set_theory.cardinal.cofinality | 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

7c2ce0c2

(last sync)

refactor(set_theory/cardinal/basic): redefine cardinal.is_limit in terms of is_succ_limit (#18523)

We redefine cardinal.is_limit x as x ≠ 0 ∧ is_succ_limit x. This will allow us to make use of the extensive is_succ_limit API in the future.

Diff

@@ -20,7 +20,6 @@ This file contains the definition of cofinality of an ordinal number and regular
 * `ordinal.cof o` is the cofinality of the ordinal `o`.
   If `o` is the order type of the relation `<` on `α`, then `o.cof` is the smallest cardinality of a
   subset `s` of α that is *cofinal* in `α`, i.e. `∀ x : α, ∃ y ∈ s, ¬ y < x`.
-* `cardinal.is_limit c` means that `c` is a (weak) limit cardinal: `c ≠ 0 ∧ ∀ x < c, succ x < c`.
 * `cardinal.is_strong_limit c` means that `c` is a strong limit cardinal:
   `c ≠ 0 ∧ ∀ x < c, 2 ^ x < c`.
 * `cardinal.is_regular c` means that `c` is a regular cardinal: `ℵ₀ ≤ c ∧ c.ord.cof = c`.
@@ -715,25 +714,6 @@ open ordinal
 
 local infixr (name := cardinal.pow) ^ := @pow cardinal.{u} cardinal cardinal.has_pow
 
-/-- A cardinal is a limit if it is not zero or a successor
-  cardinal. Note that `ℵ₀` is a limit cardinal by this definition. -/
-def is_limit (c : cardinal) : Prop :=
-c ≠ 0 ∧ ∀ x < c, succ x < c
-
-theorem is_limit.ne_zero {c} (h : is_limit c) : c ≠ 0 :=
-h.1
-
-theorem is_limit.succ_lt {x c} (h : is_limit c) : x < c → succ x < c :=
-h.2 x
-
-theorem is_limit.aleph_0_le {c} (h : is_limit c) : ℵ₀ ≤ c :=
-begin
-  by_contra' h',
-  rcases lt_aleph_0.1 h' with ⟨_ | n, rfl⟩,
-  { exact h.1.irrefl },
-  { simpa using h.2 n }
-end
-
 /-- A cardinal is a strong limit if it is not zero and it is
   closed under powersets. Note that `ℵ₀` is a strong limit by this definition. -/
 def is_strong_limit (c : cardinal) : Prop :=
@@ -751,23 +731,23 @@ theorem is_strong_limit_aleph_0 : is_strong_limit ℵ₀ :=
   exact_mod_cast nat_lt_aleph_0 (pow 2 n)
 end⟩
 
-theorem is_strong_limit.is_limit {c} (H : is_strong_limit c) : is_limit c :=
-⟨H.1, λ x h, (succ_le_of_lt $ cantor x).trans_lt (H.2 _ h)⟩
+protected theorem is_strong_limit.is_succ_limit {c} (H : is_strong_limit c) : is_succ_limit c :=
+is_succ_limit_of_succ_lt $ λ x h, (succ_le_of_lt $ cantor x).trans_lt (H.two_power_lt h)
 
-theorem is_limit_aleph_0 : is_limit ℵ₀ :=
-is_strong_limit_aleph_0.is_limit
+theorem is_strong_limit.is_limit {c} (H : is_strong_limit c) : is_limit c :=
+⟨H.ne_zero, H.is_succ_limit⟩
 
-theorem is_strong_limit_beth {o : ordinal} (H : ∀ a < o, succ a < o) : is_strong_limit (beth o) :=
+theorem is_strong_limit_beth {o : ordinal} (H : is_succ_limit o) : is_strong_limit (beth o) :=
 begin
   rcases eq_or_ne o 0 with rfl | h,
   { rw beth_zero,
     exact is_strong_limit_aleph_0 },
   { refine ⟨beth_ne_zero o, λ a ha, _⟩,
-    rw beth_limit ⟨h, H⟩ at ha,
+    rw beth_limit ⟨h, is_succ_limit_iff_succ_lt.1 H⟩ at ha,
     rcases exists_lt_of_lt_csupr' ha with ⟨⟨i, hi⟩, ha⟩,
     have := power_le_power_left two_ne_zero ha.le,
     rw ←beth_succ at this,
-    exact this.trans_lt (beth_lt.2 (H i hi)) }
+    exact this.trans_lt (beth_lt.2 (H.succ_lt hi)) }
 end
 
 theorem mk_bounded_subset {α : Type*} (h : ∀ x < #α, 2 ^ x < #α) {r : α → α → Prop}

bb168510

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

7c2ce0c2

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -271,9 +271,9 @@ theorem cof_eq_sInf_lsub (o : Ordinal.{u}) :
           fun s t hst => by
           let H := congr_arg f hst
           rwa [Classical.choose_spec s.prop, Classical.choose_spec t.prop, typein_inj,
-            Subtype.coe_inj] at H )
+            Subtype.coe_inj] at H)
     have := typein_lt_self a
-    simp_rw [← hf, lt_lsub_iff] at this 
+    simp_rw [← hf, lt_lsub_iff] at this
     cases' this with i hi
     refine' ⟨enum (· < ·) (f i) _, _, _⟩
     · rw [type_lt, ← hf]; apply lt_lsub
@@ -283,10 +283,10 @@ theorem cof_eq_sInf_lsub (o : Ordinal.{u}) :
     let f : S → Ordinal := fun s => typein (· < ·) s.val
     refine'
       ⟨S, f, le_antisymm (lsub_le fun i => typein_lt_self i) (le_of_forall_lt fun a ha => _), by
-        rwa [type_lt o] at hS' ⟩
-    rw [← type_lt o] at ha 
+        rwa [type_lt o] at hS'⟩
+    rw [← type_lt o] at ha
     rcases hS (enum (· < ·) a ha) with ⟨b, hb, hb'⟩
-    rw [← typein_le_typein, typein_enum] at hb' 
+    rw [← typein_le_typein, typein_enum] at hb'
     exact hb'.trans_lt (lt_lsub.{u, u} f ⟨b, hb⟩)
 #align ordinal.cof_eq_Inf_lsub Ordinal.cof_eq_sInf_lsub
 -/
@@ -310,8 +310,8 @@ theorem lift_cof (o) : (cof o).lift = cof o.lift :=
   · rcases cof_eq r with ⟨S, H, e'⟩
     have : (#ULift.down ⁻¹' S) ≤ (#S).lift :=
       ⟨⟨fun ⟨⟨x⟩, h⟩ => ⟨⟨x, h⟩⟩, fun ⟨⟨x⟩, h₁⟩ ⟨⟨y⟩, h₂⟩ e => by
-          simp at e  <;> congr <;> injections⟩⟩
-    rw [e'] at this 
+          simp at e <;> congr <;> injections⟩⟩
+    rw [e'] at this
     refine' (cof_type_le _).trans this
     exact fun ⟨a⟩ =>
       let ⟨b, bs, br⟩ := H a
@@ -386,7 +386,7 @@ theorem lsub_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof
 
 #print Ordinal.cof_sup_le_lift /-
 theorem cof_sup_le_lift {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup f) : cof (sup f) ≤ (#ι).lift := by
-  rw [← sup_eq_lsub_iff_lt_sup] at H ; rw [H]; exact cof_lsub_le_lift f
+  rw [← sup_eq_lsub_iff_lt_sup] at H; rw [H]; exact cof_lsub_le_lift f
 #align ordinal.cof_sup_le_lift Ordinal.cof_sup_le_lift
 -/
 
@@ -478,7 +478,7 @@ theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, b
   by
   rcases exists_lsub_cof o with ⟨ι, f, hf, hι⟩
   rcases Cardinal.ord_eq ι with ⟨r, hr, hι'⟩
-  rw [← @blsub_eq_lsub' ι r hr] at hf 
+  rw [← @blsub_eq_lsub' ι r hr] at hf
   rw [← hι, hι']
   exact ⟨_, hf⟩
 #align ordinal.exists_blsub_cof Ordinal.exists_blsub_cof
@@ -491,7 +491,7 @@ theorem le_cof_iff_blsub {b : Ordinal} {a : Cardinal} :
     ⟨fun H o f hf => by simpa using H _ hf, fun H ι f hf =>
       by
       rcases Cardinal.ord_eq ι with ⟨r, hr, hι'⟩
-      rw [← @blsub_eq_lsub' ι r hr] at hf 
+      rw [← @blsub_eq_lsub' ι r hr] at hf
       simpa using H _ hf⟩
 #align ordinal.le_cof_iff_blsub Ordinal.le_cof_iff_blsub
 -/
@@ -526,7 +526,7 @@ theorem blsub_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho :
 
