set_theory.cardinal.schroeder_bernstein

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

1e05171a

(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

@@ -71,10 +71,10 @@ theorem schroeder_bernstein {f : α → β} {g : β → α} (hf : Function.Injec
     · intro x hx y hy hxy
       obtain ⟨x', hx', rfl⟩ : x ∈ g '' (f '' s)ᶜ := by rwa [hns]
       obtain ⟨y', hy', rfl⟩ : y ∈ g '' (f '' s)ᶜ := by rwa [hns]
-      rw [g'g _, g'g _] at hxy ; rw [hxy]
+      rw [g'g _, g'g _] at hxy; rw [hxy]
     · intro x hx y hy hxy
       obtain ⟨y', hy', rfl⟩ : y ∈ g '' (f '' s)ᶜ := by rwa [hns]
-      rw [g'g _] at hxy 
+      rw [g'g _] at hxy
       exact hy' ⟨x, hx, hxy⟩
   exact ⟨h, ‹injective h›, ‹surjective h›⟩
 #align function.embedding.schroeder_bernstein Function.Embedding.schroeder_bernstein

c3291da4

bump to nightly-2023-10-21-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

a2dc86f8

Diff

@@ -116,7 +116,7 @@ theorem min_injective [I : Nonempty ι] : ∃ i, Nonempty (∀ j, β i ↪ β j)
     show ∃ i, ∀ y, ∃ x ∈ s, (x : ∀ i, β i) i = y from
       by_contradiction fun h =>
         have h : ∀ i, ∃ y, ∀ x ∈ s, (x : ∀ i, β i) i ≠ y := by
-          simpa only [not_exists, not_forall] using h
+          simpa only [not_exists, Classical.not_forall] using h
         let ⟨f, hf⟩ := Classical.axiom_of_choice h
         have : f ∈ s :=
           have : insert f s ∈ sets := fun x hx y hy =>

c3291da4

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) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro
 -/
-import Mathbin.Order.FixedPoints
-import Mathbin.Order.Zorn
+import Order.FixedPoints
+import Order.Zorn
 
 #align_import set_theory.cardinal.schroeder_bernstein 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

@@ -2,15 +2,12 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro
-
-! This file was ported from Lean 3 source module set_theory.cardinal.schroeder_bernstein
-! 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.FixedPoints
 import Mathbin.Order.Zorn
 
+#align_import set_theory.cardinal.schroeder_bernstein from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
 /-!
 # Schröder-Bernstein theorem, well-ordering of cardinals

c3291da4

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -97,11 +97,11 @@ end antisymm
 
 section Wo
 
-parameter {ι : Type u}(β : ι → Type v)
+parameter {ι : Type u} (β : ι → Type v)
 
 @[reducible]
 private def sets :=
-  { s : Set (∀ i, β i) | ∀ x ∈ s, ∀ y ∈ s, ∀ (i), (x : ∀ i, β i) i = y i → x = y }
+  {s : Set (∀ i, β i) | ∀ x ∈ s, ∀ y ∈ s, ∀ (i), (x : ∀ i, β i) i = y i → x = y}
 
 #print Function.Embedding.min_injective /-
 /-- The cardinals are well-ordered. We express it here by the fact that in any set of cardinals

c3291da4

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -74,10 +74,10 @@ theorem schroeder_bernstein {f : α → β} {g : β → α} (hf : Function.Injec
     · intro x hx y hy hxy
       obtain ⟨x', hx', rfl⟩ : x ∈ g '' (f '' s)ᶜ := by rwa [hns]
       obtain ⟨y', hy', rfl⟩ : y ∈ g '' (f '' s)ᶜ := by rwa [hns]
-      rw [g'g _, g'g _] at hxy; rw [hxy]
+      rw [g'g _, g'g _] at hxy ; rw [hxy]
     · intro x hx y hy hxy
       obtain ⟨y', hy', rfl⟩ : y ∈ g '' (f '' s)ᶜ := by rwa [hns]
-      rw [g'g _] at hxy
+      rw [g'g _] at hxy 
       exact hy' ⟨x, hx, hxy⟩
   exact ⟨h, ‹injective h›, ‹surjective h›⟩
 #align function.embedding.schroeder_bernstein Function.Embedding.schroeder_bernstein

c3291da4

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -35,7 +35,7 @@ Cardinals are defined and further developed in the file `set_theory.cardinal`.
 
