (nsmul_le_nsmul hδ hnm)
+
+lemma abs_sub_addNsmul_le (hδ : 0 ≤ δ) {t : Icc a b} (n : ℕ)
+ (ht : t ∈ Icc (addNsmul h δ n) (addNsmul h δ (n+1))) :
+ (|t - addNsmul h δ n| : α) ≤ δ :=
+ (abs_eq_self.2 <| sub_nonneg.2 ht.1).trans_le <| (sub_le_sub_right (by exact ht.2) _).trans <|
+ (le_abs_self _).trans <| (abs_projIcc_sub_projIcc h).trans <| by
+ rw [add_sub_add_comm, sub_self, zero_add, succ_nsmul, add_sub_cancel]
+ exact (abs_eq_self.mpr hδ).le
+
+end Set.Icc
+
+open scoped unitInterval
+
+/-- Any open cover `c` of a closed interval `[a, b]` in ℝ can be refined to
+ a finite partition into subintervals. -/
+lemma exists_monotone_Icc_subset_open_cover_Icc {ι} {a b : ℝ} (h : a ≤ b) {c : ι → Set (Icc a b)}
+ (hc₁ : ∀ i, IsOpen (c i)) (hc₂ : univ ⊆ ⋃ i, c i) : ∃ t : ℕ → Icc a b, t 0 = a ∧
+ Monotone t ∧ (∃ m, ∀ n ≥ m, t n = b) ∧ ∀ n, ∃ i, Icc (t n) (t (n + 1)) ⊆ c i := by
+ obtain ⟨δ, δ_pos, ball_subset⟩ := lebesgue_number_lemma_of_metric isCompact_univ hc₁ hc₂
+ have hδ := half_pos δ_pos
+ refine ⟨addNsmul h (δ/2), addNsmul_zero h,
+ monotone_addNsmul h hδ.le, addNsmul_eq_right h hδ, fun n ↦ ?_⟩
+ obtain ⟨i, hsub⟩ := ball_subset (addNsmul h (δ/2) n) trivial
+ exact ⟨i, fun t ht ↦ hsub ((abs_sub_addNsmul_le h hδ.le n ht).trans_lt <| half_lt_self δ_pos)⟩
+
+/-- Any open cover of the unit interval can be refined to a finite partition into subintervals. -/
+lemma exists_monotone_Icc_subset_open_cover_unitInterval {ι} {c : ι → Set I}
+ (hc₁ : ∀ i, IsOpen (c i)) (hc₂ : univ ⊆ ⋃ i, c i) : ∃ t : ℕ → I, t 0 = 0 ∧
+ Monotone t ∧ (∃ n, ∀ m ≥ n, t m = 1) ∧ ∀ n, ∃ i, Icc (t n) (t (n + 1)) ⊆ c i := by
+ simp_rw [← Subtype.coe_inj]
+ exact exists_monotone_Icc_subset_open_cover_Icc zero_le_one hc₁ hc₂
+
+lemma exists_monotone_Icc_subset_open_cover_unitInterval_prod_self {ι} {c : ι → Set (I × I)}
+ (hc₁ : ∀ i, IsOpen (c i)) (hc₂ : univ ⊆ ⋃ i, c i) :
+ ∃ t : ℕ → I, t 0 = 0 ∧ Monotone t ∧ (∃ n, ∀ m ≥ n, t m = 1) ∧
+ ∀ n m, ∃ i, Icc (t n) (t (n + 1)) ×ˢ Icc (t m) (t (m + 1)) ⊆ c i := by
+ obtain ⟨δ, δ_pos, ball_subset⟩ := lebesgue_number_lemma_of_metric isCompact_univ hc₁ hc₂
+ have hδ := half_pos δ_pos
+ simp_rw [Subtype.ext_iff]
+ have h : (0 : ℝ) ≤ 1 := zero_le_one
+ refine ⟨addNsmul h (δ/2), addNsmul_zero h,
+ monotone_addNsmul h hδ.le, addNsmul_eq_right h hδ, fun n m ↦ ?_⟩
+ obtain ⟨i, hsub⟩ := ball_subset (addNsmul h (δ/2) n, addNsmul h (δ/2) m) trivial
+ exact ⟨i, fun t ht ↦ hsub (Metric.mem_ball.mpr <| (max_le (abs_sub_addNsmul_le h hδ.le n ht.1) <|
+ abs_sub_addNsmul_le h hδ.le m ht.2).trans_lt <| half_lt_self δ_pos)⟩
+
+end partition
+
@[simp]
theorem projIcc_eq_zero {x : ℝ} : projIcc (0 : ℝ) 1 zero_le_one x = 0 ↔ x ≤ 0 :=
projIcc_eq_left zero_lt_one
Mirrors the corresponding proofs for connectedness.
