order.monotone.unionMathlib.Order.Monotone.Union

This file has been ported!

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.

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -3,7 +3,7 @@ Copyright (c) 2022 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel
 -/
-import Mathbin.Order.Bounds.Basic
+import Order.Bounds.Basic
 
 #align_import order.monotone.union from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
 
Diff
@@ -2,14 +2,11 @@
 Copyright (c) 2022 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module order.monotone.union
-! 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.Bounds.Basic
 
+#align_import order.monotone.union from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
 /-!
 # Monotonicity on intervals
 
Diff
@@ -27,6 +27,7 @@ open Set
 
 variable {α β : Type _} [LinearOrder α] [Preorder β] {a : α} {f : α → β}
 
+#print StrictMonoOn.union /-
 /-- If `f` is strictly monotone both on `s` and `t`, with `s` to the left of `t` and the center
 point belonging to both `s` and `t`, then `f` is strictly monotone on `s ∪ t` -/
 protected theorem StrictMonoOn.union {s t : Set α} {c : α} (h₁ : StrictMonoOn f s)
@@ -54,7 +55,9 @@ protected theorem StrictMonoOn.union {s t : Set α} {c : α} (h₁ : StrictMonoO
     have yt : y ∈ t := B _ hy (hcx.trans hxy.le)
     exact h₂ xt yt hxy
 #align strict_mono_on.union StrictMonoOn.union
+-/
 
+#print StrictMonoOn.Iic_union_Ici /-
 /-- If `f` is strictly monotone both on `(-∞, a]` and `[a, ∞)`, then it is strictly monotone on the
 whole line. -/
 protected theorem StrictMonoOn.Iic_union_Ici (h₁ : StrictMonoOn f (Iic a))
@@ -63,21 +66,27 @@ protected theorem StrictMonoOn.Iic_union_Ici (h₁ : StrictMonoOn f (Iic a))
   rw [← strictMonoOn_univ, ← @Iic_union_Ici _ _ a]
   exact StrictMonoOn.union h₁ h₂ isGreatest_Iic isLeast_Ici
 #align strict_mono_on.Iic_union_Ici StrictMonoOn.Iic_union_Ici
+-/
 
+#print StrictAntiOn.union /-
 /-- If `f` is strictly antitone both on `s` and `t`, with `s` to the left of `t` and the center
 point belonging to both `s` and `t`, then `f` is strictly antitone on `s ∪ t` -/
 protected theorem StrictAntiOn.union {s t : Set α} {c : α} (h₁ : StrictAntiOn f s)
     (h₂ : StrictAntiOn f t) (hs : IsGreatest s c) (ht : IsLeast t c) : StrictAntiOn f (s ∪ t) :=
   (h₁.dual_right.union h₂.dual_right hs ht).dual_right
 #align strict_anti_on.union StrictAntiOn.union
+-/
 
+#print StrictAntiOn.Iic_union_Ici /-
 /-- If `f` is strictly antitone both on `(-∞, a]` and `[a, ∞)`, then it is strictly antitone on the
 whole line. -/
 protected theorem StrictAntiOn.Iic_union_Ici (h₁ : StrictAntiOn f (Iic a))
     (h₂ : StrictAntiOn f (Ici a)) : StrictAnti f :=
   (h₁.dual_right.Iic_union_Ici h₂.dual_right).dual_right
 #align strict_anti_on.Iic_union_Ici StrictAntiOn.Iic_union_Ici
+-/
 
+#print MonotoneOn.union_right /-
 /-- If `f` is monotone both on `s` and `t`, with `s` to the left of `t` and the center
 point belonging to both `s` and `t`, then `f` is monotone on `s ∪ t` -/
 protected theorem MonotoneOn.union_right {s t : Set α} {c : α} (h₁ : MonotoneOn f s)
@@ -105,24 +114,31 @@ protected theorem MonotoneOn.union_right {s t : Set α} {c : α} (h₁ : Monoton
     have yt : y ∈ t := B _ hy (hcx.trans hxy)
     exact h₂ xt yt hxy
 #align monotone_on.union_right MonotoneOn.union_right
+-/
 
