PR contents

(last sync)

refactor(tactic/wlog): simplify and speed up wlog (#16495)

Benefits:

The tactic is faster
The tactic is easier to port to Lean 4

Downside:

The tactic doesn't do any heavy-lifting for the user

Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/wlog/near/296996966

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

Diff

@@ -165,8 +165,8 @@ begin
   rcases mem_Union₂.1 hx₁ with ⟨a, has, ha⟩, clear hx₁,
   rcases mem_Union₂.1 hx₂ with ⟨b, hbt, hb⟩, clear hx₂,
   rw [mem_ord_connected_component, subset_inter_iff] at ha hb,
-  wlog hab : a ≤ b := le_total a b using [a b s t, b a t s] tactic.skip,
-  rotate, from λ h₁ h₂ h₃ h₄, this h₂ h₁ h₄ h₃,
+  wlog hab : a ≤ b,
+  { exact this b hbt a has ha hb (le_of_not_le hab) },
   cases ha with ha ha', cases hb with hb hb',
   have hsub : [a, b] ⊆ (ord_separating_set s t).ord_connected_sectionᶜ,
   { rw [ord_separating_set_comm, uIcc_comm] at hb',

Zulip: https://leanprover.zulipchat.com/#narrow/stream/116395-maths/topic/Set.20intervals.20names

chore(data/set/intervals/unordered_interval): Rename to uIcc/uIoc (#18104)

Rename

set.interval → set.uIcc
set.interval_oc → set.uIoc
finset.interval→ finset.uIcc

Closes #17982

Diff

@@ -13,7 +13,7 @@ import tactic.wlog
 > Any changes to this file require a corresponding PR to mathlib4.
 
 In this file we define `set.ord_connected_component s x` to be the set of `y` such that
-`set.interval x y ⊆ s` and prove some basic facts about this definition. At the moment of writing,
+`set.uIcc x y ⊆ s` and prove some basic facts about this definition. At the moment of writing,
 this construction is used only to prove that any linear order with order topology is a T₅ space,
 so we only add API needed for this lemma.
 -/
@@ -26,7 +26,7 @@ namespace set
 variables {α : Type*} [linear_order α] {s t : set α} {x y z : α}
 
 /-- Order-connected component of a point `x` in a set `s`. It is defined as the set of `y` such that
-`set.interval x y ⊆ s`. Note that it is empty if and only if `x ∉ s`. -/
+`set.uIcc x y ⊆ s`. Note that it is empty if and only if `x ∉ s`. -/
 def ord_connected_component (s : set α) (x : α) : set α := {y | [x, y] ⊆ s}
 
 lemma mem_ord_connected_component : y ∈ ord_connected_component s x ↔ [x, y] ⊆ s := iff.rfl
@@ -34,20 +34,19 @@ lemma mem_ord_connected_component : y ∈ ord_connected_component s x ↔ [x, y]
 lemma dual_ord_connected_component :
   ord_connected_component (of_dual ⁻¹' s) (to_dual x) = of_dual ⁻¹' (ord_connected_component s x) :=
 ext $ to_dual.surjective.forall.2 $ λ x,
-  by { rw [mem_ord_connected_component, dual_interval], refl }
+  by { rw [mem_ord_connected_component, dual_uIcc], refl }
 
-lemma ord_connected_component_subset : ord_connected_component s x ⊆ s :=
-λ y hy, hy right_mem_interval
+lemma ord_connected_component_subset : ord_connected_component s x ⊆ s := λ y hy, hy right_mem_uIcc
 
 lemma subset_ord_connected_component {t} [h : ord_connected s] (hs : x ∈ s) (ht : s ⊆ t) :
   s ⊆ ord_connected_component t x :=
-λ y hy, (h.interval_subset hs hy).trans ht
+λ y hy, (h.uIcc_subset hs hy).trans ht
 
 @[simp] lemma self_mem_ord_connected_component : x ∈ ord_connected_component s x ↔ x ∈ s :=
-by rw [mem_ord_connected_component, interval_self, singleton_subset_iff]
+by rw [mem_ord_connected_component, uIcc_self, singleton_subset_iff]
 
 @[simp] lemma nonempty_ord_connected_component : (ord_connected_component s x).nonempty ↔ x ∈ s :=
-⟨λ ⟨y, hy⟩, hy $ left_mem_interval, λ h, ⟨x, self_mem_ord_connected_component.2 h⟩⟩
+⟨λ ⟨y, hy⟩, hy $ left_mem_uIcc, λ h, ⟨x, self_mem_ord_connected_component.2 h⟩⟩
 
 @[simp] lemma ord_connected_component_eq_empty : ord_connected_component s x = ∅ ↔ x ∉ s :=
 by rw [← not_nonempty_iff_eq_empty, nonempty_ord_connected_component]
@@ -64,11 +63,11 @@ by simp [ord_connected_component, set_of_and]
 
 lemma mem_ord_connected_component_comm :
   y ∈ ord_connected_component s x ↔ x ∈ ord_connected_component s y :=
-by rw [mem_ord_connected_component, mem_ord_connected_component, interval_swap]
+by rw [mem_ord_connected_component, mem_ord_connected_component, uIcc_comm]
 
 lemma mem_ord_connected_component_trans (hxy : y ∈ ord_connected_component s x)
   (hyz : z ∈ ord_connected_component s y) : z ∈ ord_connected_component s x :=
-calc [x, z] ⊆ [x, y] ∪ [y, z] : interval_subset_interval_union_interval
+calc [x, z] ⊆ [x, y] ∪ [y, z] : uIcc_subset_uIcc_union_uIcc
 ... ⊆ s : union_subset hxy hyz
 
 lemma ord_connected_component_eq (h : [x, y] ⊆ s) :
@@ -77,7 +76,7 @@ ext $ λ z, ⟨mem_ord_connected_component_trans (mem_ord_connected_component_co
   mem_ord_connected_component_trans h⟩
 
 instance : ord_connected (ord_connected_component s x) :=
-ord_connected_of_interval_subset_left $ λ y hy z hz, (interval_subset_interval_left hz).trans hy
+ord_connected_of_uIcc_subset_left $ λ y hy z hz, (uIcc_subset_uIcc_left hz).trans hy
 
 /-- Projection from `s : set α` to `α` sending each order connected component of `s` to a single
 point of this component. -/
@@ -123,7 +122,7 @@ end
 lemma ord_connected_section_subset : ord_connected_section s ⊆ s :=
 range_subset_iff.2 $ λ x, ord_connected_component_subset $ nonempty.some_mem _
 
-lemma eq_of_mem_ord_connected_section_of_interval_subset (hx : x ∈ ord_connected_section s)
+lemma eq_of_mem_ord_connected_section_of_uIcc_subset (hx : x ∈ ord_connected_section s)
   (hy : y ∈ ord_connected_section s) (h : [x, y] ⊆ s) : x = y :=
 begin
   rcases hx with ⟨x, rfl⟩, rcases hy with ⟨y, rfl⟩,
@@ -170,25 +169,25 @@ begin
   rotate, from λ h₁ h₂ h₃ h₄, this h₂ h₁ h₄ h₃,
   cases ha with ha ha', cases hb with hb hb',
   have hsub : [a, b] ⊆ (ord_separating_set s t).ord_connected_sectionᶜ,
-  { rw [ord_separating_set_comm, interval_swap] at hb',
-    calc [a, b] ⊆ [a, x] ∪ [x, b] : interval_subset_interval_union_interval
+  { rw [ord_separating_set_comm, uIcc_comm] at hb',
+    calc [a, b] ⊆ [a, x] ∪ [x, b] : uIcc_subset_uIcc_union_uIcc
     ... ⊆ (ord_separating_set s t).ord_connected_sectionᶜ : union_subset ha' hb' },
   clear ha' hb',
   cases le_total x a with hxa hax,
-  { exact hb (Icc_subset_interval' ⟨hxa, hab⟩) has },
+  { exact hb (Icc_subset_uIcc' ⟨hxa, hab⟩) has },
   cases le_total b x with hbx hxb,
-  { exact ha (Icc_subset_interval ⟨hab, hbx⟩) hbt },
+  { exact ha (Icc_subset_uIcc ⟨hab, hbx⟩) hbt },
   have : x ∈ ord_separating_set s t,
   { exact ⟨mem_Union₂.2 ⟨a, has, ha⟩, mem_Union₂.2 ⟨b, hbt, hb⟩⟩ },
   lift x to ord_separating_set s t using this,
   suffices : ord_connected_component (ord_separating_set s t) x ⊆ [a, b],
     from hsub (this $ ord_connected_proj_mem_ord_connected_component _ _) (mem_range_self _),
   rintros y (hy : [↑x, y] ⊆ ord_separating_set s t),
-  rw [interval_of_le hab, mem_Icc, ← not_lt, ← not_lt],
+  rw [uIcc_of_le hab, mem_Icc, ← not_lt, ← not_lt],
   exact ⟨λ hya, disjoint_left.1 disjoint_left_ord_separating_set has
-    (hy $ Icc_subset_interval' ⟨hya.le, hax⟩),
+    (hy $ Icc_subset_uIcc' ⟨hya.le, hax⟩),
     λ hyb, disjoint_left.1 disjoint_right_ord_separating_set hbt
-      (hy $ Icc_subset_interval ⟨hxb, hyb.le⟩)⟩
+      (hy $ Icc_subset_uIcc ⟨hxb, hyb.le⟩)⟩
 end
 
