data.W.cardinal | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

6eeb941c

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

ee05e9ce

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -53,7 +53,7 @@ theorem cardinal_mk_eq_sum : (#WType β) = Sum fun a : α => (#WType β) ^ (#β
 theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (Sum fun a : α => κ ^ (#β a)) ≤ κ) :
     (#WType β) ≤ κ := by
   induction' κ using Cardinal.inductionOn with γ
-  simp only [Cardinal.power_def, ← Cardinal.mk_sigma, Cardinal.le_def] at hκ 
+  simp only [Cardinal.power_def, ← Cardinal.mk_sigma, Cardinal.le_def] at hκ
   cases hκ
   exact Cardinal.mk_le_of_injective (elim_injective _ hκ.1 hκ.2)
 #align W_type.cardinal_mk_le_of_le WType.cardinal_mk_le_of_le

ee05e9ce

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) 2021 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 -/
-import Mathbin.Data.W.Basic
-import Mathbin.SetTheory.Cardinal.Ordinal
+import Data.W.Basic
+import SetTheory.Cardinal.Ordinal
 
 #align_import data.W.cardinal from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"

ee05e9ce

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) 2021 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module data.W.cardinal
-! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.W.Basic
 import Mathbin.SetTheory.Cardinal.Ordinal
 
+#align_import data.W.cardinal from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
+
 /-!
 # Cardinality of W-types

ee05e9ce

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -62,6 +62,7 @@ theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (Sum fun a : α => κ ^
 #align W_type.cardinal_mk_le_of_le WType.cardinal_mk_le_of_le
 -/
 
+#print WType.cardinal_mk_le_max_aleph0_of_finite /-
 /-- If, for any `a : α`, `β a` is finite, then the cardinality of `W_type β`
   is at most the maximum of the cardinality of `α` and `ℵ₀`  -/
 theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : (#WType β) ≤ max (#α) ℵ₀ :=
@@ -90,6 +91,7 @@ theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : (#WType β)
                     power_le_power_left
                       (pos_iff_ne_zero.1 (aleph_0_pos.trans_le (le_max_right _ _))) (zero_le _))
 #align W_type.cardinal_mk_le_max_aleph_0_of_finite WType.cardinal_mk_le_max_aleph0_of_finite
+-/
 
 end WType

ee05e9ce

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -89,7 +89,6 @@ theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : (#WType β)
                   exact
                     power_le_power_left
                       (pos_iff_ne_zero.1 (aleph_0_pos.trans_le (le_max_right _ _))) (zero_le _))
-        
 #align W_type.cardinal_mk_le_max_aleph_0_of_finite WType.cardinal_mk_le_max_aleph0_of_finite
 
 end WType

ee05e9ce

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -56,7 +56,7 @@ theorem cardinal_mk_eq_sum : (#WType β) = Sum fun a : α => (#WType β) ^ (#β
 theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (Sum fun a : α => κ ^ (#β a)) ≤ κ) :
     (#WType β) ≤ κ := by
   induction' κ using Cardinal.inductionOn with γ
-  simp only [Cardinal.power_def, ← Cardinal.mk_sigma, Cardinal.le_def] at hκ
+  simp only [Cardinal.power_def, ← Cardinal.mk_sigma, Cardinal.le_def] at hκ 
   cases hκ
   exact Cardinal.mk_le_of_injective (elim_injective _ hκ.1 hκ.2)
 #align W_type.cardinal_mk_le_of_le WType.cardinal_mk_le_of_le

ee05e9ce

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -39,7 +39,7 @@ noncomputable section
 
 namespace WType
 
-open Cardinal
+open scoped Cardinal
 
 open Cardinal

ee05e9ce

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -62,12 +62,6 @@ theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (Sum fun a : α => κ ^
 #align W_type.cardinal_mk_le_of_le WType.cardinal_mk_le_of_le
 -/
 
