order.monotone.extension | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

422e70f7

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

c3291da4

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -47,7 +47,7 @@ theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow
   · rcases not_disjoint_iff_nonempty_inter.1 hy with ⟨z, hz⟩
     exact le_csSup_of_le (hu' _) (mem_image_of_mem _ hz) (ha <| mem_image_of_mem _ hz.2)
   · exact (hx <| hy.mono_left <| Iic_subset_Iic.2 hxy).elim
-  · rw [not_disjoint_iff_nonempty_inter] at hx hy 
+  · rw [not_disjoint_iff_nonempty_inter] at hx hy
     refine' csSup_le_csSup (hu' _) (hx.image _) (image_subset _ _)
     exact inter_subset_inter_left _ (Iic_subset_Iic.2 hxy)
 #align monotone_on.exists_monotone_extension MonotoneOn.exists_monotone_extension

c3291da4

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -27,13 +27,33 @@ variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β]
 /-- If a function is monotone and is bounded on a set `s`, then it admits a monotone extension to
 the whole space. -/
 theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow (f '' s))
-    (hu : BddAbove (f '' s)) : ∃ g : α → β, Monotone g ∧ EqOn f g s := by classical
+    (hu : BddAbove (f '' s)) : ∃ g : α → β, Monotone g ∧ EqOn f g s := by
+  classical
+  /- The extension is defined by `f x = f a` for `x ≤ a`, and `f x` is the supremum of the values
+    of `f`  to the left of `x` for `x ≥ a`. -/
+  rcases hl with ⟨a, ha⟩
+  have hu' : ∀ x, BddAbove (f '' (Iic x ∩ s)) := fun x =>
+    hu.mono (image_subset _ (inter_subset_right _ _))
+  set g : α → β := fun x => if Disjoint (Iic x) s then a else Sup (f '' (Iic x ∩ s))
+  have hgs : eq_on f g s := by
+    intro x hx
+    simp only [g]
+    have : IsGreatest (Iic x ∩ s) x := ⟨⟨right_mem_Iic, hx⟩, fun y hy => hy.1⟩
+    rw [if_neg this.nonempty.not_disjoint,
+      ((h.mono <| inter_subset_right _ _).map_isGreatest this).csSup_eq]
+  refine' ⟨g, fun x y hxy => _, hgs⟩
+  by_cases hx : Disjoint (Iic x) s <;> by_cases hy : Disjoint (Iic y) s <;>
+    simp only [g, if_pos, if_neg, not_false_iff, *]
+  · rcases not_disjoint_iff_nonempty_inter.1 hy with ⟨z, hz⟩
+    exact le_csSup_of_le (hu' _) (mem_image_of_mem _ hz) (ha <| mem_image_of_mem _ hz.2)
+  · exact (hx <| hy.mono_left <| Iic_subset_Iic.2 hxy).elim
+  · rw [not_disjoint_iff_nonempty_inter] at hx hy 
+    refine' csSup_le_csSup (hu' _) (hx.image _) (image_subset _ _)
+    exact inter_subset_inter_left _ (Iic_subset_Iic.2 hxy)
 #align monotone_on.exists_monotone_extension MonotoneOn.exists_monotone_extension
 -/
 
 #print AntitoneOn.exists_antitone_extension /-
-/- The extension is defined by `f x = f a` for `x ≤ a`, and `f x` is the supremum of the values
-  of `f`  to the left of `x` for `x ≥ a`. -/
 /-- If a function is antitone and is bounded on a set `s`, then it admits an antitone extension to
 the whole space. -/
 theorem AntitoneOn.exists_antitone_extension (h : AntitoneOn f s) (hl : BddBelow (f '' s))

