data.set.intervals.group
⟷
Mathlib.Data.Set.Intervals.Group
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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This PR will split most of the lemmas in data.set.pairwise
which are independent of the data.set.lattice
. It makes a lot of files no longer depend on data.set.lattice
.
mathlib4 PR: https://github.com/leanprover-community/mathlib4/pull/1184
Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-/
import data.set.intervals.basic
-import data.set.pairwise
+import data.set.pairwise.basic
import algebra.order.group.abs
import algebra.group_power.lemmas
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@@ -4,12 +4,15 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-/
import data.set.intervals.basic
+import data.set.pairwise
import algebra.order.group.abs
+import algebra.group_power.lemmas
-/-! ### Lemmas about arithmetic operations and intervals.
+/-! ### Lemmas about arithmetic operations and intervals.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
-> Any changes to this file require a corresponding PR to mathlib4.-/
+> Any changes to this file require a corresponding PR to mathlib4.
+-/
variables {α : Type*}
@@ -98,4 +101,99 @@ end
end linear_ordered_add_comm_group
+/-! ### Lemmas about disjointness of translates of intervals -/
+section pairwise_disjoint
+
+section ordered_comm_group
+
+variables [ordered_comm_group α] (a b : α)
+
+@[to_additive]
+lemma pairwise_disjoint_Ioc_mul_zpow :
+ pairwise (disjoint on λ n : ℤ, Ioc (a * b ^ n) (a * b ^ (n + 1))) :=
+begin
+ simp_rw [function.on_fun, set.disjoint_iff],
+ intros m n hmn x hx,
+ apply hmn,
+ have hb : 1 < b,
+ { have : a * b ^ m < a * b ^ (m + 1), from hx.1.1.trans_le hx.1.2,
+ rwa [mul_lt_mul_iff_left, ←mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this },
+ have i1 := hx.1.1.trans_le hx.2.2,
+ have i2 := hx.2.1.trans_le hx.1.2,
+ rw [mul_lt_mul_iff_left, zpow_lt_zpow_iff hb, int.lt_add_one_iff] at i1 i2,
+ exact le_antisymm i1 i2
+end
+
+@[to_additive]
+lemma pairwise_disjoint_Ico_mul_zpow :
+ pairwise (disjoint on λ n : ℤ, Ico (a * b ^ n) (a * b ^ (n + 1))) :=
+begin
+ simp_rw [function.on_fun, set.disjoint_iff],
+ intros m n hmn x hx,
+ apply hmn,
+ have hb : 1 < b,
+ { have : a * b ^ m < a * b ^ (m + 1), from hx.1.1.trans_lt hx.1.2,
+ rwa [mul_lt_mul_iff_left, ←mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this },
+ have i1 := hx.1.1.trans_lt hx.2.2,
+ have i2 := hx.2.1.trans_lt hx.1.2,
+ rw [mul_lt_mul_iff_left, zpow_lt_zpow_iff hb, int.lt_add_one_iff] at i1 i2,
+ exact le_antisymm i1 i2,
+end
+
+@[to_additive]
+lemma pairwise_disjoint_Ioo_mul_zpow :
+ pairwise (disjoint on λ n : ℤ, Ioo (a * b ^ n) (a * b ^ (n + 1))) :=
+λ m n hmn, (pairwise_disjoint_Ioc_mul_zpow a b hmn).mono Ioo_subset_Ioc_self Ioo_subset_Ioc_self
+
+@[to_additive]
+lemma pairwise_disjoint_Ioc_zpow :
+ pairwise (disjoint on λ n : ℤ, Ioc (b ^ n) (b ^ (n + 1))) :=
+by simpa only [one_mul] using pairwise_disjoint_Ioc_mul_zpow 1 b
+
+@[to_additive]
+lemma pairwise_disjoint_Ico_zpow :
+ pairwise (disjoint on λ n : ℤ, Ico (b ^ n) (b ^ (n + 1))) :=
+by simpa only [one_mul] using pairwise_disjoint_Ico_mul_zpow 1 b
+
+@[to_additive]
+lemma pairwise_disjoint_Ioo_zpow :
+ pairwise (disjoint on λ n : ℤ, Ioo (b ^ n) (b ^ (n + 1))) :=
+by simpa only [one_mul] using pairwise_disjoint_Ioo_mul_zpow 1 b
+
+end ordered_comm_group
+
+section ordered_ring
+
+variables [ordered_ring α] (a : α)
+
+lemma pairwise_disjoint_Ioc_add_int_cast :
+ pairwise (disjoint on λ n : ℤ, Ioc (a + n) (a + n + 1)) :=
+by simpa only [zsmul_one, int.cast_add, int.cast_one, ←add_assoc]
+ using pairwise_disjoint_Ioc_add_zsmul a (1 : α)
+
+lemma pairwise_disjoint_Ico_add_int_cast :
+ pairwise (disjoint on λ n : ℤ, Ico (a + n) (a + n + 1)) :=
+by simpa only [zsmul_one, int.cast_add, int.cast_one, ←add_assoc]
+ using pairwise_disjoint_Ico_add_zsmul a (1 : α)
+
+lemma pairwise_disjoint_Ioo_add_int_cast :
+ pairwise (disjoint on λ n : ℤ, Ioo (a + n) (a + n + 1)) :=
+by simpa only [zsmul_one, int.cast_add, int.cast_one, ←add_assoc]
+ using pairwise_disjoint_Ioo_add_zsmul a (1 : α)
+
+variables (α)
+
+lemma pairwise_disjoint_Ico_int_cast : pairwise (disjoint on λ n : ℤ, Ico (n : α) (n + 1)) :=
+by simpa only [zero_add] using pairwise_disjoint_Ico_add_int_cast (0 : α)
+
+lemma pairwise_disjoint_Ioo_int_cast : pairwise (disjoint on λ n : ℤ, Ioo (n : α) (n + 1)) :=
+by simpa only [zero_add] using pairwise_disjoint_Ioo_add_int_cast (0 : α)
+
+lemma pairwise_disjoint_Ioc_int_cast : pairwise (disjoint on λ n : ℤ, Ioc (n : α) (n + 1)) :=
+by simpa only [zero_add] using pairwise_disjoint_Ioc_add_int_cast (0 : α)
+
+end ordered_ring
+
+end pairwise_disjoint
+
end set
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(first ported)
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -3,7 +3,7 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-/
-import Data.Set.Intervals.Basic
+import Order.Interval.Set.Basic
import Data.Set.Pairwise.Basic
import Algebra.Order.Group.Abs
import Algebra.GroupPower.Lemmas
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -31,7 +31,7 @@ variable [OrderedCommGroup α] {a b c d : α}
#print Set.inv_mem_Icc_iff /-
@[to_additive]
theorem inv_mem_Icc_iff : a⁻¹ ∈ Set.Icc c d ↔ a ∈ Set.Icc d⁻¹ c⁻¹ :=
- (and_comm' _ _).trans <| and_congr inv_le' le_inv'
+ (and_comm _ _).trans <| and_congr inv_le' le_inv'
#align set.inv_mem_Icc_iff Set.inv_mem_Icc_iff
#align set.neg_mem_Icc_iff Set.neg_mem_Icc_iff
-/
@@ -39,7 +39,7 @@ theorem inv_mem_Icc_iff : a⁻¹ ∈ Set.Icc c d ↔ a ∈ Set.Icc d⁻¹ c⁻¹
#print Set.inv_mem_Ico_iff /-
@[to_additive]
theorem inv_mem_Ico_iff : a⁻¹ ∈ Set.Ico c d ↔ a ∈ Set.Ioc d⁻¹ c⁻¹ :=
- (and_comm' _ _).trans <| and_congr inv_lt' le_inv'
+ (and_comm _ _).trans <| and_congr inv_lt' le_inv'
#align set.inv_mem_Ico_iff Set.inv_mem_Ico_iff
#align set.neg_mem_Ico_iff Set.neg_mem_Ico_iff
-/
@@ -47,7 +47,7 @@ theorem inv_mem_Ico_iff : a⁻¹ ∈ Set.Ico c d ↔ a ∈ Set.Ioc d⁻¹ c⁻¹
#print Set.inv_mem_Ioc_iff /-
@[to_additive]
theorem inv_mem_Ioc_iff : a⁻¹ ∈ Set.Ioc c d ↔ a ∈ Set.Ico d⁻¹ c⁻¹ :=
- (and_comm' _ _).trans <| and_congr inv_le' lt_inv'
+ (and_comm _ _).trans <| and_congr inv_le' lt_inv'
#align set.inv_mem_Ioc_iff Set.inv_mem_Ioc_iff
#align set.neg_mem_Ioc_iff Set.neg_mem_Ioc_iff
-/
@@ -55,7 +55,7 @@ theorem inv_mem_Ioc_iff : a⁻¹ ∈ Set.Ioc c d ↔ a ∈ Set.Ico d⁻¹ c⁻¹
#print Set.inv_mem_Ioo_iff /-
@[to_additive]
theorem inv_mem_Ioo_iff : a⁻¹ ∈ Set.Ioo c d ↔ a ∈ Set.Ioo d⁻¹ c⁻¹ :=
- (and_comm' _ _).trans <| and_congr inv_lt' lt_inv'
+ (and_comm _ _).trans <| and_congr inv_lt' lt_inv'
#align set.inv_mem_Ioo_iff Set.inv_mem_Ioo_iff
#align set.neg_mem_Ioo_iff Set.neg_mem_Ioo_iff
-/
@@ -152,25 +152,25 @@ theorem sub_mem_Ioo_iff_left : a - b ∈ Set.Ioo c d ↔ a ∈ Set.Ioo (c + b) (
#print Set.sub_mem_Icc_iff_right /-
theorem sub_mem_Icc_iff_right : a - b ∈ Set.Icc c d ↔ b ∈ Set.Icc (a - d) (a - c) :=
- (and_comm' _ _).trans <| and_congr sub_le_comm le_sub_comm
+ (and_comm _ _).trans <| and_congr sub_le_comm le_sub_comm
#align set.sub_mem_Icc_iff_right Set.sub_mem_Icc_iff_right
-/
#print Set.sub_mem_Ico_iff_right /-
theorem sub_mem_Ico_iff_right : a - b ∈ Set.Ico c d ↔ b ∈ Set.Ioc (a - d) (a - c) :=
- (and_comm' _ _).trans <| and_congr sub_lt_comm le_sub_comm
+ (and_comm _ _).trans <| and_congr sub_lt_comm le_sub_comm
#align set.sub_mem_Ico_iff_right Set.sub_mem_Ico_iff_right
-/
#print Set.sub_mem_Ioc_iff_right /-
theorem sub_mem_Ioc_iff_right : a - b ∈ Set.Ioc c d ↔ b ∈ Set.Ico (a - d) (a - c) :=
- (and_comm' _ _).trans <| and_congr sub_le_comm lt_sub_comm
+ (and_comm _ _).trans <| and_congr sub_le_comm lt_sub_comm
#align set.sub_mem_Ioc_iff_right Set.sub_mem_Ioc_iff_right
-/
#print Set.sub_mem_Ioo_iff_right /-
theorem sub_mem_Ioo_iff_right : a - b ∈ Set.Ioo c d ↔ b ∈ Set.Ioo (a - d) (a - c) :=
- (and_comm' _ _).trans <| and_congr sub_lt_comm lt_sub_comm
+ (and_comm _ _).trans <| and_congr sub_lt_comm lt_sub_comm
#align set.sub_mem_Ioo_iff_right Set.sub_mem_Ioo_iff_right
-/
@@ -179,7 +179,7 @@ theorem sub_mem_Ioo_iff_right : a - b ∈ Set.Ioo c d ↔ b ∈ Set.Ioo (a - d)
-- for instance when considering metric balls in `ℝ`.