 #print Ordinal.cof_bsup_le_lift /-
 theorem cof_bsup_le_lift {o : Ordinal} {f : ∀ a < o, Ordinal} (H : ∀ i h, f i h < bsup o f) :
-    cof (bsup o f) ≤ o.card.lift := by rw [← bsup_eq_blsub_iff_lt_bsup] at H ; rw [H];
+    cof (bsup o f) ≤ o.card.lift := by rw [← bsup_eq_blsub_iff_lt_bsup] at H; rw [H];
   exact cof_blsub_le_lift f
 #align ordinal.cof_bsup_le_lift Ordinal.cof_bsup_le_lift
 -/
@@ -603,7 +603,7 @@ theorem cof_succ (o) : cof (succ o) = 1 :=
 theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
   ⟨inductionOn o fun α r _ z => by
       skip
-      rcases cof_eq r with ⟨S, hl, e⟩; rw [z] at e 
+      rcases cof_eq r with ⟨S, hl, e⟩; rw [z] at e
       cases' mk_ne_zero_iff.1 (by rw [e] <;> exact one_ne_zero) with a
       refine'
         ⟨typein r a,
@@ -619,7 +619,7 @@ theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
         · exact Or.inl h
         · exact Or.inr ⟨PUnit.unit, h.symm⟩
         · rcases hl x with ⟨a', aS, hn⟩
-          rw [(_ : ↑a = a')] at h ; · exact absurd h hn
+          rw [(_ : ↑a = a')] at h; · exact absurd h hn
           refine' congr_arg Subtype.val (_ : a = ⟨a', aS⟩)
           haveI := le_one_iff_subsingleton.1 (le_of_eq e)
           apply Subsingleton.elim,
@@ -682,8 +682,8 @@ protected theorem succ : IsFundamentalSequence (succ o) 1 fun _ _ => o :=
   by
   refine' ⟨_, fun i j hi hj h => _, blsub_const Ordinal.one_ne_zero o⟩
   · rw [cof_succ, ord_one]
-  · rw [lt_one_iff_zero] at hi hj 
-    rw [hi, hj] at h 
+  · rw [lt_one_iff_zero] at hi hj
+    rw [hi, hj] at h
     exact h.false.elim
 #align ordinal.is_fundamental_sequence.succ Ordinal.IsFundamentalSequence.succ
 -/
@@ -739,7 +739,7 @@ theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequ
     · refine' ⟨typein r' ⟨i, h⟩, typein_lt_type _ _, _⟩
       rw [bfamily_of_family'_typein]
       rfl
-    · push_neg at h 
+    · push_neg at h
       cases' wo.wf.min_mem _ h with hji hij
       refine' ⟨typein r' ⟨_, fun k hkj => lt_of_lt_of_le _ hij⟩, typein_lt_type _ _, _⟩
       · by_contra! H
@@ -773,12 +773,12 @@ protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u
     have H : ∀ i, ∃ b < a, f' i ≤ f b := fun i =>
       by
       have := lt_lsub.{u, u} f' i
-      rwa [hf', ← IsNormal.blsub_eq.{u, u} hf ha, lt_blsub_iff] at this 
+      rwa [hf', ← IsNormal.blsub_eq.{u, u} hf ha, lt_blsub_iff] at this
     refine' (lsub_le fun i => _).antisymm (le_of_forall_lt fun b hb => _)
     · rcases H i with ⟨b, hb, hb'⟩
       exact lt_of_le_of_lt (csInf_le' hb') hb
     · have := hf.strict_mono hb
-      rw [← hf', lt_lsub_iff] at this 
+      rw [← hf', lt_lsub_iff] at this
       cases' this with i hi
       rcases H i with ⟨b, _, hb⟩
       exact
@@ -829,11 +829,11 @@ theorem aleph0_le_cof {o} : ℵ₀ ≤ cof o ↔ IsLimit o :=
   · simp [l]; refine' le_of_not_lt fun h => _
     cases' Cardinal.lt_aleph0.1 h with n e
     have := cof_cof o
-    rw [e, ord_nat] at this 
+    rw [e, ord_nat] at this
     cases n
-    · simp at e ; simpa [e, not_zero_is_limit] using l
-    · rw [nat_cast_succ, cof_succ] at this 
-      rw [← this, cof_eq_one_iff_is_succ] at e 
+    · simp at e; simpa [e, not_zero_is_limit] using l
+    · rw [nat_cast_succ, cof_succ] at this
+      rw [← this, cof_eq_one_iff_is_succ] at e
       rcases e with ⟨a, rfl⟩
       exact not_succ_is_limit _ l
 #align ordinal.aleph_0_le_cof Ordinal.aleph0_le_cof
@@ -908,7 +908,7 @@ theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder
     (h₁ : Unbounded r <| ⋃₀ s) (h₂ : (#s) < StrictOrder.cof r) : ∃ x ∈ s, Unbounded r x :=
   by
   by_contra! h
-  simp_rw [not_unbounded_iff] at h 
+  simp_rw [not_unbounded_iff] at h
   let f : s → α := fun x : s => wo.wf.sup x (h x.1 x.2)
   refine' h₂.not_le (le_trans (csInf_le' ⟨range f, fun x => _, rfl⟩) mk_range_le)
   rcases h₁ x with ⟨y, ⟨c, hc, hy⟩, hxy⟩
@@ -922,7 +922,7 @@ theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder
 theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
     (s : β → Set α) (h₁ : Unbounded r <| ⋃ x, s x) (h₂ : (#β) < StrictOrder.cof r) :
     ∃ x : β, Unbounded r (s x) := by
-  rw [← sUnion_range] at h₁ 
+  rw [← sUnion_range] at h₁
   rcases unbounded_of_unbounded_sUnion r h₁ (mk_range_le.trans_lt h₂) with ⟨_, ⟨x, rfl⟩, u⟩
   exact ⟨x, u⟩
 #align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_iUnion
@@ -1034,10 +1034,10 @@ theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (be
   · rw [beth_zero]
     exact is_strong_limit_aleph_0
   · refine' ⟨beth_ne_zero o, fun a ha => _⟩
-    rw [beth_limit ⟨h, is_succ_limit_iff_succ_lt.1 H⟩] at ha 
+    rw [beth_limit ⟨h, is_succ_limit_iff_succ_lt.1 H⟩] at ha
     rcases exists_lt_of_lt_ciSup' ha with ⟨⟨i, hi⟩, ha⟩
     have := power_le_power_left two_ne_zero ha.le
-    rw [← beth_succ] at this 
+    rw [← beth_succ] at this
     exact this.trans_lt (beth_lt.2 (H.succ_lt hi))
 #align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_beth
 -/
@@ -1086,7 +1086,7 @@ theorem mk_subset_mk_lt_cof {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) :
   apply le_antisymm
   · nth_rw_rhs 1 [← mk_bounded_subset h hr]
     apply mk_le_mk_of_subset fun s hs => _
-    rw [hr] at hs 
+    rw [hr] at hs
     exact lt_cof_type hs
   · refine' @mk_le_of_injective α _ (fun x => Subtype.mk {x} _) _
     · rw [mk_singleton]
@@ -1144,7 +1144,7 @@ theorem isRegular_succ {c : Cardinal.{u}} (h : ℵ₀ ≤ c) : IsRegular (succ c
   ⟨h.trans (le_succ c),
     succ_le_of_lt
       (by
-        cases' Quotient.exists_rep (@succ Cardinal _ _ c) with α αe; simp at αe 
+        cases' Quotient.exists_rep (@succ Cardinal _ _ c) with α αe; simp at αe
         rcases ord_eq α with ⟨r, wo, re⟩; skip
         have := ord_is_limit (h.trans (le_succ _))
         rw [← αe, re] at this ⊢
@@ -1221,13 +1221,13 @@ theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α 
     rw [w]
     exact infinite_univ
   by_contra h
-  simp only [not_le] at h 
+  simp only [not_le] at h
   let u : ∀ b, ∃ a, b ∈ f a := fun b => by simpa using (w.ge : _) (Set.mem_univ b)
   let u' : β → range f := fun b => ⟨f (u b).some, by simp⟩
   have v' : ∀ a, u' ⁻¹' {⟨f a, by simp⟩} ≤ f a :=
     by
     rintro a p m
-    simp at m 
+    simp at m
     rw [← m]
     apply fun b => (u b).choose_spec
   obtain ⟨⟨-, ⟨a, rfl⟩⟩, p⟩ := exists_infinite_fiber u' h k
@@ -1458,7 +1458,7 @@ theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
           let ⟨b, h, ab⟩ := H a
           ⟨⟨⟨_, h⟩, _, ab⟩, rfl⟩
     · have := typein_lt_type r i
-      rwa [← re, lt_ord] at this 
+      rwa [← re, lt_ord] at this
 #align cardinal.lt_power_cof Cardinal.lt_power_cof
 -/

7c2ce0c2

bump to nightly-2023-12-06-06

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

d09917f6

Diff

@@ -742,7 +742,7 @@ theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequ
     · push_neg at h 
       cases' wo.wf.min_mem _ h with hji hij
       refine' ⟨typein r' ⟨_, fun k hkj => lt_of_lt_of_le _ hij⟩, typein_lt_type _ _, _⟩
-      · by_contra' H
+      · by_contra! H
         exact (wo.wf.not_lt_min _ h ⟨IsTrans.trans _ _ _ hkj hji, H⟩) hkj
       · rwa [bfamily_of_family'_typein]
 #align ordinal.exists_fundamental_sequence Ordinal.exists_fundamental_sequence
@@ -907,7 +907,7 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ :=
 theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder α r] {s : Set (Set α)}
     (h₁ : Unbounded r <| ⋃₀ s) (h₂ : (#s) < StrictOrder.cof r) : ∃ x ∈ s, Unbounded r x :=
   by
-  by_contra' h
+  by_contra! h
   simp_rw [not_unbounded_iff] at h 
   let f : s → α := fun x : s => wo.wf.sup x (h x.1 x.2)
   refine' h₂.not_le (le_trans (csInf_le' ⟨range f, fun x => _, rfl⟩) mk_range_le)
@@ -934,7 +934,7 @@ theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤
     ∃ a : α, (#f ⁻¹' {a}) = (#β) :=
   by
   have : ∃ a, (#β) ≤ (#f ⁻¹' {a}) := by
-    by_contra' h
+    by_contra! h
     apply mk_univ.not_lt
     rw [← preimage_univ, ← Union_of_singleton, preimage_Union]
     exact

7c2ce0c2

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 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios
 -/
-import Mathbin.SetTheory.Cardinal.Ordinal
-import Mathbin.SetTheory.Ordinal.FixedPoint
+import SetTheory.Cardinal.Ordinal
+import SetTheory.Ordinal.FixedPoint
 
 #align_import set_theory.cardinal.cofinality from "leanprover-community/mathlib"@"7c2ce0c2da15516b4e65d0c9e254bb6dc93abd1f"

7c2ce0c2

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 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios
-
-! This file was ported from Lean 3 source module set_theory.cardinal.cofinality
-! leanprover-community/mathlib commit 7c2ce0c2da15516b4e65d0c9e254bb6dc93abd1f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.SetTheory.Cardinal.Ordinal
 import Mathbin.SetTheory.Ordinal.FixedPoint
 
+#align_import set_theory.cardinal.cofinality from "leanprover-community/mathlib"@"7c2ce0c2da15516b4e65d0c9e254bb6dc93abd1f"
+
 /-!
 # Cofinality

7c2ce0c2

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -74,16 +74,21 @@ def cof (r : α → α → Prop) : Cardinal :=
 #align order.cof Order.cof
 -/
 
+#print Order.cof_nonempty /-
 /-- The set in the definition of `order.cof` is nonempty. -/
 theorem cof_nonempty (r : α → α → Prop) [IsRefl α r] :
     {c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c}.Nonempty :=
   ⟨_, Set.univ, fun a => ⟨a, ⟨⟩, refl _⟩, rfl⟩
 #align order.cof_nonempty Order.cof_nonempty
+-/
 
+#print Order.cof_le /-
 theorem cof_le (r : α → α → Prop) {S : Set α} (h : ∀ a, ∃ b ∈ S, r a b) : cof r ≤ (#S) :=
   csInf_le' ⟨S, h, rfl⟩
 #align order.cof_le Order.cof_le
+-/
 
+#print Order.le_cof /-
 theorem le_cof {r : α → α → Prop} [IsRefl α r] (c : Cardinal) :
     c ≤ cof r ↔ ∀ {S : Set α}, (∀ a, ∃ b ∈ S, r a b) → c ≤ (#S) :=
   by
@@ -92,6 +97,7 @@ theorem le_cof {r : α → α → Prop} [IsRefl α r] (c : Cardinal) :
   rintro H d ⟨S, h, rfl⟩
   exact H h
 #align order.le_cof Order.le_cof
+-/
 
 end Order
 
@@ -253,6 +259,7 @@ theorem cof_lsub_def_nonempty (o) :
 #align ordinal.cof_lsub_def_nonempty Ordinal.cof_lsub_def_nonempty
 -/
 