c3291da4

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -27,33 +27,13 @@ variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β]
 /-- If a function is monotone and is bounded on a set `s`, then it admits a monotone extension to
 the whole space. -/
 theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow (f '' s))
-    (hu : BddAbove (f '' s)) : ∃ g : α → β, Monotone g ∧ EqOn f g s := by
-  classical
-  /- The extension is defined by `f x = f a` for `x ≤ a`, and `f x` is the supremum of the values
-    of `f`  to the left of `x` for `x ≥ a`. -/
-  rcases hl with ⟨a, ha⟩
-  have hu' : ∀ x, BddAbove (f '' (Iic x ∩ s)) := fun x =>
-    hu.mono (image_subset _ (inter_subset_right _ _))
-  set g : α → β := fun x => if Disjoint (Iic x) s then a else Sup (f '' (Iic x ∩ s))
-  have hgs : eq_on f g s := by
-    intro x hx
-    simp only [g]
-    have : IsGreatest (Iic x ∩ s) x := ⟨⟨right_mem_Iic, hx⟩, fun y hy => hy.1⟩
-    rw [if_neg this.nonempty.not_disjoint,
-      ((h.mono <| inter_subset_right _ _).map_isGreatest this).csSup_eq]
-  refine' ⟨g, fun x y hxy => _, hgs⟩
-  by_cases hx : Disjoint (Iic x) s <;> by_cases hy : Disjoint (Iic y) s <;>
-    simp only [g, if_pos, if_neg, not_false_iff, *]
-  · rcases not_disjoint_iff_nonempty_inter.1 hy with ⟨z, hz⟩
-    exact le_csSup_of_le (hu' _) (mem_image_of_mem _ hz) (ha <| mem_image_of_mem _ hz.2)
-  · exact (hx <| hy.mono_left <| Iic_subset_Iic.2 hxy).elim
-  · rw [not_disjoint_iff_nonempty_inter] at hx hy 
-    refine' csSup_le_csSup (hu' _) (hx.image _) (image_subset _ _)
-    exact inter_subset_inter_left _ (Iic_subset_Iic.2 hxy)
+    (hu : BddAbove (f '' s)) : ∃ g : α → β, Monotone g ∧ EqOn f g s := by classical
 #align monotone_on.exists_monotone_extension MonotoneOn.exists_monotone_extension
 -/
 
 #print AntitoneOn.exists_antitone_extension /-
+/- The extension is defined by `f x = f a` for `x ≤ a`, and `f x` is the supremum of the values
+  of `f`  to the left of `x` for `x ≥ a`. -/
 /-- If a function is antitone and is bounded on a set `s`, then it admits an antitone extension to
 the whole space. -/
 theorem AntitoneOn.exists_antitone_extension (h : AntitoneOn f s) (hl : BddBelow (f '' s))

c3291da4

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yury Kudryashov
 -/
-import Mathbin.Order.ConditionallyCompleteLattice.Basic
+import Order.ConditionallyCompleteLattice.Basic
 
 #align_import order.monotone.extension from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"

c3291da4

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yury Kudryashov
-
-! This file was ported from Lean 3 source module order.monotone.extension
-! 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.ConditionallyCompleteLattice.Basic
 
+#align_import order.monotone.extension from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
 /-!
 # Extension of a monotone function from a set to the whole space

c3291da4

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -26,6 +26,7 @@ open Set
 variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β] {f : α → β} {s : Set α}
   {a b : α}
 
+#print MonotoneOn.exists_monotone_extension /-
 /-- If a function is monotone and is bounded on a set `s`, then it admits a monotone extension to
 the whole space. -/
 theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow (f '' s))
@@ -53,11 +54,14 @@ theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow
     refine' csSup_le_csSup (hu' _) (hx.image _) (image_subset _ _)
     exact inter_subset_inter_left _ (Iic_subset_Iic.2 hxy)
 #align monotone_on.exists_monotone_extension MonotoneOn.exists_monotone_extension
+-/
 