theorem mem_Icc_iff_abs_le {R : Type _} [LinearOrderedAddCommGroup R] {x y z : R} :
|x - y| ≤ z ↔ y ∈ Icc (x - z) (x + z) :=
- abs_le.trans <| (and_comm' _ _).trans <| and_congr sub_le_comm neg_le_sub_iff_le_add
+ abs_le.trans <| (and_comm _ _).trans <| and_congr sub_le_comm neg_le_sub_iff_le_add
#align set.mem_Icc_iff_abs_le Set.mem_Icc_iff_abs_le
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -293,48 +293,48 @@ section OrderedRing
variable [OrderedRing α] (a : α)
-#print Set.pairwise_disjoint_Ioc_add_int_cast /-
-theorem pairwise_disjoint_Ioc_add_int_cast :
+#print Set.pairwise_disjoint_Ioc_add_intCast /-
+theorem pairwise_disjoint_Ioc_add_intCast :
Pairwise (Disjoint on fun n : ℤ => Ioc (a + n) (a + n + 1)) := by
simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
pairwise_disjoint_Ioc_add_zsmul a (1 : α)
-#align set.pairwise_disjoint_Ioc_add_int_cast Set.pairwise_disjoint_Ioc_add_int_cast
+#align set.pairwise_disjoint_Ioc_add_int_cast Set.pairwise_disjoint_Ioc_add_intCast
-/
-#print Set.pairwise_disjoint_Ico_add_int_cast /-
-theorem pairwise_disjoint_Ico_add_int_cast :
+#print Set.pairwise_disjoint_Ico_add_intCast /-
+theorem pairwise_disjoint_Ico_add_intCast :
Pairwise (Disjoint on fun n : ℤ => Ico (a + n) (a + n + 1)) := by
simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
pairwise_disjoint_Ico_add_zsmul a (1 : α)
-#align set.pairwise_disjoint_Ico_add_int_cast Set.pairwise_disjoint_Ico_add_int_cast
+#align set.pairwise_disjoint_Ico_add_int_cast Set.pairwise_disjoint_Ico_add_intCast
-/
-#print Set.pairwise_disjoint_Ioo_add_int_cast /-
-theorem pairwise_disjoint_Ioo_add_int_cast :
+#print Set.pairwise_disjoint_Ioo_add_intCast /-
+theorem pairwise_disjoint_Ioo_add_intCast :
Pairwise (Disjoint on fun n : ℤ => Ioo (a + n) (a + n + 1)) := by
simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
pairwise_disjoint_Ioo_add_zsmul a (1 : α)
-#align set.pairwise_disjoint_Ioo_add_int_cast Set.pairwise_disjoint_Ioo_add_int_cast
+#align set.pairwise_disjoint_Ioo_add_int_cast Set.pairwise_disjoint_Ioo_add_intCast
-/
variable (α)
-#print Set.pairwise_disjoint_Ico_int_cast /-
-theorem pairwise_disjoint_Ico_int_cast : Pairwise (Disjoint on fun n : ℤ => Ico (n : α) (n + 1)) :=
+#print Set.pairwise_disjoint_Ico_intCast /-
+theorem pairwise_disjoint_Ico_intCast : Pairwise (Disjoint on fun n : ℤ => Ico (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ico_add_int_cast (0 : α)
-#align set.pairwise_disjoint_Ico_int_cast Set.pairwise_disjoint_Ico_int_cast
+#align set.pairwise_disjoint_Ico_int_cast Set.pairwise_disjoint_Ico_intCast
-/
-#print Set.pairwise_disjoint_Ioo_int_cast /-
-theorem pairwise_disjoint_Ioo_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioo (n : α) (n + 1)) :=
+#print Set.pairwise_disjoint_Ioo_intCast /-
+theorem pairwise_disjoint_Ioo_intCast : Pairwise (Disjoint on fun n : ℤ => Ioo (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ioo_add_int_cast (0 : α)
-#align set.pairwise_disjoint_Ioo_int_cast Set.pairwise_disjoint_Ioo_int_cast
+#align set.pairwise_disjoint_Ioo_int_cast Set.pairwise_disjoint_Ioo_intCast
-/
-#print Set.pairwise_disjoint_Ioc_int_cast /-
-theorem pairwise_disjoint_Ioc_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioc (n : α) (n + 1)) :=
+#print Set.pairwise_disjoint_Ioc_intCast /-
+theorem pairwise_disjoint_Ioc_intCast : Pairwise (Disjoint on fun n : ℤ => Ioc (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ioc_add_int_cast (0 : α)
-#align set.pairwise_disjoint_Ioc_int_cast Set.pairwise_disjoint_Ioc_int_cast
+#align set.pairwise_disjoint_Ioc_int_cast Set.pairwise_disjoint_Ioc_intCast
-/
end OrderedRing
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -222,10 +222,10 @@ theorem pairwise_disjoint_Ioc_mul_zpow :
have hb : 1 < b :=
by
have : a * b ^ m < a * b ^ (m + 1) := hx.1.1.trans_le hx.1.2
- rwa [mul_lt_mul_iff_left, ← mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this
+ rwa [mul_lt_mul_iff_left, ← mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this
have i1 := hx.1.1.trans_le hx.2.2
have i2 := hx.2.1.trans_le hx.1.2
- rw [mul_lt_mul_iff_left, zpow_lt_zpow_iff hb, Int.lt_add_one_iff] at i1 i2
+ rw [mul_lt_mul_iff_left, zpow_lt_zpow_iff hb, Int.lt_add_one_iff] at i1 i2
exact le_antisymm i1 i2
#align set.pairwise_disjoint_Ioc_mul_zpow Set.pairwise_disjoint_Ioc_mul_zpow
#align set.pairwise_disjoint_Ioc_add_zsmul Set.pairwise_disjoint_Ioc_add_zsmul
@@ -242,10 +242,10 @@ theorem pairwise_disjoint_Ico_mul_zpow :
have hb : 1 < b :=
by
have : a * b ^ m < a * b ^ (m + 1) := hx.1.1.trans_lt hx.1.2
- rwa [mul_lt_mul_iff_left, ← mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this
+ rwa [mul_lt_mul_iff_left, ← mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this
have i1 := hx.1.1.trans_lt hx.2.2
have i2 := hx.2.1.trans_lt hx.1.2
- rw [mul_lt_mul_iff_left, zpow_lt_zpow_iff hb, Int.lt_add_one_iff] at i1 i2
+ rw [mul_lt_mul_iff_left, zpow_lt_zpow_iff hb, Int.lt_add_one_iff] at i1 i2
exact le_antisymm i1 i2
#align set.pairwise_disjoint_Ico_mul_zpow Set.pairwise_disjoint_Ico_mul_zpow
#align set.pairwise_disjoint_Ico_add_zsmul Set.pairwise_disjoint_Ico_add_zsmul
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,10 +3,10 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-/
-import Mathbin.Data.Set.Intervals.Basic
-import Mathbin.Data.Set.Pairwise.Basic
-import Mathbin.Algebra.Order.Group.Abs
-import Mathbin.Algebra.GroupPower.Lemmas
+import Data.Set.Intervals.Basic
+import Data.Set.Pairwise.Basic
+import Algebra.Order.Group.Abs
+import Algebra.GroupPower.Lemmas
#align_import data.set.intervals.group from "leanprover-community/mathlib"@"c227d107bbada5d0d9d20287e3282c0a7f1651a0"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,17 +2,14 @@
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-
-! This file was ported from Lean 3 source module data.set.intervals.group
-! leanprover-community/mathlib commit c227d107bbada5d0d9d20287e3282c0a7f1651a0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Set.Intervals.Basic
import Mathbin.Data.Set.Pairwise.Basic
import Mathbin.Algebra.Order.Group.Abs
import Mathbin.Algebra.GroupPower.Lemmas
+#align_import data.set.intervals.group from "leanprover-community/mathlib"@"c227d107bbada5d0d9d20287e3282c0a7f1651a0"
+
/-! ### Lemmas about arithmetic operations and intervals.
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -31,29 +31,37 @@ variable [OrderedCommGroup α] {a b c d : α}
/-! `inv_mem_Ixx_iff`, `sub_mem_Ixx_iff` -/
+#print Set.inv_mem_Icc_iff /-
@[to_additive]
theorem inv_mem_Icc_iff : a⁻¹ ∈ Set.Icc c d ↔ a ∈ Set.Icc d⁻¹ c⁻¹ :=
(and_comm' _ _).trans <| and_congr inv_le' le_inv'
#align set.inv_mem_Icc_iff Set.inv_mem_Icc_iff
#align set.neg_mem_Icc_iff Set.neg_mem_Icc_iff
+-/
+#print Set.inv_mem_Ico_iff /-
@[to_additive]
theorem inv_mem_Ico_iff : a⁻¹ ∈ Set.Ico c d ↔ a ∈ Set.Ioc d⁻¹ c⁻¹ :=
(and_comm' _ _).trans <| and_congr inv_lt' le_inv'
#align set.inv_mem_Ico_iff Set.inv_mem_Ico_iff
#align set.neg_mem_Ico_iff Set.neg_mem_Ico_iff
+-/
+#print Set.inv_mem_Ioc_iff /-
@[to_additive]
theorem inv_mem_Ioc_iff : a⁻¹ ∈ Set.Ioc c d ↔ a ∈ Set.Ico d⁻¹ c⁻¹ :=
(and_comm' _ _).trans <| and_congr inv_le' lt_inv'
#align set.inv_mem_Ioc_iff Set.inv_mem_Ioc_iff
#align set.neg_mem_Ioc_iff Set.neg_mem_Ioc_iff
+-/
+#print Set.inv_mem_Ioo_iff /-
@[to_additive]
theorem inv_mem_Ioo_iff : a⁻¹ ∈ Set.Ioo c d ↔ a ∈ Set.Ioo d⁻¹ c⁻¹ :=
(and_comm' _ _).trans <| and_congr inv_lt' lt_inv'
#align set.inv_mem_Ioo_iff Set.inv_mem_Ioo_iff
#align set.neg_mem_Ioo_iff Set.neg_mem_Ioo_iff
+-/
end OrderedCommGroup
@@ -64,85 +72,119 @@ variable [OrderedAddCommGroup α] {a b c d : α}
/-! `add_mem_Ixx_iff_left` -/
+#print Set.add_mem_Icc_iff_left /-
theorem add_mem_Icc_iff_left : a + b ∈ Set.Icc c d ↔ a ∈ Set.Icc (c - b) (d - b) :=
(and_congr sub_le_iff_le_add le_sub_iff_add_le).symm
#align set.add_mem_Icc_iff_left Set.add_mem_Icc_iff_left
+-/
+#print Set.add_mem_Ico_iff_left /-
theorem add_mem_Ico_iff_left : a + b ∈ Set.Ico c d ↔ a ∈ Set.Ico (c - b) (d - b) :=
(and_congr sub_le_iff_le_add lt_sub_iff_add_lt).symm
#align set.add_mem_Ico_iff_left Set.add_mem_Ico_iff_left
+-/
+#print Set.add_mem_Ioc_iff_left /-
theorem add_mem_Ioc_iff_left : a + b ∈ Set.Ioc c d ↔ a ∈ Set.Ioc (c - b) (d - b) :=
(and_congr sub_lt_iff_lt_add le_sub_iff_add_le).symm
#align set.add_mem_Ioc_iff_left Set.add_mem_Ioc_iff_left
+-/
+#print Set.add_mem_Ioo_iff_left /-
theorem add_mem_Ioo_iff_left : a + b ∈ Set.Ioo c d ↔ a ∈ Set.Ioo (c - b) (d - b) :=
(and_congr sub_lt_iff_lt_add lt_sub_iff_add_lt).symm
#align set.add_mem_Ioo_iff_left Set.add_mem_Ioo_iff_left
+-/
/-! `add_mem_Ixx_iff_right` -/
+#print Set.add_mem_Icc_iff_right /-
theorem add_mem_Icc_iff_right : a + b ∈ Set.Icc c d ↔ b ∈ Set.Icc (c - a) (d - a) :=
(and_congr sub_le_iff_le_add' le_sub_iff_add_le').symm
#align set.add_mem_Icc_iff_right Set.add_mem_Icc_iff_right
+-/
+#print Set.add_mem_Ico_iff_right /-
theorem add_mem_Ico_iff_right : a + b ∈ Set.Ico c d ↔ b ∈ Set.Ico (c - a) (d - a) :=
(and_congr sub_le_iff_le_add' lt_sub_iff_add_lt').symm
#align set.add_mem_Ico_iff_right Set.add_mem_Ico_iff_right
+-/
+#print Set.add_mem_Ioc_iff_right /-
theorem add_mem_Ioc_iff_right : a + b ∈ Set.Ioc c d ↔ b ∈ Set.Ioc (c - a) (d - a) :=
(and_congr sub_lt_iff_lt_add' le_sub_iff_add_le').symm
#align set.add_mem_Ioc_iff_right Set.add_mem_Ioc_iff_right
+-/
+#print Set.add_mem_Ioo_iff_right /-
theorem add_mem_Ioo_iff_right : a + b ∈ Set.Ioo c d ↔ b ∈ Set.Ioo (c - a) (d - a) :=
(and_congr sub_lt_iff_lt_add' lt_sub_iff_add_lt').symm
#align set.add_mem_Ioo_iff_right Set.add_mem_Ioo_iff_right
+-/
/-! `sub_mem_Ixx_iff_left` -/
+#print Set.sub_mem_Icc_iff_left /-
theorem sub_mem_Icc_iff_left : a - b ∈ Set.Icc c d ↔ a ∈ Set.Icc (c + b) (d + b) :=
and_congr le_sub_iff_add_le sub_le_iff_le_add
#align set.sub_mem_Icc_iff_left Set.sub_mem_Icc_iff_left
+-/
+#print Set.sub_mem_Ico_iff_left /-
theorem sub_mem_Ico_iff_left : a - b ∈ Set.Ico c d ↔ a ∈ Set.Ico (c + b) (d + b) :=
and_congr le_sub_iff_add_le sub_lt_iff_lt_add
#align set.sub_mem_Ico_iff_left Set.sub_mem_Ico_iff_left
+-/
+#print Set.sub_mem_Ioc_iff_left /-
theorem sub_mem_Ioc_iff_left : a - b ∈ Set.Ioc c d ↔ a ∈ Set.Ioc (c + b) (d + b) :=
and_congr lt_sub_iff_add_lt sub_le_iff_le_add
#align set.sub_mem_Ioc_iff_left Set.sub_mem_Ioc_iff_left
+-/
+#print Set.sub_mem_Ioo_iff_left /-
theorem sub_mem_Ioo_iff_left : a - b ∈ Set.Ioo c d ↔ a ∈ Set.Ioo (c + b) (d + b) :=
and_congr lt_sub_iff_add_lt sub_lt_iff_lt_add
#align set.sub_mem_Ioo_iff_left Set.sub_mem_Ioo_iff_left
+-/
/-! `sub_mem_Ixx_iff_right` -/
+#print Set.sub_mem_Icc_iff_right /-
theorem sub_mem_Icc_iff_right : a - b ∈ Set.Icc c d ↔ b ∈ Set.Icc (a - d) (a - c) :=
(and_comm' _ _).trans <| and_congr sub_le_comm le_sub_comm
#align set.sub_mem_Icc_iff_right Set.sub_mem_Icc_iff_right
+-/
+#print Set.sub_mem_Ico_iff_right /-
theorem sub_mem_Ico_iff_right : a - b ∈ Set.Ico c d ↔ b ∈ Set.Ioc (a - d) (a - c) :=
(and_comm' _ _).trans <| and_congr sub_lt_comm le_sub_comm
#align set.sub_mem_Ico_iff_right Set.sub_mem_Ico_iff_right
+-/
+#print Set.sub_mem_Ioc_iff_right /-
theorem sub_mem_Ioc_iff_right : a - b ∈ Set.Ioc c d ↔ b ∈ Set.Ico (a - d) (a - c) :=
(and_comm' _ _).trans <| and_congr sub_le_comm lt_sub_comm
#align set.sub_mem_Ioc_iff_right Set.sub_mem_Ioc_iff_right
+-/
+#print Set.sub_mem_Ioo_iff_right /-
theorem sub_mem_Ioo_iff_right : a - b ∈ Set.Ioo c d ↔ b ∈ Set.Ioo (a - d) (a - c) :=
(and_comm' _ _).trans <| and_congr sub_lt_comm lt_sub_comm
#align set.sub_mem_Ioo_iff_right Set.sub_mem_Ioo_iff_right
+-/
+#print Set.mem_Icc_iff_abs_le /-
-- I think that symmetric intervals deserve attention and API: they arise all the time,
-- for instance when considering metric balls in `ℝ`.