 end set

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-26-08

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

ab3b6a0f

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
 -/
-import Data.Set.Intervals.OrdConnected
+import Order.Interval.Set.OrdConnected
 import Tactic.Wlog
 
 #align_import data.set.intervals.ord_connected_component from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -266,13 +266,13 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) :=
   rintro x ⟨hx₁, hx₂⟩
   rcases mem_Union₂.1 hx₁ with ⟨a, has, ha⟩; clear hx₁
   rcases mem_Union₂.1 hx₂ with ⟨b, hbt, hb⟩; clear hx₂
-  rw [mem_ord_connected_component, subset_inter_iff] at ha hb 
+  rw [mem_ord_connected_component, subset_inter_iff] at ha hb
   wlog hab : a ≤ b
   · exact this b hbt a has ha hb (le_of_not_le hab)
   cases' ha with ha ha'; cases' hb with hb hb'
   have hsub : [a, b] ⊆ (ord_separating_set s t).ordConnectedSectionᶜ :=
     by
-    rw [ord_separating_set_comm, uIcc_comm] at hb' 
+    rw [ord_separating_set_comm, uIcc_comm] at hb'
     calc
       [a, b] ⊆ [a, x] ∪ [x, b] := uIcc_subset_uIcc_union_uIcc
       _ ⊆ (ord_separating_set s t).ordConnectedSectionᶜ := union_subset ha' hb'

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -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.Data.Set.Intervals.OrdConnected
-import Mathbin.Tactic.Wlog
+import Data.Set.Intervals.OrdConnected
+import Tactic.Wlog
 
 #align_import data.set.intervals.ord_connected_component from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -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 data.set.intervals.ord_connected_component
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.Intervals.OrdConnected
 import Mathbin.Tactic.Wlog
 
+#align_import data.set.intervals.ord_connected_component from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"
+
 /-!
 # Order connected components of a set

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -100,10 +100,12 @@ theorem ordConnectedComponent_univ : ordConnectedComponent univ x = univ := by
 #align set.ord_connected_component_univ Set.ordConnectedComponent_univ
 -/
 
+#print Set.ordConnectedComponent_inter /-
 theorem ordConnectedComponent_inter (s t : Set α) (x : α) :
     ordConnectedComponent (s ∩ t) x = ordConnectedComponent s x ∩ ordConnectedComponent t x := by
   simp [ord_connected_component, set_of_and]
 #align set.ord_connected_component_inter Set.ordConnectedComponent_inter
+-/
 
 #print Set.mem_ordConnectedComponent_comm /-
 theorem mem_ordConnectedComponent_comm :
@@ -231,15 +233,19 @@ theorem ordSeparatingSet_comm (s t : Set α) : ordSeparatingSet s t = ordSeparat
 #align set.ord_separating_set_comm Set.ordSeparatingSet_comm
 -/
 
+#print Set.disjoint_left_ordSeparatingSet /-
 theorem disjoint_left_ordSeparatingSet : Disjoint s (ordSeparatingSet s t) :=
   Disjoint.inter_right' _ <|
     disjoint_iUnion₂_right.2 fun x hx =>
       disjoint_compl_right.mono_right <| ordConnectedComponent_subset
 #align set.disjoint_left_ord_separating_set Set.disjoint_left_ordSeparatingSet
+-/
 
+#print Set.disjoint_right_ordSeparatingSet /-
 theorem disjoint_right_ordSeparatingSet : Disjoint t (ordSeparatingSet s t) :=
   ordSeparatingSet_comm t s ▸ disjoint_left_ordSeparatingSet
 #align set.disjoint_right_ord_separating_set Set.disjoint_right_ordSeparatingSet
+-/
 
 #print Set.dual_ordSeparatingSet /-
 theorem dual_ordSeparatingSet :
@@ -256,6 +262,7 @@ def ordT5Nhd (s t : Set α) : Set α :=
 #align set.ord_t5_nhd Set.ordT5Nhd
 -/
 
+#print Set.disjoint_ordT5Nhd /-
 theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) :=
   by
   rw [disjoint_iff_inf_le]
@@ -289,6 +296,7 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) :=
       fun hyb =>
       disjoint_left.1 disjoint_right_ord_separating_set hbt (hy <| Icc_subset_uIcc ⟨hxb, hyb.le⟩)⟩
 #align set.disjoint_ord_t5_nhd Set.disjoint_ordT5Nhd
+-/
 
 end Set

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -118,7 +118,6 @@ theorem mem_ordConnectedComponent_trans (hxy : y ∈ ordConnectedComponent s x)
   calc
     [x, z] ⊆ [x, y] ∪ [y, z] := uIcc_subset_uIcc_union_uIcc
     _ ⊆ s := union_subset hxy hyz
-    
 #align set.mem_ord_connected_component_trans Set.mem_ordConnectedComponent_trans
 -/
 
@@ -273,7 +272,6 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) :=
     calc
       [a, b] ⊆ [a, x] ∪ [x, b] := uIcc_subset_uIcc_union_uIcc
       _ ⊆ (ord_separating_set s t).ordConnectedSectionᶜ := union_subset ha' hb'
-      
   clear ha' hb'
   cases' le_total x a with hxa hax
   · exact hb (Icc_subset_uIcc' ⟨hxa, hab⟩) has

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -36,7 +36,7 @@ variable {α : Type _} [LinearOrder α] {s t : Set α} {x y z : α}
 /-- Order-connected component of a point `x` in a set `s`. It is defined as the set of `y` such that
 `set.uIcc x y ⊆ s`. Note that it is empty if and only if `x ∉ s`. -/
 def ordConnectedComponent (s : Set α) (x : α) : Set α :=
-  { y | [x, y] ⊆ s }
+  {y | [x, y] ⊆ s}
 #align set.ord_connected_component Set.ordConnectedComponent
 -/

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -263,13 +263,13 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) :=
   rintro x ⟨hx₁, hx₂⟩
   rcases mem_Union₂.1 hx₁ with ⟨a, has, ha⟩; clear hx₁
   rcases mem_Union₂.1 hx₂ with ⟨b, hbt, hb⟩; clear hx₂
-  rw [mem_ord_connected_component, subset_inter_iff] at ha hb
+  rw [mem_ord_connected_component, subset_inter_iff] at ha hb 
   wlog hab : a ≤ b
   · exact this b hbt a has ha hb (le_of_not_le hab)
   cases' ha with ha ha'; cases' hb with hb hb'
   have hsub : [a, b] ⊆ (ord_separating_set s t).ordConnectedSectionᶜ :=
     by
-    rw [ord_separating_set_comm, uIcc_comm] at hb'
+    rw [ord_separating_set_comm, uIcc_comm] at hb' 
     calc
       [a, b] ⊆ [a, x] ∪ [x, b] := uIcc_subset_uIcc_union_uIcc
       _ ⊆ (ord_separating_set s t).ordConnectedSectionᶜ := union_subset ha' hb'

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -26,7 +26,7 @@ so we only add API needed for this lemma.
 
 open Function OrderDual
 
-open Interval
+open scoped Interval
 
 namespace Set

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -100,12 +100,6 @@ theorem ordConnectedComponent_univ : ordConnectedComponent univ x = univ := by
 #align set.ord_connected_component_univ Set.ordConnectedComponent_univ
 -/
 