+#print MonotoneOn.Iic_union_Ici /-
 /-- If `f` is monotone both on `(-∞, a]` and `[a, ∞)`, then it is monotone on the whole line. -/
 protected theorem MonotoneOn.Iic_union_Ici (h₁ : MonotoneOn f (Iic a)) (h₂ : MonotoneOn f (Ici a)) :
     Monotone f := by
   rw [← monotoneOn_univ, ← @Iic_union_Ici _ _ a]
   exact MonotoneOn.union_right h₁ h₂ isGreatest_Iic isLeast_Ici
 #align monotone_on.Iic_union_Ici MonotoneOn.Iic_union_Ici
+-/
 
+#print AntitoneOn.union_right /-
 /-- If `f` is antitone both on `s` and `t`, with `s` to the left of `t` and the center
 point belonging to both `s` and `t`, then `f` is antitone on `s ∪ t` -/
 protected theorem AntitoneOn.union_right {s t : Set α} {c : α} (h₁ : AntitoneOn f s)
     (h₂ : AntitoneOn f t) (hs : IsGreatest s c) (ht : IsLeast t c) : AntitoneOn f (s ∪ t) :=
   (h₁.dual_right.union_right h₂.dual_right hs ht).dual_right
 #align antitone_on.union_right AntitoneOn.union_right
+-/
 
+#print AntitoneOn.Iic_union_Ici /-
 /-- If `f` is antitone both on `(-∞, a]` and `[a, ∞)`, then it is antitone on the whole line. -/
 protected theorem AntitoneOn.Iic_union_Ici (h₁ : AntitoneOn f (Iic a)) (h₂ : AntitoneOn f (Ici a)) :
     Antitone f :=
   (h₁.dual_right.Iic_union_Ici h₂.dual_right).dual_right
 #align antitone_on.Iic_union_Ici AntitoneOn.Iic_union_Ici
+-/
 
Diff
@@ -27,12 +27,6 @@ open Set
 
 variable {α β : Type _} [LinearOrder α] [Preorder β] {a : α} {f : α → β}
 
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-Case conversion may be inaccurate. Consider using '#align strict_mono_on.union StrictMonoOn.unionₓ'. -/
 /-- If `f` is strictly monotone both on `s` and `t`, with `s` to the left of `t` and the center
 point belonging to both `s` and `t`, then `f` is strictly monotone on `s ∪ t` -/
 protected theorem StrictMonoOn.union {s t : Set α} {c : α} (h₁ : StrictMonoOn f s)
@@ -61,12 +55,6 @@ protected theorem StrictMonoOn.union {s t : Set α} {c : α} (h₁ : StrictMonoO
     exact h₂ xt yt hxy
 #align strict_mono_on.union StrictMonoOn.union
 
-/- warning: strict_mono_on.Iic_union_Ici -> StrictMonoOn.Iic_union_Ici is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align strict_mono_on.Iic_union_Ici StrictMonoOn.Iic_union_Iciₓ'. -/
 /-- If `f` is strictly monotone both on `(-∞, a]` and `[a, ∞)`, then it is strictly monotone on the
 whole line. -/
 protected theorem StrictMonoOn.Iic_union_Ici (h₁ : StrictMonoOn f (Iic a))
@@ -76,12 +64,6 @@ protected theorem StrictMonoOn.Iic_union_Ici (h₁ : StrictMonoOn f (Iic a))
   exact StrictMonoOn.union h₁ h₂ isGreatest_Iic isLeast_Ici
 #align strict_mono_on.Iic_union_Ici StrictMonoOn.Iic_union_Ici
 
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-Case conversion may be inaccurate. Consider using '#align strict_anti_on.union StrictAntiOn.unionₓ'. -/
 /-- If `f` is strictly antitone both on `s` and `t`, with `s` to the left of `t` and the center
 point belonging to both `s` and `t`, then `f` is strictly antitone on `s ∪ t` -/
 protected theorem StrictAntiOn.union {s t : Set α} {c : α} (h₁ : StrictAntiOn f s)
@@ -89,12 +71,6 @@ protected theorem StrictAntiOn.union {s t : Set α} {c : α} (h₁ : StrictAntiO
   (h₁.dual_right.union h₂.dual_right hs ht).dual_right
 #align strict_anti_on.union StrictAntiOn.union
 
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-Case conversion may be inaccurate. Consider using '#align strict_anti_on.Iic_union_Ici StrictAntiOn.Iic_union_Iciₓ'. -/
 /-- If `f` is strictly antitone both on `(-∞, a]` and `[a, ∞)`, then it is strictly antitone on the
 whole line. -/
 protected theorem StrictAntiOn.Iic_union_Ici (h₁ : StrictAntiOn f (Iic a))
@@ -102,12 +78,6 @@ protected theorem StrictAntiOn.Iic_union_Ici (h₁ : StrictAntiOn f (Iic a))
   (h₁.dual_right.Iic_union_Ici h₂.dual_right).dual_right
 #align strict_anti_on.Iic_union_Ici StrictAntiOn.Iic_union_Ici
 