theorem mem_Icc_iff_abs_le {R : Type _} [LinearOrderedAddCommGroup R] {x y z : R} :
|x - y| ≤ z ↔ y ∈ Icc (x - z) (x + z) :=
abs_le.trans <| (and_comm' _ _).trans <| and_congr sub_le_comm neg_le_sub_iff_le_add
#align set.mem_Icc_iff_abs_le Set.mem_Icc_iff_abs_le
+-/
end OrderedAddCommGroup
@@ -150,6 +192,7 @@ section LinearOrderedAddCommGroup
variable [LinearOrderedAddCommGroup α]
+#print Set.nonempty_Ico_sdiff /-
/-- If we remove a smaller interval from a larger, the result is nonempty -/
theorem nonempty_Ico_sdiff {x dx y dy : α} (h : dy < dx) (hx : 0 < dx) :
Nonempty ↥(Ico x (x + dx) \ Ico y (y + dy)) :=
@@ -158,6 +201,7 @@ theorem nonempty_Ico_sdiff {x dx y dy : α} (h : dy < dx) (hx : 0 < dx) :
· use x; simp [*, not_le.2 h']
· use max x (x + dy); simp [*, le_refl]
#align set.nonempty_Ico_sdiff Set.nonempty_Ico_sdiff
+-/
end LinearOrderedAddCommGroup
@@ -170,6 +214,7 @@ section OrderedCommGroup
variable [OrderedCommGroup α] (a b : α)
+#print Set.pairwise_disjoint_Ioc_mul_zpow /-
@[to_additive]
theorem pairwise_disjoint_Ioc_mul_zpow :
Pairwise (Disjoint on fun n : ℤ => Ioc (a * b ^ n) (a * b ^ (n + 1))) :=
@@ -187,7 +232,9 @@ theorem pairwise_disjoint_Ioc_mul_zpow :
exact le_antisymm i1 i2
#align set.pairwise_disjoint_Ioc_mul_zpow Set.pairwise_disjoint_Ioc_mul_zpow
#align set.pairwise_disjoint_Ioc_add_zsmul Set.pairwise_disjoint_Ioc_add_zsmul
+-/
+#print Set.pairwise_disjoint_Ico_mul_zpow /-
@[to_additive]
theorem pairwise_disjoint_Ico_mul_zpow :
Pairwise (Disjoint on fun n : ℤ => Ico (a * b ^ n) (a * b ^ (n + 1))) :=
@@ -205,34 +252,43 @@ theorem pairwise_disjoint_Ico_mul_zpow :
exact le_antisymm i1 i2
#align set.pairwise_disjoint_Ico_mul_zpow Set.pairwise_disjoint_Ico_mul_zpow
#align set.pairwise_disjoint_Ico_add_zsmul Set.pairwise_disjoint_Ico_add_zsmul
+-/
+#print Set.pairwise_disjoint_Ioo_mul_zpow /-
@[to_additive]
theorem pairwise_disjoint_Ioo_mul_zpow :
Pairwise (Disjoint on fun n : ℤ => Ioo (a * b ^ n) (a * b ^ (n + 1))) := fun m n hmn =>
(pairwise_disjoint_Ioc_mul_zpow a b hmn).mono Ioo_subset_Ioc_self Ioo_subset_Ioc_self
#align set.pairwise_disjoint_Ioo_mul_zpow Set.pairwise_disjoint_Ioo_mul_zpow
#align set.pairwise_disjoint_Ioo_add_zsmul Set.pairwise_disjoint_Ioo_add_zsmul
+-/
+#print Set.pairwise_disjoint_Ioc_zpow /-
@[to_additive]
theorem pairwise_disjoint_Ioc_zpow :
Pairwise (Disjoint on fun n : ℤ => Ioc (b ^ n) (b ^ (n + 1))) := by
simpa only [one_mul] using pairwise_disjoint_Ioc_mul_zpow 1 b
#align set.pairwise_disjoint_Ioc_zpow Set.pairwise_disjoint_Ioc_zpow
#align set.pairwise_disjoint_Ioc_zsmul Set.pairwise_disjoint_Ioc_zsmul
+-/
+#print Set.pairwise_disjoint_Ico_zpow /-
@[to_additive]
theorem pairwise_disjoint_Ico_zpow :
Pairwise (Disjoint on fun n : ℤ => Ico (b ^ n) (b ^ (n + 1))) := by
simpa only [one_mul] using pairwise_disjoint_Ico_mul_zpow 1 b
#align set.pairwise_disjoint_Ico_zpow Set.pairwise_disjoint_Ico_zpow
#align set.pairwise_disjoint_Ico_zsmul Set.pairwise_disjoint_Ico_zsmul
+-/
+#print Set.pairwise_disjoint_Ioo_zpow /-
@[to_additive]
theorem pairwise_disjoint_Ioo_zpow :
Pairwise (Disjoint on fun n : ℤ => Ioo (b ^ n) (b ^ (n + 1))) := by
simpa only [one_mul] using pairwise_disjoint_Ioo_mul_zpow 1 b
#align set.pairwise_disjoint_Ioo_zpow Set.pairwise_disjoint_Ioo_zpow
#align set.pairwise_disjoint_Ioo_zsmul Set.pairwise_disjoint_Ioo_zsmul
+-/
end OrderedCommGroup
@@ -240,37 +296,49 @@ section OrderedRing
variable [OrderedRing α] (a : α)
+#print Set.pairwise_disjoint_Ioc_add_int_cast /-
theorem pairwise_disjoint_Ioc_add_int_cast :
Pairwise (Disjoint on fun n : ℤ => Ioc (a + n) (a + n + 1)) := by
simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
pairwise_disjoint_Ioc_add_zsmul a (1 : α)
#align set.pairwise_disjoint_Ioc_add_int_cast Set.pairwise_disjoint_Ioc_add_int_cast
+-/
+#print Set.pairwise_disjoint_Ico_add_int_cast /-
theorem pairwise_disjoint_Ico_add_int_cast :
Pairwise (Disjoint on fun n : ℤ => Ico (a + n) (a + n + 1)) := by
simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
pairwise_disjoint_Ico_add_zsmul a (1 : α)
#align set.pairwise_disjoint_Ico_add_int_cast Set.pairwise_disjoint_Ico_add_int_cast
+-/
+#print Set.pairwise_disjoint_Ioo_add_int_cast /-
theorem pairwise_disjoint_Ioo_add_int_cast :
Pairwise (Disjoint on fun n : ℤ => Ioo (a + n) (a + n + 1)) := by
simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
pairwise_disjoint_Ioo_add_zsmul a (1 : α)
#align set.pairwise_disjoint_Ioo_add_int_cast Set.pairwise_disjoint_Ioo_add_int_cast
+-/
variable (α)
+#print Set.pairwise_disjoint_Ico_int_cast /-
theorem pairwise_disjoint_Ico_int_cast : Pairwise (Disjoint on fun n : ℤ => Ico (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ico_add_int_cast (0 : α)
#align set.pairwise_disjoint_Ico_int_cast Set.pairwise_disjoint_Ico_int_cast
+-/
+#print Set.pairwise_disjoint_Ioo_int_cast /-
theorem pairwise_disjoint_Ioo_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioo (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ioo_add_int_cast (0 : α)
#align set.pairwise_disjoint_Ioo_int_cast Set.pairwise_disjoint_Ioo_int_cast
+-/
+#print Set.pairwise_disjoint_Ioc_int_cast /-
theorem pairwise_disjoint_Ioc_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioc (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ioc_add_int_cast (0 : α)
#align set.pairwise_disjoint_Ioc_int_cast Set.pairwise_disjoint_Ioc_int_cast
+-/
end OrderedRing
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -180,10 +180,10 @@ theorem pairwise_disjoint_Ioc_mul_zpow :
have hb : 1 < b :=
by
have : a * b ^ m < a * b ^ (m + 1) := hx.1.1.trans_le hx.1.2
- rwa [mul_lt_mul_iff_left, ← mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this
+ rwa [mul_lt_mul_iff_left, ← mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this
have i1 := hx.1.1.trans_le hx.2.2
have i2 := hx.2.1.trans_le hx.1.2
- rw [mul_lt_mul_iff_left, zpow_lt_zpow_iff hb, Int.lt_add_one_iff] at i1 i2
+ rw [mul_lt_mul_iff_left, zpow_lt_zpow_iff hb, Int.lt_add_one_iff] at i1 i2
exact le_antisymm i1 i2
#align set.pairwise_disjoint_Ioc_mul_zpow Set.pairwise_disjoint_Ioc_mul_zpow
#align set.pairwise_disjoint_Ioc_add_zsmul Set.pairwise_disjoint_Ioc_add_zsmul
@@ -198,10 +198,10 @@ theorem pairwise_disjoint_Ico_mul_zpow :
have hb : 1 < b :=
by
have : a * b ^ m < a * b ^ (m + 1) := hx.1.1.trans_lt hx.1.2
- rwa [mul_lt_mul_iff_left, ← mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this
+ rwa [mul_lt_mul_iff_left, ← mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this
have i1 := hx.1.1.trans_lt hx.2.2
have i2 := hx.2.1.trans_lt hx.1.2
- rw [mul_lt_mul_iff_left, zpow_lt_zpow_iff hb, Int.lt_add_one_iff] at i1 i2
+ rw [mul_lt_mul_iff_left, zpow_lt_zpow_iff hb, Int.lt_add_one_iff] at i1 i2
exact le_antisymm i1 i2
#align set.pairwise_disjoint_Ico_mul_zpow Set.pairwise_disjoint_Ico_mul_zpow
#align set.pairwise_disjoint_Ico_add_zsmul Set.pairwise_disjoint_Ico_add_zsmul
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -31,48 +31,24 @@ variable [OrderedCommGroup α] {a b c d : α}
/-! `inv_mem_Ixx_iff`, `sub_mem_Ixx_iff` -/
-/- warning: set.inv_mem_Icc_iff -> Set.inv_mem_Icc_iff is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] {a : α} {c : α} {d : α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))) a) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))) d) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))) c)))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] {a : α} {c : α} {d : α}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Inv.inv.{u1} α (InvOneClass.toInv.{u1} α (DivInvOneMonoid.toInvOneClass.{u1} α (DivisionMonoid.toDivInvOneMonoid.{u1} α (DivisionCommMonoid.toDivisionMonoid.{u1} α (CommGroup.toDivisionCommMonoid.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))))) a) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (Inv.inv.{u1} α (InvOneClass.toInv.{u1} α (DivInvOneMonoid.toInvOneClass.{u1} α (DivisionMonoid.toDivInvOneMonoid.{u1} α (DivisionCommMonoid.toDivisionMonoid.{u1} α (CommGroup.toDivisionCommMonoid.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))))) d) (Inv.inv.{u1} α (InvOneClass.toInv.{u1} α (DivInvOneMonoid.toInvOneClass.{u1} α (DivisionMonoid.toDivInvOneMonoid.{u1} α (DivisionCommMonoid.toDivisionMonoid.{u1} α (CommGroup.toDivisionCommMonoid.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))))) c)))
-Case conversion may be inaccurate. Consider using '#align set.inv_mem_Icc_iff Set.inv_mem_Icc_iffₓ'. -/
@[to_additive]
theorem inv_mem_Icc_iff : a⁻¹ ∈ Set.Icc c d ↔ a ∈ Set.Icc d⁻¹ c⁻¹ :=
(and_comm' _ _).trans <| and_congr inv_le' le_inv'
#align set.inv_mem_Icc_iff Set.inv_mem_Icc_iff
#align set.neg_mem_Icc_iff Set.neg_mem_Icc_iff
-/- warning: set.inv_mem_Ico_iff -> Set.inv_mem_Ico_iff is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] {a : α} {c : α} {d : α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))) a) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))) d) (Inv.inv.{u1} α (DivInvMonoid.toHasInv.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))) c)))
-but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] {a : α} {c : α} {d : α}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Inv.inv.{u1} α (InvOneClass.toInv.{u1} α (DivInvOneMonoid.toInvOneClass.{u1} α (DivisionMonoid.toDivInvOneMonoid.{u1} α (DivisionCommMonoid.toDivisionMonoid.{u1} α (CommGroup.toDivisionCommMonoid.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))))) a) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (Inv.inv.{u1} α (InvOneClass.toInv.{u1} α (DivInvOneMonoid.toInvOneClass.{u1} α (DivisionMonoid.toDivInvOneMonoid.{u1} α (DivisionCommMonoid.toDivisionMonoid.{u1} α (CommGroup.toDivisionCommMonoid.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))))) d) (Inv.inv.{u1} α (InvOneClass.toInv.{u1} α (DivInvOneMonoid.toInvOneClass.{u1} α (DivisionMonoid.toDivInvOneMonoid.{u1} α (DivisionCommMonoid.toDivisionMonoid.{u1} α (CommGroup.toDivisionCommMonoid.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1)))))) c)))
-Case conversion may be inaccurate. Consider using '#align set.inv_mem_Ico_iff Set.inv_mem_Ico_iffₓ'. -/
@[to_additive]
theorem inv_mem_Ico_iff : a⁻¹ ∈ Set.Ico c d ↔ a ∈ Set.Ioc d⁻¹ c⁻¹ :=
(and_comm' _ _).trans <| and_congr inv_lt' le_inv'
#align set.inv_mem_Ico_iff Set.inv_mem_Ico_iff
#align set.neg_mem_Ico_iff Set.neg_mem_Ico_iff
-/- warning: set.inv_mem_Ioc_iff -> Set.inv_mem_Ioc_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.inv_mem_Ioc_iff Set.inv_mem_Ioc_iffₓ'. -/
@[to_additive]
theorem inv_mem_Ioc_iff : a⁻¹ ∈ Set.Ioc c d ↔ a ∈ Set.Ico d⁻¹ c⁻¹ :=
(and_comm' _ _).trans <| and_congr inv_le' lt_inv'
#align set.inv_mem_Ioc_iff Set.inv_mem_Ioc_iff
#align set.neg_mem_Ioc_iff Set.neg_mem_Ioc_iff
-/- warning: set.inv_mem_Ioo_iff -> Set.inv_mem_Ioo_iff is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.inv_mem_Ioo_iff Set.inv_mem_Ioo_iffₓ'. -/
@[to_additive]
theorem inv_mem_Ioo_iff : a⁻¹ ∈ Set.Ioo c d ↔ a ∈ Set.Ioo d⁻¹ c⁻¹ :=