+#print AntitoneOn.exists_antitone_extension /-
 /-- If a function is antitone and is bounded on a set `s`, then it admits an antitone extension to
 the whole space. -/
 theorem AntitoneOn.exists_antitone_extension (h : AntitoneOn f s) (hl : BddBelow (f '' s))
     (hu : BddAbove (f '' s)) : ∃ g : α → β, Antitone g ∧ EqOn f g s :=
   h.dual_right.exists_monotone_extension hu hl
 #align antitone_on.exists_antitone_extension AntitoneOn.exists_antitone_extension
+-/

c3291da4

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -31,27 +31,27 @@ the whole space. -/
 theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow (f '' s))
     (hu : BddAbove (f '' s)) : ∃ g : α → β, Monotone g ∧ EqOn f g s := by
   classical
-    /- The extension is defined by `f x = f a` for `x ≤ a`, and `f x` is the supremum of the values
-      of `f`  to the left of `x` for `x ≥ a`. -/
-    rcases hl with ⟨a, ha⟩
-    have hu' : ∀ x, BddAbove (f '' (Iic x ∩ s)) := fun x =>
-      hu.mono (image_subset _ (inter_subset_right _ _))
-    set g : α → β := fun x => if Disjoint (Iic x) s then a else Sup (f '' (Iic x ∩ s))
-    have hgs : eq_on f g s := by
-      intro x hx
-      simp only [g]
-      have : IsGreatest (Iic x ∩ s) x := ⟨⟨right_mem_Iic, hx⟩, fun y hy => hy.1⟩
-      rw [if_neg this.nonempty.not_disjoint,
-        ((h.mono <| inter_subset_right _ _).map_isGreatest this).csSup_eq]
-    refine' ⟨g, fun x y hxy => _, hgs⟩
-    by_cases hx : Disjoint (Iic x) s <;> by_cases hy : Disjoint (Iic y) s <;>
-      simp only [g, if_pos, if_neg, not_false_iff, *]
-    · rcases not_disjoint_iff_nonempty_inter.1 hy with ⟨z, hz⟩
-      exact le_csSup_of_le (hu' _) (mem_image_of_mem _ hz) (ha <| mem_image_of_mem _ hz.2)
-    · exact (hx <| hy.mono_left <| Iic_subset_Iic.2 hxy).elim
-    · rw [not_disjoint_iff_nonempty_inter] at hx hy 
-      refine' csSup_le_csSup (hu' _) (hx.image _) (image_subset _ _)
-      exact inter_subset_inter_left _ (Iic_subset_Iic.2 hxy)
+  /- The extension is defined by `f x = f a` for `x ≤ a`, and `f x` is the supremum of the values
+    of `f`  to the left of `x` for `x ≥ a`. -/
+  rcases hl with ⟨a, ha⟩
+  have hu' : ∀ x, BddAbove (f '' (Iic x ∩ s)) := fun x =>
+    hu.mono (image_subset _ (inter_subset_right _ _))
+  set g : α → β := fun x => if Disjoint (Iic x) s then a else Sup (f '' (Iic x ∩ s))
+  have hgs : eq_on f g s := by
+    intro x hx
+    simp only [g]
+    have : IsGreatest (Iic x ∩ s) x := ⟨⟨right_mem_Iic, hx⟩, fun y hy => hy.1⟩
+    rw [if_neg this.nonempty.not_disjoint,
+      ((h.mono <| inter_subset_right _ _).map_isGreatest this).csSup_eq]
+  refine' ⟨g, fun x y hxy => _, hgs⟩
+  by_cases hx : Disjoint (Iic x) s <;> by_cases hy : Disjoint (Iic y) s <;>
+    simp only [g, if_pos, if_neg, not_false_iff, *]
+  · rcases not_disjoint_iff_nonempty_inter.1 hy with ⟨z, hz⟩
+    exact le_csSup_of_le (hu' _) (mem_image_of_mem _ hz) (ha <| mem_image_of_mem _ hz.2)
+  · exact (hx <| hy.mono_left <| Iic_subset_Iic.2 hxy).elim
+  · rw [not_disjoint_iff_nonempty_inter] at hx hy 
+    refine' csSup_le_csSup (hu' _) (hx.image _) (image_subset _ _)
+    exact inter_subset_inter_left _ (Iic_subset_Iic.2 hxy)
 #align monotone_on.exists_monotone_extension MonotoneOn.exists_monotone_extension
 