-/- warning: set.ord_connected_component_inter -> Set.ordConnectedComponent_inter is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α) (x : α), Eq.{succ u1} (Set.{u1} α) (Set.ordConnectedComponent.{u1} α _inst_1 (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t) x) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (Set.ordConnectedComponent.{u1} α _inst_1 s x) (Set.ordConnectedComponent.{u1} α _inst_1 t x))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] (s : Set.{u1} α) (t : Set.{u1} α) (x : α), Eq.{succ u1} (Set.{u1} α) (Set.ordConnectedComponent.{u1} α _inst_1 (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t) x) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (Set.ordConnectedComponent.{u1} α _inst_1 s x) (Set.ordConnectedComponent.{u1} α _inst_1 t x))
-Case conversion may be inaccurate. Consider using '#align set.ord_connected_component_inter Set.ordConnectedComponent_interₓ'. -/
 theorem ordConnectedComponent_inter (s t : Set α) (x : α) :
     ordConnectedComponent (s ∩ t) x = ordConnectedComponent s x ∩ ordConnectedComponent t x := by
   simp [ord_connected_component, set_of_and]
@@ -238,24 +232,12 @@ theorem ordSeparatingSet_comm (s t : Set α) : ordSeparatingSet s t = ordSeparat
 #align set.ord_separating_set_comm Set.ordSeparatingSet_comm
 -/
 
-/- warning: set.disjoint_left_ord_separating_set -> Set.disjoint_left_ordSeparatingSet is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, 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))) s (Set.ordSeparatingSet.{u1} α _inst_1 s t)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, 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)))))) s (Set.ordSeparatingSet.{u1} α _inst_1 s t)
-Case conversion may be inaccurate. Consider using '#align set.disjoint_left_ord_separating_set Set.disjoint_left_ordSeparatingSetₓ'. -/
 theorem disjoint_left_ordSeparatingSet : Disjoint s (ordSeparatingSet s t) :=
   Disjoint.inter_right' _ <|
     disjoint_iUnion₂_right.2 fun x hx =>
       disjoint_compl_right.mono_right <| ordConnectedComponent_subset
 #align set.disjoint_left_ord_separating_set Set.disjoint_left_ordSeparatingSet
 
-/- warning: set.disjoint_right_ord_separating_set -> Set.disjoint_right_ordSeparatingSet is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, 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))) t (Set.ordSeparatingSet.{u1} α _inst_1 s t)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, 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)))))) t (Set.ordSeparatingSet.{u1} α _inst_1 s t)
-Case conversion may be inaccurate. Consider using '#align set.disjoint_right_ord_separating_set Set.disjoint_right_ordSeparatingSetₓ'. -/
 theorem disjoint_right_ordSeparatingSet : Disjoint t (ordSeparatingSet s t) :=
   ordSeparatingSet_comm t s ▸ disjoint_left_ordSeparatingSet
 #align set.disjoint_right_ord_separating_set Set.disjoint_right_ordSeparatingSet
@@ -275,12 +257,6 @@ def ordT5Nhd (s t : Set α) : Set α :=
 #align set.ord_t5_nhd Set.ordT5Nhd
 -/
 
-/- warning: set.disjoint_ord_t5_nhd -> Set.disjoint_ordT5Nhd is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, 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))) (Set.ordT5Nhd.{u1} α _inst_1 s t) (Set.ordT5Nhd.{u1} α _inst_1 t s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : LinearOrder.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, 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)))))) (Set.ordT5Nhd.{u1} α _inst_1 s t) (Set.ordT5Nhd.{u1} α _inst_1 t s)
-Case conversion may be inaccurate. Consider using '#align set.disjoint_ord_t5_nhd Set.disjoint_ordT5Nhdₓ'. -/
 theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) :=
   by
   rw [disjoint_iff_inf_le]

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -49,11 +49,7 @@ theorem mem_ordConnectedComponent : y ∈ ordConnectedComponent s x ↔ [x, y] 
 #print Set.dual_ordConnectedComponent /-
 theorem dual_ordConnectedComponent :
     ordConnectedComponent (ofDual ⁻¹' s) (toDual x) = ofDual ⁻¹' ordConnectedComponent s x :=
-  ext <|
-    toDual.Surjective.forall.2 fun x =>
-      by
-      rw [mem_ord_connected_component, dual_uIcc]
-      rfl
+  ext <| toDual.Surjective.forall.2 fun x => by rw [mem_ord_connected_component, dual_uIcc]; rfl
 #align set.dual_ord_connected_component Set.dual_ordConnectedComponent
 -/
 
@@ -289,15 +285,12 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) :=
   by
   rw [disjoint_iff_inf_le]
   rintro x ⟨hx₁, hx₂⟩
-  rcases mem_Union₂.1 hx₁ with ⟨a, has, ha⟩
-  clear hx₁
-  rcases mem_Union₂.1 hx₂ with ⟨b, hbt, hb⟩
-  clear hx₂
+  rcases mem_Union₂.1 hx₁ with ⟨a, has, ha⟩; clear hx₁
+  rcases mem_Union₂.1 hx₂ with ⟨b, hbt, hb⟩; clear hx₂
   rw [mem_ord_connected_component, subset_inter_iff] at ha hb
   wlog hab : a ≤ b
   · exact this b hbt a has ha hb (le_of_not_le hab)
-  cases' ha with ha ha'
-  cases' hb with hb hb'
+  cases' ha with ha ha'; cases' hb with hb hb'
   have hsub : [a, b] ⊆ (ord_separating_set s t).ordConnectedSectionᶜ :=
     by
     rw [ord_separating_set_comm, uIcc_comm] at hb'

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -250,7 +250,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align set.disjoint_left_ord_separating_set Set.disjoint_left_ordSeparatingSetₓ'. -/
 theorem disjoint_left_ordSeparatingSet : Disjoint s (ordSeparatingSet s t) :=
   Disjoint.inter_right' _ <|
-    disjoint_unionᵢ₂_right.2 fun x hx =>
+    disjoint_iUnion₂_right.2 fun x hx =>
       disjoint_compl_right.mono_right <| ordConnectedComponent_subset
 #align set.disjoint_left_ord_separating_set Set.disjoint_left_ordSeparatingSet

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: Move intervals (#11765)

Move Set.Ixx, Finset.Ixx, Multiset.Ixx together under two different folders:

Order.Interval for their definition and basic properties
Algebra.Order.Interval for their algebraic properties

Move 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.

c7fa7063

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
 -/
-import Mathlib.Data.Set.Intervals.OrdConnected
+import Mathlib.Order.Interval.Set.OrdConnected
 import Mathlib.Data.Set.Lattice
 
 #align_import data.set.intervals.ord_connected_component from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"

chore(Data/Set/Intervals/OrdConnectedComponent): resolve porting note about lift not being … (#12102)

…implemented

By now, it has been implemented; use it.

c411fe2e

Diff

@@ -219,11 +219,10 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) := by
   rcases le_total b x with hbx | hxb
   · exact ha (Icc_subset_uIcc ⟨hab, hbx⟩) hbt
   have h' : x ∈ ordSeparatingSet s t := ⟨mem_iUnion₂.2 ⟨a, has, ha⟩, mem_iUnion₂.2 ⟨b, hbt, hb⟩⟩
-  -- Porting note: lift not implemented yet
-  -- lift x to ordSeparatingSet s t using this
+  lift x to ordSeparatingSet s t using h'
   suffices ordConnectedComponent (ordSeparatingSet s t) x ⊆ [[a, b]] from
-    hsub (this <| ordConnectedProj_mem_ordConnectedComponent _ ⟨x, h'⟩) (mem_range_self _)
-  rintro y (hy : [[x, y]] ⊆ ordSeparatingSet s t)
+    hsub (this <| ordConnectedProj_mem_ordConnectedComponent _ x) (mem_range_self _)
+  rintro y hy
   rw [uIcc_of_le hab, mem_Icc, ← not_lt, ← not_lt]
   have sol1 := fun (hya : y < a) =>
       (disjoint_left (t := ordSeparatingSet s t)).1 disjoint_left_ordSeparatingSet has

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -219,7 +219,7 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) := by
   rcases le_total b x with hbx | hxb
   · exact ha (Icc_subset_uIcc ⟨hab, hbx⟩) hbt
   have h' : x ∈ ordSeparatingSet s t := ⟨mem_iUnion₂.2 ⟨a, has, ha⟩, mem_iUnion₂.2 ⟨b, hbt, hb⟩⟩
-  -- porting note: lift not implemented yet
+  -- Porting note: lift not implemented yet
   -- lift x to ordSeparatingSet s t using this
   suffices ordConnectedComponent (ordSeparatingSet s t) x ⊆ [[a, b]] from
     hsub (this <| ordConnectedProj_mem_ordConnectedComponent _ ⟨x, h'⟩) (mem_range_self _)

chore(Order/*): move SupSet, Set.sUnion etc to a new file (#10232)

d18f1d0b

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
 import Mathlib.Data.Set.Intervals.OrdConnected
+import Mathlib.Data.Set.Lattice
 
 #align_import data.set.intervals.ord_connected_component from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"

chore: address wlog porting note in OrdConnectedComponent (#9183)

Data.Set.Intervals.OrdConnectedComponent was ported in #1303 and wlog was added later in #2144.