+#print Ordinal.cof_eq_sInf_lsub /-
 theorem cof_eq_sInf_lsub (o : Ordinal.{u}) :
     cof o = sInf {a : Cardinal | ∃ (ι : Type u) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a} :=
   by
@@ -285,7 +292,9 @@ theorem cof_eq_sInf_lsub (o : Ordinal.{u}) :
     rw [← typein_le_typein, typein_enum] at hb' 
     exact hb'.trans_lt (lt_lsub.{u, u} f ⟨b, hb⟩)
 #align ordinal.cof_eq_Inf_lsub Ordinal.cof_eq_sInf_lsub
+-/
 
+#print Ordinal.lift_cof /-
 @[simp]
 theorem lift_cof (o) : (cof o).lift = cof o.lift :=
   by
@@ -311,6 +320,7 @@ theorem lift_cof (o) : (cof o).lift = cof o.lift :=
       let ⟨b, bs, br⟩ := H a
       ⟨⟨b⟩, bs, br⟩
 #align ordinal.lift_cof Ordinal.lift_cof
+-/
 
 #print Ordinal.cof_le_card /-
 theorem cof_le_card (o) : cof o ≤ card o := by rw [cof_eq_Inf_lsub]; exact csInf_le' card_mem_cof
@@ -403,6 +413,7 @@ theorem sup_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof)
 #align ordinal.sup_lt_ord Ordinal.sup_lt_ord
 -/
 
+#print Ordinal.iSup_lt_lift /-
 theorem iSup_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal} (hι : Cardinal.lift (#ι) < c.ord.cof)
     (hf : ∀ i, f i < c) : iSup f < c :=
   by
@@ -411,11 +422,14 @@ theorem iSup_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal} (hι : Cardinal.l
   rw [ord_lt_ord]
   apply hf
 #align ordinal.supr_lt_lift Ordinal.iSup_lt_lift
+-/
 
+#print Ordinal.iSup_lt /-
 theorem iSup_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : (#ι) < c.ord.cof) :
     (∀ i, f i < c) → iSup f < c :=
   iSup_lt_lift (by rwa [(#ι).lift_id])
 #align ordinal.supr_lt Ordinal.iSup_lt
+-/
 
 #print Ordinal.nfpFamily_lt_ord_lift /-
 theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
@@ -666,6 +680,7 @@ protected theorem zero {f : ∀ b < (0 : Ordinal), Ordinal} : IsFundamentalSeque
 #align ordinal.is_fundamental_sequence.zero Ordinal.IsFundamentalSequence.zero
 -/
 
+#print Ordinal.IsFundamentalSequence.succ /-
 protected theorem succ : IsFundamentalSequence (succ o) 1 fun _ _ => o :=
   by
   refine' ⟨_, fun i j hi hj h => _, blsub_const Ordinal.one_ne_zero o⟩
@@ -674,6 +689,7 @@ protected theorem succ : IsFundamentalSequence (succ o) 1 fun _ _ => o :=
     rw [hi, hj] at h 
     exact h.false.elim
 #align ordinal.is_fundamental_sequence.succ Ordinal.IsFundamentalSequence.succ
+-/
 
 #print Ordinal.IsFundamentalSequence.monotone /-
 protected theorem monotone (hf : IsFundamentalSequence a o f) {i j : Ordinal} (hi : i < o)
@@ -847,6 +863,7 @@ theorem cof_omega : cof ω = ℵ₀ :=
 #align ordinal.cof_omega Ordinal.cof_omega
 -/
 
+#print Ordinal.cof_eq' /-
 theorem cof_eq' (r : α → α → Prop) [IsWellOrder α r] (h : IsLimit (type r)) :
     ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = cof (type r) :=
   let ⟨S, H, e⟩ := cof_eq r
@@ -859,6 +876,7 @@ theorem cof_eq' (r : α → α → Prop) [IsWellOrder α r] (h : IsLimit (type r
         ab⟩,
     e⟩
 #align ordinal.cof_eq' Ordinal.cof_eq'
+-/
 
 #print Ordinal.cof_univ /-
 @[simp]
@@ -886,6 +904,7 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ :=
 /-! ### Infinite pigeonhole principle -/
 
 
+#print Ordinal.unbounded_of_unbounded_sUnion /-
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
 theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder α r] {s : Set (Set α)}
@@ -898,6 +917,7 @@ theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder
   rcases h₁ x with ⟨y, ⟨c, hc, hy⟩, hxy⟩
   exact ⟨f ⟨c, hc⟩, mem_range_self _, fun hxz => hxy (trans (wo.wf.lt_sup _ hy) hxz)⟩
 #align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_sUnion
+-/
 
 #print Ordinal.unbounded_of_unbounded_iUnion /-
 /-- If the union of s is unbounded and s is smaller than the cofinality,
@@ -968,7 +988,6 @@ namespace Cardinal
 
 open Ordinal
 
--- mathport name: cardinal.pow
 local infixr:0 "^" => @pow Cardinal.{u} Cardinal Cardinal.hasPow
 
 #print Cardinal.IsStrongLimit /-
@@ -985,9 +1004,11 @@ theorem IsStrongLimit.ne_zero {c} (h : IsStrongLimit c) : c ≠ 0 :=
 #align cardinal.is_strong_limit.ne_zero Cardinal.IsStrongLimit.ne_zero
 -/
 
+#print Cardinal.IsStrongLimit.two_power_lt /-
 theorem IsStrongLimit.two_power_lt {x c} (h : IsStrongLimit c) : x < c → (2^x) < c :=
   h.2 x
 #align cardinal.is_strong_limit.two_power_lt Cardinal.IsStrongLimit.two_power_lt
+-/
 
 #print Cardinal.isStrongLimit_aleph0 /-
 theorem isStrongLimit_aleph0 : IsStrongLimit ℵ₀ :=
@@ -1024,6 +1045,7 @@ theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (be
 #align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_beth
 -/
 
+#print Cardinal.mk_bounded_subset /-
 theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α → α → Prop}
     [IsWellOrder α r] (hr : (#α).ord = type r) : (#{ s : Set α // Bounded r s }) = (#α) :=
   by
@@ -1052,7 +1074,9 @@ theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α
     · intro a b hab
       simpa only [singleton_eq_singleton_iff] using hab
 #align cardinal.mk_bounded_subset Cardinal.mk_bounded_subset
+-/
 
+#print Cardinal.mk_subset_mk_lt_cof /-
 theorem mk_subset_mk_lt_cof {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) :
     (#{ s : Set α // (#s) < cof (#α).ord }) = (#α) :=
   by
@@ -1073,6 +1097,7 @@ theorem mk_subset_mk_lt_cof {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) :
     · intro a b hab
       simpa only [singleton_eq_singleton_iff] using hab
 #align cardinal.mk_subset_mk_lt_cof Cardinal.mk_subset_mk_lt_cof
+-/
 
 #print Cardinal.IsRegular /-
 /-- A cardinal is regular if it is infinite and it equals its own cofinality. -/
@@ -1117,6 +1142,7 @@ theorem isRegular_aleph0 : IsRegular ℵ₀ :=
 #align cardinal.is_regular_aleph_0 Cardinal.isRegular_aleph0
 -/
 
+#print Cardinal.isRegular_succ /-
 theorem isRegular_succ {c : Cardinal.{u}} (h : ℵ₀ ≤ c) : IsRegular (succ c) :=
   ⟨h.trans (le_succ c),
     succ_le_of_lt
@@ -1138,10 +1164,13 @@ theorem isRegular_succ {c : Cardinal.{u}} (h : ℵ₀ ≤ c) : IsRegular (succ c
         · rw [← lt_succ_iff, ← lt_ord, ← αe, re]
           apply typein_lt_type)⟩
 #align cardinal.is_regular_succ Cardinal.isRegular_succ
+-/
 
+#print Cardinal.isRegular_aleph_one /-
 theorem isRegular_aleph_one : IsRegular (aleph 1) := by rw [← succ_aleph_0];
   exact is_regular_succ le_rfl
 #align cardinal.is_regular_aleph_one Cardinal.isRegular_aleph_one
+-/
 
 #print Cardinal.isRegular_aleph'_succ /-
 theorem isRegular_aleph'_succ {o : Ordinal} (h : ω ≤ o) : IsRegular (aleph' (succ o)) := by
@@ -1181,6 +1210,7 @@ theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : (#α) < (#β
 #align cardinal.exists_infinite_fiber Cardinal.exists_infinite_fiber
 -/
 
+#print Cardinal.le_range_of_union_finset_eq_top /-
 /-- If an infinite type `β` can be expressed as a union of finite sets,
 then the cardinality of the collection of those finite sets
 must be at least the cardinality of `β`.
@@ -1206,6 +1236,7 @@ theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α 
   obtain ⟨⟨-, ⟨a, rfl⟩⟩, p⟩ := exists_infinite_fiber u' h k
   exact (@Infinite.of_injective _ _ p (inclusion (v' a)) (inclusion_injective _)).False
 #align cardinal.le_range_of_union_finset_eq_top Cardinal.le_range_of_union_finset_eq_top
+-/
 
 #print Cardinal.lsub_lt_ord_lift_of_isRegular /-
 theorem lsub_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
@@ -1263,15 +1294,19 @@ theorem bsup_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc
 #align cardinal.bsup_lt_ord_of_is_regular Cardinal.bsup_lt_ord_of_isRegular
 -/
 
+#print Cardinal.iSup_lt_lift_of_isRegular /-
 theorem iSup_lt_lift_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c) → iSup f < c :=
   iSup_lt_lift (by rwa [hc.cof_eq])
 #align cardinal.supr_lt_lift_of_is_regular Cardinal.iSup_lt_lift_of_isRegular
+-/
 
+#print Cardinal.iSup_lt_of_isRegular /-
 theorem iSup_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c) → iSup f < c :=
   iSup_lt (by rwa [hc.cof_eq])
 #align cardinal.supr_lt_of_is_regular Cardinal.iSup_lt_of_isRegular
+-/
 
 #print Cardinal.sum_lt_lift_of_isRegular /-
 theorem sum_lt_lift_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
@@ -1390,10 +1425,12 @@ def IsInaccessible (c : Cardinal) :=
 #align cardinal.is_inaccessible Cardinal.IsInaccessible
 -/
 
+#print Cardinal.IsInaccessible.mk /-
 theorem IsInaccessible.mk {c} (h₁ : ℵ₀ < c) (h₂ : c ≤ c.ord.cof) (h₃ : ∀ x < c, (2^x) < c) :
     IsInaccessible c :=
   ⟨h₁, ⟨h₁.le, h₂⟩, (aleph0_pos.trans h₁).ne', h₃⟩
 #align cardinal.is_inaccessible.mk Cardinal.IsInaccessible.mk
+-/
 