Co-authored-by: @ADedecker
@@ -163,6 +163,8 @@ theorem le_one' {t : I} : t ≤ 1 :=
t.2.2
#align unit_interval.le_one' unitInterval.le_one'
+instance : NeZero (1 : I) := ⟨fun h ↦ one_ne_zero <| congrArg Subtype.val h⟩
+
theorem mul_pos_mem_iff {a t : ℝ} (ha : 0 < a) : a * t ∈ I ↔ t ∈ Set.Icc (0 : ℝ) (1 / a) := by
constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor
· exact nonneg_of_mul_nonneg_right h₁ ha
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -205,7 +205,7 @@ end Tactic.Interactive
section
-variable {𝕜 : Type _} [LinearOrderedField 𝕜] [TopologicalSpace 𝕜] [TopologicalRing 𝕜]
+variable {𝕜 : Type*} [LinearOrderedField 𝕜] [TopologicalSpace 𝕜] [TopologicalRing 𝕜]
-- We only need the ordering on `𝕜` here to avoid talking about flipping the interval over.
-- At the end of the day I only care about `ℝ`, so I'm hesitant to put work into generalizing.
@@ -2,17 +2,14 @@
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Scott Morrison
-
-! This file was ported from Lean 3 source module topology.unit_interval
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Topology.Instances.Real
import Mathlib.Topology.Algebra.Field
import Mathlib.Data.Set.Intervals.ProjIcc
import Mathlib.Data.Set.Intervals.Instances
+#align_import topology.unit_interval from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
/-!
# The unit interval, as a topological space
@@ -129,7 +129,7 @@ theorem coe_symm_eq (x : I) : (σ x : ℝ) = 1 - x :=
-- Porting note: Proof used to be `by continuity!`
@[continuity]
theorem continuous_symm : Continuous σ :=
-(continuous_const.add continuous_induced_dom.neg).subtype_mk _
+ (continuous_const.add continuous_induced_dom.neg).subtype_mk _
#align unit_interval.continuous_symm unitInterval.continuous_symm
instance : ConnectedSpace I :=
@@ -175,7 +175,7 @@ theorem mul_pos_mem_iff {a t : ℝ} (ha : 0 < a) : a * t ∈ I ↔ t ∈ Set.Icc
#align unit_interval.mul_pos_mem_iff unitInterval.mul_pos_mem_iff
theorem two_mul_sub_one_mem_iff {t : ℝ} : 2 * t - 1 ∈ I ↔ t ∈ Set.Icc (1 / 2 : ℝ) 1 := by
-constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor <;> linarith
+ constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor <;> linarith
#align unit_interval.two_mul_sub_one_mem_iff unitInterval.two_mul_sub_one_mem_iff
end unitInterval
This fixes a bunch of spacing bugs in tactics. Mathlib counterpart of:
@@ -194,7 +194,7 @@ namespace Tactic.Interactive
-- Porting note: This replaces an unsafe def tactic
/-- A tactic that solves `0 ≤ ↑x`, `0 ≤ 1 - ↑x`, `↑x ≤ 1`, and `1 - ↑x ≤ 1` for `x : I`. -/
-macro "unit_interval ": tactic =>
+macro "unit_interval" : tactic =>
`(tactic| (first
| apply unitInterval.nonneg
| apply unitInterval.one_minus_nonneg
Enable the cancelDenoms
preprocessor in linarith
. Closes #2714.
Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -175,14 +175,7 @@ theorem mul_pos_mem_iff {a t : ℝ} (ha : 0 < a) : a * t ∈ I ↔ t ∈ Set.Icc
#align unit_interval.mul_pos_mem_iff unitInterval.mul_pos_mem_iff
theorem two_mul_sub_one_mem_iff {t : ℝ} : 2 * t - 1 ∈ I ↔ t ∈ Set.Icc (1 / 2 : ℝ) 1 := by
--- Porting note: used to be
--- constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor <;> linarith
-letI : NeZero 1 := inferInstance
-constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor <;> try {linarith}
-· rw [← (mul_le_mul_left (zero_lt_two))]
- simp [le_of_sub_nonneg h₁]
-· rw [sub_nonneg]
- exact (div_le_iff' (zero_lt_two)).1 h₁
+constructor <;> rintro ⟨h₁, h₂⟩ <;> constructor <;> linarith
#align unit_interval.two_mul_sub_one_mem_iff unitInterval.two_mul_sub_one_mem_iff
end unitInterval
@@ -16,7 +16,7 @@ import Mathlib.Data.Set.Intervals.Instances
/-!
# The unit interval, as a topological space
-Use `open_locale unitInterval` to turn on the notation `I := Set.Icc (0 : ℝ) (1 : ℝ)`.
+Use `open unitInterval` to turn on the notation `I := Set.Icc (0 : ℝ) (1 : ℝ)`.
We provide basic instances, as well as a custom tactic for discharging
`0 ≤ ↑x`, `0 ≤ 1 - ↑x`, `↑x ≤ 1`, and `1 - ↑x ≤ 1` when `x : I`.
The unported dependencies are
algebra.order.module
init.core
algebra.order.monoid.cancel.defs
algebra.abs
algebra.group_power.lemmas
init.data.list.basic
algebra.order.monoid.cancel.basic
init.data.list.default
topology.subset_properties
init.logic
The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file