 /-- If a function is antitone and is bounded on a set `s`, then it admits an antitone extension to

c3291da4

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -49,7 +49,7 @@ theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow
     · rcases not_disjoint_iff_nonempty_inter.1 hy with ⟨z, hz⟩
       exact le_csSup_of_le (hu' _) (mem_image_of_mem _ hz) (ha <| mem_image_of_mem _ hz.2)
     · exact (hx <| hy.mono_left <| Iic_subset_Iic.2 hxy).elim
-    · rw [not_disjoint_iff_nonempty_inter] at hx hy
+    · rw [not_disjoint_iff_nonempty_inter] at hx hy 
       refine' csSup_le_csSup (hu' _) (hx.image _) (image_subset _ _)
       exact inter_subset_inter_left _ (Iic_subset_Iic.2 hxy)
 #align monotone_on.exists_monotone_extension MonotoneOn.exists_monotone_extension

c3291da4

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -26,12 +26,6 @@ open Set
 variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β] {f : α → β} {s : Set α}
   {a b : α}
 
-/- warning: monotone_on.exists_monotone_extension -> MonotoneOn.exists_monotone_extension is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] {f : α -> β} {s : Set.{u1} α}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f s) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) (Set.image.{u1, u2} α β f s)) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) (Set.image.{u1, u2} α β f s)) -> (Exists.{max (succ u1) (succ u2)} (α -> β) (fun (g : α -> β) => And (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) g) (Set.EqOn.{u1, u2} α β f g s)))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] {f : α -> β} {s : Set.{u2} α}, (MonotoneOn.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f s) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) (Set.image.{u2, u1} α β f s)) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) (Set.image.{u2, u1} α β f s)) -> (Exists.{max (succ u2) (succ u1)} (α -> β) (fun (g : α -> β) => And (Monotone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) g) (Set.EqOn.{u2, u1} α β f g s)))
-Case conversion may be inaccurate. Consider using '#align monotone_on.exists_monotone_extension MonotoneOn.exists_monotone_extensionₓ'. -/
 /-- If a function is monotone and is bounded on a set `s`, then it admits a monotone extension to
 the whole space. -/
 theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow (f '' s))
@@ -60,12 +54,6 @@ theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow
       exact inter_subset_inter_left _ (Iic_subset_Iic.2 hxy)
 #align monotone_on.exists_monotone_extension MonotoneOn.exists_monotone_extension
 
-/- warning: antitone_on.exists_antitone_extension -> AntitoneOn.exists_antitone_extension is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u2} β] {f : α -> β} {s : Set.{u1} α}, (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) f s) -> (BddBelow.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) (Set.image.{u1, u2} α β f s)) -> (BddAbove.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) (Set.image.{u1, u2} α β f s)) -> (Exists.{max (succ u1) (succ u2)} (α -> β) (fun (g : α -> β) => And (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_2))))) g) (Set.EqOn.{u1, u2} α β f g s)))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : ConditionallyCompleteLinearOrder.{u1} β] {f : α -> β} {s : Set.{u2} α}, (AntitoneOn.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) f s) -> (BddBelow.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) (Set.image.{u2, u1} α β f s)) -> (BddAbove.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) (Set.image.{u2, u1} α β f s)) -> (Exists.{max (succ u2) (succ u1)} (α -> β) (fun (g : α -> β) => And (Antitone.{u2, u1} α β (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_2))))) g) (Set.EqOn.{u2, u1} α β f g s)))
-Case conversion may be inaccurate. Consider using '#align antitone_on.exists_antitone_extension AntitoneOn.exists_antitone_extensionₓ'. -/
 /-- If a function is antitone and is bounded on a set `s`, then it admits an antitone extension to
 the whole space. -/
 theorem AntitoneOn.exists_antitone_extension (h : AntitoneOn f s) (hl : BddBelow (f '' s))