 #print Cardinal.univ_inaccessible /-
 -- Lean's foundations prove the existence of ℵ₀ many inaccessible cardinals

7c2ce0c2

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -70,13 +70,13 @@ namespace Order
 /-- Cofinality of a reflexive order `≼`. This is the smallest cardinality
   of a subset `S : set α` such that `∀ a, ∃ b ∈ S, a ≼ b`. -/
 def cof (r : α → α → Prop) : Cardinal :=
-  sInf { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c }
+  sInf {c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c}
 #align order.cof Order.cof
 -/
 
 /-- The set in the definition of `order.cof` is nonempty. -/
 theorem cof_nonempty (r : α → α → Prop) [IsRefl α r] :
-    { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c }.Nonempty :=
+    {c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c}.Nonempty :=
   ⟨_, Set.univ, fun a => ⟨a, ⟨⟩, refl _⟩, rfl⟩
 #align order.cof_nonempty Order.cof_nonempty
 
@@ -144,7 +144,7 @@ def StrictOrder.cof (r : α → α → Prop) : Cardinal :=
 #print StrictOrder.cof_nonempty /-
 /-- The set in the definition of `order.strict_order.cof` is nonempty. -/
 theorem StrictOrder.cof_nonempty (r : α → α → Prop) [IsIrrefl α r] :
-    { c | ∃ S : Set α, Unbounded r S ∧ (#S) = c }.Nonempty :=
+    {c | ∃ S : Set α, Unbounded r S ∧ (#S) = c}.Nonempty :=
   @Order.cof_nonempty α _ (IsRefl.swap (rᶜ))
 #align strict_order.cof_nonempty StrictOrder.cof_nonempty
 -/
@@ -209,7 +209,7 @@ theorem ord_cof_eq (r : α → α → Prop) [IsWellOrder α r] :
   by
   let ⟨S, hS, e⟩ := cof_eq r
   let ⟨s, _, e'⟩ := Cardinal.ord_eq S
-  let T : Set α := { a | ∃ aS : a ∈ S, ∀ b : S, s b ⟨_, aS⟩ → r b a }
+  let T : Set α := {a | ∃ aS : a ∈ S, ∀ b : S, s b ⟨_, aS⟩ → r b a}
   skip; suffices
   · refine' ⟨T, this, le_antisymm _ (Cardinal.ord_le.2 <| cof_type_le this)⟩
     rw [← e, e']
@@ -228,7 +228,7 @@ theorem ord_cof_eq (r : α → α → Prop) [IsWellOrder α r] :
     · intro e; injection e with e; subst b
       exact irrefl _ h
   · intro a
-    have : { b : S | ¬r b a }.Nonempty :=
+    have : {b : S | ¬r b a}.Nonempty :=
       let ⟨b, bS, ba⟩ := hS a
       ⟨⟨b, bS⟩, ba⟩
     let b := IsWellFounded.wf.min _ this
@@ -248,14 +248,13 @@ private theorem card_mem_cof {o} : ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u
 #print Ordinal.cof_lsub_def_nonempty /-
 /-- The set in the `lsub` characterization of `cof` is nonempty. -/
 theorem cof_lsub_def_nonempty (o) :
-    { a : Cardinal | ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a }.Nonempty :=
+    {a : Cardinal | ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a}.Nonempty :=
   ⟨_, card_mem_cof⟩
 #align ordinal.cof_lsub_def_nonempty Ordinal.cof_lsub_def_nonempty
 -/
 
 theorem cof_eq_sInf_lsub (o : Ordinal.{u}) :
-    cof o =
-      sInf { a : Cardinal | ∃ (ι : Type u) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } :=
+    cof o = sInf {a : Cardinal | ∃ (ι : Type u) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a} :=
   by
   refine' le_antisymm (le_csInf (cof_lsub_def_nonempty o) _) (csInf_le' _)
   · rintro a ⟨ι, f, hf, rfl⟩
@@ -710,7 +709,7 @@ theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequ
   rcases exists_lsub_cof a with ⟨ι, f, hf, hι⟩
   rcases ord_eq ι with ⟨r, wo, hr⟩
   haveI := wo
-  let r' := Subrel r { i | ∀ j, r j i → f j < f i }
+  let r' := Subrel r {i | ∀ j, r j i → f j < f i}
   let hrr' : r' ↪r r := Subrel.relEmbedding _ _
   haveI := hrr'.is_well_order
   refine'
@@ -727,7 +726,7 @@ theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequ
     · refine' ⟨typein r' ⟨i, h⟩, typein_lt_type _ _, _⟩
       rw [bfamily_of_family'_typein]
       rfl
-    · push_neg  at h 
+    · push_neg at h 
       cases' wo.wf.min_mem _ h with hji hij
       refine' ⟨typein r' ⟨_, fun k hkj => lt_of_lt_of_le _ hij⟩, typein_lt_type _ _, _⟩
       · by_contra' H
@@ -754,7 +753,7 @@ protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u
   refine' ⟨_, fun i j _ _ h => hf.strict_mono (hg.2.1 _ _ h), _⟩
   · rcases exists_lsub_cof (f a) with ⟨ι, f', hf', hι⟩
     rw [← hg.cof_eq, ord_le_ord, ← hι]
-    suffices (lsub.{u, u} fun i => Inf { b : Ordinal | f' i ≤ f b }) = a
+    suffices (lsub.{u, u} fun i => Inf {b : Ordinal | f' i ≤ f b}) = a
       by
       rw [← this]
       apply cof_lsub_le
@@ -949,7 +948,7 @@ theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ
     ∃ (a : α) (t : Set β) (h : t ⊆ s), θ ≤ (#t) ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a :=
   by
   cases' infinite_pigeonhole_card f θ hθ h₁ h₂ with a ha
-  refine' ⟨a, { x | ∃ h, f ⟨x, h⟩ = a }, _, _, _⟩
+  refine' ⟨a, {x | ∃ h, f ⟨x, h⟩ = a}, _, _, _⟩
   · rintro x ⟨hx, hx'⟩; exact hx
   · refine'
       ha.trans
@@ -1038,7 +1037,7 @@ theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α
   have h' : is_strong_limit (#α) := ⟨ha, h⟩
   have ha := h'.is_limit.aleph_0_le
   apply le_antisymm
-  · have : { s : Set α | bounded r s } = ⋃ i, 𝒫{ j | r j i } := set_of_exists _
+  · have : {s : Set α | bounded r s} = ⋃ i, 𝒫{j | r j i} := set_of_exists _
     rw [← coe_set_of, this]
     convert mk_Union_le_sum_mk.trans ((sum_le_supr _).trans (mul_le_max_of_aleph_0_le_left ha))
     apply (max_eq_left _).symm; apply ciSup_le' fun i => _

7c2ce0c2

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -242,19 +242,20 @@ theorem ord_cof_eq (r : α → α → Prop) [IsWellOrder α r] :
 /-! ### Cofinality of suprema and least strict upper bounds -/
 
 
-private theorem card_mem_cof {o} : ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = o.card :=
+private theorem card_mem_cof {o} : ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = o.card :=
   ⟨_, _, lsub_typein o, mk_ordinal_out o⟩
 
 #print Ordinal.cof_lsub_def_nonempty /-
 /-- The set in the `lsub` characterization of `cof` is nonempty. -/
 theorem cof_lsub_def_nonempty (o) :
-    { a : Cardinal | ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a }.Nonempty :=
+    { a : Cardinal | ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a }.Nonempty :=
   ⟨_, card_mem_cof⟩
 #align ordinal.cof_lsub_def_nonempty Ordinal.cof_lsub_def_nonempty
 -/
 
 theorem cof_eq_sInf_lsub (o : Ordinal.{u}) :
-    cof o = sInf { a : Cardinal | ∃ (ι : Type u)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } :=
+    cof o =
+      sInf { a : Cardinal | ∃ (ι : Type u) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } :=
   by
   refine' le_antisymm (le_csInf (cof_lsub_def_nonempty o) _) (csInf_le' _)
   · rintro a ⟨ι, f, hf, rfl⟩
@@ -267,9 +268,9 @@ theorem cof_eq_sInf_lsub (o : Ordinal.{u}) :
           fun s t hst => by
           let H := congr_arg f hst
           rwa [Classical.choose_spec s.prop, Classical.choose_spec t.prop, typein_inj,
-            Subtype.coe_inj] at H)
+            Subtype.coe_inj] at H )
     have := typein_lt_self a
-    simp_rw [← hf, lt_lsub_iff] at this
+    simp_rw [← hf, lt_lsub_iff] at this 
     cases' this with i hi
     refine' ⟨enum (· < ·) (f i) _, _, _⟩
     · rw [type_lt, ← hf]; apply lt_lsub
@@ -279,10 +280,10 @@ theorem cof_eq_sInf_lsub (o : Ordinal.{u}) :
     let f : S → Ordinal := fun s => typein (· < ·) s.val
     refine'
       ⟨S, f, le_antisymm (lsub_le fun i => typein_lt_self i) (le_of_forall_lt fun a ha => _), by
-        rwa [type_lt o] at hS'⟩
-    rw [← type_lt o] at ha
+        rwa [type_lt o] at hS' ⟩
+    rw [← type_lt o] at ha 
     rcases hS (enum (· < ·) a ha) with ⟨b, hb, hb'⟩
-    rw [← typein_le_typein, typein_enum] at hb'
+    rw [← typein_le_typein, typein_enum] at hb' 
     exact hb'.trans_lt (lt_lsub.{u, u} f ⟨b, hb⟩)
 #align ordinal.cof_eq_Inf_lsub Ordinal.cof_eq_sInf_lsub
 
@@ -304,8 +305,8 @@ theorem lift_cof (o) : (cof o).lift = cof o.lift :=
   · rcases cof_eq r with ⟨S, H, e'⟩
     have : (#ULift.down ⁻¹' S) ≤ (#S).lift :=
       ⟨⟨fun ⟨⟨x⟩, h⟩ => ⟨⟨x, h⟩⟩, fun ⟨⟨x⟩, h₁⟩ ⟨⟨y⟩, h₂⟩ e => by
-          simp at e <;> congr <;> injections⟩⟩
-    rw [e'] at this
+          simp at e  <;> congr <;> injections⟩⟩
+    rw [e'] at this 
     refine' (cof_type_le _).trans this
     exact fun ⟨a⟩ =>
       let ⟨b, bs, br⟩ := H a
@@ -330,7 +331,7 @@ theorem ord_cof_le (o : Ordinal.{u}) : o.cof.ord ≤ o :=
 