Before this change, trace.profiler reports that elaborating this proof takes 0.13 seconds. After this change, it reports 0.10 seconds.

760ba709

Diff

@@ -203,35 +203,32 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) := by
   rcases mem_iUnion₂.1 hx₂ with ⟨b, hbt, hb⟩
   clear hx₂
   rw [mem_ordConnectedComponent, subset_inter_iff] at ha hb
-  rcases le_total a b with hab | hab
-  on_goal 2 => swap_var a ↔ b, s ↔ t, ha ↔ hb, has ↔ hbt
-  all_goals
--- porting note: wlog not implemented yet, the following replaces the three previous lines
--- wlog (discharger := tactic.skip) hab : a ≤ b := le_total a b using a b s t, b a t s
-    cases' ha with ha ha'
-    cases' hb with hb hb'
-    have hsub : [[a, b]] ⊆ (ordSeparatingSet s t).ordConnectedSectionᶜ := by
-      rw [ordSeparatingSet_comm, uIcc_comm] at hb'
-      calc
-        [[a, b]] ⊆ [[a, x]] ∪ [[x, b]] := uIcc_subset_uIcc_union_uIcc
-        _ ⊆ (ordSeparatingSet s t).ordConnectedSectionᶜ := union_subset ha' hb'
-    clear ha' hb'
-    rcases le_total x a with hxa | hax
-    · exact hb (Icc_subset_uIcc' ⟨hxa, hab⟩) has
-    rcases le_total b x with hbx | hxb
-    · exact ha (Icc_subset_uIcc ⟨hab, hbx⟩) hbt
-    have h' : x ∈ ordSeparatingSet s t := ⟨mem_iUnion₂.2 ⟨a, has, ha⟩, mem_iUnion₂.2 ⟨b, hbt, hb⟩⟩
-    -- porting note: lift not implemented yet
-    -- lift x to ordSeparatingSet s t using this
-    suffices ordConnectedComponent (ordSeparatingSet s t) x ⊆ [[a, b]] from
-      hsub (this <| ordConnectedProj_mem_ordConnectedComponent _ ⟨x, h'⟩) (mem_range_self _)
-    rintro y (hy : [[x, y]] ⊆ ordSeparatingSet s t)
-    rw [uIcc_of_le hab, mem_Icc, ← not_lt, ← not_lt]
-    have sol1 := fun (hya : y < a) =>
-        (disjoint_left (t := ordSeparatingSet s t)).1 disjoint_left_ordSeparatingSet has
-          (hy <| Icc_subset_uIcc' ⟨hya.le, hax⟩)
-    have sol2 := fun (hby : b < y) =>
-        (disjoint_left (t := ordSeparatingSet s t)).1 disjoint_right_ordSeparatingSet hbt
-          (hy <| Icc_subset_uIcc ⟨hxb, hby.le⟩)
-    exact ⟨sol1, sol2⟩
+  wlog hab : a ≤ b with H
+  · exact H (x := x) (y := y) (z := z) b hbt hb a has ha (le_of_not_le hab)
+  cases' ha with ha ha'
+  cases' hb with hb hb'
+  have hsub : [[a, b]] ⊆ (ordSeparatingSet s t).ordConnectedSectionᶜ := by
+    rw [ordSeparatingSet_comm, uIcc_comm] at hb'
+    calc
+      [[a, b]] ⊆ [[a, x]] ∪ [[x, b]] := uIcc_subset_uIcc_union_uIcc
+      _ ⊆ (ordSeparatingSet s t).ordConnectedSectionᶜ := union_subset ha' hb'
+  clear ha' hb'
+  rcases le_total x a with hxa | hax
+  · exact hb (Icc_subset_uIcc' ⟨hxa, hab⟩) has
+  rcases le_total b x with hbx | hxb
+  · exact ha (Icc_subset_uIcc ⟨hab, hbx⟩) hbt
+  have h' : x ∈ ordSeparatingSet s t := ⟨mem_iUnion₂.2 ⟨a, has, ha⟩, mem_iUnion₂.2 ⟨b, hbt, hb⟩⟩
+  -- porting note: lift not implemented yet
+  -- lift x to ordSeparatingSet s t using this
+  suffices ordConnectedComponent (ordSeparatingSet s t) x ⊆ [[a, b]] from
+    hsub (this <| ordConnectedProj_mem_ordConnectedComponent _ ⟨x, h'⟩) (mem_range_self _)
+  rintro y (hy : [[x, y]] ⊆ ordSeparatingSet s t)
+  rw [uIcc_of_le hab, mem_Icc, ← not_lt, ← not_lt]
+  have sol1 := fun (hya : y < a) =>
+      (disjoint_left (t := ordSeparatingSet s t)).1 disjoint_left_ordSeparatingSet has
+        (hy <| Icc_subset_uIcc' ⟨hya.le, hax⟩)
+  have sol2 := fun (hby : b < y) =>
+      (disjoint_left (t := ordSeparatingSet s t)).1 disjoint_right_ordSeparatingSet hbt
+        (hy <| Icc_subset_uIcc ⟨hxb, hby.le⟩)
+  exact ⟨sol1, sol2⟩
 #align set.disjoint_ord_t5_nhd Set.disjoint_ordT5Nhd

chore: remove uses of cases' (#9171)

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

3fca282c

Diff

@@ -203,7 +203,7 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) := by
   rcases mem_iUnion₂.1 hx₂ with ⟨b, hbt, hb⟩
   clear hx₂
   rw [mem_ordConnectedComponent, subset_inter_iff] at ha hb
-  cases' le_total a b with hab hab
+  rcases le_total a b with hab | hab
   on_goal 2 => swap_var a ↔ b, s ↔ t, ha ↔ hb, has ↔ hbt
   all_goals
 -- porting note: wlog not implemented yet, the following replaces the three previous lines
@@ -216,9 +216,9 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) := by
         [[a, b]] ⊆ [[a, x]] ∪ [[x, b]] := uIcc_subset_uIcc_union_uIcc
         _ ⊆ (ordSeparatingSet s t).ordConnectedSectionᶜ := union_subset ha' hb'
     clear ha' hb'
-    cases' le_total x a with hxa hax
+    rcases le_total x a with hxa | hax
     · exact hb (Icc_subset_uIcc' ⟨hxa, hab⟩) has
-    cases' le_total b x with hbx hxb
+    rcases le_total b x with hbx | hxb
     · exact ha (Icc_subset_uIcc ⟨hab, hbx⟩) hbt
     have h' : x ∈ ordSeparatingSet s t := ⟨mem_iUnion₂.2 ⟨a, has, ha⟩, mem_iUnion₂.2 ⟨b, hbt, hb⟩⟩
     -- porting note: lift not implemented yet

chore: bump to v4.3.0-rc2 (#8366)

PR contents

This is the supremum of

#8284
#8056
#8023
#8332
#8226 (already approved)
#7834 (already approved)

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.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

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).

leanprover/lean4#2722

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}).

leanprover/lean4#2783

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:

switching to using explicit lemmas that have the intended level of application
(config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
Using @[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>

40b64f79

Diff

@@ -140,7 +140,8 @@ def ordConnectedSection (s : Set α) : Set α :=
 
 theorem dual_ordConnectedSection (s : Set α) :
     ordConnectedSection (ofDual ⁻¹' s) = ofDual ⁻¹' ordConnectedSection s := by
-  simp_rw [ordConnectedSection, ordConnectedProj]
+  simp only [ordConnectedSection]
+  simp (config := { unfoldPartialApp := true }) only [ordConnectedProj]
   ext x
   simp only [mem_range, Subtype.exists, mem_preimage, OrderDual.exists, dual_ordConnectedComponent,
     ofDual_toDual]

chore: remove nonterminal simp (#7580)

Removes nonterminal simps on lines looking like simp [...]