-/- warning: W_type.cardinal_mk_le_max_aleph_0_of_finite -> WType.cardinal_mk_le_max_aleph0_of_finite is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : α -> Type.{u1}} [_inst_1 : forall (a : α), Finite.{succ u1} (β a)], LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (WType.{u1, u1} α β)) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
-but is expected to have type
-  forall {α : Type.{u1}} {β : α -> Type.{u1}} [_inst_1 : forall (a : α), Finite.{succ u1} (β a)], LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (WType.{u1, u1} α β)) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
-Case conversion may be inaccurate. Consider using '#align W_type.cardinal_mk_le_max_aleph_0_of_finite WType.cardinal_mk_le_max_aleph0_of_finiteₓ'. -/
 /-- If, for any `a : α`, `β a` is finite, then the cardinality of `W_type β`
   is at most the maximum of the cardinality of `α` and `ℵ₀`  -/
 theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : (#WType β) ≤ max (#α) ℵ₀ :=

ee05e9ce

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -80,17 +80,17 @@ theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : (#WType β)
     let m := max (#α) ℵ₀
     cardinal_mk_le_of_le <|
       calc
-        (Cardinal.sum fun a => m ^ (#β a)) ≤ (#α) * ⨆ a, m ^ (#β a) := Cardinal.sum_le_supᵢ _
+        (Cardinal.sum fun a => m ^ (#β a)) ≤ (#α) * ⨆ a, m ^ (#β a) := Cardinal.sum_le_iSup _
         _ ≤ m * ⨆ a, m ^ (#β a) := (mul_le_mul' (le_max_left _ _) le_rfl)
         _ = m :=
           mul_eq_left.{u} (le_max_right _ _)
-              (csupᵢ_le' fun i => pow_le (le_max_right _ _) (lt_aleph0_of_finite _)) <|
+              (ciSup_le' fun i => pow_le (le_max_right _ _) (lt_aleph0_of_finite _)) <|
             pos_iff_ne_zero.1 <|
               Order.succ_le_iff.1
                 (by
                   rw [succ_zero]
                   obtain ⟨a⟩ : Nonempty α; exact hn
-                  refine' le_trans _ (le_csupᵢ (bddAbove_range.{u, u} _) a)
+                  refine' le_trans _ (le_ciSup (bddAbove_range.{u, u} _) a)
                   rw [← power_zero]
                   exact
                     power_le_power_left

ee05e9ce

bump to nightly-2023-04-03-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095

8477bcac

Diff

@@ -64,7 +64,7 @@ theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (Sum fun a : α => κ ^
 
 /- warning: W_type.cardinal_mk_le_max_aleph_0_of_finite -> WType.cardinal_mk_le_max_aleph0_of_finite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : α -> Type.{u1}} [_inst_1 : forall (a : α), Finite.{succ u1} (β a)], LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (WType.{u1, u1} α β)) (LinearOrder.max.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toLinearOrder.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1})) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
+  forall {α : Type.{u1}} {β : α -> Type.{u1}} [_inst_1 : forall (a : α), Finite.{succ u1} (β a)], LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (WType.{u1, u1} α β)) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
 but is expected to have type
   forall {α : Type.{u1}} {β : α -> Type.{u1}} [_inst_1 : forall (a : α), Finite.{succ u1} (β a)], LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (WType.{u1, u1} α β)) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
 Case conversion may be inaccurate. Consider using '#align W_type.cardinal_mk_le_max_aleph_0_of_finite WType.cardinal_mk_le_max_aleph0_of_finiteₓ'. -/

ee05e9ce

bump to nightly-2023-03-02-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

db7421c3

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
 
 ! This file was ported from Lean 3 source module data.W.cardinal
-! leanprover-community/mathlib commit 6eeb941cf39066417a09b1bbc6e74761cadfcb1a
+! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.SetTheory.Cardinal.Ordinal
 /-!
 # Cardinality of W-types
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves some theorems about the cardinality of W-types. The main result is
 `cardinal_mk_le_max_aleph_0_of_fintype` which says that if for any `a : α`,
 `β a` is finite, then the cardinality of `W_type β` is at most the maximum of the

6eeb941c

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -78,7 +78,7 @@ theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : (#WType β)
     cardinal_mk_le_of_le <|
       calc
         (Cardinal.sum fun a => m ^ (#β a)) ≤ (#α) * ⨆ a, m ^ (#β a) := Cardinal.sum_le_supᵢ _
-        _ ≤ m * ⨆ a, m ^ (#β a) := mul_le_mul' (le_max_left _ _) le_rfl
+        _ ≤ m * ⨆ a, m ^ (#β a) := (mul_le_mul' (le_max_left _ _) le_rfl)
         _ = m :=
           mul_eq_left.{u} (le_max_right _ _)
               (csupᵢ_le' fun i => pow_le (le_max_right _ _) (lt_aleph0_of_finite _)) <|