 open Set Function
 
-open Classical
+open scoped Classical
 
 universe u v

c3291da4

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -74,8 +74,7 @@ theorem schroeder_bernstein {f : α → β} {g : β → α} (hf : Function.Injec
     · intro x hx y hy hxy
       obtain ⟨x', hx', rfl⟩ : x ∈ g '' (f '' s)ᶜ := by rwa [hns]
       obtain ⟨y', hy', rfl⟩ : y ∈ g '' (f '' s)ᶜ := by rwa [hns]
-      rw [g'g _, g'g _] at hxy
-      rw [hxy]
+      rw [g'g _, g'g _] at hxy; rw [hxy]
     · intro x hx y hy hxy
       obtain ⟨y', hy', rfl⟩ : y ∈ g '' (f '' s)ᶜ := by rwa [hns]
       rw [g'g _] at hxy
@@ -126,10 +125,8 @@ theorem min_injective [I : Nonempty ι] : ∃ i, Nonempty (∀ j, β i ↪ β j)
           have : insert f s ∈ sets := fun x hx y hy =>
             by
             cases hx <;> cases hy; · simp [hx, hy]
-            · subst x
-              exact fun i e => (hf i y hy e.symm).elim
-            · subst y
-              exact fun i e => (hf i x hx e).elim
+            · subst x; exact fun i e => (hf i y hy e.symm).elim
+            · subst y; exact fun i e => (hf i x hx e).elim
             · exact hs x hx y hy
           ms _ this (subset_insert f s) ▸ mem_insert _ _
         let ⟨i⟩ := I

c3291da4

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -103,7 +103,6 @@ parameter {ι : Type u}(β : ι → Type v)
 @[reducible]
 private def sets :=
   { s : Set (∀ i, β i) | ∀ x ∈ s, ∀ y ∈ s, ∀ (i), (x : ∀ i, β i) i = y i → x = y }
-#align function.embedding.sets function.embedding.sets
 
 #print Function.Embedding.min_injective /-
 /-- The cardinals are well-ordered. We express it here by the fact that in any set of cardinals

c3291da4

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -116,7 +116,7 @@ theorem min_injective [I : Nonempty ι] : ∃ i, Nonempty (∀ j, β i ↪ β j)
         ⟨⋃₀ c, fun x ⟨p, hpc, hxp⟩ y ⟨q, hqc, hyq⟩ i hi =>
           (hcc.Total hpc hqc).elim (fun h => hc hqc x (h hxp) y hyq i hi) fun h =>
             hc hpc x hxp y (h hyq) i hi,
-          fun _ => subset_unionₛ_of_mem⟩
+          fun _ => subset_sUnion_of_mem⟩
   let ⟨i, e⟩ :=
     show ∃ i, ∀ y, ∃ x ∈ s, (x : ∀ i, β i) i = y from
       by_contradiction fun h =>

c3291da4

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

1e05171a

chore: scope open Classical (#11199)

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

c747be0a

Diff

@@ -30,7 +30,7 @@ Cardinals are defined and further developed in the folder `SetTheory.Cardinal`.
 
 open Set Function
 
-open Classical
+open scoped Classical
 
 universe u v

1e05171a

chore: Move zpow lemmas (#9720)

These lemmas can be proved much earlier with little to no change to their proofs.

Part of #9411

1564a327

Diff

@@ -3,6 +3,7 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro
 -/
+import Mathlib.Init.Classical
 import Mathlib.Order.FixedPoints
 import Mathlib.Order.Zorn

1e05171a

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

@@ -2,15 +2,12 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro
-
-! This file was ported from Lean 3 source module set_theory.cardinal.schroeder_bernstein
-! leanprover-community/mathlib commit 1e05171a5e8cf18d98d9cf7b207540acb044acae
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Order.FixedPoints
 import Mathlib.Order.Zorn
 
+#align_import set_theory.cardinal.schroeder_bernstein from "leanprover-community/mathlib"@"1e05171a5e8cf18d98d9cf7b207540acb044acae"
+
 /-!
 # Schröder-Bernstein theorem, well-ordering of cardinals