6fc8e6ec

Diff

@@ -142,7 +142,8 @@ theorem dual_ordConnectedSection (s : Set α) :
     ordConnectedSection (ofDual ⁻¹' s) = ofDual ⁻¹' ordConnectedSection s := by
   simp_rw [ordConnectedSection, ordConnectedProj]
   ext x
-  simp [dual_ordConnectedComponent]
+  simp only [mem_range, Subtype.exists, mem_preimage, OrderDual.exists, dual_ordConnectedComponent,
+    ofDual_toDual]
   tauto
 #align set.dual_ord_connected_section Set.dual_ordConnectedSection

chore: avoid lean3 style have/suffices (#6964)

Many proofs use the "stream of consciousness" style from Lean 3, rather than have ... := or suffices ... from/by.

This PR updates a fraction of these to the preferred Lean 4 style.

I think a good goal would be to delete the "deferred" versions of have, suffices, and let at the bottom of Mathlib.Tactic.Have

(Anyone who would like to contribute more cleanup is welcome to push directly to this branch.)

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

bdc47f68

Diff

@@ -221,8 +221,8 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) := by
     have h' : x ∈ ordSeparatingSet s t := ⟨mem_iUnion₂.2 ⟨a, has, ha⟩, mem_iUnion₂.2 ⟨b, hbt, hb⟩⟩
     -- porting note: lift not implemented yet
     -- lift x to ordSeparatingSet s t using this
-    suffices : ordConnectedComponent (ordSeparatingSet s t) x ⊆ [[a, b]]
-    exact hsub (this <| ordConnectedProj_mem_ordConnectedComponent _ ⟨x, h'⟩) (mem_range_self _)
+    suffices ordConnectedComponent (ordSeparatingSet s t) x ⊆ [[a, b]] from
+      hsub (this <| ordConnectedProj_mem_ordConnectedComponent _ ⟨x, h'⟩) (mem_range_self _)
     rintro y (hy : [[x, y]] ⊆ ordSeparatingSet s t)
     rw [uIcc_of_le hab, mem_Icc, ← not_lt, ← not_lt]
     have sol1 := fun (hya : y < a) =>

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

@@ -21,7 +21,7 @@ open Interval Function OrderDual
 
 namespace Set
 
-variable {α : Type _} [LinearOrder α] {s t : Set α} {x y z : α}
+variable {α : Type*} [LinearOrder α] {s t : Set α} {x y z : α}
 
 /-- Order-connected component of a point `x` in a set `s`. It is defined as the set of `y` such that
 `Set.uIcc x y ⊆ s`. Note that it is empty if and only if `x ∉ s`. -/

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 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 data.set.intervals.ord_connected_component
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Set.Intervals.OrdConnected
 
+#align_import data.set.intervals.ord_connected_component from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"
+
 /-!
 # Order connected components of a set

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

@@ -32,7 +32,7 @@ def ordConnectedComponent (s : Set α) (x : α) : Set α :=
   { y | [[x, y]] ⊆ s }
 #align set.ord_connected_component Set.ordConnectedComponent
 
-theorem mem_ordConnectedComponent : y ∈ ordConnectedComponent s x ↔  [[x, y]] ⊆ s :=
+theorem mem_ordConnectedComponent : y ∈ ordConnectedComponent s x ↔ [[x, y]] ⊆ s :=
   Iff.rfl
 #align set.mem_ord_connected_component Set.mem_ordConnectedComponent

fix: change compl precedence (#5586)

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

4d4f0f25

Diff

@@ -168,7 +168,7 @@ belong both to some `Set.ordConnectedComponent tᶜ x`, `x ∈ s`, and to some
 `Set.ordConnectedComponent sᶜ x`, `x ∈ t`. In the case of two disjoint closed sets, this is the
 union of all open intervals $(a, b)$ such that their endpoints belong to different sets. -/
 def ordSeparatingSet (s t : Set α) : Set α :=
-  (⋃ x ∈ s, ordConnectedComponent (tᶜ) x) ∩ ⋃ x ∈ t, ordConnectedComponent (sᶜ) x
+  (⋃ x ∈ s, ordConnectedComponent tᶜ x) ∩ ⋃ x ∈ t, ordConnectedComponent sᶜ x
 #align set.ord_separating_set Set.ordSeparatingSet
 
 theorem ordSeparatingSet_comm (s t : Set α) : ordSeparatingSet s t = ordSeparatingSet t s :=

feat: add Mathlib.Tactic.Common, and import (#4056)

This makes a mathlib4 version of mathlib3's tactic.basic, now called Mathlib.Tactic.Common, which imports all tactics which do not have significant theory requirements, and then is imported all across the base of the hierarchy.

This ensures that all common tactics are available nearly everywhere in the library, rather than having to be imported one-by-one as you need them.

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

a4eaf1c4

Diff

@@ -9,7 +9,7 @@ Authors: Yury Kudryashov
 ! if you have ported upstream changes.
 -/
 import Mathlib.Data.Set.Intervals.OrdConnected
-import Mathlib.Tactic.SwapVar
+
 /-!
 # Order connected components of a set

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

@@ -177,7 +177,7 @@ theorem ordSeparatingSet_comm (s t : Set α) : ordSeparatingSet s t = ordSeparat
 
 theorem disjoint_left_ordSeparatingSet : Disjoint s (ordSeparatingSet s t) :=
   Disjoint.inter_right' _ <|
-    disjoint_unionᵢ₂_right.2 fun _ _ =>
+    disjoint_iUnion₂_right.2 fun _ _ =>
       disjoint_compl_right.mono_right <| ordConnectedComponent_subset
 #align set.disjoint_left_ord_separating_set Set.disjoint_left_ordSeparatingSet
 
@@ -187,8 +187,8 @@ theorem disjoint_right_ordSeparatingSet : Disjoint t (ordSeparatingSet s t) :=
 
 theorem dual_ordSeparatingSet :
     ordSeparatingSet (ofDual ⁻¹' s) (ofDual ⁻¹' t) = ofDual ⁻¹' ordSeparatingSet s t := by
-  simp only [ordSeparatingSet, mem_preimage, ← toDual.surjective.unionᵢ_comp, ofDual_toDual,
-    dual_ordConnectedComponent, ← preimage_compl, preimage_inter, preimage_unionᵢ]
+  simp only [ordSeparatingSet, mem_preimage, ← toDual.surjective.iUnion_comp, ofDual_toDual,
+    dual_ordConnectedComponent, ← preimage_compl, preimage_inter, preimage_iUnion]
 #align set.dual_ord_separating_set Set.dual_ordSeparatingSet
 
 /-- An auxiliary neighborhood that will be used in the proof of `OrderTopology.t5Space`. -/
@@ -199,9 +199,9 @@ def ordT5Nhd (s t : Set α) : Set α :=
 theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) := by
   rw [disjoint_iff_inf_le]
   rintro x ⟨hx₁, hx₂⟩
-  rcases mem_unionᵢ₂.1 hx₁ with ⟨a, has, ha⟩
+  rcases mem_iUnion₂.1 hx₁ with ⟨a, has, ha⟩
   clear hx₁
-  rcases mem_unionᵢ₂.1 hx₂ with ⟨b, hbt, hb⟩
+  rcases mem_iUnion₂.1 hx₂ with ⟨b, hbt, hb⟩
   clear hx₂
   rw [mem_ordConnectedComponent, subset_inter_iff] at ha hb
   cases' le_total a b with hab hab
@@ -221,7 +221,7 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) := by
     · exact hb (Icc_subset_uIcc' ⟨hxa, hab⟩) has
     cases' le_total b x with hbx hxb
     · exact ha (Icc_subset_uIcc ⟨hab, hbx⟩) hbt
-    have h' : x ∈ ordSeparatingSet s t := ⟨mem_unionᵢ₂.2 ⟨a, has, ha⟩, mem_unionᵢ₂.2 ⟨b, hbt, hb⟩⟩
+    have h' : x ∈ ordSeparatingSet s t := ⟨mem_iUnion₂.2 ⟨a, has, ha⟩, mem_iUnion₂.2 ⟨b, hbt, hb⟩⟩
     -- porting note: lift not implemented yet
     -- lift x to ordSeparatingSet s t using this
     suffices : ordConnectedComponent (ordSeparatingSet s t) x ⊆ [[a, b]]

chore: bye-bye, solo bys! (#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 bys".