6eeb941c

bump to nightly-2023-02-25-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

aca219f8

Diff

@@ -40,12 +40,15 @@ open Cardinal
 
 open Cardinal
 
+#print WType.cardinal_mk_eq_sum /-
 theorem cardinal_mk_eq_sum : (#WType β) = Sum fun a : α => (#WType β) ^ (#β a) :=
   by
   simp only [Cardinal.power_def, ← Cardinal.mk_sigma]
   exact mk_congr (equiv_sigma β)
 #align W_type.cardinal_mk_eq_sum WType.cardinal_mk_eq_sum
+-/
 
+#print WType.cardinal_mk_le_of_le /-
 /-- `#(W_type β)` is the least cardinal `κ` such that `sum (λ a : α, κ ^ #(β a)) ≤ κ` -/
 theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (Sum fun a : α => κ ^ (#β a)) ≤ κ) :
     (#WType β) ≤ κ := by
@@ -54,7 +57,14 @@ theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (Sum fun a : α => κ ^
   cases hκ
   exact Cardinal.mk_le_of_injective (elim_injective _ hκ.1 hκ.2)
 #align W_type.cardinal_mk_le_of_le WType.cardinal_mk_le_of_le
+-/
 
+/- warning: W_type.cardinal_mk_le_max_aleph_0_of_finite -> WType.cardinal_mk_le_max_aleph0_of_finite is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : α -> Type.{u1}} [_inst_1 : forall (a : α), Finite.{succ u1} (β a)], LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (WType.{u1, u1} α β)) (LinearOrder.max.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toLinearOrder.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1})) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
+but is expected to have type
+  forall {α : Type.{u1}} {β : α -> Type.{u1}} [_inst_1 : forall (a : α), Finite.{succ u1} (β a)], LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (WType.{u1, u1} α β)) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
+Case conversion may be inaccurate. Consider using '#align W_type.cardinal_mk_le_max_aleph_0_of_finite WType.cardinal_mk_le_max_aleph0_of_finiteₓ'. -/
 /-- If, for any `a : α`, `β a` is finite, then the cardinality of `W_type β`
   is at most the maximum of the cardinality of `α` and `ℵ₀`  -/
 theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : (#WType β) ≤ max (#α) ℵ₀ :=

6eeb941c

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

6eeb941c

chore: replace λ by fun (#11301)

Per the style guidelines, λ is disallowed in mathlib. This is close to exhaustive; I left some tactic code alone when it seemed to me that tactic could be upstreamed soon.

Notes

In lines I was modifying anyway, I also converted => to ↦.
Also contains some mild in-passing indentation fixes in Mathlib/Order/SupClosed.
Some doc comments still contained Lean 3 syntax λ x, , which I also replaced.

af0f54a9

Diff

@@ -42,7 +42,7 @@ theorem cardinal_mk_eq_sum' : #(WType β) = sum (fun a : α => #(WType β) ^ lif
   (mk_congr <| equivSigma β).trans <| by
     simp_rw [mk_sigma, mk_arrow]; rw [lift_id'.{v, u}, lift_umax.{v, u}]
 
-/-- `#(WType β)` is the least cardinal `κ` such that `sum (λ a : α, κ ^ #(β a)) ≤ κ` -/
+/-- `#(WType β)` is the least cardinal `κ` such that `sum (fun a : α ↦ κ ^ #(β a)) ≤ κ` -/
 theorem cardinal_mk_le_of_le' {κ : Cardinal.{max u v}}
     (hκ : (sum fun a : α => κ ^ lift.{u} #(β a)) ≤ κ) :
     #(WType β) ≤ κ := by
@@ -89,7 +89,7 @@ theorem cardinal_mk_eq_sum : #(WType β) = sum (fun a : α => #(WType β) ^ #(β
   cardinal_mk_eq_sum'.trans <| by simp_rw [lift_id]
 #align W_type.cardinal_mk_eq_sum WType.cardinal_mk_eq_sum
 
-/-- `#(WType β)` is the least cardinal `κ` such that `sum (λ a : α, κ ^ #(β a)) ≤ κ` -/
+/-- `#(WType β)` is the least cardinal `κ` such that `sum (fun a : α ↦ κ ^ #(β a)) ≤ κ` -/
 theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (sum fun a : α => κ ^ #(β a)) ≤ κ) :
     #(WType β) ≤ κ := cardinal_mk_le_of_le' <| by simp_rw [lift_id]; exact hκ
 #align W_type.cardinal_mk_le_of_le WType.cardinal_mk_le_of_le

6eeb941c

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

@@ -35,7 +35,7 @@ namespace WType
 
 open Cardinal
 
--- porting note: `W` is a special name, exceptionally in upper case in Lean3
+-- Porting note: `W` is a special name, exceptionally in upper case in Lean3
 set_option linter.uppercaseLean3 false
 
 theorem cardinal_mk_eq_sum' : #(WType β) = sum (fun a : α => #(WType β) ^ lift.{u} #(β a)) :=

6eeb941c

feat: cardinality of Subfield.closure (#8942)

Also generalize results about the cardinality of WType to be universe polymorphic.