 #print Ordinal.exists_lsub_cof /-
 theorem exists_lsub_cof (o : Ordinal) :
-    ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = cof o := by rw [cof_eq_Inf_lsub];
+    ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = cof o := by rw [cof_eq_Inf_lsub];
   exact csInf_mem (cof_lsub_def_nonempty o)
 #align ordinal.exists_lsub_cof Ordinal.exists_lsub_cof
 -/
@@ -379,7 +380,7 @@ theorem lsub_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof
 
 #print Ordinal.cof_sup_le_lift /-
 theorem cof_sup_le_lift {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup f) : cof (sup f) ≤ (#ι).lift := by
-  rw [← sup_eq_lsub_iff_lt_sup] at H; rw [H]; exact cof_lsub_le_lift f
+  rw [← sup_eq_lsub_iff_lt_sup] at H ; rw [H]; exact cof_lsub_le_lift f
 #align ordinal.cof_sup_le_lift Ordinal.cof_sup_le_lift
 -/
 
@@ -467,7 +468,7 @@ theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, b
   by
   rcases exists_lsub_cof o with ⟨ι, f, hf, hι⟩
   rcases Cardinal.ord_eq ι with ⟨r, hr, hι'⟩
-  rw [← @blsub_eq_lsub' ι r hr] at hf
+  rw [← @blsub_eq_lsub' ι r hr] at hf 
   rw [← hι, hι']
   exact ⟨_, hf⟩
 #align ordinal.exists_blsub_cof Ordinal.exists_blsub_cof
@@ -480,7 +481,7 @@ theorem le_cof_iff_blsub {b : Ordinal} {a : Cardinal} :
     ⟨fun H o f hf => by simpa using H _ hf, fun H ι f hf =>
       by
       rcases Cardinal.ord_eq ι with ⟨r, hr, hι'⟩
-      rw [← @blsub_eq_lsub' ι r hr] at hf
+      rw [← @blsub_eq_lsub' ι r hr] at hf 
       simpa using H _ hf⟩
 #align ordinal.le_cof_iff_blsub Ordinal.le_cof_iff_blsub
 -/
@@ -515,7 +516,7 @@ theorem blsub_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho :
 
 #print Ordinal.cof_bsup_le_lift /-
 theorem cof_bsup_le_lift {o : Ordinal} {f : ∀ a < o, Ordinal} (H : ∀ i h, f i h < bsup o f) :
-    cof (bsup o f) ≤ o.card.lift := by rw [← bsup_eq_blsub_iff_lt_bsup] at H; rw [H];
+    cof (bsup o f) ≤ o.card.lift := by rw [← bsup_eq_blsub_iff_lt_bsup] at H ; rw [H];
   exact cof_blsub_le_lift f
 #align ordinal.cof_bsup_le_lift Ordinal.cof_bsup_le_lift
 -/
@@ -592,14 +593,14 @@ theorem cof_succ (o) : cof (succ o) = 1 :=
 theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
   ⟨inductionOn o fun α r _ z => by
       skip
-      rcases cof_eq r with ⟨S, hl, e⟩; rw [z] at e
+      rcases cof_eq r with ⟨S, hl, e⟩; rw [z] at e 
       cases' mk_ne_zero_iff.1 (by rw [e] <;> exact one_ne_zero) with a
       refine'
         ⟨typein r a,
           Eq.symm <|
             Quotient.sound
               ⟨RelIso.ofSurjective (RelEmbedding.ofMonotone _ fun x y => _) fun x => _⟩⟩
-      · apply Sum.rec <;> [exact Subtype.val;exact fun _ => a]
+      · apply Sum.rec <;> [exact Subtype.val; exact fun _ => a]
       · rcases x with (x | ⟨⟨⟨⟩⟩⟩) <;> rcases y with (y | ⟨⟨⟨⟩⟩⟩) <;>
           simp [Subrel, Order.Preimage, EmptyRelation]
         exact x.2
@@ -608,7 +609,7 @@ theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
         · exact Or.inl h
         · exact Or.inr ⟨PUnit.unit, h.symm⟩
         · rcases hl x with ⟨a', aS, hn⟩
-          rw [(_ : ↑a = a')] at h; · exact absurd h hn
+          rw [(_ : ↑a = a')] at h ; · exact absurd h hn
           refine' congr_arg Subtype.val (_ : a = ⟨a', aS⟩)
           haveI := le_one_iff_subsingleton.1 (le_of_eq e)
           apply Subsingleton.elim,
@@ -670,8 +671,8 @@ protected theorem succ : IsFundamentalSequence (succ o) 1 fun _ _ => o :=
   by
   refine' ⟨_, fun i j hi hj h => _, blsub_const Ordinal.one_ne_zero o⟩
   · rw [cof_succ, ord_one]
-  · rw [lt_one_iff_zero] at hi hj
-    rw [hi, hj] at h
+  · rw [lt_one_iff_zero] at hi hj 
+    rw [hi, hj] at h 
     exact h.false.elim
 #align ordinal.is_fundamental_sequence.succ Ordinal.IsFundamentalSequence.succ
 
@@ -726,7 +727,7 @@ theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequ
     · refine' ⟨typein r' ⟨i, h⟩, typein_lt_type _ _, _⟩
       rw [bfamily_of_family'_typein]
       rfl
-    · push_neg  at h
+    · push_neg  at h 
       cases' wo.wf.min_mem _ h with hji hij
       refine' ⟨typein r' ⟨_, fun k hkj => lt_of_lt_of_le _ hij⟩, typein_lt_type _ _, _⟩
       · by_contra' H
@@ -760,12 +761,12 @@ protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u
     have H : ∀ i, ∃ b < a, f' i ≤ f b := fun i =>
       by
       have := lt_lsub.{u, u} f' i
-      rwa [hf', ← IsNormal.blsub_eq.{u, u} hf ha, lt_blsub_iff] at this
+      rwa [hf', ← IsNormal.blsub_eq.{u, u} hf ha, lt_blsub_iff] at this 
     refine' (lsub_le fun i => _).antisymm (le_of_forall_lt fun b hb => _)
     · rcases H i with ⟨b, hb, hb'⟩
       exact lt_of_le_of_lt (csInf_le' hb') hb
     · have := hf.strict_mono hb
-      rw [← hf', lt_lsub_iff] at this
+      rw [← hf', lt_lsub_iff] at this 
       cases' this with i hi
       rcases H i with ⟨b, _, hb⟩
       exact
@@ -816,11 +817,11 @@ theorem aleph0_le_cof {o} : ℵ₀ ≤ cof o ↔ IsLimit o :=
   · simp [l]; refine' le_of_not_lt fun h => _
     cases' Cardinal.lt_aleph0.1 h with n e
     have := cof_cof o
-    rw [e, ord_nat] at this
+    rw [e, ord_nat] at this 
     cases n
-    · simp at e; simpa [e, not_zero_is_limit] using l
-    · rw [nat_cast_succ, cof_succ] at this
-      rw [← this, cof_eq_one_iff_is_succ] at e
+    · simp at e ; simpa [e, not_zero_is_limit] using l
+    · rw [nat_cast_succ, cof_succ] at this 
+      rw [← this, cof_eq_one_iff_is_succ] at e 
       rcases e with ⟨a, rfl⟩
       exact not_succ_is_limit _ l
 #align ordinal.aleph_0_le_cof Ordinal.aleph0_le_cof
@@ -892,7 +893,7 @@ theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder
     (h₁ : Unbounded r <| ⋃₀ s) (h₂ : (#s) < StrictOrder.cof r) : ∃ x ∈ s, Unbounded r x :=
   by
   by_contra' h
-  simp_rw [not_unbounded_iff] at h
+  simp_rw [not_unbounded_iff] at h 
   let f : s → α := fun x : s => wo.wf.sup x (h x.1 x.2)
   refine' h₂.not_le (le_trans (csInf_le' ⟨range f, fun x => _, rfl⟩) mk_range_le)
   rcases h₁ x with ⟨y, ⟨c, hc, hy⟩, hxy⟩
@@ -905,7 +906,7 @@ theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder
 theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
     (s : β → Set α) (h₁ : Unbounded r <| ⋃ x, s x) (h₂ : (#β) < StrictOrder.cof r) :
     ∃ x : β, Unbounded r (s x) := by
-  rw [← sUnion_range] at h₁
+  rw [← sUnion_range] at h₁ 
   rcases unbounded_of_unbounded_sUnion r h₁ (mk_range_le.trans_lt h₂) with ⟨_, ⟨x, rfl⟩, u⟩
   exact ⟨x, u⟩
 #align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_iUnion
@@ -945,7 +946,7 @@ theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal
 #print Ordinal.infinite_pigeonhole_set /-
 theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ : Cardinal)
     (hθ : θ ≤ (#s)) (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) :
-    ∃ (a : α)(t : Set β)(h : t ⊆ s), θ ≤ (#t) ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a :=
+    ∃ (a : α) (t : Set β) (h : t ⊆ s), θ ≤ (#t) ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a :=
   by
   cases' infinite_pigeonhole_card f θ hθ h₁ h₂ with a ha
   refine' ⟨a, { x | ∃ h, f ⟨x, h⟩ = a }, _, _, _⟩
@@ -1016,10 +1017,10 @@ theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (be
   · rw [beth_zero]
     exact is_strong_limit_aleph_0
   · refine' ⟨beth_ne_zero o, fun a ha => _⟩
-    rw [beth_limit ⟨h, is_succ_limit_iff_succ_lt.1 H⟩] at ha
+    rw [beth_limit ⟨h, is_succ_limit_iff_succ_lt.1 H⟩] at ha 
     rcases exists_lt_of_lt_ciSup' ha with ⟨⟨i, hi⟩, ha⟩
     have := power_le_power_left two_ne_zero ha.le
-    rw [← beth_succ] at this
+    rw [← beth_succ] at this 
     exact this.trans_lt (beth_lt.2 (H.succ_lt hi))
 #align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_beth
 -/
@@ -1065,7 +1066,7 @@ theorem mk_subset_mk_lt_cof {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) :
   apply le_antisymm
   · nth_rw_rhs 1 [← mk_bounded_subset h hr]
     apply mk_le_mk_of_subset fun s hs => _
-    rw [hr] at hs
+    rw [hr] at hs 
     exact lt_cof_type hs
   · refine' @mk_le_of_injective α _ (fun x => Subtype.mk {x} _) _
     · rw [mk_singleton]
@@ -1121,10 +1122,10 @@ theorem isRegular_succ {c : Cardinal.{u}} (h : ℵ₀ ≤ c) : IsRegular (succ c
   ⟨h.trans (le_succ c),
     succ_le_of_lt
       (by
-        cases' Quotient.exists_rep (@succ Cardinal _ _ c) with α αe; simp at αe
+        cases' Quotient.exists_rep (@succ Cardinal _ _ c) with α αe; simp at αe 
         rcases ord_eq α with ⟨r, wo, re⟩; skip
         have := ord_is_limit (h.trans (le_succ _))
-        rw [← αe, re] at this⊢
+        rw [← αe, re] at this ⊢
         rcases cof_eq' r this with ⟨S, H, Se⟩
         rw [← Se]
         apply lt_imp_lt_of_le_imp_le fun h => mul_le_mul_right' h c
@@ -1175,7 +1176,7 @@ has an infinite fiber.
 theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : (#α) < (#β)) (w' : Infinite α) :
     ∃ a : α, Infinite (f ⁻¹' {a}) :=
   by
-  simp_rw [Cardinal.infinite_iff] at w'⊢
+  simp_rw [Cardinal.infinite_iff] at w' ⊢
   cases' infinite_pigeonhole_card_lt f w w' with a ha
   exact ⟨a, w'.trans ha.le⟩
 #align cardinal.exists_infinite_fiber Cardinal.exists_infinite_fiber
@@ -1194,13 +1195,13 @@ theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α 
     rw [w]
     exact infinite_univ
   by_contra h
-  simp only [not_le] at h
+  simp only [not_le] at h 
   let u : ∀ b, ∃ a, b ∈ f a := fun b => by simpa using (w.ge : _) (Set.mem_univ b)
   let u' : β → range f := fun b => ⟨f (u b).some, by simp⟩
   have v' : ∀ a, u' ⁻¹' {⟨f a, by simp⟩} ≤ f a :=
     by
     rintro a p m
-    simp at m
+    simp at m 
     rw [← m]
     apply fun b => (u b).choose_spec
   obtain ⟨⟨-, ⟨a, rfl⟩⟩, p⟩ := exists_infinite_fiber u' h k
@@ -1412,10 +1413,10 @@ theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
     by
     rcases ord_eq α with ⟨r, wo, re⟩; skip
     have := ord_is_limit h
-    rw [mk_def, re] at this⊢
+    rw [mk_def, re] at this ⊢
     rcases cof_eq' r this with ⟨S, H, Se⟩
     have := sum_lt_prod (fun a : S => #{ x // r x a }) (fun _ => #α) fun i => _
-    · simp only [Cardinal.prod_const, Cardinal.lift_id, ← Se, ← mk_sigma, power_def] at this⊢
+    · simp only [Cardinal.prod_const, Cardinal.lift_id, ← Se, ← mk_sigma, power_def] at this ⊢
       refine' lt_of_le_of_lt _ this
       refine' ⟨embedding.of_surjective _ _⟩
       · exact fun x => x.2.1
@@ -1424,7 +1425,7 @@ theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
           let ⟨b, h, ab⟩ := H a
           ⟨⟨⟨_, h⟩, _, ab⟩, rfl⟩
     · have := typein_lt_type r i
-      rwa [← re, lt_ord] at this
+      rwa [← re, lt_ord] at this 
 #align cardinal.lt_power_cof Cardinal.lt_power_cof
 -/