c3291da4

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -48,15 +48,15 @@ theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow
       simp only [g]
       have : IsGreatest (Iic x ∩ s) x := ⟨⟨right_mem_Iic, hx⟩, fun y hy => hy.1⟩
       rw [if_neg this.nonempty.not_disjoint,
-        ((h.mono <| inter_subset_right _ _).map_isGreatest this).csupₛ_eq]
+        ((h.mono <| inter_subset_right _ _).map_isGreatest this).csSup_eq]
     refine' ⟨g, fun x y hxy => _, hgs⟩
     by_cases hx : Disjoint (Iic x) s <;> by_cases hy : Disjoint (Iic y) s <;>
       simp only [g, if_pos, if_neg, not_false_iff, *]
     · rcases not_disjoint_iff_nonempty_inter.1 hy with ⟨z, hz⟩
-      exact le_csupₛ_of_le (hu' _) (mem_image_of_mem _ hz) (ha <| mem_image_of_mem _ hz.2)
+      exact le_csSup_of_le (hu' _) (mem_image_of_mem _ hz) (ha <| mem_image_of_mem _ hz.2)
     · exact (hx <| hy.mono_left <| Iic_subset_Iic.2 hxy).elim
     · rw [not_disjoint_iff_nonempty_inter] at hx hy
-      refine' csupₛ_le_csupₛ (hu' _) (hx.image _) (image_subset _ _)
+      refine' csSup_le_csSup (hu' _) (hx.image _) (image_subset _ _)
       exact inter_subset_inter_left _ (Iic_subset_Iic.2 hxy)
 #align monotone_on.exists_monotone_extension MonotoneOn.exists_monotone_extension

c3291da4

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

422e70f7

chore: more backporting of simp changes from #10995 (#11001)

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

d9589c14

Diff

@@ -33,13 +33,13 @@ theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow
     let g : α → β := fun x => if Disjoint (Iic x) s then a else sSup (f '' (Iic x ∩ s))
     have hgs : EqOn f g s := by
       intro x hx
-      simp only []
+      simp only [g]
       have : IsGreatest (Iic x ∩ s) x := ⟨⟨right_mem_Iic, hx⟩, fun y hy => hy.1⟩
       rw [if_neg this.nonempty.not_disjoint,
         ((h.mono <| inter_subset_right _ _).map_isGreatest this).csSup_eq]
     refine' ⟨g, fun x y hxy => _, hgs⟩
     by_cases hx : Disjoint (Iic x) s <;> by_cases hy : Disjoint (Iic y) s <;>
-      simp only [if_pos, if_neg, not_false_iff, *, refl]
+      simp only [g, if_pos, if_neg, not_false_iff, *, refl]
     · rcases not_disjoint_iff_nonempty_inter.1 hy with ⟨z, hz⟩
       exact le_csSup_of_le (hu' _) (mem_image_of_mem _ hz) (ha <| mem_image_of_mem _ hz.2)
     · exact (hx <| hy.mono_left <| Iic_subset_Iic.2 hxy).elim

422e70f7

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -17,7 +17,7 @@ monotone extension to the whole space.
 
 open Set
 
-variable {α β : Type _} [LinearOrder α] [ConditionallyCompleteLinearOrder β] {f : α → β} {s : Set α}
+variable {α β : Type*} [LinearOrder α] [ConditionallyCompleteLinearOrder β] {f : α → β} {s : Set α}
   {a b : α}
 
 /-- If a function is monotone and is bounded on a set `s`, then it admits a monotone extension to

