order.monotone.odd
⟷
Mathlib.Order.Monotone.Odd
The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathbin.Order.Monotone.Union
-import Mathbin.Algebra.Order.Group.Instances
+import Order.Monotone.Union
+import Algebra.Order.Group.Instances
#align_import order.monotone.odd from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module order.monotone.odd
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Order.Monotone.Union
import Mathbin.Algebra.Order.Group.Instances
+#align_import order.monotone.odd from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
/-!
# Monotonicity of odd functions
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -27,6 +27,7 @@ open Set
variable {G H : Type _} [LinearOrderedAddCommGroup G] [OrderedAddCommGroup H]
+#print strictMono_of_odd_strictMonoOn_nonneg /-
/-- An odd function on a linear ordered additive commutative group is strictly monotone on the whole
group provided that it is strictly monotone on `set.Ici 0`. -/
theorem strictMono_of_odd_strictMonoOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
@@ -36,14 +37,18 @@ theorem strictMono_of_odd_strictMonoOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x
rw [← h₁, ← h₁]
exact h₂ (neg_nonneg.2 hy) (neg_nonneg.2 hx) (neg_lt_neg hxy)
#align strict_mono_of_odd_strict_mono_on_nonneg strictMono_of_odd_strictMonoOn_nonneg
+-/
+#print strictAnti_of_odd_strictAntiOn_nonneg /-
/-- An odd function on a linear ordered additive commutative group is strictly antitone on the whole
group provided that it is strictly antitone on `set.Ici 0`. -/
theorem strictAnti_of_odd_strictAntiOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
(h₂ : StrictAntiOn f (Ici 0)) : StrictAnti f :=
@strictMono_of_odd_strictMonoOn_nonneg G Hᵒᵈ _ _ _ h₁ h₂
#align strict_anti_of_odd_strict_anti_on_nonneg strictAnti_of_odd_strictAntiOn_nonneg
+-/
+#print monotone_of_odd_of_monotoneOn_nonneg /-
/-- An odd function on a linear ordered additive commutative group is monotone on the whole group
provided that it is monotone on `set.Ici 0`. -/
theorem monotone_of_odd_of_monotoneOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
@@ -53,11 +58,14 @@ theorem monotone_of_odd_of_monotoneOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x)
rw [← h₁, ← h₁]
exact h₂ (neg_nonneg.2 hy) (neg_nonneg.2 hx) (neg_le_neg hxy)
#align monotone_of_odd_of_monotone_on_nonneg monotone_of_odd_of_monotoneOn_nonneg
+-/
+#print antitone_of_odd_of_monotoneOn_nonneg /-
/-- An odd function on a linear ordered additive commutative group is antitone on the whole group
provided that it is monotone on `set.Ici 0`. -/
theorem antitone_of_odd_of_monotoneOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
(h₂ : AntitoneOn f (Ici 0)) : Antitone f :=
@monotone_of_odd_of_monotoneOn_nonneg G Hᵒᵈ _ _ _ h₁ h₂
#align antitone_of_odd_of_monotone_on_nonneg antitone_of_odd_of_monotoneOn_nonneg
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -27,12 +27,6 @@ open Set
variable {G H : Type _} [LinearOrderedAddCommGroup G] [OrderedAddCommGroup H]
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-Case conversion may be inaccurate. Consider using '#align strict_mono_of_odd_strict_mono_on_nonneg strictMono_of_odd_strictMonoOn_nonnegₓ'. -/
/-- An odd function on a linear ordered additive commutative group is strictly monotone on the whole
group provided that it is strictly monotone on `set.Ici 0`. -/
theorem strictMono_of_odd_strictMonoOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
@@ -43,12 +37,6 @@ theorem strictMono_of_odd_strictMonoOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x
exact h₂ (neg_nonneg.2 hy) (neg_nonneg.2 hx) (neg_lt_neg hxy)
#align strict_mono_of_odd_strict_mono_on_nonneg strictMono_of_odd_strictMonoOn_nonneg
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-Case conversion may be inaccurate. Consider using '#align strict_anti_of_odd_strict_anti_on_nonneg strictAnti_of_odd_strictAntiOn_nonnegₓ'. -/
/-- An odd function on a linear ordered additive commutative group is strictly antitone on the whole
group provided that it is strictly antitone on `set.Ici 0`. -/
theorem strictAnti_of_odd_strictAntiOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
@@ -56,12 +44,6 @@ theorem strictAnti_of_odd_strictAntiOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x
@strictMono_of_odd_strictMonoOn_nonneg G Hᵒᵈ _ _ _ h₁ h₂
#align strict_anti_of_odd_strict_anti_on_nonneg strictAnti_of_odd_strictAntiOn_nonneg
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-Case conversion may be inaccurate. Consider using '#align monotone_of_odd_of_monotone_on_nonneg monotone_of_odd_of_monotoneOn_nonnegₓ'. -/
/-- An odd function on a linear ordered additive commutative group is monotone on the whole group
provided that it is monotone on `set.Ici 0`. -/
theorem monotone_of_odd_of_monotoneOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
@@ -72,12 +54,6 @@ theorem monotone_of_odd_of_monotoneOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x)
exact h₂ (neg_nonneg.2 hy) (neg_nonneg.2 hx) (neg_le_neg hxy)
#align monotone_of_odd_of_monotone_on_nonneg monotone_of_odd_of_monotoneOn_nonneg
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-Case conversion may be inaccurate. Consider using '#align antitone_of_odd_of_monotone_on_nonneg antitone_of_odd_of_monotoneOn_nonnegₓ'. -/
/-- An odd function on a linear ordered additive commutative group is antitone on the whole group
provided that it is monotone on `set.Ici 0`. -/
theorem antitone_of_odd_of_monotoneOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -19,7 +19,7 @@ prove versions of this lemma for `Antitone`, `StrictMono`, and `StrictAnti`.