(and_comm' _ _).trans <| and_congr inv_lt' lt_inv'
@@ -88,42 +64,18 @@ variable [OrderedAddCommGroup α] {a b c d : α}
/-! `add_mem_Ixx_iff_left` -/
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-Case conversion may be inaccurate. Consider using '#align set.add_mem_Icc_iff_left Set.add_mem_Icc_iff_leftₓ'. -/
theorem add_mem_Icc_iff_left : a + b ∈ Set.Icc c d ↔ a ∈ Set.Icc (c - b) (d - b) :=
(and_congr sub_le_iff_le_add le_sub_iff_add_le).symm
#align set.add_mem_Icc_iff_left Set.add_mem_Icc_iff_left
-/- warning: set.add_mem_Ico_iff_left -> Set.add_mem_Ico_iff_left is a dubious translation:
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- forall {α : Type.{u1}} [_inst_1 : OrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))))) a b) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) c b) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) d b)))
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-Case conversion may be inaccurate. Consider using '#align set.add_mem_Ico_iff_left Set.add_mem_Ico_iff_leftₓ'. -/
theorem add_mem_Ico_iff_left : a + b ∈ Set.Ico c d ↔ a ∈ Set.Ico (c - b) (d - b) :=
(and_congr sub_le_iff_le_add lt_sub_iff_add_lt).symm
#align set.add_mem_Ico_iff_left Set.add_mem_Ico_iff_left
-/- warning: set.add_mem_Ioc_iff_left -> Set.add_mem_Ioc_iff_left is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.add_mem_Ioc_iff_left Set.add_mem_Ioc_iff_leftₓ'. -/
theorem add_mem_Ioc_iff_left : a + b ∈ Set.Ioc c d ↔ a ∈ Set.Ioc (c - b) (d - b) :=
(and_congr sub_lt_iff_lt_add le_sub_iff_add_le).symm
#align set.add_mem_Ioc_iff_left Set.add_mem_Ioc_iff_left
-/- warning: set.add_mem_Ioo_iff_left -> Set.add_mem_Ioo_iff_left is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.add_mem_Ioo_iff_left Set.add_mem_Ioo_iff_leftₓ'. -/
theorem add_mem_Ioo_iff_left : a + b ∈ Set.Ioo c d ↔ a ∈ Set.Ioo (c - b) (d - b) :=
(and_congr sub_lt_iff_lt_add lt_sub_iff_add_lt).symm
#align set.add_mem_Ioo_iff_left Set.add_mem_Ioo_iff_left
@@ -131,42 +83,18 @@ theorem add_mem_Ioo_iff_left : a + b ∈ Set.Ioo c d ↔ a ∈ Set.Ioo (c - b) (
/-! `add_mem_Ixx_iff_right` -/
-/- warning: set.add_mem_Icc_iff_right -> Set.add_mem_Icc_iff_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.add_mem_Icc_iff_right Set.add_mem_Icc_iff_rightₓ'. -/
theorem add_mem_Icc_iff_right : a + b ∈ Set.Icc c d ↔ b ∈ Set.Icc (c - a) (d - a) :=
(and_congr sub_le_iff_le_add' le_sub_iff_add_le').symm
#align set.add_mem_Icc_iff_right Set.add_mem_Icc_iff_right
-/- warning: set.add_mem_Ico_iff_right -> Set.add_mem_Ico_iff_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))))) a b) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) c a) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) d a)))
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-Case conversion may be inaccurate. Consider using '#align set.add_mem_Ico_iff_right Set.add_mem_Ico_iff_rightₓ'. -/
theorem add_mem_Ico_iff_right : a + b ∈ Set.Ico c d ↔ b ∈ Set.Ico (c - a) (d - a) :=
(and_congr sub_le_iff_le_add' lt_sub_iff_add_lt').symm
#align set.add_mem_Ico_iff_right Set.add_mem_Ico_iff_right
-/- warning: set.add_mem_Ioc_iff_right -> Set.add_mem_Ioc_iff_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))))) a b) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) c a) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) d a)))
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-Case conversion may be inaccurate. Consider using '#align set.add_mem_Ioc_iff_right Set.add_mem_Ioc_iff_rightₓ'. -/
theorem add_mem_Ioc_iff_right : a + b ∈ Set.Ioc c d ↔ b ∈ Set.Ioc (c - a) (d - a) :=
(and_congr sub_lt_iff_lt_add' le_sub_iff_add_le').symm
#align set.add_mem_Ioc_iff_right Set.add_mem_Ioc_iff_right
-/- warning: set.add_mem_Ioo_iff_right -> Set.add_mem_Ioo_iff_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))))) a b) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) c a) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) d a)))
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-Case conversion may be inaccurate. Consider using '#align set.add_mem_Ioo_iff_right Set.add_mem_Ioo_iff_rightₓ'. -/
theorem add_mem_Ioo_iff_right : a + b ∈ Set.Ioo c d ↔ b ∈ Set.Ioo (c - a) (d - a) :=
(and_congr sub_lt_iff_lt_add' lt_sub_iff_add_lt').symm
#align set.add_mem_Ioo_iff_right Set.add_mem_Ioo_iff_right
@@ -174,42 +102,18 @@ theorem add_mem_Ioo_iff_right : a + b ∈ Set.Ioo c d ↔ b ∈ Set.Ioo (c - a)
/-! `sub_mem_Ixx_iff_left` -/
-/- warning: set.sub_mem_Icc_iff_left -> Set.sub_mem_Icc_iff_left is a dubious translation:
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- forall {α : Type.{u1}} [_inst_1 : OrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a b) (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Icc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))))) c b) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))))) d b)))
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-Case conversion may be inaccurate. Consider using '#align set.sub_mem_Icc_iff_left Set.sub_mem_Icc_iff_leftₓ'. -/
theorem sub_mem_Icc_iff_left : a - b ∈ Set.Icc c d ↔ a ∈ Set.Icc (c + b) (d + b) :=
and_congr le_sub_iff_add_le sub_le_iff_le_add
#align set.sub_mem_Icc_iff_left Set.sub_mem_Icc_iff_left
-/- warning: set.sub_mem_Ico_iff_left -> Set.sub_mem_Ico_iff_left is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a b) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))))) c b) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))))) d b)))
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-Case conversion may be inaccurate. Consider using '#align set.sub_mem_Ico_iff_left Set.sub_mem_Ico_iff_leftₓ'. -/
theorem sub_mem_Ico_iff_left : a - b ∈ Set.Ico c d ↔ a ∈ Set.Ico (c + b) (d + b) :=
and_congr le_sub_iff_add_le sub_lt_iff_lt_add
#align set.sub_mem_Ico_iff_left Set.sub_mem_Ico_iff_left
-/- warning: set.sub_mem_Ioc_iff_left -> Set.sub_mem_Ioc_iff_left is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align set.sub_mem_Ioc_iff_left Set.sub_mem_Ioc_iff_leftₓ'. -/
theorem sub_mem_Ioc_iff_left : a - b ∈ Set.Ioc c d ↔ a ∈ Set.Ioc (c + b) (d + b) :=
and_congr lt_sub_iff_add_lt sub_le_iff_le_add
#align set.sub_mem_Ioc_iff_left Set.sub_mem_Ioc_iff_left
-/- warning: set.sub_mem_Ioo_iff_left -> Set.sub_mem_Ioo_iff_left is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a b) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))))) c b) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))))) d b)))
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-Case conversion may be inaccurate. Consider using '#align set.sub_mem_Ioo_iff_left Set.sub_mem_Ioo_iff_leftₓ'. -/
theorem sub_mem_Ioo_iff_left : a - b ∈ Set.Ioo c d ↔ a ∈ Set.Ioo (c + b) (d + b) :=
and_congr lt_sub_iff_add_lt sub_lt_iff_lt_add
#align set.sub_mem_Ioo_iff_left Set.sub_mem_Ioo_iff_left
@@ -217,52 +121,22 @@ theorem sub_mem_Ioo_iff_left : a - b ∈ Set.Ioo c d ↔ a ∈ Set.Ioo (c + b) (
/-! `sub_mem_Ixx_iff_right` -/
-/- warning: set.sub_mem_Icc_iff_right -> Set.sub_mem_Icc_iff_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.sub_mem_Icc_iff_right Set.sub_mem_Icc_iff_rightₓ'. -/
theorem sub_mem_Icc_iff_right : a - b ∈ Set.Icc c d ↔ b ∈ Set.Icc (a - d) (a - c) :=
(and_comm' _ _).trans <| and_congr sub_le_comm le_sub_comm
#align set.sub_mem_Icc_iff_right Set.sub_mem_Icc_iff_right
-/- warning: set.sub_mem_Ico_iff_right -> Set.sub_mem_Ico_iff_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.sub_mem_Ico_iff_right Set.sub_mem_Ico_iff_rightₓ'. -/
theorem sub_mem_Ico_iff_right : a - b ∈ Set.Ico c d ↔ b ∈ Set.Ioc (a - d) (a - c) :=
(and_comm' _ _).trans <| and_congr sub_lt_comm le_sub_comm
#align set.sub_mem_Ico_iff_right Set.sub_mem_Ico_iff_right
-/- warning: set.sub_mem_Ioc_iff_right -> Set.sub_mem_Ioc_iff_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a b) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a d) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a c)))
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- forall {α : Type.{u1}} [_inst_1 : OrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a b) (Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a d) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a c)))
-Case conversion may be inaccurate. Consider using '#align set.sub_mem_Ioc_iff_right Set.sub_mem_Ioc_iff_rightₓ'. -/
theorem sub_mem_Ioc_iff_right : a - b ∈ Set.Ioc c d ↔ b ∈ Set.Ico (a - d) (a - c) :=
(and_comm' _ _).trans <| and_congr sub_le_comm lt_sub_comm
#align set.sub_mem_Ioc_iff_right Set.sub_mem_Ioc_iff_right
-/- warning: set.sub_mem_Ioo_iff_right -> Set.sub_mem_Ioo_iff_right is a dubious translation:
-lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a b) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a d) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toHasSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a c)))
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- forall {α : Type.{u1}} [_inst_1 : OrderedAddCommGroup.{u1} α] {a : α} {b : α} {c : α} {d : α}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a b) (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) c d)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b (Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α _inst_1)) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a d) (HSub.hSub.{u1, u1, u1} α α α (instHSub.{u1} α (SubNegMonoid.toSub.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α _inst_1))))) a c)))
-Case conversion may be inaccurate. Consider using '#align set.sub_mem_Ioo_iff_right Set.sub_mem_Ioo_iff_rightₓ'. -/
theorem sub_mem_Ioo_iff_right : a - b ∈ Set.Ioo c d ↔ b ∈ Set.Ioo (a - d) (a - c) :=
(and_comm' _ _).trans <| and_congr sub_lt_comm lt_sub_comm
#align set.sub_mem_Ioo_iff_right Set.sub_mem_Ioo_iff_right
-/- warning: set.mem_Icc_iff_abs_le -> Set.mem_Icc_iff_abs_le is a dubious translation:
-lean 3 declaration is
- forall {R : Type.{u1}} [_inst_2 : LinearOrderedAddCommGroup.{u1} R] {x : R} {y : R} {z : R}, Iff (LE.le.{u1} R (Preorder.toHasLe.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))) (Abs.abs.{u1} R (Neg.toHasAbs.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2))))) (SemilatticeSup.toHasSup.{u1} R (Lattice.toSemilatticeSup.{u1} R (LinearOrder.toLattice.{u1} R (LinearOrderedAddCommGroup.toLinearOrder.{u1} R _inst_2))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))) x y)) z) (Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) y (Set.Icc.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))) x z) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))))) x z)))
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-Case conversion may be inaccurate. Consider using '#align set.mem_Icc_iff_abs_le Set.mem_Icc_iff_abs_leₓ'. -/
-- I think that symmetric intervals deserve attention and API: they arise all the time,
-- for instance when considering metric balls in `ℝ`.