14167e48

Diff

@@ -38,11 +38,9 @@ theorem mem_ordConnectedComponent : y ∈ ordConnectedComponent s x ↔  [[x, y]
 
 theorem dual_ordConnectedComponent :
     ordConnectedComponent (ofDual ⁻¹' s) (toDual x) = ofDual ⁻¹' ordConnectedComponent s x :=
-  ext <|
-      (Surjective.forall toDual.surjective).2 fun x =>
-      by
-      rw [mem_ordConnectedComponent, dual_uIcc]
-      rfl
+  ext <| (Surjective.forall toDual.surjective).2 fun x => by
+    rw [mem_ordConnectedComponent, dual_uIcc]
+    rfl
 #align set.dual_ord_connected_component Set.dual_ordConnectedComponent
 
 theorem ordConnectedComponent_subset : ordConnectedComponent s x ⊆ s := fun _ hy =>
@@ -213,8 +211,7 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) := by
 -- wlog (discharger := tactic.skip) hab : a ≤ b := le_total a b using a b s t, b a t s
     cases' ha with ha ha'
     cases' hb with hb hb'
-    have hsub : [[a, b]] ⊆ (ordSeparatingSet s t).ordConnectedSectionᶜ :=
-      by
+    have hsub : [[a, b]] ⊆ (ordSeparatingSet s t).ordConnectedSectionᶜ := by
       rw [ordSeparatingSet_comm, uIcc_comm] at hb'
       calc
         [[a, b]] ⊆ [[a, x]] ∪ [[x, b]] := uIcc_subset_uIcc_union_uIcc

chore: fix #align lines (#3640)

This PR fixes two things:

Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

2b42dc7c

Diff

@@ -93,7 +93,6 @@ theorem mem_ordConnectedComponent_trans (hxy : y ∈ ordConnectedComponent s x)
   calc
     [[x, z]] ⊆ [[x, y]] ∪ [[y, z]] := uIcc_subset_uIcc_union_uIcc
     _ ⊆ s := union_subset hxy hyz
-
 #align set.mem_ord_connected_component_trans Set.mem_ordConnectedComponent_trans
 
 theorem ordConnectedComponent_eq (h : [[x, y]] ⊆ s) :
@@ -150,7 +149,6 @@ theorem dual_ordConnectedSection (s : Set α) :
   ext x
   simp [dual_ordConnectedComponent]
   tauto
-
 #align set.dual_ord_connected_section Set.dual_ordConnectedSection
 
 theorem ordConnectedSection_subset : ordConnectedSection s ⊆ s :=
@@ -165,8 +163,7 @@ theorem eq_of_mem_ordConnectedSection_of_uIcc_subset (hx : x ∈ ordConnectedSec
       (mem_ordConnectedComponent_trans
         (mem_ordConnectedComponent_trans (ordConnectedProj_mem_ordConnectedComponent _ _) h)
         (mem_ordConnectedComponent_ordConnectedProj _ _))
-#align set.eq_of_mem_ord_connected_section_of_uIcc_subset
-  Set.eq_of_mem_ordConnectedSection_of_uIcc_subset
+#align set.eq_of_mem_ord_connected_section_of_uIcc_subset Set.eq_of_mem_ordConnectedSection_of_uIcc_subset
 
 /-- Given two sets `s t : Set α`, the set `Set.orderSeparatingSet s t` is the set of points that
 belong both to some `Set.ordConnectedComponent tᶜ x`, `x ∈ s`, and to some

chore: resync ported files (#2135)

This PR resyncs the first 28 entries of https://leanprover-community.github.io/mathlib-port-status/out-of-sync.html after sorting by diff size.

resync Mathlib/Data/Bool/Count
resync Mathlib/Order/Max
resync Mathlib/Algebra/EuclideanDomain/Instances
resync Mathlib/Data/List/Duplicate
resync Mathlib/Data/Multiset/Nodup
resync Mathlib/Data/Set/Pointwise/ListOfFn
resync Mathlib/Dynamics/FixedPoints/Basic
resync Mathlib/Order/OmegaCompletePartialOrder
resync Mathlib/Order/PropInstances
resync Mathlib/Topology/LocallyFinite
resync Mathlib/Data/Bool/Set
resync Mathlib/Data/Fintype/Card
resync Mathlib/Data/Multiset/Bind
resync Mathlib/Data/Rat/Floor
resync Mathlib/Algebra/Order/Floor
resync Mathlib/Data/Int/Basic
resync Mathlib/Data/Int/Dvd/Basic
resync Mathlib/Data/List/Sort
resync Mathlib/Data/Nat/GCD/Basic
resync Mathlib/Data/Set/Enumerate
resync Mathlib/Data/Set/Intervals/OrdConnectedComponent
resync Mathlib/GroupTheory/Subsemigroup/Basic
resync Mathlib/Topology/Connected
resync Mathlib/Topology/NhdsSet
resync Mathlib/Algebra/BigOperators/Multiset/Lemmas
resync Mathlib/Algebra/CharZero/Infinite
resync Mathlib/Data/Multiset/Range
resync Mathlib/Data/Set/Pointwise/Finite

a7eb5ab3

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module data.set.intervals.ord_connected_component
-! leanprover-community/mathlib commit 9003f28797c0664a49e4179487267c494477d853
+! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

chore: bump to nightly-2023-02-03 (#1999)

78fc778d

Diff

@@ -90,7 +90,6 @@ theorem mem_ordConnectedComponent_comm :
 
 theorem mem_ordConnectedComponent_trans (hxy : y ∈ ordConnectedComponent s x)
     (hyz : z ∈ ordConnectedComponent s y) : z ∈ ordConnectedComponent s x :=
-  show _ ⊆ _ from -- lean4#2073
   calc
     [[x, z]] ⊆ [[x, y]] ∪ [[y, z]] := uIcc_subset_uIcc_union_uIcc
     _ ⊆ s := union_subset hxy hyz

chore: bump lean 01-29 (#1927)

1abd74a8

Diff

@@ -90,6 +90,7 @@ theorem mem_ordConnectedComponent_comm :
 
 theorem mem_ordConnectedComponent_trans (hxy : y ∈ ordConnectedComponent s x)
     (hyz : z ∈ ordConnectedComponent s y) : z ∈ ordConnectedComponent s x :=
+  show _ ⊆ _ from -- lean4#2073
   calc
     [[x, z]] ⊆ [[x, y]] ∪ [[y, z]] := uIcc_subset_uIcc_union_uIcc
     _ ⊆ s := union_subset hxy hyz

feat: port Data.Finset.LocallyFinite (#1837)

Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Jon Eugster <eugster.jon@gmail.com> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

e2c39a45

Diff

@@ -20,7 +20,7 @@ so we only add API needed for this lemma.
 -/
 
 
-open Function OrderDual
+open Interval Function OrderDual
 
 namespace Set

Match https://github.com/leanprover-community/mathlib/pull/18104

chore: Rename intervals to uIcc/uIoc (#1496)

bd0eb8a4

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module data.set.intervals.ord_connected_component
-! leanprover-community/mathlib commit 1e05171a5e8cf18d98d9cf7b207540acb044acae
+! leanprover-community/mathlib commit 9003f28797c0664a49e4179487267c494477d853
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,7 +14,7 @@ import Mathlib.Tactic.SwapVar
 # Order connected components of a set
 
 In this file we define `Set.ordConnectedComponent s x` to be the set of `y` such that
-`Set.interval x y ⊆ s` and prove some basic facts about this definition. At the moment of writing,
+`Set.uIcc x y ⊆ s` and prove some basic facts about this definition. At the moment of writing,
 this construction is used only to prove that any linear order with order topology is a T₅ space,
 so we only add API needed for this lemma.
 -/
@@ -27,7 +27,7 @@ namespace Set
 variable {α : Type _} [LinearOrder α] {s t : Set α} {x y z : α}
 