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-Case conversion may be inaccurate. Consider using '#align monotone_on.union_right MonotoneOn.union_rightₓ'. -/
 /-- If `f` is monotone both on `s` and `t`, with `s` to the left of `t` and the center
 point belonging to both `s` and `t`, then `f` is monotone on `s ∪ t` -/
 protected theorem MonotoneOn.union_right {s t : Set α} {c : α} (h₁ : MonotoneOn f s)
@@ -136,12 +106,6 @@ protected theorem MonotoneOn.union_right {s t : Set α} {c : α} (h₁ : Monoton
     exact h₂ xt yt hxy
 #align monotone_on.union_right MonotoneOn.union_right
 
-/- warning: monotone_on.Iic_union_Ici -> MonotoneOn.Iic_union_Ici is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Preorder.{u2} β] {a : α} {f : α -> β}, (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 f (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a)) -> (MonotoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 f (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a)) -> (Monotone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 f)
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : Preorder.{u1} β] {a : α} {f : α -> β}, (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))))) _inst_2 f (Set.Iic.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a)) -> (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))))) _inst_2 f (Set.Ici.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a)) -> (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))))) _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align monotone_on.Iic_union_Ici MonotoneOn.Iic_union_Iciₓ'. -/
 /-- If `f` is monotone both on `(-∞, a]` and `[a, ∞)`, then it is monotone on the whole line. -/
 protected theorem MonotoneOn.Iic_union_Ici (h₁ : MonotoneOn f (Iic a)) (h₂ : MonotoneOn f (Ici a)) :
     Monotone f := by
@@ -149,12 +113,6 @@ protected theorem MonotoneOn.Iic_union_Ici (h₁ : MonotoneOn f (Iic a)) (h₂ :
   exact MonotoneOn.union_right h₁ h₂ isGreatest_Iic isLeast_Ici
 #align monotone_on.Iic_union_Ici MonotoneOn.Iic_union_Ici
 
-/- warning: antitone_on.union_right -> AntitoneOn.union_right is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Preorder.{u2} β] {f : α -> β} {s : Set.{u1} α} {t : Set.{u1} α} {c : α}, (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 f s) -> (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 f t) -> (IsGreatest.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) s c) -> (IsLeast.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) t c) -> (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 f (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : Preorder.{u1} β] {f : α -> β} {s : Set.{u2} α} {t : Set.{u2} α} {c : 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))))) _inst_2 f s) -> (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))))) _inst_2 f t) -> (IsGreatest.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) s c) -> (IsLeast.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) t c) -> (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))))) _inst_2 f (Union.union.{u2} (Set.{u2} α) (Set.instUnionSet.{u2} α) s t))
-Case conversion may be inaccurate. Consider using '#align antitone_on.union_right AntitoneOn.union_rightₓ'. -/
 /-- If `f` is antitone both on `s` and `t`, with `s` to the left of `t` and the center
 point belonging to both `s` and `t`, then `f` is antitone on `s ∪ t` -/
 protected theorem AntitoneOn.union_right {s t : Set α} {c : α} (h₁ : AntitoneOn f s)
@@ -162,12 +120,6 @@ protected theorem AntitoneOn.union_right {s t : Set α} {c : α} (h₁ : Antiton
   (h₁.dual_right.union_right h₂.dual_right hs ht).dual_right
 #align antitone_on.union_right AntitoneOn.union_right
 