theorem mem_Icc_iff_abs_le {R : Type _} [LinearOrderedAddCommGroup R] {x y z : R} :
@@ -276,12 +150,6 @@ section LinearOrderedAddCommGroup
variable [LinearOrderedAddCommGroup α]
-/- warning: set.nonempty_Ico_sdiff -> Set.nonempty_Ico_sdiff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.nonempty_Ico_sdiff Set.nonempty_Ico_sdiffₓ'. -/
/-- If we remove a smaller interval from a larger, the result is nonempty -/
theorem nonempty_Ico_sdiff {x dx y dy : α} (h : dy < dx) (hx : 0 < dx) :
Nonempty ↥(Ico x (x + dx) \ Ico y (y + dy)) :=
@@ -302,12 +170,6 @@ section OrderedCommGroup
variable [OrderedCommGroup α] (a b : α)
-/- warning: set.pairwise_disjoint_Ioc_mul_zpow -> Set.pairwise_disjoint_Ioc_mul_zpow is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_mul_zpow Set.pairwise_disjoint_Ioc_mul_zpowₓ'. -/
@[to_additive]
theorem pairwise_disjoint_Ioc_mul_zpow :
Pairwise (Disjoint on fun n : ℤ => Ioc (a * b ^ n) (a * b ^ (n + 1))) :=
@@ -326,12 +188,6 @@ theorem pairwise_disjoint_Ioc_mul_zpow :
#align set.pairwise_disjoint_Ioc_mul_zpow Set.pairwise_disjoint_Ioc_mul_zpow
#align set.pairwise_disjoint_Ioc_add_zsmul Set.pairwise_disjoint_Ioc_add_zsmul
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_mul_zpow Set.pairwise_disjoint_Ico_mul_zpowₓ'. -/
@[to_additive]
theorem pairwise_disjoint_Ico_mul_zpow :
Pairwise (Disjoint on fun n : ℤ => Ico (a * b ^ n) (a * b ^ (n + 1))) :=
@@ -350,12 +206,6 @@ theorem pairwise_disjoint_Ico_mul_zpow :
#align set.pairwise_disjoint_Ico_mul_zpow Set.pairwise_disjoint_Ico_mul_zpow
#align set.pairwise_disjoint_Ico_add_zsmul Set.pairwise_disjoint_Ico_add_zsmul
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_mul_zpow Set.pairwise_disjoint_Ioo_mul_zpowₓ'. -/
@[to_additive]
theorem pairwise_disjoint_Ioo_mul_zpow :
Pairwise (Disjoint on fun n : ℤ => Ioo (a * b ^ n) (a * b ^ (n + 1))) := fun m n hmn =>
@@ -363,12 +213,6 @@ theorem pairwise_disjoint_Ioo_mul_zpow :
#align set.pairwise_disjoint_Ioo_mul_zpow Set.pairwise_disjoint_Ioo_mul_zpow
#align set.pairwise_disjoint_Ioo_add_zsmul Set.pairwise_disjoint_Ioo_add_zsmul
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_zpow Set.pairwise_disjoint_Ioc_zpowₓ'. -/
@[to_additive]
theorem pairwise_disjoint_Ioc_zpow :
Pairwise (Disjoint on fun n : ℤ => Ioc (b ^ n) (b ^ (n + 1))) := by
@@ -376,12 +220,6 @@ theorem pairwise_disjoint_Ioc_zpow :
#align set.pairwise_disjoint_Ioc_zpow Set.pairwise_disjoint_Ioc_zpow
#align set.pairwise_disjoint_Ioc_zsmul Set.pairwise_disjoint_Ioc_zsmul
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_zpow Set.pairwise_disjoint_Ico_zpowₓ'. -/
@[to_additive]
theorem pairwise_disjoint_Ico_zpow :
Pairwise (Disjoint on fun n : ℤ => Ico (b ^ n) (b ^ (n + 1))) := by
@@ -389,12 +227,6 @@ theorem pairwise_disjoint_Ico_zpow :
#align set.pairwise_disjoint_Ico_zpow Set.pairwise_disjoint_Ico_zpow
#align set.pairwise_disjoint_Ico_zsmul Set.pairwise_disjoint_Ico_zsmul
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@[to_additive]
theorem pairwise_disjoint_Ioo_zpow :
Pairwise (Disjoint on fun n : ℤ => Ioo (b ^ n) (b ^ (n + 1))) := by
@@ -408,36 +240,18 @@ section OrderedRing
variable [OrderedRing α] (a : α)
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_add_int_cast Set.pairwise_disjoint_Ioc_add_int_castₓ'. -/
theorem pairwise_disjoint_Ioc_add_int_cast :
Pairwise (Disjoint on fun n : ℤ => Ioc (a + n) (a + n + 1)) := by
simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
pairwise_disjoint_Ioc_add_zsmul a (1 : α)
#align set.pairwise_disjoint_Ioc_add_int_cast Set.pairwise_disjoint_Ioc_add_int_cast
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_add_int_cast Set.pairwise_disjoint_Ico_add_int_castₓ'. -/
theorem pairwise_disjoint_Ico_add_int_cast :
Pairwise (Disjoint on fun n : ℤ => Ico (a + n) (a + n + 1)) := by
simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
pairwise_disjoint_Ico_add_zsmul a (1 : α)
#align set.pairwise_disjoint_Ico_add_int_cast Set.pairwise_disjoint_Ico_add_int_cast
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_add_int_cast Set.pairwise_disjoint_Ioo_add_int_castₓ'. -/
theorem pairwise_disjoint_Ioo_add_int_cast :
Pairwise (Disjoint on fun n : ℤ => Ioo (a + n) (a + n + 1)) := by
simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
@@ -446,32 +260,14 @@ theorem pairwise_disjoint_Ioo_add_int_cast :
variable (α)
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_int_cast Set.pairwise_disjoint_Ico_int_castₓ'. -/
theorem pairwise_disjoint_Ico_int_cast : Pairwise (Disjoint on fun n : ℤ => Ico (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ico_add_int_cast (0 : α)
#align set.pairwise_disjoint_Ico_int_cast Set.pairwise_disjoint_Ico_int_cast
-/- warning: set.pairwise_disjoint_Ioo_int_cast -> Set.pairwise_disjoint_Ioo_int_cast is a dubious translation:
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- forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (OrderedSemiring.toSemiring.{u1} α (OrderedRing.toOrderedSemiring.{u1} α _inst_1))))))))
-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_int_cast Set.pairwise_disjoint_Ioo_int_castₓ'. -/
theorem pairwise_disjoint_Ioo_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioo (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ioo_add_int_cast (0 : α)
#align set.pairwise_disjoint_Ioo_int_cast Set.pairwise_disjoint_Ioo_int_cast
-/- warning: set.pairwise_disjoint_Ioc_int_cast -> Set.pairwise_disjoint_Ioc_int_cast is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_int_cast Set.pairwise_disjoint_Ioc_int_castₓ'. -/
theorem pairwise_disjoint_Ioc_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioc (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ioc_add_int_cast (0 : α)
#align set.pairwise_disjoint_Ioc_int_cast Set.pairwise_disjoint_Ioc_int_cast
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -287,10 +287,8 @@ theorem nonempty_Ico_sdiff {x dx y dy : α} (h : dy < dx) (hx : 0 < dx) :
Nonempty ↥(Ico x (x + dx) \ Ico y (y + dy)) :=
by
cases' lt_or_le x y with h' h'
- · use x
- simp [*, not_le.2 h']
- · use max x (x + dy)
- simp [*, le_refl]
+ · use x; simp [*, not_le.2 h']
+ · use max x (x + dy); simp [*, le_refl]
#align set.nonempty_Ico_sdiff Set.nonempty_Ico_sdiff
end LinearOrderedAddCommGroup
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -259,7 +259,7 @@ theorem sub_mem_Ioo_iff_right : a - b ∈ Set.Ioo c d ↔ b ∈ Set.Ioo (a - d)
/- warning: set.mem_Icc_iff_abs_le -> Set.mem_Icc_iff_abs_le is a dubious translation:
lean 3 declaration is
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+ forall {R : Type.{u1}} [_inst_2 : LinearOrderedAddCommGroup.{u1} R] {x : R} {y : R} {z : R}, Iff (LE.le.{u1} R (Preorder.toHasLe.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))) (Abs.abs.{u1} R (Neg.toHasAbs.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2))))) (SemilatticeSup.toHasSup.{u1} R (Lattice.toSemilatticeSup.{u1} R (LinearOrder.toLattice.{u1} R (LinearOrderedAddCommGroup.toLinearOrder.{u1} R _inst_2))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))) x y)) z) (Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) y (Set.Icc.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))) x z) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))))) x z)))
but is expected to have type
forall {R : Type.{u1}} [_inst_2 : LinearOrderedAddCommGroup.{u1} R] {x : R} {y : R} {z : R}, Iff (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))) (Abs.abs.{u1} R (Neg.toHasAbs.{u1} R (NegZeroClass.toNeg.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (SubtractionCommMonoid.toSubtractionMonoid.{u1} R (AddCommGroup.toDivisionAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2))))))) (SemilatticeSup.toSup.{u1} R (Lattice.toSemilatticeSup.{u1} R (DistribLattice.toLattice.{u1} R (instDistribLattice.{u1} R (LinearOrderedAddCommGroup.toLinearOrder.{u1} R _inst_2)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))) x y)) z) (Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) y (Set.Icc.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))) x z) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))))) x z)))
Case conversion may be inaccurate. Consider using '#align set.mem_Icc_iff_abs_le Set.mem_Icc_iff_abs_leₓ'. -/
@@ -278,7 +278,7 @@ variable [LinearOrderedAddCommGroup α]
/- warning: set.nonempty_Ico_sdiff -> Set.nonempty_Ico_sdiff is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {x : α} {dx : α} {y : α} {dy : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) dy dx) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) dx) -> (Nonempty.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) x (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) x dx)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) y (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) y dy)))))
+ forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {x : α} {dx : α} {y : α} {dy : α}, (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) dy dx) -> (LT.lt.{u1} α (Preorder.toHasLt.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (OfNat.mk.{u1} α 0 (Zero.zero.{u1} α (AddZeroClass.toHasZero.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))))) dx) -> (Nonempty.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) x (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) x dx)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) y (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toHasAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) y dy)))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : LinearOrderedAddCommGroup.{u1} α] {x : α} {dx : α} {y : α} {dy : α}, (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) dy dx) -> (LT.lt.{u1} α (Preorder.toLT.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))) (OfNat.ofNat.{u1} α 0 (Zero.toOfNat0.{u1} α (NegZeroClass.toZero.{u1} α (SubNegZeroMonoid.toNegZeroClass.{u1} α (SubtractionMonoid.toSubNegZeroMonoid.{u1} α (SubtractionCommMonoid.toSubtractionMonoid.{u1} α (AddCommGroup.toDivisionAddCommMonoid.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))))))))) dx) -> (Nonempty.{succ u1} (Set.Elem.{u1} α (SDiff.sdiff.{u1} (Set.{u1} α) (Set.instSDiffSet.{u1} α) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) x (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) x dx)) (Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1))) y (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (AddZeroClass.toAdd.{u1} α (AddMonoid.toAddZeroClass.{u1} α (SubNegMonoid.toAddMonoid.{u1} α (AddGroup.toSubNegMonoid.{u1} α (AddCommGroup.toAddGroup.{u1} α (OrderedAddCommGroup.toAddCommGroup.{u1} α (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} α _inst_1)))))))) y dy)))))
Case conversion may be inaccurate. Consider using '#align set.nonempty_Ico_sdiff Set.nonempty_Ico_sdiffₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/08e1d8d4d989df3a6df86f385e9053ec8a372cc1
@@ -414,7 +414,7 @@ variable [OrderedRing α] (a : α)
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (OrderedSemiring.toSemiring.{u1} α (OrderedRing.toOrderedSemiring.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_add_int_cast Set.pairwise_disjoint_Ioc_add_int_castₓ'. -/
theorem pairwise_disjoint_Ioc_add_int_cast :
Pairwise (Disjoint on fun n : ℤ => Ioc (a + n) (a + n + 1)) := by
@@ -426,7 +426,7 @@ theorem pairwise_disjoint_Ioc_add_int_cast :
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (OrderedSemiring.toSemiring.{u1} α (OrderedRing.toOrderedSemiring.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_add_int_cast Set.pairwise_disjoint_Ico_add_int_castₓ'. -/
theorem pairwise_disjoint_Ico_add_int_cast :
Pairwise (Disjoint on fun n : ℤ => Ico (a + n) (a + n + 1)) := by
@@ -438,7 +438,7 @@ theorem pairwise_disjoint_Ico_add_int_cast :
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (OrderedSemiring.toSemiring.{u1} α (OrderedRing.toOrderedSemiring.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_add_int_cast Set.pairwise_disjoint_Ioo_add_int_castₓ'. -/
theorem pairwise_disjoint_Ioo_add_int_cast :
Pairwise (Disjoint on fun n : ℤ => Ioo (a + n) (a + n + 1)) := by
@@ -452,7 +452,7 @@ variable (α)
lean 3 declaration is
forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
- forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
+ forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (OrderedSemiring.toSemiring.{u1} α (OrderedRing.toOrderedSemiring.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_int_cast Set.pairwise_disjoint_Ico_int_castₓ'. -/
theorem pairwise_disjoint_Ico_int_cast : Pairwise (Disjoint on fun n : ℤ => Ico (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ico_add_int_cast (0 : α)
@@ -462,7 +462,7 @@ theorem pairwise_disjoint_Ico_int_cast : Pairwise (Disjoint on fun n : ℤ => Ic
lean 3 declaration is
forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
- forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
+ forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (OrderedSemiring.toSemiring.{u1} α (OrderedRing.toOrderedSemiring.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_int_cast Set.pairwise_disjoint_Ioo_int_castₓ'. -/
theorem pairwise_disjoint_Ioo_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioo (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ioo_add_int_cast (0 : α)
@@ -472,7 +472,7 @@ theorem pairwise_disjoint_Ioo_int_cast : Pairwise (Disjoint on fun n : ℤ => Io
lean 3 declaration is
forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
- forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
+ forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (Semiring.toOne.{u1} α (OrderedSemiring.toSemiring.{u1} α (OrderedRing.toOrderedSemiring.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_int_cast Set.pairwise_disjoint_Ioc_int_castₓ'. -/
theorem pairwise_disjoint_Ioc_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioc (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ioc_add_int_cast (0 : α)
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1
@@ -308,7 +308,7 @@ variable [OrderedCommGroup α] (a b : α)
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_mul_zpow Set.pairwise_disjoint_Ioc_mul_zpowₓ'. -/
@[to_additive]
theorem pairwise_disjoint_Ioc_mul_zpow :
@@ -332,7 +332,7 @@ theorem pairwise_disjoint_Ioc_mul_zpow :
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_mul_zpow Set.pairwise_disjoint_Ico_mul_zpowₓ'. -/
@[to_additive]
theorem pairwise_disjoint_Ico_mul_zpow :
@@ -356,7 +356,7 @@ theorem pairwise_disjoint_Ico_mul_zpow :
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_mul_zpow Set.pairwise_disjoint_Ioo_mul_zpowₓ'. -/
@[to_additive]
theorem pairwise_disjoint_Ioo_mul_zpow :
@@ -369,7 +369,7 @@ theorem pairwise_disjoint_Ioo_mul_zpow :
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_zpow Set.pairwise_disjoint_Ioc_zpowₓ'. -/
@[to_additive]
theorem pairwise_disjoint_Ioc_zpow :
@@ -382,7 +382,7 @@ theorem pairwise_disjoint_Ioc_zpow :
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_zpow Set.pairwise_disjoint_Ico_zpowₓ'. -/
@[to_additive]
theorem pairwise_disjoint_Ico_zpow :
@@ -395,7 +395,7 @@ theorem pairwise_disjoint_Ico_zpow :
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_zpow Set.pairwise_disjoint_Ioo_zpowₓ'. -/
@[to_additive]
theorem pairwise_disjoint_Ioo_zpow :
@@ -414,7 +414,7 @@ variable [OrderedRing α] (a : α)
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_add_int_cast Set.pairwise_disjoint_Ioc_add_int_castₓ'. -/
theorem pairwise_disjoint_Ioc_add_int_cast :
Pairwise (Disjoint on fun n : ℤ => Ioc (a + n) (a + n + 1)) := by
@@ -426,7 +426,7 @@ theorem pairwise_disjoint_Ioc_add_int_cast :
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_add_int_cast Set.pairwise_disjoint_Ico_add_int_castₓ'. -/
theorem pairwise_disjoint_Ico_add_int_cast :
Pairwise (Disjoint on fun n : ℤ => Ico (a + n) (a + n + 1)) := by
@@ -438,7 +438,7 @@ theorem pairwise_disjoint_Ico_add_int_cast :
lean 3 declaration is
forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
- forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_add_int_cast Set.pairwise_disjoint_Ioo_add_int_castₓ'. -/
theorem pairwise_disjoint_Ioo_add_int_cast :
Pairwise (Disjoint on fun n : ℤ => Ioo (a + n) (a + n + 1)) := by
@@ -452,7 +452,7 @@ variable (α)
lean 3 declaration is
forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
- forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
+ forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_int_cast Set.pairwise_disjoint_Ico_int_castₓ'. -/
theorem pairwise_disjoint_Ico_int_cast : Pairwise (Disjoint on fun n : ℤ => Ico (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ico_add_int_cast (0 : α)
@@ -462,7 +462,7 @@ theorem pairwise_disjoint_Ico_int_cast : Pairwise (Disjoint on fun n : ℤ => Ic
lean 3 declaration is
forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
- forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
+ forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_int_cast Set.pairwise_disjoint_Ioo_int_castₓ'. -/
theorem pairwise_disjoint_Ioo_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioo (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ioo_add_int_cast (0 : α)
@@ -472,7 +472,7 @@ theorem pairwise_disjoint_Ioo_int_cast : Pairwise (Disjoint on fun n : ℤ => Io
lean 3 declaration is
forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
- forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
+ forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (CoheytingAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BiheytingAlgebra.toCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toBiheytingAlgebra.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α))))))))) (BooleanAlgebra.toBoundedOrder.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_int_cast Set.pairwise_disjoint_Ioc_int_castₓ'. -/
theorem pairwise_disjoint_Ioc_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioc (n : α) (n + 1)) :=
by simpa only [zero_add] using pairwise_disjoint_Ioc_add_int_cast (0 : α)
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1
@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
! This file was ported from Lean 3 source module data.set.intervals.group
-! leanprover-community/mathlib commit 740acc0e6f9adf4423f92a485d0456fc271482da
+! leanprover-community/mathlib commit c227d107bbada5d0d9d20287e3282c0a7f1651a0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathbin.Data.Set.Intervals.Basic
-import Mathbin.Data.Set.Pairwise
+import Mathbin.Data.Set.Pairwise.Basic
import Mathbin.Algebra.Order.Group.Abs
import Mathbin.Algebra.GroupPower.Lemmas
@@ -306,7 +306,7 @@ variable [OrderedCommGroup α] (a b : α)
/- warning: set.pairwise_disjoint_Ioc_mul_zpow -> Set.pairwise_disjoint_Ioc_mul_zpow is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_mul_zpow Set.pairwise_disjoint_Ioc_mul_zpowₓ'. -/
@@ -330,7 +330,7 @@ theorem pairwise_disjoint_Ioc_mul_zpow :
/- warning: set.pairwise_disjoint_Ico_mul_zpow -> Set.pairwise_disjoint_Ico_mul_zpow is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_mul_zpow Set.pairwise_disjoint_Ico_mul_zpowₓ'. -/
@@ -354,7 +354,7 @@ theorem pairwise_disjoint_Ico_mul_zpow :
/- warning: set.pairwise_disjoint_Ioo_mul_zpow -> Set.pairwise_disjoint_Ioo_mul_zpow is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne))))))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (a : α) (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n)) (HMul.hMul.{u1, u1, u1} α α α (instHMul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α (DivInvMonoid.toMonoid.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))))) a (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1)))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_mul_zpow Set.pairwise_disjoint_Ioo_mul_zpowₓ'. -/
@@ -367,7 +367,7 @@ theorem pairwise_disjoint_Ioo_mul_zpow :
/- warning: set.pairwise_disjoint_Ioc_zpow -> Set.pairwise_disjoint_Ioc_zpow is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_zpow Set.pairwise_disjoint_Ioc_zpowₓ'. -/
@@ -380,7 +380,7 @@ theorem pairwise_disjoint_Ioc_zpow :
/- warning: set.pairwise_disjoint_Ico_zpow -> Set.pairwise_disjoint_Ico_zpow is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_zpow Set.pairwise_disjoint_Ico_zpowₓ'. -/
@@ -393,7 +393,7 @@ theorem pairwise_disjoint_Ico_zpow :
/- warning: set.pairwise_disjoint_Ioo_zpow -> Set.pairwise_disjoint_Ioo_zpow is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.hasAdd) n (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : OrderedCommGroup.{u1} α] (b : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedCommGroup.toPartialOrder.{u1} α _inst_1)) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b n) (HPow.hPow.{u1, 0, u1} α Int α (instHPow.{u1, 0} α Int (DivInvMonoid.Pow.{u1} α (Group.toDivInvMonoid.{u1} α (CommGroup.toGroup.{u1} α (OrderedCommGroup.toCommGroup.{u1} α _inst_1))))) b (HAdd.hAdd.{0, 0, 0} Int Int Int (instHAdd.{0} Int Int.instAddInt) n (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_zpow Set.pairwise_disjoint_Ioo_zpowₓ'. -/
@@ -412,7 +412,7 @@ variable [OrderedRing α] (a : α)
/- warning: set.pairwise_disjoint_Ioc_add_int_cast -> Set.pairwise_disjoint_Ioc_add_int_cast is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_add_int_cast Set.pairwise_disjoint_Ioc_add_int_castₓ'. -/
@@ -424,7 +424,7 @@ theorem pairwise_disjoint_Ioc_add_int_cast :
/- warning: set.pairwise_disjoint_Ico_add_int_cast -> Set.pairwise_disjoint_Ico_add_int_cast is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_add_int_cast Set.pairwise_disjoint_Ico_add_int_castₓ'. -/
@@ -436,7 +436,7 @@ theorem pairwise_disjoint_Ico_add_int_cast :
/- warning: set.pairwise_disjoint_Ioo_add_int_cast -> Set.pairwise_disjoint_Ioo_add_int_cast is a dubious translation:
lean 3 declaration is
- forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
+ forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) a ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n)) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
forall {α : Type.{u1}} [_inst_1 : OrderedRing.{u1} α] (a : α), Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) a (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n)) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_add_int_cast Set.pairwise_disjoint_Ioo_add_int_castₓ'. -/
@@ -450,7 +450,7 @@ variable (α)
/- warning: set.pairwise_disjoint_Ico_int_cast -> Set.pairwise_disjoint_Ico_int_cast is a dubious translation:
lean 3 declaration is
- forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
+ forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ico.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ico_int_cast Set.pairwise_disjoint_Ico_int_castₓ'. -/
@@ -460,7 +460,7 @@ theorem pairwise_disjoint_Ico_int_cast : Pairwise (Disjoint on fun n : ℤ => Ic
/- warning: set.pairwise_disjoint_Ioo_int_cast -> Set.pairwise_disjoint_Ioo_int_cast is a dubious translation:
lean 3 declaration is
- forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
+ forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioo.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioo_int_cast Set.pairwise_disjoint_Ioo_int_castₓ'. -/
@@ -470,7 +470,7 @@ theorem pairwise_disjoint_Ioo_int_cast : Pairwise (Disjoint on fun n : ℤ => Io
/- warning: set.pairwise_disjoint_Ioc_int_cast -> Set.pairwise_disjoint_Ioc_int_cast is a dubious translation:
lean 3 declaration is
- forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (NonAssocRing.toAddGroupWithOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
+ forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (SemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (Lattice.toSemilatticeInf.{u1} (Set.{u1} α) (GeneralizedCoheytingAlgebra.toLattice.{u1} (Set.{u1} α) (GeneralizedBooleanAlgebra.toGeneralizedCoheytingAlgebra.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedAddCommGroup.toPartialOrder.{u1} α (OrderedRing.toOrderedAddCommGroup.{u1} α _inst_1))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toHasAdd.{u1} α (Ring.toDistrib.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))) ((fun (a : Type) (b : Type.{u1}) [self : HasLiftT.{1, succ u1} a b] => self.0) Int α (HasLiftT.mk.{1, succ u1} Int α (CoeTCₓ.coe.{1, succ u1} Int α (Int.castCoe.{u1} α (AddGroupWithOne.toHasIntCast.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) n) (OfNat.ofNat.{u1} α 1 (OfNat.mk.{u1} α 1 (One.one.{u1} α (AddMonoidWithOne.toOne.{u1} α (AddGroupWithOne.toAddMonoidWithOne.{u1} α (AddCommGroupWithOne.toAddGroupWithOne.{u1} α (Ring.toAddCommGroupWithOne.{u1} α (OrderedRing.toRing.{u1} α _inst_1)))))))))))