7c2ce0c2

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -55,7 +55,7 @@ noncomputable section
 
 open Function Cardinal Set Order
 
-open Classical Cardinal Ordinal
+open scoped Classical Cardinal Ordinal
 
 universe u v w
 
@@ -191,9 +191,11 @@ theorem cof_type_le [IsWellOrder α r] {S : Set α} (h : Unbounded r S) : cof (t
 #align ordinal.cof_type_le Ordinal.cof_type_le
 -/
 
+#print Ordinal.lt_cof_type /-
 theorem lt_cof_type [IsWellOrder α r] {S : Set α} : (#S) < cof (type r) → Bounded r S := by
   simpa using not_imp_not.2 cof_type_le
 #align ordinal.lt_cof_type Ordinal.lt_cof_type
+-/
 
 #print Ordinal.cof_eq /-
 theorem cof_eq (r : α → α → Prop) [IsWellOrder α r] : ∃ S, Unbounded r S ∧ (#S) = cof (type r) :=
@@ -320,9 +322,11 @@ theorem cof_ord_le (c : Cardinal) : c.ord.cof ≤ c := by simpa using cof_le_car
 #align ordinal.cof_ord_le Ordinal.cof_ord_le
 -/
 
+#print Ordinal.ord_cof_le /-
 theorem ord_cof_le (o : Ordinal.{u}) : o.cof.ord ≤ o :=
   (ord_le_ord.2 (cof_le_card o)).trans (ord_card_le o)
 #align ordinal.ord_cof_le Ordinal.ord_cof_le
+-/
 
 #print Ordinal.exists_lsub_cof /-
 theorem exists_lsub_cof (o : Ordinal) :
@@ -359,33 +363,45 @@ theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
 #align ordinal.le_cof_iff_lsub Ordinal.le_cof_iff_lsub
 -/
 
+#print Ordinal.lsub_lt_ord_lift /-
 theorem lsub_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : lsub.{u, v} f < c :=
   lt_of_le_of_ne (lsub_le hf) fun h => by subst h; exact (cof_lsub_le_lift f).not_lt hι
 #align ordinal.lsub_lt_ord_lift Ordinal.lsub_lt_ord_lift
+-/
 
+#print Ordinal.lsub_lt_ord /-
 theorem lsub_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
     (∀ i, f i < c) → lsub.{u, u} f < c :=
   lsub_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.lsub_lt_ord Ordinal.lsub_lt_ord
+-/
 
+#print Ordinal.cof_sup_le_lift /-
 theorem cof_sup_le_lift {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup f) : cof (sup f) ≤ (#ι).lift := by
   rw [← sup_eq_lsub_iff_lt_sup] at H; rw [H]; exact cof_lsub_le_lift f
 #align ordinal.cof_sup_le_lift Ordinal.cof_sup_le_lift
+-/
 
+#print Ordinal.cof_sup_le /-
 theorem cof_sup_le {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup.{u, u} f) :
     cof (sup.{u, u} f) ≤ (#ι) := by rw [← (#ι).lift_id]; exact cof_sup_le_lift H
 #align ordinal.cof_sup_le Ordinal.cof_sup_le
+-/
 
+#print Ordinal.sup_lt_ord_lift /-
 theorem sup_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : sup.{u, v} f < c :=
   (sup_le_lsub.{u, v} f).trans_lt (lsub_lt_ord_lift hι hf)
 #align ordinal.sup_lt_ord_lift Ordinal.sup_lt_ord_lift
+-/
 
+#print Ordinal.sup_lt_ord /-
 theorem sup_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
     (∀ i, f i < c) → sup.{u, u} f < c :=
   sup_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.sup_lt_ord Ordinal.sup_lt_ord
+-/
 
 theorem iSup_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal} (hι : Cardinal.lift (#ι) < c.ord.cof)
     (hf : ∀ i, f i < c) : iSup f < c :=
@@ -401,6 +417,7 @@ theorem iSup_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : (#ι) < c.ord.c
   iSup_lt_lift (by rwa [(#ι).lift_id])
 #align ordinal.supr_lt Ordinal.iSup_lt
 
+#print Ordinal.nfpFamily_lt_ord_lift /-
 theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : (#ι).lift < cof c) (hf : ∀ (i), ∀ b < c, f i b < c) {a} (ha : a < c) :
     nfpFamily.{u, v} f a < c :=
@@ -413,29 +430,39 @@ theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : 
     · exact ha
     · exact hf _ _ H
 #align ordinal.nfp_family_lt_ord_lift Ordinal.nfpFamily_lt_ord_lift
+-/
 
+#print Ordinal.nfpFamily_lt_ord /-
 theorem nfpFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hc' : (#ι) < cof c)
     (hf : ∀ (i), ∀ b < c, f i b < c) {a} : a < c → nfpFamily.{u, u} f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [(#ι).lift_id]) hf
 #align ordinal.nfp_family_lt_ord Ordinal.nfpFamily_lt_ord
+-/
 
+#print Ordinal.nfpBFamily_lt_ord_lift /-
 theorem nfpBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : o.card.lift < cof c) (hf : ∀ (i hi), ∀ b < c, f i hi b < c) {a} :
     a < c → nfpBFamily.{u, v} o f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [mk_ordinal_out]) fun i => hf _ _
 #align ordinal.nfp_bfamily_lt_ord_lift Ordinal.nfpBFamily_lt_ord_lift
+-/
 
+#print Ordinal.nfpBFamily_lt_ord /-
 theorem nfpBFamily_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : o.card < cof c) (hf : ∀ (i hi), ∀ b < c, f i hi b < c) {a} :
     a < c → nfpBFamily.{u, u} o f a < c :=
   nfpBFamily_lt_ord_lift hc (by rwa [o.card.lift_id]) hf
 #align ordinal.nfp_bfamily_lt_ord Ordinal.nfpBFamily_lt_ord
+-/
 
+#print Ordinal.nfp_lt_ord /-
 theorem nfp_lt_ord {f : Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hf : ∀ i < c, f i < c) {a} :
     a < c → nfp f a < c :=
   nfpFamily_lt_ord_lift hc (by simpa using cardinal.one_lt_aleph_0.trans hc) fun _ => hf
 #align ordinal.nfp_lt_ord Ordinal.nfp_lt_ord
+-/
 
+#print Ordinal.exists_blsub_cof /-
 theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, blsub.{u, u} _ f = o :=
   by
   rcases exists_lsub_cof o with ⟨ι, f, hf, hι⟩
@@ -444,7 +471,9 @@ theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, b
   rw [← hι, hι']
   exact ⟨_, hf⟩
 #align ordinal.exists_blsub_cof Ordinal.exists_blsub_cof
+-/
 
+#print Ordinal.le_cof_iff_blsub /-
 theorem le_cof_iff_blsub {b : Ordinal} {a : Cardinal} :
     a ≤ cof b ↔ ∀ {o} (f : ∀ a < o, Ordinal), blsub.{u, u} o f = b → a ≤ o.card :=
   le_cof_iff_lsub.trans
@@ -454,46 +483,63 @@ theorem le_cof_iff_blsub {b : Ordinal} {a : Cardinal} :
       rw [← @blsub_eq_lsub' ι r hr] at hf
       simpa using H _ hf⟩
 #align ordinal.le_cof_iff_blsub Ordinal.le_cof_iff_blsub
+-/
 
+#print Ordinal.cof_blsub_le_lift /-
 theorem cof_blsub_le_lift {o} (f : ∀ a < o, Ordinal) :
     cof (blsub o f) ≤ Cardinal.lift.{v, u} o.card := by convert cof_lsub_le_lift _;
   exact (mk_ordinal_out o).symm
 #align ordinal.cof_blsub_le_lift Ordinal.cof_blsub_le_lift
+-/
 