-/- warning: antitone_on.Iic_union_Ici -> AntitoneOn.Iic_union_Ici is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u1} α] [_inst_2 : Preorder.{u2} β] {a : α} {f : α -> β}, (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 f (Set.Iic.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a)) -> (AntitoneOn.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 f (Set.Ici.{u1} α (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) a)) -> (Antitone.{u1, u2} α β (PartialOrder.toPreorder.{u1} α (SemilatticeInf.toPartialOrder.{u1} α (Lattice.toSemilatticeInf.{u1} α (LinearOrder.toLattice.{u1} α _inst_1)))) _inst_2 f)
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : LinearOrder.{u2} α] [_inst_2 : Preorder.{u1} β] {a : α} {f : α -> β}, (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))))) _inst_2 f (Set.Iic.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a)) -> (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))))) _inst_2 f (Set.Ici.{u2} α (PartialOrder.toPreorder.{u2} α (SemilatticeInf.toPartialOrder.{u2} α (Lattice.toSemilatticeInf.{u2} α (DistribLattice.toLattice.{u2} α (instDistribLattice.{u2} α _inst_1))))) a)) -> (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))))) _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align antitone_on.Iic_union_Ici AntitoneOn.Iic_union_Iciₓ'. -/
 /-- If `f` is antitone both on `(-∞, a]` and `[a, ∞)`, then it is antitone on the whole line. -/
 protected theorem AntitoneOn.Iic_union_Ici (h₁ : AntitoneOn f (Iic a)) (h₂ : AntitoneOn f (Ici a)) :
     Antitone f :=
Diff
@@ -41,19 +41,14 @@ protected theorem StrictMonoOn.union {s t : Set α} {c : α} (h₁ : StrictMonoO
   have A : ∀ x, x ∈ s ∪ t → x ≤ c → x ∈ s :=
     by
     intro x hx hxc
-    cases hx
-    · exact hx
-    rcases eq_or_lt_of_le hxc with (rfl | h'x)
-    · exact hs.1
+    cases hx; · exact hx
+    rcases eq_or_lt_of_le hxc with (rfl | h'x); · exact hs.1
     exact (lt_irrefl _ (h'x.trans_le (ht.2 hx))).elim
   have B : ∀ x, x ∈ s ∪ t → c ≤ x → x ∈ t :=
     by
     intro x hx hxc
-    cases hx
-    swap
-    · exact hx
-    rcases eq_or_lt_of_le hxc with (rfl | h'x)
-    · exact ht.1
+    cases hx; swap; · exact hx
+    rcases eq_or_lt_of_le hxc with (rfl | h'x); · exact ht.1
     exact (lt_irrefl _ (h'x.trans_le (hs.2 hx))).elim
   intro x hx y hy hxy
   rcases lt_or_le x c with (hxc | hcx)
@@ -121,19 +116,14 @@ protected theorem MonotoneOn.union_right {s t : Set α} {c : α} (h₁ : Monoton
   have A : ∀ x, x ∈ s ∪ t → x ≤ c → x ∈ s :=
     by
     intro x hx hxc
-    cases hx
-    · exact hx
-    rcases eq_or_lt_of_le hxc with (rfl | h'x)
-    · exact hs.1
+    cases hx; · exact hx
+    rcases eq_or_lt_of_le hxc with (rfl | h'x); · exact hs.1
     exact (lt_irrefl _ (h'x.trans_le (ht.2 hx))).elim
   have B : ∀ x, x ∈ s ∪ t → c ≤ x → x ∈ t :=
     by
     intro x hx hxc
-    cases hx
-    swap
-    · exact hx
-    rcases eq_or_lt_of_le hxc with (rfl | h'x)
-    · exact ht.1
+    cases hx; swap; · exact hx
+    rcases eq_or_lt_of_le hxc with (rfl | h'x); · exact ht.1
     exact (lt_irrefl _ (h'x.trans_le (hs.2 hx))).elim
   intro x hx y hy hxy
   rcases lt_or_le x c with (hxc | hcx)

Changes in mathlib4

mathlib3
mathlib4
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.

Diff
@@ -19,7 +19,7 @@ set.
 
 open Set
 
-variable {α β : Type _} [LinearOrder α] [Preorder β] {a : α} {f : α → β}
+variable {α β : Type*} [LinearOrder α] [Preorder β] {a : α} {f : α → β}
 
 /-- If `f` is strictly monotone both on `s` and `t`, with `s` to the left of `t` and the center
 point belonging to both `s` and `t`, then `f` is strictly monotone on `s ∪ t` -/
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

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

Diff
@@ -2,14 +2,11 @@
 Copyright (c) 2022 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module order.monotone.union
-! leanprover-community/mathlib commit d012cd09a9b256d870751284dd6a29882b0be105
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Order.Bounds.Basic
 
+#align_import order.monotone.union from "leanprover-community/mathlib"@"d012cd09a9b256d870751284dd6a29882b0be105"
+
 /-!
 # Monotonicity on intervals
 
feat port: Order.Monotone.Union (#1083)

d012cd09

Dependencies 43

44 files ported (100.0%)
24895 lines ported (100.0%)

All dependencies are ported!