Zulip discussion about the approach

depends on: #8941

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

2e77db72

Diff

@@ -25,9 +25,9 @@ W, W type, cardinal, first order
 -/
 
 
-universe u
+universe u v
 
-variable {α : Type u} {β : α → Type u}
+variable {α : Type u} {β : α → Type v}
 
 noncomputable section
 
@@ -38,47 +38,65 @@ open Cardinal
 -- porting note: `W` is a special name, exceptionally in upper case in Lean3
 set_option linter.uppercaseLean3 false
 
-theorem cardinal_mk_eq_sum : #(WType β) = sum (fun a : α => #(WType β) ^ #(β a)) := by
-  simp only [Cardinal.power_def, ← Cardinal.mk_sigma]
-  exact mk_congr (equivSigma β)
-#align W_type.cardinal_mk_eq_sum WType.cardinal_mk_eq_sum
+theorem cardinal_mk_eq_sum' : #(WType β) = sum (fun a : α => #(WType β) ^ lift.{u} #(β a)) :=
+  (mk_congr <| equivSigma β).trans <| by
+    simp_rw [mk_sigma, mk_arrow]; rw [lift_id'.{v, u}, lift_umax.{v, u}]
 
 /-- `#(WType β)` is the least cardinal `κ` such that `sum (λ a : α, κ ^ #(β a)) ≤ κ` -/
-theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (sum fun a : α => κ ^ #(β a)) ≤ κ) :
+theorem cardinal_mk_le_of_le' {κ : Cardinal.{max u v}}
+    (hκ : (sum fun a : α => κ ^ lift.{u} #(β a)) ≤ κ) :
     #(WType β) ≤ κ := by
   induction' κ using Cardinal.inductionOn with γ
-  simp only [Cardinal.power_def, ← Cardinal.mk_sigma, Cardinal.le_def] at hκ
+  simp_rw [← lift_umax.{v, u}] at hκ
+  nth_rewrite 1 [← lift_id'.{v, u} #γ] at hκ
+  simp_rw [← mk_arrow, ← mk_sigma, le_def] at hκ
   cases' hκ with hκ
   exact Cardinal.mk_le_of_injective (elim_injective _ hκ.1 hκ.2)
-#align W_type.cardinal_mk_le_of_le WType.cardinal_mk_le_of_le
 