422e70f7

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel, Yury Kudryashov
-
-! This file was ported from Lean 3 source module order.monotone.extension
-! leanprover-community/mathlib commit 422e70f7ce183d2900c586a8cda8381e788a0c62
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Order.ConditionallyCompleteLattice.Basic
 
+#align_import order.monotone.extension from "leanprover-community/mathlib"@"422e70f7ce183d2900c586a8cda8381e788a0c62"
+
 /-!
 # Extension of a monotone function from a set to the whole space

422e70f7

chore: cleanup whitespace (#5988)

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

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

12343aa5

Diff

@@ -29,7 +29,7 @@ theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow
     (hu : BddAbove (f '' s)) : ∃ g : α → β, Monotone g ∧ EqOn f g s := by
   classical
     /- The extension is defined by `f x = f a` for `x ≤ a`, and `f x` is the supremum of the values
-      of `f`  to the left of `x` for `x ≥ a`. -/
+      of `f` to the left of `x` for `x ≥ a`. -/
     rcases hl with ⟨a, ha⟩
     have hu' : ∀ x, BddAbove (f '' (Iic x ∩ s)) := fun x =>
       hu.mono (image_subset _ (inter_subset_right _ _))

422e70f7

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

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

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

d1eb6264

Diff

@@ -33,21 +33,21 @@ theorem MonotoneOn.exists_monotone_extension (h : MonotoneOn f s) (hl : BddBelow
     rcases hl with ⟨a, ha⟩
     have hu' : ∀ x, BddAbove (f '' (Iic x ∩ s)) := fun x =>
       hu.mono (image_subset _ (inter_subset_right _ _))
-    let g : α → β := fun x => if Disjoint (Iic x) s then a else supₛ (f '' (Iic x ∩ s))
+    let g : α → β := fun x => if Disjoint (Iic x) s then a else sSup (f '' (Iic x ∩ s))
     have hgs : EqOn f g s := by
       intro x hx
       simp only []
       have : IsGreatest (Iic x ∩ s) x := ⟨⟨right_mem_Iic, hx⟩, fun y hy => hy.1⟩
       rw [if_neg this.nonempty.not_disjoint,
-        ((h.mono <| inter_subset_right _ _).map_isGreatest this).csupₛ_eq]
+        ((h.mono <| inter_subset_right _ _).map_isGreatest this).csSup_eq]
     refine' ⟨g, fun x y hxy => _, hgs⟩
     by_cases hx : Disjoint (Iic x) s <;> by_cases hy : Disjoint (Iic y) s <;>
       simp only [if_pos, if_neg, not_false_iff, *, refl]
     · rcases not_disjoint_iff_nonempty_inter.1 hy with ⟨z, hz⟩
-      exact le_csupₛ_of_le (hu' _) (mem_image_of_mem _ hz) (ha <| mem_image_of_mem _ hz.2)
+      exact le_csSup_of_le (hu' _) (mem_image_of_mem _ hz) (ha <| mem_image_of_mem _ hz.2)
     · exact (hx <| hy.mono_left <| Iic_subset_Iic.2 hxy).elim
     · rw [not_disjoint_iff_nonempty_inter] at hx hy
-      refine' csupₛ_le_csupₛ (hu' _) (hx.image _) (image_subset _ _)
+      refine' csSup_le_csSup (hu' _) (hx.image _) (image_subset _ _)
       exact inter_subset_inter_left _ (Iic_subset_Iic.2 hxy)
 #align monotone_on.exists_monotone_extension MonotoneOn.exists_monotone_extension

422e70f7

feat: port order.monotone.extension (#1262)

751f7c13

`order.monotone.extension` ⟷ `Mathlib.Order.Monotone.Extension`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 61

order.monotone.extension ⟷ Mathlib.Order.Monotone.Extension

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 61

`order.monotone.extension` ⟷ `Mathlib.Order.Monotone.Extension`