 /-- Order-connected component of a point `x` in a set `s`. It is defined as the set of `y` such that
-`Set.interval x y ⊆ s`. Note that it is empty if and only if `x ∉ s`. -/
+`Set.uIcc x y ⊆ s`. Note that it is empty if and only if `x ∉ s`. -/
 def ordConnectedComponent (s : Set α) (x : α) : Set α :=
   { y | [[x, y]] ⊆ s }
 #align set.ord_connected_component Set.ordConnectedComponent
@@ -41,26 +41,26 @@ theorem dual_ordConnectedComponent :
   ext <|
       (Surjective.forall toDual.surjective).2 fun x =>
       by
-      rw [mem_ordConnectedComponent, dual_interval]
+      rw [mem_ordConnectedComponent, dual_uIcc]
       rfl
 #align set.dual_ord_connected_component Set.dual_ordConnectedComponent
 
 theorem ordConnectedComponent_subset : ordConnectedComponent s x ⊆ s := fun _ hy =>
-  hy right_mem_interval
+  hy right_mem_uIcc
 #align set.ord_connected_component_subset Set.ordConnectedComponent_subset
 
 theorem subset_ordConnectedComponent {t} [h : OrdConnected s] (hs : x ∈ s) (ht : s ⊆ t) :
-    s ⊆ ordConnectedComponent t x := fun _ hy => (h.interval_subset hs hy).trans ht
+    s ⊆ ordConnectedComponent t x := fun _ hy => (h.uIcc_subset hs hy).trans ht
 #align set.subset_ord_connected_component Set.subset_ordConnectedComponent
 
 @[simp]
 theorem self_mem_ordConnectedComponent : x ∈ ordConnectedComponent s x ↔ x ∈ s := by
-  rw [mem_ordConnectedComponent, interval_self, singleton_subset_iff]
+  rw [mem_ordConnectedComponent, uIcc_self, singleton_subset_iff]
 #align set.self_mem_ord_connected_component Set.self_mem_ordConnectedComponent
 
 @[simp]
 theorem nonempty_ordConnectedComponent : (ordConnectedComponent s x).Nonempty ↔ x ∈ s :=
-  ⟨fun ⟨_, hy⟩ => hy <| left_mem_interval, fun h => ⟨x, self_mem_ordConnectedComponent.2 h⟩⟩
+  ⟨fun ⟨_, hy⟩ => hy <| left_mem_uIcc, fun h => ⟨x, self_mem_ordConnectedComponent.2 h⟩⟩
 #align set.nonempty_ord_connected_component Set.nonempty_ordConnectedComponent
 
 @[simp]
@@ -85,13 +85,13 @@ theorem ordConnectedComponent_inter (s t : Set α) (x : α) :
 
 theorem mem_ordConnectedComponent_comm :
     y ∈ ordConnectedComponent s x ↔ x ∈ ordConnectedComponent s y := by
-  rw [mem_ordConnectedComponent, mem_ordConnectedComponent, interval_swap]
+  rw [mem_ordConnectedComponent, mem_ordConnectedComponent, uIcc_comm]
 #align set.mem_ord_connected_component_comm Set.mem_ordConnectedComponent_comm
 
 theorem mem_ordConnectedComponent_trans (hxy : y ∈ ordConnectedComponent s x)
     (hyz : z ∈ ordConnectedComponent s y) : z ∈ ordConnectedComponent s x :=
   calc
-    [[x, z]] ⊆ [[x, y]] ∪ [[y, z]] := interval_subset_interval_union_interval
+    [[x, z]] ⊆ [[x, y]] ∪ [[y, z]] := uIcc_subset_uIcc_union_uIcc
     _ ⊆ s := union_subset hxy hyz
 
 #align set.mem_ord_connected_component_trans Set.mem_ordConnectedComponent_trans
@@ -104,7 +104,7 @@ theorem ordConnectedComponent_eq (h : [[x, y]] ⊆ s) :
 #align set.ord_connected_component_eq Set.ordConnectedComponent_eq
 
 instance : OrdConnected (ordConnectedComponent s x) :=
-  ordConnected_of_interval_subset_left fun _ hy _ hz => (interval_subset_interval_left hz).trans hy
+  ordConnected_of_uIcc_subset_left fun _ hy _ hz => (uIcc_subset_uIcc_left hz).trans hy
 
 /-- Projection from `s : Set α` to `α` sending each order connected component of `s` to a single
 point of this component. -/
@@ -157,7 +157,7 @@ theorem ordConnectedSection_subset : ordConnectedSection s ⊆ s :=
   range_subset_iff.2 fun _ => ordConnectedComponent_subset <| Nonempty.some_mem _
 #align set.ord_connected_section_subset Set.ordConnectedSection_subset
 
-theorem eq_of_mem_ordConnectedSection_of_interval_subset (hx : x ∈ ordConnectedSection s)
+theorem eq_of_mem_ordConnectedSection_of_uIcc_subset (hx : x ∈ ordConnectedSection s)
     (hy : y ∈ ordConnectedSection s) (h : [[x, y]] ⊆ s) : x = y := by
   rcases hx with ⟨x, rfl⟩; rcases hy with ⟨y, rfl⟩
   exact
@@ -165,7 +165,8 @@ theorem eq_of_mem_ordConnectedSection_of_interval_subset (hx : x ∈ ordConnecte
       (mem_ordConnectedComponent_trans
         (mem_ordConnectedComponent_trans (ordConnectedProj_mem_ordConnectedComponent _ _) h)
         (mem_ordConnectedComponent_ordConnectedProj _ _))
-#align set.eq_of_mem_ord_connected_section_of_interval_subset Set.eq_of_mem_ordConnectedSection_of_interval_subset
+#align set.eq_of_mem_ord_connected_section_of_uIcc_subset
+  Set.eq_of_mem_ordConnectedSection_of_uIcc_subset
 
 /-- Given two sets `s t : Set α`, the set `Set.orderSeparatingSet s t` is the set of points that
 belong both to some `Set.ordConnectedComponent tᶜ x`, `x ∈ s`, and to some
@@ -217,27 +218,27 @@ theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) := by
     cases' hb with hb hb'
     have hsub : [[a, b]] ⊆ (ordSeparatingSet s t).ordConnectedSectionᶜ :=
       by
-      rw [ordSeparatingSet_comm, interval_swap] at hb'
+      rw [ordSeparatingSet_comm, uIcc_comm] at hb'
       calc
-        [[a, b]] ⊆ [[a, x]] ∪ [[x, b]] := interval_subset_interval_union_interval
+        [[a, b]] ⊆ [[a, x]] ∪ [[x, b]] := uIcc_subset_uIcc_union_uIcc
         _ ⊆ (ordSeparatingSet s t).ordConnectedSectionᶜ := union_subset ha' hb'
     clear ha' hb'
     cases' le_total x a with hxa hax
-    · exact hb (Icc_subset_interval' ⟨hxa, hab⟩) has
+    · exact hb (Icc_subset_uIcc' ⟨hxa, hab⟩) has
     cases' le_total b x with hbx hxb
-    · exact ha (Icc_subset_interval ⟨hab, hbx⟩) hbt
+    · exact ha (Icc_subset_uIcc ⟨hab, hbx⟩) hbt
     have h' : x ∈ ordSeparatingSet s t := ⟨mem_unionᵢ₂.2 ⟨a, has, ha⟩, mem_unionᵢ₂.2 ⟨b, hbt, hb⟩⟩
     -- porting note: lift not implemented yet
     -- lift x to ordSeparatingSet s t using this
     suffices : ordConnectedComponent (ordSeparatingSet s t) x ⊆ [[a, b]]
     exact hsub (this <| ordConnectedProj_mem_ordConnectedComponent _ ⟨x, h'⟩) (mem_range_self _)
     rintro y (hy : [[x, y]] ⊆ ordSeparatingSet s t)
-    rw [interval_of_le hab, mem_Icc, ← not_lt, ← not_lt]
+    rw [uIcc_of_le hab, mem_Icc, ← not_lt, ← not_lt]
     have sol1 := fun (hya : y < a) =>
         (disjoint_left (t := ordSeparatingSet s t)).1 disjoint_left_ordSeparatingSet has
-          (hy <| Icc_subset_interval' ⟨hya.le, hax⟩)
+          (hy <| Icc_subset_uIcc' ⟨hya.le, hax⟩)
     have sol2 := fun (hby : b < y) =>
         (disjoint_left (t := ordSeparatingSet s t)).1 disjoint_right_ordSeparatingSet hbt
-          (hy <| Icc_subset_interval ⟨hxb, hby.le⟩)
+          (hy <| Icc_subset_uIcc ⟨hxb, hby.le⟩)
     exact ⟨sol1, sol2⟩
 #align set.disjoint_ord_t5_nhd Set.disjoint_ordT5Nhd

chore: format by line breaks (#1523)

During porting, I usually fix the desired format we seem to want for the line breaks around by with

awk '{do {{if (match($0, "^  by$") && length(p) < 98) {p=p " by";} else {if (NR!=1) {print p}; p=$0}}} while (getline == 1) if (getline==0) print p}' Mathlib/File/Im/Working/On.lean

I noticed there are some more files that slipped through.