 /-- If, for any `a : α`, `β a` is finite, then the cardinality of `WType β`
   is at most the maximum of the cardinality of `α` and `ℵ₀`  -/
-theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : #(WType β) ≤ max #α ℵ₀ :=
+theorem cardinal_mk_le_max_aleph0_of_finite' [∀ a, Finite (β a)] :
+    #(WType β) ≤ max (lift.{v} #α) ℵ₀ :=
   (isEmpty_or_nonempty α).elim
     (by
       intro h
       rw [Cardinal.mk_eq_zero (WType β)]
       exact zero_le _)
     fun hn =>
-    let m := max #α ℵ₀
-    cardinal_mk_le_of_le <|
+    let m := max (lift.{v} #α) ℵ₀
+    cardinal_mk_le_of_le' <|
       calc
-        (Cardinal.sum fun a => m ^ #(β a)) ≤ #α * ⨆ a, m ^ #(β a) := Cardinal.sum_le_iSup _
-        _ ≤ m * ⨆ a, m ^ #(β a) := mul_le_mul' (le_max_left _ _) le_rfl
+        (Cardinal.sum fun a => m ^ lift.{u} #(β a)) ≤ lift.{v} #α * ⨆ a, m ^ lift.{u} #(β a) :=
+          Cardinal.sum_le_iSup_lift _
+        _ ≤ m * ⨆ a, m ^ lift.{u} #(β a) := mul_le_mul' (le_max_left _ _) le_rfl
         _ = m :=
-          mul_eq_left.{u} (le_max_right _ _)
+          mul_eq_left (le_max_right _ _)
               (ciSup_le' fun i => pow_le (le_max_right _ _) (lt_aleph0_of_finite _)) <|
             pos_iff_ne_zero.1 <|
               Order.succ_le_iff.1
                 (by
                   rw [succ_zero]
                   obtain ⟨a⟩ : Nonempty α := hn
-                  refine' le_trans _ (le_ciSup (bddAbove_range.{u, u} _) a)
+                  refine' le_trans _ (le_ciSup (bddAbove_range.{_, v} _) a)
                   rw [← power_zero]
                   exact
                     power_le_power_left
                       (pos_iff_ne_zero.1 (aleph0_pos.trans_le (le_max_right _ _))) (zero_le _))
-#align W_type.cardinal_mk_le_max_aleph_0_of_finite WType.cardinal_mk_le_max_aleph0_of_finite
+
+variable {β : α → Type u}
+
+theorem cardinal_mk_eq_sum : #(WType β) = sum (fun a : α => #(WType β) ^ #(β a)) :=
+  cardinal_mk_eq_sum'.trans <| by simp_rw [lift_id]
+#align W_type.cardinal_mk_eq_sum WType.cardinal_mk_eq_sum
+
+/-- `#(WType β)` is the least cardinal `κ` such that `sum (λ a : α, κ ^ #(β a)) ≤ κ` -/
+theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (sum fun a : α => κ ^ #(β a)) ≤ κ) :
+    #(WType β) ≤ κ := cardinal_mk_le_of_le' <| by simp_rw [lift_id]; exact hκ
+#align W_type.cardinal_mk_le_of_le WType.cardinal_mk_le_of_le
+
+/-- If, for any `a : α`, `β a` is finite, then the cardinality of `WType β`
+  is at most the maximum of the cardinality of `α` and `ℵ₀`  -/
+theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : #(WType β) ≤ max #α ℵ₀ :=
+  cardinal_mk_le_max_aleph0_of_finite'.trans_eq <| by rw [lift_id]
 
 end WType

6eeb941c

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) 2021 Chris Hughes. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module data.W.cardinal
-! leanprover-community/mathlib commit 6eeb941cf39066417a09b1bbc6e74761cadfcb1a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.W.Basic
 import Mathlib.SetTheory.Cardinal.Ordinal
 
+#align_import data.W.cardinal from "leanprover-community/mathlib"@"6eeb941cf39066417a09b1bbc6e74761cadfcb1a"
+
 /-!
 # Cardinality of W-types

6eeb941c

fix: precedence of # (#5623)

d450fcd7

Diff

@@ -41,14 +41,14 @@ open Cardinal
 -- porting note: `W` is a special name, exceptionally in upper case in Lean3
 set_option linter.uppercaseLean3 false
 
-theorem cardinal_mk_eq_sum : (#WType β) = sum (fun a : α => (#WType β) ^ (#β a)) := by
+theorem cardinal_mk_eq_sum : #(WType β) = sum (fun a : α => #(WType β) ^ #(β a)) := by
   simp only [Cardinal.power_def, ← Cardinal.mk_sigma]
   exact mk_congr (equivSigma β)
 #align W_type.cardinal_mk_eq_sum WType.cardinal_mk_eq_sum
 
 /-- `#(WType β)` is the least cardinal `κ` such that `sum (λ a : α, κ ^ #(β a)) ≤ κ` -/
-theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (sum fun a : α => κ ^ (#β a)) ≤ κ) :
-    (#WType β) ≤ κ := by
+theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (sum fun a : α => κ ^ #(β a)) ≤ κ) :
+    #(WType β) ≤ κ := by
   induction' κ using Cardinal.inductionOn with γ
   simp only [Cardinal.power_def, ← Cardinal.mk_sigma, Cardinal.le_def] at hκ
   cases' hκ with hκ
@@ -57,18 +57,18 @@ theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (sum fun a : α => κ ^
 
 /-- If, for any `a : α`, `β a` is finite, then the cardinality of `WType β`
   is at most the maximum of the cardinality of `α` and `ℵ₀`  -/
-theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : (#WType β) ≤ max (#α) ℵ₀ :=
+theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : #(WType β) ≤ max #α ℵ₀ :=
   (isEmpty_or_nonempty α).elim
     (by
       intro h
       rw [Cardinal.mk_eq_zero (WType β)]
       exact zero_le _)
     fun hn =>
-    let m := max (#α) ℵ₀
+    let m := max #α ℵ₀
     cardinal_mk_le_of_le <|
       calc
-        (Cardinal.sum fun a => m ^ (#β a)) ≤ (#α) * ⨆ a, m ^ (#β a) := Cardinal.sum_le_iSup _
-        _ ≤ m * ⨆ a, m ^ (#β a) := mul_le_mul' (le_max_left _ _) le_rfl
+        (Cardinal.sum fun a => m ^ #(β a)) ≤ #α * ⨆ a, m ^ #(β a) := Cardinal.sum_le_iSup _
+        _ ≤ m * ⨆ a, m ^ #(β a) := mul_le_mul' (le_max_left _ _) le_rfl
         _ = m :=
           mul_eq_left.{u} (le_max_right _ _)
               (ciSup_le' fun i => pow_le (le_max_right _ _) (lt_aleph0_of_finite _)) <|