+#print Ordinal.cof_blsub_le /-
 theorem cof_blsub_le {o} (f : ∀ a < o, Ordinal) : cof (blsub.{u, u} o f) ≤ o.card := by
   rw [← o.card.lift_id]; exact cof_blsub_le_lift f
 #align ordinal.cof_blsub_le Ordinal.cof_blsub_le
+-/
 
+#print Ordinal.blsub_lt_ord_lift /-
 theorem blsub_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : o.card.lift < c.cof) (hf : ∀ i hi, f i hi < c) : blsub.{u, v} o f < c :=
   lt_of_le_of_ne (blsub_le hf) fun h =>
     ho.not_le (by simpa [← supr_ord, hf, h] using cof_blsub_le_lift.{u} f)
 #align ordinal.blsub_lt_ord_lift Ordinal.blsub_lt_ord_lift
+-/
 
+#print Ordinal.blsub_lt_ord /-
 theorem blsub_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof)
     (hf : ∀ i hi, f i hi < c) : blsub.{u, u} o f < c :=
   blsub_lt_ord_lift (by rwa [o.card.lift_id]) hf
 #align ordinal.blsub_lt_ord Ordinal.blsub_lt_ord
+-/
 
+#print Ordinal.cof_bsup_le_lift /-
 theorem cof_bsup_le_lift {o : Ordinal} {f : ∀ a < o, Ordinal} (H : ∀ i h, f i h < bsup o f) :
     cof (bsup o f) ≤ o.card.lift := by rw [← bsup_eq_blsub_iff_lt_bsup] at H; rw [H];
   exact cof_blsub_le_lift f
 #align ordinal.cof_bsup_le_lift Ordinal.cof_bsup_le_lift
+-/
 
+#print Ordinal.cof_bsup_le /-
 theorem cof_bsup_le {o : Ordinal} {f : ∀ a < o, Ordinal} :
     (∀ i h, f i h < bsup.{u, u} o f) → cof (bsup.{u, u} o f) ≤ o.card := by rw [← o.card.lift_id];
   exact cof_bsup_le_lift
 #align ordinal.cof_bsup_le Ordinal.cof_bsup_le
+-/
 
+#print Ordinal.bsup_lt_ord_lift /-
 theorem bsup_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : o.card.lift < c.cof) (hf : ∀ i hi, f i hi < c) : bsup.{u, v} o f < c :=
   (bsup_le_blsub f).trans_lt (blsub_lt_ord_lift ho hf)
 #align ordinal.bsup_lt_ord_lift Ordinal.bsup_lt_ord_lift
+-/
 
+#print Ordinal.bsup_lt_ord /-
 theorem bsup_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof) :
     (∀ i hi, f i hi < c) → bsup.{u, u} o f < c :=
   bsup_lt_ord_lift (by rwa [o.card.lift_id])
 #align ordinal.bsup_lt_ord Ordinal.bsup_lt_ord
+-/
 
 /-! ### Basic results -/
 
@@ -570,41 +616,55 @@ theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
 #align ordinal.cof_eq_one_iff_is_succ Ordinal.cof_eq_one_iff_is_succ
 -/
 
+#print Ordinal.IsFundamentalSequence /-
 /-- A fundamental sequence for `a` is an increasing sequence of length `o = cof a` that converges at
     `a`. We provide `o` explicitly in order to avoid type rewrites. -/
 def IsFundamentalSequence (a o : Ordinal.{u}) (f : ∀ b < o, Ordinal.{u}) : Prop :=
   o ≤ a.cof.ord ∧ (∀ {i j} (hi hj), i < j → f i hi < f j hj) ∧ blsub.{u, u} o f = a
 #align ordinal.is_fundamental_sequence Ordinal.IsFundamentalSequence
+-/
 
 namespace IsFundamentalSequence
 
 variable {a o : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}}
 
+#print Ordinal.IsFundamentalSequence.cof_eq /-
 protected theorem cof_eq (hf : IsFundamentalSequence a o f) : a.cof.ord = o :=
   hf.1.antisymm' <| by rw [← hf.2.2]; exact (ord_le_ord.2 (cof_blsub_le f)).trans (ord_card_le o)
 #align ordinal.is_fundamental_sequence.cof_eq Ordinal.IsFundamentalSequence.cof_eq
+-/
 
+#print Ordinal.IsFundamentalSequence.strict_mono /-
 protected theorem strict_mono (hf : IsFundamentalSequence a o f) {i j} :
     ∀ hi hj, i < j → f i hi < f j hj :=
   hf.2.1
 #align ordinal.is_fundamental_sequence.strict_mono Ordinal.IsFundamentalSequence.strict_mono
+-/
 
+#print Ordinal.IsFundamentalSequence.blsub_eq /-
 theorem blsub_eq (hf : IsFundamentalSequence a o f) : blsub.{u, u} o f = a :=
   hf.2.2
 #align ordinal.is_fundamental_sequence.blsub_eq Ordinal.IsFundamentalSequence.blsub_eq
+-/
 
+#print Ordinal.IsFundamentalSequence.ord_cof /-
 theorem ord_cof (hf : IsFundamentalSequence a o f) :
     IsFundamentalSequence a a.cof.ord fun i hi => f i (hi.trans_le (by rw [hf.cof_eq])) := by
   have H := hf.cof_eq; subst H; exact hf
 #align ordinal.is_fundamental_sequence.ord_cof Ordinal.IsFundamentalSequence.ord_cof
+-/
 
+#print Ordinal.IsFundamentalSequence.id_of_le_cof /-
 theorem id_of_le_cof (h : o ≤ o.cof.ord) : IsFundamentalSequence o o fun a _ => a :=
   ⟨h, fun _ _ _ _ => id, blsub_id o⟩
 #align ordinal.is_fundamental_sequence.id_of_le_cof Ordinal.IsFundamentalSequence.id_of_le_cof
+-/
 
+#print Ordinal.IsFundamentalSequence.zero /-
 protected theorem zero {f : ∀ b < (0 : Ordinal), Ordinal} : IsFundamentalSequence 0 0 f :=
   ⟨by rw [cof_zero, ord_zero], fun i j hi => (Ordinal.not_lt_zero i hi).elim, blsub_zero f⟩
 #align ordinal.is_fundamental_sequence.zero Ordinal.IsFundamentalSequence.zero
+-/
 
 protected theorem succ : IsFundamentalSequence (succ o) 1 fun _ _ => o :=
   by
@@ -615,6 +675,7 @@ protected theorem succ : IsFundamentalSequence (succ o) 1 fun _ _ => o :=
     exact h.false.elim
 #align ordinal.is_fundamental_sequence.succ Ordinal.IsFundamentalSequence.succ
 
+#print Ordinal.IsFundamentalSequence.monotone /-
 protected theorem monotone (hf : IsFundamentalSequence a o f) {i j : Ordinal} (hi : i < o)
     (hj : j < o) (hij : i ≤ j) : f i hi ≤ f j hj :=
   by
@@ -622,7 +683,9 @@ protected theorem monotone (hf : IsFundamentalSequence a o f) {i j : Ordinal} (h
   · exact (hf.2.1 hi hj hij).le
   · rfl
 #align ordinal.is_fundamental_sequence.monotone Ordinal.IsFundamentalSequence.monotone
+-/
 
+#print Ordinal.IsFundamentalSequence.trans /-
 theorem trans {a o o' : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}} (hf : IsFundamentalSequence a o f)
     {g : ∀ b < o', Ordinal.{u}} (hg : IsFundamentalSequence o o' g) :
     IsFundamentalSequence a o' fun i hi => f (g i hi) (by rw [← hg.2.2]; apply lt_blsub) :=
@@ -633,9 +696,11 @@ theorem trans {a o o' : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}} (hf : IsFundam
   · rw [@blsub_comp.{u, u, u} o _ f (@is_fundamental_sequence.monotone _ _ f hf)]
     exact hf.2.2
 #align ordinal.is_fundamental_sequence.trans Ordinal.IsFundamentalSequence.trans
+-/
 
 end IsFundamentalSequence
 
+#print Ordinal.exists_fundamental_sequence /-
 /-- Every ordinal has a fundamental sequence. -/
 theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequence a a.cof.ord f :=
   by
@@ -668,6 +733,7 @@ theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequ
         exact (wo.wf.not_lt_min _ h ⟨IsTrans.trans _ _ _ hkj hji, H⟩) hkj
       · rwa [bfamily_of_family'_typein]
 #align ordinal.exists_fundamental_sequence Ordinal.exists_fundamental_sequence
+-/
 
 #print Ordinal.cof_cof /-
 @[simp]
@@ -679,6 +745,7 @@ theorem cof_cof (a : Ordinal.{u}) : cof (cof a).ord = cof a :=
 #align ordinal.cof_cof Ordinal.cof_cof
 -/
 
+#print Ordinal.IsNormal.isFundamentalSequence /-
 protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u}} (hf : IsNormal f)
     {a o} (ha : IsLimit a) {g} (hg : IsFundamentalSequence a o g) :
     IsFundamentalSequence (f a) o fun b hb => f (g b hb) :=
@@ -708,6 +775,7 @@ protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u
         hg.2.2]
     exact IsNormal.blsub_eq.{u, u} hf ha
 #align ordinal.is_normal.is_fundamental_sequence Ordinal.IsNormal.isFundamentalSequence
+-/
 
 #print Ordinal.IsNormal.cof_eq /-
 theorem IsNormal.cof_eq {f} (hf : IsNormal f) {a} (ha : IsLimit a) : cof (f a) = cof a :=
@@ -831,6 +899,7 @@ theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder
   exact ⟨f ⟨c, hc⟩, mem_range_self _, fun hxz => hxy (trans (wo.wf.lt_sup _ hy) hxz)⟩
 #align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_sUnion
 
+#print Ordinal.unbounded_of_unbounded_iUnion /-
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
 theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
@@ -840,7 +909,9 @@ theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop)
   rcases unbounded_of_unbounded_sUnion r h₁ (mk_range_le.trans_lt h₂) with ⟨_, ⟨x, rfl⟩, u⟩
   exact ⟨x, u⟩
 #align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_iUnion
+-/
 
+#print Ordinal.infinite_pigeonhole /-
 /-- The infinite pigeonhole principle -/
 theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤ (#β)) (h₂ : (#α) < (#β).ord.cof) :
     ∃ a : α, (#f ⁻¹' {a}) = (#β) :=
@@ -857,7 +928,9 @@ theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤
   rw [le_mk_iff_exists_set]
   exact ⟨_, rfl⟩
 #align ordinal.infinite_pigeonhole Ordinal.infinite_pigeonhole
+-/
 