but is expected to have type
forall (α : Type.{u1}) [_inst_1 : OrderedRing.{u1} α], Pairwise.{0} Int (Function.onFun.{1, succ u1, 1} Int (Set.{u1} α) Prop (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α))))))) (fun (n : Int) => Set.Ioc.{u1} α (PartialOrder.toPreorder.{u1} α (OrderedRing.toPartialOrder.{u1} α _inst_1)) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (HAdd.hAdd.{u1, u1, u1} α α α (instHAdd.{u1} α (Distrib.toAdd.{u1} α (NonUnitalNonAssocSemiring.toDistrib.{u1} α (NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring.{u1} α (NonAssocRing.toNonUnitalNonAssocRing.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))) (Int.cast.{u1} α (Ring.toIntCast.{u1} α (OrderedRing.toRing.{u1} α _inst_1)) n) (OfNat.ofNat.{u1} α 1 (One.toOfNat1.{u1} α (NonAssocRing.toOne.{u1} α (Ring.toNonAssocRing.{u1} α (OrderedRing.toRing.{u1} α _inst_1))))))))
Case conversion may be inaccurate. Consider using '#align set.pairwise_disjoint_Ioc_int_cast Set.pairwise_disjoint_Ioc_int_castₓ'. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -261,7 +261,7 @@ theorem sub_mem_Ioo_iff_right : a - b ∈ Set.Ioo c d ↔ b ∈ Set.Ioo (a - d)
lean 3 declaration is
forall {R : Type.{u1}} [_inst_2 : LinearOrderedAddCommGroup.{u1} R] {x : R} {y : R} {z : R}, Iff (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))) (Abs.abs.{u1} R (Neg.toHasAbs.{u1} R (SubNegMonoid.toHasNeg.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2))))) (SemilatticeSup.toHasSup.{u1} R (Lattice.toSemilatticeSup.{u1} R (LinearOrder.toLattice.{u1} R (LinearOrderedAddCommGroup.toLinearOrder.{u1} R _inst_2))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))) x y)) z) (Membership.Mem.{u1, u1} R (Set.{u1} R) (Set.hasMem.{u1} R) y (Set.Icc.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toHasSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))) x z) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toHasAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))))) x z)))
but is expected to have type
- forall {R : Type.{u1}} [_inst_2 : LinearOrderedAddCommGroup.{u1} R] {x : R} {y : R} {z : R}, Iff (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))) (Abs.abs.{u1} R (Neg.toHasAbs.{u1} R (NegZeroClass.toNeg.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (SubtractionCommMonoid.toSubtractionMonoid.{u1} R (AddCommGroup.toDivisionAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2))))))) (SemilatticeSup.toHasSup.{u1} R (Lattice.toSemilatticeSup.{u1} R (DistribLattice.toLattice.{u1} R (instDistribLattice.{u1} R (LinearOrderedAddCommGroup.toLinearOrder.{u1} R _inst_2)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))) x y)) z) (Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) y (Set.Icc.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))) x z) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))))) x z)))
+ forall {R : Type.{u1}} [_inst_2 : LinearOrderedAddCommGroup.{u1} R] {x : R} {y : R} {z : R}, Iff (LE.le.{u1} R (Preorder.toLE.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))) (Abs.abs.{u1} R (Neg.toHasAbs.{u1} R (NegZeroClass.toNeg.{u1} R (SubNegZeroMonoid.toNegZeroClass.{u1} R (SubtractionMonoid.toSubNegZeroMonoid.{u1} R (SubtractionCommMonoid.toSubtractionMonoid.{u1} R (AddCommGroup.toDivisionAddCommMonoid.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2))))))) (SemilatticeSup.toSup.{u1} R (Lattice.toSemilatticeSup.{u1} R (DistribLattice.toLattice.{u1} R (instDistribLattice.{u1} R (LinearOrderedAddCommGroup.toLinearOrder.{u1} R _inst_2)))))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))) x y)) z) (Membership.mem.{u1, u1} R (Set.{u1} R) (Set.instMembershipSet.{u1} R) y (Set.Icc.{u1} R (PartialOrder.toPreorder.{u1} R (OrderedAddCommGroup.toPartialOrder.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2))) (HSub.hSub.{u1, u1, u1} R R R (instHSub.{u1} R (SubNegMonoid.toSub.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))) x z) (HAdd.hAdd.{u1, u1, u1} R R R (instHAdd.{u1} R (AddZeroClass.toAdd.{u1} R (AddMonoid.toAddZeroClass.{u1} R (SubNegMonoid.toAddMonoid.{u1} R (AddGroup.toSubNegMonoid.{u1} R (AddCommGroup.toAddGroup.{u1} R (OrderedAddCommGroup.toAddCommGroup.{u1} R (LinearOrderedAddCommGroup.toOrderedAddCommGroup.{u1} R _inst_2)))))))) x z)))
Case conversion may be inaccurate. Consider using '#align set.mem_Icc_iff_abs_le Set.mem_Icc_iff_abs_leₓ'. -/
-- I think that symmetric intervals deserve attention and API: they arise all the time,
-- for instance when considering metric balls in `ℝ`.
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
.
@@ -5,7 +5,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy
-/
import Mathlib.Algebra.GroupPower.Order
import Mathlib.Data.Int.Cast.Lemmas
-import Mathlib.Data.Set.Intervals.Basic
+import Mathlib.Order.Interval.Set.Basic
import Mathlib.Logic.Pairwise
#align_import data.set.intervals.group from "leanprover-community/mathlib"@"c227d107bbada5d0d9d20287e3282c0a7f1651a0"
nat_cast
/int_cast
/rat_cast
to natCast
/intCast
/ratCast
(#11486)
Now that I am defining NNRat.cast
, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast
/intCast
/ratCast
over nat_cast
/int_cast
/rat_cast
, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.
@@ -232,37 +232,37 @@ section OrderedRing
variable [OrderedRing α] (a : α)
-theorem pairwise_disjoint_Ioc_add_int_cast :
+theorem pairwise_disjoint_Ioc_add_intCast :
Pairwise (Disjoint on fun n : ℤ => Ioc (a + n) (a + n + 1)) := by
simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
pairwise_disjoint_Ioc_add_zsmul a (1 : α)
-#align set.pairwise_disjoint_Ioc_add_int_cast Set.pairwise_disjoint_Ioc_add_int_cast
+#align set.pairwise_disjoint_Ioc_add_int_cast Set.pairwise_disjoint_Ioc_add_intCast
-theorem pairwise_disjoint_Ico_add_int_cast :
+theorem pairwise_disjoint_Ico_add_intCast :
Pairwise (Disjoint on fun n : ℤ => Ico (a + n) (a + n + 1)) := by
simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
pairwise_disjoint_Ico_add_zsmul a (1 : α)
-#align set.pairwise_disjoint_Ico_add_int_cast Set.pairwise_disjoint_Ico_add_int_cast
+#align set.pairwise_disjoint_Ico_add_int_cast Set.pairwise_disjoint_Ico_add_intCast
-theorem pairwise_disjoint_Ioo_add_int_cast :
+theorem pairwise_disjoint_Ioo_add_intCast :
Pairwise (Disjoint on fun n : ℤ => Ioo (a + n) (a + n + 1)) := by
simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
pairwise_disjoint_Ioo_add_zsmul a (1 : α)
-#align set.pairwise_disjoint_Ioo_add_int_cast Set.pairwise_disjoint_Ioo_add_int_cast
+#align set.pairwise_disjoint_Ioo_add_int_cast Set.pairwise_disjoint_Ioo_add_intCast
variable (α)
-theorem pairwise_disjoint_Ico_int_cast : Pairwise (Disjoint on fun n : ℤ => Ico (n : α) (n + 1)) :=
- by simpa only [zero_add] using pairwise_disjoint_Ico_add_int_cast (0 : α)
-#align set.pairwise_disjoint_Ico_int_cast Set.pairwise_disjoint_Ico_int_cast
+theorem pairwise_disjoint_Ico_intCast : Pairwise (Disjoint on fun n : ℤ => Ico (n : α) (n + 1)) :=
+ by simpa only [zero_add] using pairwise_disjoint_Ico_add_intCast (0 : α)
+#align set.pairwise_disjoint_Ico_int_cast Set.pairwise_disjoint_Ico_intCast
-theorem pairwise_disjoint_Ioo_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioo (n : α) (n + 1)) :=
- by simpa only [zero_add] using pairwise_disjoint_Ioo_add_int_cast (0 : α)
-#align set.pairwise_disjoint_Ioo_int_cast Set.pairwise_disjoint_Ioo_int_cast
+theorem pairwise_disjoint_Ioo_intCast : Pairwise (Disjoint on fun n : ℤ => Ioo (n : α) (n + 1)) :=
+ by simpa only [zero_add] using pairwise_disjoint_Ioo_add_intCast (0 : α)
+#align set.pairwise_disjoint_Ioo_int_cast Set.pairwise_disjoint_Ioo_intCast
-theorem pairwise_disjoint_Ioc_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioc (n : α) (n + 1)) :=
- by simpa only [zero_add] using pairwise_disjoint_Ioc_add_int_cast (0 : α)
-#align set.pairwise_disjoint_Ioc_int_cast Set.pairwise_disjoint_Ioc_int_cast
+theorem pairwise_disjoint_Ioc_intCast : Pairwise (Disjoint on fun n : ℤ => Ioc (n : α) (n + 1)) :=
+ by simpa only [zero_add] using pairwise_disjoint_Ioc_add_intCast (0 : α)
+#align set.pairwise_disjoint_Ioc_int_cast Set.pairwise_disjoint_Ioc_intCast
end OrderedRing
@@ -3,10 +3,10 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-/
+import Mathlib.Algebra.GroupPower.Order
+import Mathlib.Data.Int.Cast.Lemmas
import Mathlib.Data.Set.Intervals.Basic
-import Mathlib.Data.Set.Pairwise.Basic
-import Mathlib.Algebra.Order.Group.Abs
-import Mathlib.Algebra.GroupPower.Lemmas
+import Mathlib.Logic.Pairwise
#align_import data.set.intervals.group from "leanprover-community/mathlib"@"c227d107bbada5d0d9d20287e3282c0a7f1651a0"
This is the supremum of
along with some minor fixes from failures on nightly-testing as Mathlib master
is merged into it.
Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.
I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0
branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.
In particular this includes adjustments for the Lean PRs
We can get rid of all the
local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)
macros across Mathlib (and in any projects that want to write natural number powers of reals).
Changes the default behaviour of simp
to (config := {decide := false})
. This makes simp
(and consequentially norm_num
) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp
or norm_num
to decide
or rfl
, or adding (config := {decide := true})
.
This changed the behaviour of simp
so that simp [f]
will only unfold "fully applied" occurrences of f
. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true })
. We may in future add a syntax for this, e.g. simp [!f]
; please provide feedback! In the meantime, we have made the following changes:
(config := { unfoldPartialApp := true })
in some places, to recover the old behaviour@[eqns]
to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp
and Function.flip
.This change in Lean may require further changes down the line (e.g. adding the !f
syntax, and/or upstreaming the special treatment for Function.comp
and Function.flip
, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!
Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>
@@ -167,7 +167,8 @@ variable [OrderedCommGroup α] (a b : α)
@[to_additive]
theorem pairwise_disjoint_Ioc_mul_zpow :
Pairwise (Disjoint on fun n : ℤ => Ioc (a * b ^ n) (a * b ^ (n + 1))) := by
- simp_rw [Function.onFun, Set.disjoint_iff]
+ simp (config := { unfoldPartialApp := true }) only [Function.onFun]
+ simp_rw [Set.disjoint_iff]
intro m n hmn x hx
apply hmn
have hb : 1 < b := by
@@ -183,7 +184,8 @@ theorem pairwise_disjoint_Ioc_mul_zpow :
@[to_additive]
theorem pairwise_disjoint_Ico_mul_zpow :
Pairwise (Disjoint on fun n : ℤ => Ico (a * b ^ n) (a * b ^ (n + 1))) := by
- simp_rw [Function.onFun, Set.disjoint_iff]
+ simp (config := { unfoldPartialApp := true }) only [Function.onFun]
+ simp_rw [Set.disjoint_iff]
intro m n hmn x hx
apply hmn
have hb : 1 < b := by
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -13,7 +13,7 @@ import Mathlib.Algebra.GroupPower.Lemmas
/-! ### Lemmas about arithmetic operations and intervals. -/
-variable {α : Type _}
+variable {α : Type*}
namespace Set
@@ -133,7 +133,7 @@ theorem sub_mem_Ioo_iff_right : a - b ∈ Set.Ioo c d ↔ b ∈ Set.Ioo (a - d)
-- I think that symmetric intervals deserve attention and API: they arise all the time,
-- for instance when considering metric balls in `ℝ`.
-theorem mem_Icc_iff_abs_le {R : Type _} [LinearOrderedAddCommGroup R] {x y z : R} :
+theorem mem_Icc_iff_abs_le {R : Type*} [LinearOrderedAddCommGroup R] {x y z : R} :
|x - y| ≤ z ↔ y ∈ Icc (x - z) (x + z) :=
abs_le.trans <| and_comm.trans <| and_congr sub_le_comm neg_le_sub_iff_le_add
#align set.mem_Icc_iff_abs_le Set.mem_Icc_iff_abs_le
Briefly during the port we were adding "Ported by" headers, but only ~60 / 3000 files ended up with such a header.