6eeb941c

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

@@ -67,17 +67,17 @@ theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : (#WType β)
     let m := max (#α) ℵ₀
     cardinal_mk_le_of_le <|
       calc
-        (Cardinal.sum fun a => m ^ (#β a)) ≤ (#α) * ⨆ a, m ^ (#β a) := Cardinal.sum_le_supᵢ _
+        (Cardinal.sum fun a => m ^ (#β a)) ≤ (#α) * ⨆ a, m ^ (#β a) := Cardinal.sum_le_iSup _
         _ ≤ m * ⨆ a, m ^ (#β a) := mul_le_mul' (le_max_left _ _) le_rfl
         _ = m :=
           mul_eq_left.{u} (le_max_right _ _)
-              (csupᵢ_le' fun i => pow_le (le_max_right _ _) (lt_aleph0_of_finite _)) <|
+              (ciSup_le' fun i => pow_le (le_max_right _ _) (lt_aleph0_of_finite _)) <|
             pos_iff_ne_zero.1 <|
               Order.succ_le_iff.1
                 (by
                   rw [succ_zero]
                   obtain ⟨a⟩ : Nonempty α := hn
-                  refine' le_trans _ (le_csupᵢ (bddAbove_range.{u, u} _) a)
+                  refine' le_trans _ (le_ciSup (bddAbove_range.{u, u} _) a)
                   rw [← power_zero]
                   exact
                     power_le_power_left

6eeb941c

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

@@ -82,7 +82,6 @@ theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : (#WType β)
                   exact
                     power_le_power_left
                       (pos_iff_ne_zero.1 (aleph0_pos.trans_le (le_max_right _ _))) (zero_le _))
-
 #align W_type.cardinal_mk_le_max_aleph_0_of_finite WType.cardinal_mk_le_max_aleph0_of_finite
 
 end WType

6eeb941c

chore: tidy various files (#3530)

8cf71b01

Diff

@@ -38,7 +38,6 @@ namespace WType
 
 open Cardinal
 
-open Cardinal
 -- porting note: `W` is a special name, exceptionally in upper case in Lean3
 set_option linter.uppercaseLean3 false
 
@@ -47,7 +46,7 @@ theorem cardinal_mk_eq_sum : (#WType β) = sum (fun a : α => (#WType β) ^ (#β
   exact mk_congr (equivSigma β)
 #align W_type.cardinal_mk_eq_sum WType.cardinal_mk_eq_sum
 
-/-- `#(WType β)` is the least cardinal `κ` such that `Sum (λ a : α, κ ^ #(β a)) ≤ κ` -/
+/-- `#(WType β)` is the least cardinal `κ` such that `sum (λ a : α, κ ^ #(β a)) ≤ κ` -/
 theorem cardinal_mk_le_of_le {κ : Cardinal.{u}} (hκ : (sum fun a : α => κ ^ (#β a)) ≤ κ) :
     (#WType β) ≤ κ := by
   induction' κ using Cardinal.inductionOn with γ
@@ -77,7 +76,7 @@ theorem cardinal_mk_le_max_aleph0_of_finite [∀ a, Finite (β a)] : (#WType β)
               Order.succ_le_iff.1
                 (by
                   rw [succ_zero]
-                  obtain ⟨a⟩ : Nonempty α; exact hn
+                  obtain ⟨a⟩ : Nonempty α := hn
                   refine' le_trans _ (le_csupᵢ (bddAbove_range.{u, u} _) a)
                   rw [← power_zero]
                   exact

6eeb941c

feat: port Data.W.Cardinal (#2465)

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

cdd500c7

`data.W.cardinal` ⟷ `Mathlib.Data.W.Cardinal`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 349

data.W.cardinal ⟷ Mathlib.Data.W.Cardinal

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 349

`data.W.cardinal` ⟷ `Mathlib.Data.W.Cardinal`