1e05171a

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -55,7 +55,7 @@ theorem schroeder_bernstein {f : α → β} {g : β → α} (hf : Function.Injec
     { toFun := fun s => (g '' (f '' s)ᶜ)ᶜ
       monotone' := fun s t hst =>
         compl_subset_compl.mpr <| image_subset _ <| compl_subset_compl.mpr <| image_subset _ hst }
-  -- Porting note: dot dotation `F.lfp` doesn't work here
+  -- Porting note: dot notation `F.lfp` doesn't work here
   set s : Set α := OrderHom.lfp F
   have hs : (g '' (f '' s)ᶜ)ᶜ = s := F.map_lfp
   have hns : g '' (f '' s)ᶜ = sᶜ := compl_injective (by simp [hs])

1e05171a

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

@@ -107,7 +107,7 @@ theorem min_injective [I : Nonempty ι] : ∃ i, Nonempty (∀ j, β i ↪ β j)
         ⟨⋃₀c, fun x ⟨p, hpc, hxp⟩ y ⟨q, hqc, hyq⟩ i hi =>
           (hcc.total hpc hqc).elim (fun h => hc hqc x (h hxp) y hyq i hi) fun h =>
             hc hpc x hxp y (h hyq) i hi,
-          fun _ => subset_unionₛ_of_mem⟩
+          fun _ => subset_sUnion_of_mem⟩
   let ⟨i, e⟩ :=
     show ∃ i, ∀ y, ∃ x ∈ s, (x : ∀ i, β i) i = y from
       Classical.by_contradiction fun h =>

1e05171a

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

@@ -64,8 +64,7 @@ theorem schroeder_bernstein {f : α → β} {g : β → α} (hf : Function.Injec
   have hg'ns : g' '' sᶜ = (f '' s)ᶜ := by rw [← hns, g'g.image_image]
   set h : α → β := s.piecewise f g'
   have : Surjective h := by rw [← range_iff_surjective, range_piecewise, hg'ns, union_compl_self]
-  have : Injective h :=
-    by
+  have : Injective h := by
     refine' (injective_piecewise_iff _).2 ⟨hf.injOn _, _, _⟩
     · intro x hx y hy hxy
       obtain ⟨x', _, rfl⟩ : x ∈ g '' (f '' s)ᶜ := by rwa [hns]

1e05171a

chore: strip trailing spaces in lean files (#2828)

vscode is already configured by .vscode/settings.json to trim these on save. It's not clear how they've managed to stick around.

By doing this all in one PR now, it avoids getting random whitespace diffs in PRs later.

This was done with a regex search in vscode,

6ceb5945

Diff

@@ -99,7 +99,7 @@ private def sets :=
   { s : Set (∀ i, β i) | ∀ x ∈ s, ∀ y ∈ s, ∀ (i), (x : ∀ i, β i) i = y i → x = y }
 
 /-- The cardinals are well-ordered. We express it here by the fact that in any set of cardinals
-there is an element that injects into the others. 
+there is an element that injects into the others.
 See `Cardinal.conditionallyCompleteLinearOrderBot` for (one of) the lattice instances. -/
 theorem min_injective [I : Nonempty ι] : ∃ i, Nonempty (∀ j, β i ↪ β j) :=
   let ⟨s, hs, ms⟩ :=

1e05171a

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

@@ -47,8 +47,7 @@ variable {α : Type u} {β : Type v}
 /-- **The Schröder-Bernstein Theorem**:
 Given injections `α → β` and `β → α`, we can get a bijection `α → β`. -/
 theorem schroeder_bernstein {f : α → β} {g : β → α} (hf : Function.Injective f)
-    (hg : Function.Injective g) : ∃ h : α → β, Bijective h :=
-  by
+    (hg : Function.Injective g) : ∃ h : α → β, Bijective h := by
   cases' isEmpty_or_nonempty β with hβ hβ
   · have : IsEmpty α := Function.isEmpty f
     exact ⟨_, ((Equiv.equivEmpty α).trans (Equiv.equivEmpty β).symm).bijective⟩

1e05171a

feat: port SetTheory.Cardinal.SchroederBernstein (#1296)

Co-authored-by: Lukas Miaskiwskyi <lukas.mias@gmail.com>

2714dce0

`set_theory.cardinal.schroeder_bernstein` ⟷ `Mathlib.SetTheory.Cardinal.SchroederBernstein`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 3 + 153

set_theory.cardinal.schroeder_bernstein ⟷ Mathlib.SetTheory.Cardinal.SchroederBernstein

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 3 + 153

`set_theory.cardinal.schroeder_bernstein` ⟷ `Mathlib.SetTheory.Cardinal.SchroederBernstein`