open Set
-variable {G H : Type _} [LinearOrderedAddCommGroup G] [OrderedAddCommGroup H]
+variable {G H : Type*} [LinearOrderedAddCommGroup G] [OrderedAddCommGroup H]
/-- An odd function on a linear ordered additive commutative group is strictly monotone on the whole
group provided that it is strictly monotone on `Set.Ici 0`. -/
@@ -12,7 +12,7 @@ import Mathlib.Algebra.Order.Group.Instances
# Monotonicity of odd functions
An odd function on a linear ordered additive commutative group `G` is monotone on the whole group
-provided that is is monotone on `Set.Ici 0`, see `monotone_of_odd_of_monotoneOn_nonneg`. We also
+provided that it is monotone on `Set.Ici 0`, see `monotone_of_odd_of_monotoneOn_nonneg`. We also
prove versions of this lemma for `Antitone`, `StrictMono`, and `StrictAnti`.
-/
@@ -2,15 +2,12 @@
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module order.monotone.odd
-! leanprover-community/mathlib commit 9116dd6709f303dcf781632e15fdef382b0fc579
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Order.Monotone.Union
import Mathlib.Algebra.Order.Group.Instances
+#align_import order.monotone.odd from "leanprover-community/mathlib"@"9116dd6709f303dcf781632e15fdef382b0fc579"
+
/-!
# Monotonicity of odd functions
@@ -15,7 +15,7 @@ import Mathlib.Algebra.Order.Group.Instances
# Monotonicity of odd functions
An odd function on a linear ordered additive commutative group `G` is monotone on the whole group
-provided that is is monotone on `Set.Ici 0`, see `monotone_of_odd_of_monotone_on_nonneg`. We also
+provided that is is monotone on `Set.Ici 0`, see `monotone_of_odd_of_monotoneOn_nonneg`. We also
prove versions of this lemma for `Antitone`, `StrictMono`, and `StrictAnti`.
-/
@@ -26,32 +26,32 @@ variable {G H : Type _} [LinearOrderedAddCommGroup G] [OrderedAddCommGroup H]
/-- An odd function on a linear ordered additive commutative group is strictly monotone on the whole
group provided that it is strictly monotone on `Set.Ici 0`. -/
-theorem strictMono_of_odd_strictMono_on_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
+theorem strictMono_of_odd_strictMonoOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
(h₂ : StrictMonoOn f (Ici 0)) : StrictMono f := by
refine' StrictMonoOn.Iic_union_Ici (fun x hx y hy hxy => neg_lt_neg_iff.1 _) h₂
rw [← h₁, ← h₁]
exact h₂ (neg_nonneg.2 hy) (neg_nonneg.2 hx) (neg_lt_neg hxy)
-#align strict_mono_of_odd_strict_mono_on_nonneg strictMono_of_odd_strictMono_on_nonneg
+#align strict_mono_of_odd_strict_mono_on_nonneg strictMono_of_odd_strictMonoOn_nonneg
/-- An odd function on a linear ordered additive commutative group is strictly antitone on the whole
group provided that it is strictly antitone on `Set.Ici 0`. -/
-theorem strictAnti_of_odd_strictAnti_on_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
+theorem strictAnti_of_odd_strictAntiOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
(h₂ : StrictAntiOn f (Ici 0)) : StrictAnti f :=
- @strictMono_of_odd_strictMono_on_nonneg G Hᵒᵈ _ _ _ h₁ h₂
-#align strict_anti_of_odd_strict_anti_on_nonneg strictAnti_of_odd_strictAnti_on_nonneg
+ @strictMono_of_odd_strictMonoOn_nonneg G Hᵒᵈ _ _ _ h₁ h₂
+#align strict_anti_of_odd_strict_anti_on_nonneg strictAnti_of_odd_strictAntiOn_nonneg
/-- An odd function on a linear ordered additive commutative group is monotone on the whole group
provided that it is monotone on `Set.Ici 0`. -/
-theorem monotone_of_odd_of_monotone_on_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
+theorem monotone_of_odd_of_monotoneOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
(h₂ : MonotoneOn f (Ici 0)) : Monotone f := by
refine' MonotoneOn.Iic_union_Ici (fun x hx y hy hxy => neg_le_neg_iff.1 _) h₂
rw [← h₁, ← h₁]
exact h₂ (neg_nonneg.2 hy) (neg_nonneg.2 hx) (neg_le_neg hxy)
-#align monotone_of_odd_of_monotone_on_nonneg monotone_of_odd_of_monotone_on_nonneg
+#align monotone_of_odd_of_monotone_on_nonneg monotone_of_odd_of_monotoneOn_nonneg
/-- An odd function on a linear ordered additive commutative group is antitone on the whole group
provided that it is monotone on `Set.Ici 0`. -/
-theorem antitone_of_odd_of_monotone_on_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
+theorem antitone_of_odd_of_monotoneOn_nonneg {f : G → H} (h₁ : ∀ x, f (-x) = -f x)
(h₂ : AntitoneOn f (Ici 0)) : Antitone f :=
- @monotone_of_odd_of_monotone_on_nonneg G Hᵒᵈ _ _ _ h₁ h₂
-#align antitone_of_odd_of_monotone_on_nonneg antitone_of_odd_of_monotone_on_nonneg
+ @monotone_of_odd_of_monotoneOn_nonneg G Hᵒᵈ _ _ _ h₁ h₂
+#align antitone_of_odd_of_monotone_on_nonneg antitone_of_odd_of_monotoneOn_nonneg