I propose deleting them.
We could consider adding these uniformly via a script, as part of the great history rewrite...?
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -2,7 +2,6 @@
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
-Ported by: Winston Yin
-/
import Mathlib.Data.Set.Intervals.Basic
import Mathlib.Data.Set.Pairwise.Basic
@@ -3,17 +3,14 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy Degenne
Ported by: Winston Yin
-
-! This file was ported from Lean 3 source module data.set.intervals.group
-! leanprover-community/mathlib commit c227d107bbada5d0d9d20287e3282c0a7f1651a0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Set.Intervals.Basic
import Mathlib.Data.Set.Pairwise.Basic
import Mathlib.Algebra.Order.Group.Abs
import Mathlib.Algebra.GroupPower.Lemmas
+#align_import data.set.intervals.group from "leanprover-community/mathlib"@"c227d107bbada5d0d9d20287e3282c0a7f1651a0"
+
/-! ### Lemmas about arithmetic operations and intervals. -/
by
s! (#3825)
This PR puts, with one exception, every single remaining by
that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh
. The exception is when the by
begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.
Essentially this is s/\n *by$/ by/g
, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated by
s".
@@ -186,13 +186,11 @@ theorem pairwise_disjoint_Ioc_mul_zpow :
@[to_additive]
theorem pairwise_disjoint_Ico_mul_zpow :
- Pairwise (Disjoint on fun n : ℤ => Ico (a * b ^ n) (a * b ^ (n + 1))) :=
- by
+ Pairwise (Disjoint on fun n : ℤ => Ico (a * b ^ n) (a * b ^ (n + 1))) := by
simp_rw [Function.onFun, Set.disjoint_iff]
intro m n hmn x hx
apply hmn
- have hb : 1 < b :=
- by
+ have hb : 1 < b := by
have : a * b ^ m < a * b ^ (m + 1) := hx.1.1.trans_lt hx.1.2
rwa [mul_lt_mul_iff_left, ← mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this
have i1 := hx.1.1.trans_lt hx.2.2
data.set.pairwise
(#3117)
Match https://github.com/leanprover-community/mathlib/pull/17880
The new import of Mathlib.Data.Set.Lattice
in Mathlib.Data.Finset.Basic
was implied transitively from tactic imports present in Lean 3.
Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>
@@ -5,12 +5,12 @@ Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy
Ported by: Winston Yin
! This file was ported from Lean 3 source module data.set.intervals.group
-! leanprover-community/mathlib commit 740acc0e6f9adf4423f92a485d0456fc271482da
+! leanprover-community/mathlib commit c227d107bbada5d0d9d20287e3282c0a7f1651a0
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathlib.Data.Set.Intervals.Basic
-import Mathlib.Data.Set.Pairwise
+import Mathlib.Data.Set.Pairwise.Basic
import Mathlib.Algebra.Order.Group.Abs
import Mathlib.Algebra.GroupPower.Lemmas
Forward-port lemmas in Data.Set.Intervals.Group
about disjointness of intervals, from mathlib3 PR [#18427](https://github.com/leanprover-community/mathlib/pull/18427)
@@ -5,12 +5,14 @@ Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy
Ported by: Winston Yin
! This file was ported from Lean 3 source module data.set.intervals.group
-! leanprover-community/mathlib commit 18a5306c091183ac90884daa9373fa3b178e8607
+! leanprover-community/mathlib commit 740acc0e6f9adf4423f92a485d0456fc271482da
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathlib.Data.Set.Intervals.Basic
+import Mathlib.Data.Set.Pairwise
import Mathlib.Algebra.Order.Group.Abs
+import Mathlib.Algebra.GroupPower.Lemmas
/-! ### Lemmas about arithmetic operations and intervals. -/
@@ -158,4 +160,116 @@ theorem nonempty_Ico_sdiff {x dx y dy : α} (h : dy < dx) (hx : 0 < dx) :
end LinearOrderedAddCommGroup
+/-! ### Lemmas about disjointness of translates of intervals -/
+
+section PairwiseDisjoint
+
+section OrderedCommGroup
+
+variable [OrderedCommGroup α] (a b : α)
+
+@[to_additive]
+theorem pairwise_disjoint_Ioc_mul_zpow :
+ Pairwise (Disjoint on fun n : ℤ => Ioc (a * b ^ n) (a * b ^ (n + 1))) := by
+ simp_rw [Function.onFun, Set.disjoint_iff]
+ intro m n hmn x hx
+ apply hmn
+ have hb : 1 < b := by
+ have : a * b ^ m < a * b ^ (m + 1) := hx.1.1.trans_le hx.1.2
+ rwa [mul_lt_mul_iff_left, ← mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this
+ have i1 := hx.1.1.trans_le hx.2.2
+ have i2 := hx.2.1.trans_le hx.1.2
+ rw [mul_lt_mul_iff_left, zpow_lt_zpow_iff hb, Int.lt_add_one_iff] at i1 i2
+ exact le_antisymm i1 i2
+#align set.pairwise_disjoint_Ioc_mul_zpow Set.pairwise_disjoint_Ioc_mul_zpow
+#align set.pairwise_disjoint_Ioc_add_zsmul Set.pairwise_disjoint_Ioc_add_zsmul
+
+@[to_additive]
+theorem pairwise_disjoint_Ico_mul_zpow :
+ Pairwise (Disjoint on fun n : ℤ => Ico (a * b ^ n) (a * b ^ (n + 1))) :=
+ by
+ simp_rw [Function.onFun, Set.disjoint_iff]
+ intro m n hmn x hx
+ apply hmn
+ have hb : 1 < b :=
+ by
+ have : a * b ^ m < a * b ^ (m + 1) := hx.1.1.trans_lt hx.1.2
+ rwa [mul_lt_mul_iff_left, ← mul_one (b ^ m), zpow_add_one, mul_lt_mul_iff_left] at this
+ have i1 := hx.1.1.trans_lt hx.2.2
+ have i2 := hx.2.1.trans_lt hx.1.2
+ rw [mul_lt_mul_iff_left, zpow_lt_zpow_iff hb, Int.lt_add_one_iff] at i1 i2
+ exact le_antisymm i1 i2
+#align set.pairwise_disjoint_Ico_mul_zpow Set.pairwise_disjoint_Ico_mul_zpow
+#align set.pairwise_disjoint_Ico_add_zsmul Set.pairwise_disjoint_Ico_add_zsmul
+
+@[to_additive]
+theorem pairwise_disjoint_Ioo_mul_zpow :
+ Pairwise (Disjoint on fun n : ℤ => Ioo (a * b ^ n) (a * b ^ (n + 1))) := fun _ _ hmn =>
+ (pairwise_disjoint_Ioc_mul_zpow a b hmn).mono Ioo_subset_Ioc_self Ioo_subset_Ioc_self
+#align set.pairwise_disjoint_Ioo_mul_zpow Set.pairwise_disjoint_Ioo_mul_zpow
+#align set.pairwise_disjoint_Ioo_add_zsmul Set.pairwise_disjoint_Ioo_add_zsmul
+
+@[to_additive]
+theorem pairwise_disjoint_Ioc_zpow :
+ Pairwise (Disjoint on fun n : ℤ => Ioc (b ^ n) (b ^ (n + 1))) := by
+ simpa only [one_mul] using pairwise_disjoint_Ioc_mul_zpow 1 b
+#align set.pairwise_disjoint_Ioc_zpow Set.pairwise_disjoint_Ioc_zpow
+#align set.pairwise_disjoint_Ioc_zsmul Set.pairwise_disjoint_Ioc_zsmul
+
+@[to_additive]
+theorem pairwise_disjoint_Ico_zpow :
+ Pairwise (Disjoint on fun n : ℤ => Ico (b ^ n) (b ^ (n + 1))) := by
+ simpa only [one_mul] using pairwise_disjoint_Ico_mul_zpow 1 b
+#align set.pairwise_disjoint_Ico_zpow Set.pairwise_disjoint_Ico_zpow
+#align set.pairwise_disjoint_Ico_zsmul Set.pairwise_disjoint_Ico_zsmul
+
+@[to_additive]
+theorem pairwise_disjoint_Ioo_zpow :
+ Pairwise (Disjoint on fun n : ℤ => Ioo (b ^ n) (b ^ (n + 1))) := by
+ simpa only [one_mul] using pairwise_disjoint_Ioo_mul_zpow 1 b
+#align set.pairwise_disjoint_Ioo_zpow Set.pairwise_disjoint_Ioo_zpow
+#align set.pairwise_disjoint_Ioo_zsmul Set.pairwise_disjoint_Ioo_zsmul
+
+end OrderedCommGroup
+
+section OrderedRing
+
+variable [OrderedRing α] (a : α)
+
+theorem pairwise_disjoint_Ioc_add_int_cast :
+ Pairwise (Disjoint on fun n : ℤ => Ioc (a + n) (a + n + 1)) := by
+ simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
+ pairwise_disjoint_Ioc_add_zsmul a (1 : α)
+#align set.pairwise_disjoint_Ioc_add_int_cast Set.pairwise_disjoint_Ioc_add_int_cast
+
+theorem pairwise_disjoint_Ico_add_int_cast :
+ Pairwise (Disjoint on fun n : ℤ => Ico (a + n) (a + n + 1)) := by
+ simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
+ pairwise_disjoint_Ico_add_zsmul a (1 : α)
+#align set.pairwise_disjoint_Ico_add_int_cast Set.pairwise_disjoint_Ico_add_int_cast
+
+theorem pairwise_disjoint_Ioo_add_int_cast :
+ Pairwise (Disjoint on fun n : ℤ => Ioo (a + n) (a + n + 1)) := by
+ simpa only [zsmul_one, Int.cast_add, Int.cast_one, ← add_assoc] using
+ pairwise_disjoint_Ioo_add_zsmul a (1 : α)
+#align set.pairwise_disjoint_Ioo_add_int_cast Set.pairwise_disjoint_Ioo_add_int_cast
+
+variable (α)
+
+theorem pairwise_disjoint_Ico_int_cast : Pairwise (Disjoint on fun n : ℤ => Ico (n : α) (n + 1)) :=
+ by simpa only [zero_add] using pairwise_disjoint_Ico_add_int_cast (0 : α)
+#align set.pairwise_disjoint_Ico_int_cast Set.pairwise_disjoint_Ico_int_cast
+
+theorem pairwise_disjoint_Ioo_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioo (n : α) (n + 1)) :=
+ by simpa only [zero_add] using pairwise_disjoint_Ioo_add_int_cast (0 : α)
+#align set.pairwise_disjoint_Ioo_int_cast Set.pairwise_disjoint_Ioo_int_cast
+
+theorem pairwise_disjoint_Ioc_int_cast : Pairwise (Disjoint on fun n : ℤ => Ioc (n : α) (n + 1)) :=
+ by simpa only [zero_add] using pairwise_disjoint_Ioc_add_int_cast (0 : α)
+#align set.pairwise_disjoint_Ioc_int_cast Set.pairwise_disjoint_Ioc_int_cast
+
+end OrderedRing
+
+end PairwiseDisjoint
+
end Set
@@ -30,21 +30,25 @@ variable [OrderedCommGroup α] {a b c d : α}
theorem inv_mem_Icc_iff : a⁻¹ ∈ Set.Icc c d ↔ a ∈ Set.Icc d⁻¹ c⁻¹ :=
and_comm.trans <| and_congr inv_le' le_inv'
#align set.inv_mem_Icc_iff Set.inv_mem_Icc_iff
+#align set.neg_mem_Icc_iff Set.neg_mem_Icc_iff
@[to_additive]
theorem inv_mem_Ico_iff : a⁻¹ ∈ Set.Ico c d ↔ a ∈ Set.Ioc d⁻¹ c⁻¹ :=
and_comm.trans <| and_congr inv_lt' le_inv'
#align set.inv_mem_Ico_iff Set.inv_mem_Ico_iff
+#align set.neg_mem_Ico_iff Set.neg_mem_Ico_iff
@[to_additive]
theorem inv_mem_Ioc_iff : a⁻¹ ∈ Set.Ioc c d ↔ a ∈ Set.Ico d⁻¹ c⁻¹ :=
and_comm.trans <| and_congr inv_le' lt_inv'
#align set.inv_mem_Ioc_iff Set.inv_mem_Ioc_iff
+#align set.neg_mem_Ioc_iff Set.neg_mem_Ioc_iff
@[to_additive]
theorem inv_mem_Ioo_iff : a⁻¹ ∈ Set.Ioo c d ↔ a ∈ Set.Ioo d⁻¹ c⁻¹ :=
and_comm.trans <| and_congr inv_lt' lt_inv'
#align set.inv_mem_Ioo_iff Set.inv_mem_Ioo_iff
+#align set.neg_mem_Ioo_iff Set.neg_mem_Ioo_iff
end OrderedCommGroup
@@ -5,7 +5,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot, Yury Kudryashov, Rémy
Ported by: Winston Yin
! This file was ported from Lean 3 source module data.set.intervals.group
-! leanprover-community/mathlib commit aba57d4d3dae35460225919dcd82fe91355162f9
+! leanprover-community/mathlib commit 18a5306c091183ac90884daa9373fa3b178e8607
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
The unported dependencies are