This pull request is the result of running this command:

grep -lr "^  by\$" Mathlib | xargs -n 1 awk -i inplace '{do {{if (match($0, "^  by$") && length(p) < 98 && not (match(p, "^[ \t]*--"))) {p=p " by";} else {if (NR!=1) {print p}; p=$0}}} while (getline == 1) if (getline==0) print p}'

Co-authored-by: Moritz Firsching <firsching@google.com>

d6d859a7

Diff

@@ -130,8 +130,7 @@ theorem ordConnectedComponent_ordConnectedProj (s : Set α) (x : s) :
 
 @[simp]
 theorem ordConnectedProj_eq {x y : s} :
-    ordConnectedProj s x = ordConnectedProj s y ↔ [[(x : α), y]] ⊆ s :=
-  by
+    ordConnectedProj s x = ordConnectedProj s y ↔ [[(x : α), y]] ⊆ s := by
   constructor <;> intro h
   · rw [← mem_ordConnectedComponent, ← ordConnectedComponent_ordConnectedProj, h,
       ordConnectedComponent_ordConnectedProj, self_mem_ordConnectedComponent]
@@ -159,8 +158,7 @@ theorem ordConnectedSection_subset : ordConnectedSection s ⊆ s :=
 #align set.ord_connected_section_subset Set.ordConnectedSection_subset
 
 theorem eq_of_mem_ordConnectedSection_of_interval_subset (hx : x ∈ ordConnectedSection s)
-    (hy : y ∈ ordConnectedSection s) (h : [[x, y]] ⊆ s) : x = y :=
-  by
+    (hy : y ∈ ordConnectedSection s) (h : [[x, y]] ⊆ s) : x = y := by
   rcases hx with ⟨x, rfl⟩; rcases hy with ⟨y, rfl⟩
   exact
     ordConnectedProj_eq.2
@@ -202,8 +200,7 @@ def ordT5Nhd (s t : Set α) : Set α :=
   ⋃ x ∈ s, ordConnectedComponent (tᶜ ∩ (ordConnectedSection <| ordSeparatingSet s t)ᶜ) x
 #align set.ord_t5_nhd Set.ordT5Nhd
 
-theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) :=
-  by
+theorem disjoint_ordT5Nhd : Disjoint (ordT5Nhd s t) (ordT5Nhd t s) := by
   rw [disjoint_iff_inf_le]
   rintro x ⟨hx₁, hx₂⟩
   rcases mem_unionᵢ₂.1 hx₁ with ⟨a, has, ha⟩

chore: the style linter shouldn't complain about long #align lines (#1643)

54af0498

Diff

@@ -115,16 +115,12 @@ noncomputable def ordConnectedProj (s : Set α) : s → α := fun x : s =>
 theorem ordConnectedProj_mem_ordConnectedComponent (s : Set α) (x : s) :
     ordConnectedProj s x ∈ ordConnectedComponent s x :=
   Nonempty.some_mem _
-#align
-  set.ord_connected_proj_mem_ord_connected_component
-  Set.ordConnectedProj_mem_ordConnectedComponent
+#align set.ord_connected_proj_mem_ord_connected_component Set.ordConnectedProj_mem_ordConnectedComponent
 
 theorem mem_ordConnectedComponent_ordConnectedProj (s : Set α) (x : s) :
     ↑x ∈ ordConnectedComponent s (ordConnectedProj s x) :=
   mem_ordConnectedComponent_comm.2 <| ordConnectedProj_mem_ordConnectedComponent s x
-#align
-  set.mem_ord_connected_component_ord_connected_proj
-  Set.mem_ordConnectedComponent_ordConnectedProj
+#align set.mem_ord_connected_component_ord_connected_proj Set.mem_ordConnectedComponent_ordConnectedProj
 
 @[simp]
 theorem ordConnectedComponent_ordConnectedProj (s : Set α) (x : s) :
@@ -171,9 +167,7 @@ theorem eq_of_mem_ordConnectedSection_of_interval_subset (hx : x ∈ ordConnecte
       (mem_ordConnectedComponent_trans
         (mem_ordConnectedComponent_trans (ordConnectedProj_mem_ordConnectedComponent _ _) h)
         (mem_ordConnectedComponent_ordConnectedProj _ _))
-#align
-  set.eq_of_mem_ord_connected_section_of_interval_subset
-  Set.eq_of_mem_ordConnectedSection_of_interval_subset
+#align set.eq_of_mem_ord_connected_section_of_interval_subset Set.eq_of_mem_ordConnectedSection_of_interval_subset
 
 /-- Given two sets `s t : Set α`, the set `Set.orderSeparatingSet s t` is the set of points that
 belong both to some `Set.ordConnectedComponent tᶜ x`, `x ∈ s`, and to some

chore: tidy various files (#1412)

0ee6552e

Diff

@@ -119,30 +119,28 @@ theorem ordConnectedProj_mem_ordConnectedComponent (s : Set α) (x : s) :
   set.ord_connected_proj_mem_ord_connected_component
   Set.ordConnectedProj_mem_ordConnectedComponent
 
-theorem mem_ordConnectedComponent_ord_connected_proj (s : Set α) (x : s) :
+theorem mem_ordConnectedComponent_ordConnectedProj (s : Set α) (x : s) :
     ↑x ∈ ordConnectedComponent s (ordConnectedProj s x) :=
   mem_ordConnectedComponent_comm.2 <| ordConnectedProj_mem_ordConnectedComponent s x
 #align
   set.mem_ord_connected_component_ord_connected_proj
-  Set.mem_ordConnectedComponent_ord_connected_proj
+  Set.mem_ordConnectedComponent_ordConnectedProj
 
 @[simp]
-theorem ordConnectedComponent_ord_connected_proj (s : Set α) (x : s) :
+theorem ordConnectedComponent_ordConnectedProj (s : Set α) (x : s) :
     ordConnectedComponent s (ordConnectedProj s x) = ordConnectedComponent s x :=
-  ordConnectedComponent_eq <| mem_ordConnectedComponent_ord_connected_proj _ _
-#align set.ord_connected_component_ord_connected_proj Set.ordConnectedComponent_ord_connected_proj
+  ordConnectedComponent_eq <| mem_ordConnectedComponent_ordConnectedProj _ _
+#align set.ord_connected_component_ord_connected_proj Set.ordConnectedComponent_ordConnectedProj
 
 @[simp]
 theorem ordConnectedProj_eq {x y : s} :
     ordConnectedProj s x = ordConnectedProj s y ↔ [[(x : α), y]] ⊆ s :=
   by
   constructor <;> intro h
-  · rw [← mem_ordConnectedComponent, ← ordConnectedComponent_ord_connected_proj, h,
-      ordConnectedComponent_ord_connected_proj, self_mem_ordConnectedComponent]
+  · rw [← mem_ordConnectedComponent, ← ordConnectedComponent_ordConnectedProj, h,
+      ordConnectedComponent_ordConnectedProj, self_mem_ordConnectedComponent]
     exact y.2
-  · simp only [ordConnectedProj]
-    congr 1
-    exact ordConnectedComponent_eq h
+  · simp only [ordConnectedProj, ordConnectedComponent_eq h]
 #align set.ord_connected_proj_eq Set.ordConnectedProj_eq
 
 /-- A set that intersects each order connected component of a set by a single point. Defined as the
@@ -172,7 +170,7 @@ theorem eq_of_mem_ordConnectedSection_of_interval_subset (hx : x ∈ ordConnecte
     ordConnectedProj_eq.2
       (mem_ordConnectedComponent_trans
         (mem_ordConnectedComponent_trans (ordConnectedProj_mem_ordConnectedComponent _ _) h)
-        (mem_ordConnectedComponent_ord_connected_proj _ _))
+        (mem_ordConnectedComponent_ordConnectedProj _ _))
 #align
   set.eq_of_mem_ord_connected_section_of_interval_subset
   Set.eq_of_mem_ordConnectedSection_of_interval_subset