+#print Ordinal.infinite_pigeonhole_card /-
 /-- Pigeonhole principle for a cardinality below the cardinality of the domain -/
 theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal) (hθ : θ ≤ (#β))
     (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) : ∃ a : α, θ ≤ (#f ⁻¹' {a}) :=
@@ -867,7 +940,9 @@ theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal
   use a; rw [← ha, @preimage_comp _ _ _ Subtype.val f]
   exact mk_preimage_of_injective _ _ Subtype.val_injective
 #align ordinal.infinite_pigeonhole_card Ordinal.infinite_pigeonhole_card
+-/
 
+#print Ordinal.infinite_pigeonhole_set /-
 theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ : Cardinal)
     (hθ : θ ≤ (#s)) (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) :
     ∃ (a : α)(t : Set β)(h : t ⊆ s), θ ≤ (#t) ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a :=
@@ -882,6 +957,7 @@ theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ
     simp only [coe_eq_subtype, mem_singleton_iff, mem_preimage, mem_set_of_eq]
   rintro x ⟨hx, hx'⟩; exact hx'
 #align ordinal.infinite_pigeonhole_set Ordinal.infinite_pigeonhole_set
+-/
 
 end Ordinal
 
@@ -921,9 +997,11 @@ theorem isStrongLimit_aleph0 : IsStrongLimit ℵ₀ :=
 #align cardinal.is_strong_limit_aleph_0 Cardinal.isStrongLimit_aleph0
 -/
 
+#print Cardinal.IsStrongLimit.isSuccLimit /-
 protected theorem IsStrongLimit.isSuccLimit {c} (H : IsStrongLimit c) : IsSuccLimit c :=
   isSuccLimit_of_succ_lt fun x h => (succ_le_of_lt <| cantor x).trans_lt (H.two_power_lt h)
 #align cardinal.is_strong_limit.is_succ_limit Cardinal.IsStrongLimit.isSuccLimit
+-/
 
 #print Cardinal.IsStrongLimit.isLimit /-
 theorem IsStrongLimit.isLimit {c} (H : IsStrongLimit c) : IsLimit c :=
@@ -931,6 +1009,7 @@ theorem IsStrongLimit.isLimit {c} (H : IsStrongLimit c) : IsLimit c :=
 #align cardinal.is_strong_limit.is_limit Cardinal.IsStrongLimit.isLimit
 -/
 
+#print Cardinal.isStrongLimit_beth /-
 theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (beth o) :=
   by
   rcases eq_or_ne o 0 with (rfl | h)
@@ -943,6 +1022,7 @@ theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (be
     rw [← beth_succ] at this
     exact this.trans_lt (beth_lt.2 (H.succ_lt hi))
 #align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_beth
+-/
 
 theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α → α → Prop}
     [IsWellOrder α r] (hr : (#α).ord = type r) : (#{ s : Set α // Bounded r s }) = (#α) :=
@@ -1013,13 +1093,17 @@ theorem IsRegular.cof_eq {c : Cardinal} (H : c.IsRegular) : c.ord.cof = c :=
 #align cardinal.is_regular.cof_eq Cardinal.IsRegular.cof_eq
 -/
 
+#print Cardinal.IsRegular.pos /-
 theorem IsRegular.pos {c : Cardinal} (H : c.IsRegular) : 0 < c :=
   aleph0_pos.trans_le H.1
 #align cardinal.is_regular.pos Cardinal.IsRegular.pos
+-/
 
+#print Cardinal.IsRegular.ord_pos /-
 theorem IsRegular.ord_pos {c : Cardinal} (H : c.IsRegular) : 0 < c.ord := by rw [Cardinal.lt_ord];
   exact H.pos
 #align cardinal.is_regular.ord_pos Cardinal.IsRegular.ord_pos
+-/
 
 #print Cardinal.isRegular_cof /-
 theorem isRegular_cof {o : Ordinal} (h : o.IsLimit) : IsRegular o.cof :=
@@ -1059,9 +1143,11 @@ theorem isRegular_aleph_one : IsRegular (aleph 1) := by rw [← succ_aleph_0];
   exact is_regular_succ le_rfl
 #align cardinal.is_regular_aleph_one Cardinal.isRegular_aleph_one
 
+#print Cardinal.isRegular_aleph'_succ /-
 theorem isRegular_aleph'_succ {o : Ordinal} (h : ω ≤ o) : IsRegular (aleph' (succ o)) := by
   rw [aleph'_succ]; exact is_regular_succ (aleph_0_le_aleph'.2 h)
 #align cardinal.is_regular_aleph'_succ Cardinal.isRegular_aleph'_succ
+-/
 
 #print Cardinal.isRegular_aleph_succ /-
 theorem isRegular_aleph_succ (o : Ordinal) : IsRegular (aleph (succ o)) := by rw [aleph_succ];
@@ -1069,6 +1155,7 @@ theorem isRegular_aleph_succ (o : Ordinal) : IsRegular (aleph (succ o)) := by rw
 #align cardinal.is_regular_aleph_succ Cardinal.isRegular_aleph_succ
 -/
 
+#print Cardinal.infinite_pigeonhole_card_lt /-
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has a fiber with cardinality strictly great than the codomain.
 -/
@@ -1079,7 +1166,9 @@ theorem infinite_pigeonhole_card_lt {β α : Type u} (f : β → α) (w : (#α)
     Ordinal.infinite_pigeonhole_card f (succ (#α)) (succ_le_of_lt w) (w'.trans (lt_succ _).le)
       ((lt_succ _).trans_le (is_regular_succ w').2.ge)
 #align cardinal.infinite_pigeonhole_card_lt Cardinal.infinite_pigeonhole_card_lt
+-/
 
+#print Cardinal.exists_infinite_fiber /-
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has an infinite fiber.
 -/
@@ -1090,6 +1179,7 @@ theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : (#α) < (#β
   cases' infinite_pigeonhole_card_lt f w w' with a ha
   exact ⟨a, w'.trans ha.le⟩
 #align cardinal.exists_infinite_fiber Cardinal.exists_infinite_fiber
+-/
 
 /-- If an infinite type `β` can be expressed as a union of finite sets,
 then the cardinality of the collection of those finite sets
@@ -1117,45 +1207,61 @@ theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α 
   exact (@Infinite.of_injective _ _ p (inclusion (v' a)) (inclusion_injective _)).False
 #align cardinal.le_range_of_union_finset_eq_top Cardinal.le_range_of_union_finset_eq_top
 
+#print Cardinal.lsub_lt_ord_lift_of_isRegular /-
 theorem lsub_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_lift_of_is_regular Cardinal.lsub_lt_ord_lift_of_isRegular
+-/
 
+#print Cardinal.lsub_lt_ord_of_isRegular /-
 theorem lsub_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_of_is_regular Cardinal.lsub_lt_ord_of_isRegular
+-/
 
+#print Cardinal.sup_lt_ord_lift_of_isRegular /-
 theorem sup_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_lift_of_is_regular Cardinal.sup_lt_ord_lift_of_isRegular
+-/
 
+#print Cardinal.sup_lt_ord_of_isRegular /-
 theorem sup_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_of_is_regular Cardinal.sup_lt_ord_of_isRegular
+-/
 
+#print Cardinal.blsub_lt_ord_lift_of_isRegular /-
 theorem blsub_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (ho : Cardinal.lift o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.blsub o f < c.ord :=
   blsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.blsub_lt_ord_lift_of_is_regular Cardinal.blsub_lt_ord_lift_of_isRegular
+-/
 
+#print Cardinal.blsub_lt_ord_of_isRegular /-
 theorem blsub_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (ho : o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.blsub o f < c.ord :=
   blsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.blsub_lt_ord_of_is_regular Cardinal.blsub_lt_ord_of_isRegular
+-/
 
+#print Cardinal.bsup_lt_ord_lift_of_isRegular /-
 theorem bsup_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.bsup o f < c.ord :=
   bsup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_lift_of_is_regular Cardinal.bsup_lt_ord_lift_of_isRegular
+-/
 
+#print Cardinal.bsup_lt_ord_of_isRegular /-
 theorem bsup_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (hι : o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.bsup o f < c.ord :=
   bsup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_of_is_regular Cardinal.bsup_lt_ord_of_isRegular
+-/
 
 theorem iSup_lt_lift_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c) → iSup f < c :=
@@ -1167,47 +1273,62 @@ theorem iSup_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c) (
   iSup_lt (by rwa [hc.cof_eq])
 #align cardinal.supr_lt_of_is_regular Cardinal.iSup_lt_of_isRegular
 
+#print Cardinal.sum_lt_lift_of_isRegular /-
 theorem sum_lt_lift_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : Cardinal.lift.{v, u} (#ι) < c) (hf : ∀ i, f i < c) : sum f < c :=
   (sum_le_iSup_lift _).trans_lt <| mul_lt_of_lt hc.1 hι (iSup_lt_lift_of_isRegular hc hι hf)
 #align cardinal.sum_lt_lift_of_is_regular Cardinal.sum_lt_lift_of_isRegular
+-/
 
+#print Cardinal.sum_lt_of_isRegular /-
 theorem sum_lt_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : (#ι) < c) : (∀ i, f i < c) → sum f < c :=
   sum_lt_lift_of_isRegular.{u, u} hc (by rwa [lift_id])
 #align cardinal.sum_lt_of_is_regular Cardinal.sum_lt_of_isRegular
+-/
 
+#print Cardinal.nfpFamily_lt_ord_lift_of_isRegular /-
 theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a}
     (ha : a < c.ord) : nfpFamily.{u, v} f a < c.ord := by
   apply nfp_family_lt_ord_lift _ _ hf ha <;> rwa [hc.cof_eq]; exact lt_of_le_of_ne hc.1 hc'.symm
 #align cardinal.nfp_family_lt_ord_lift_of_is_regular Cardinal.nfpFamily_lt_ord_lift_of_isRegular
+-/
 
+#print Cardinal.nfpFamily_lt_ord_of_isRegular /-
 theorem nfpFamily_lt_ord_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι) < c) (hc' : c ≠ ℵ₀) {a} (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) :
     a < c.ord → nfpFamily.{u, u} f a < c.ord :=
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_family_lt_ord_of_is_regular Cardinal.nfpFamily_lt_ord_of_isRegular
+-/
 
+#print Cardinal.nfpBFamily_lt_ord_lift_of_isRegular /-
 theorem nfpBFamily_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (ho : o.card.lift < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → nfpBFamily.{u, v} o f a < c.ord :=
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [mk_ordinal_out]) hc' fun i => hf _ _
 #align cardinal.nfp_bfamily_lt_ord_lift_of_is_regular Cardinal.nfpBFamily_lt_ord_lift_of_isRegular
+-/
 
+#print Cardinal.nfpBFamily_lt_ord_of_isRegular /-
 theorem nfpBFamily_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (ho : o.card < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → nfpBFamily.{u, u} o f a < c.ord :=
   nfpBFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_bfamily_lt_ord_of_is_regular Cardinal.nfpBFamily_lt_ord_of_isRegular
+-/
 
+#print Cardinal.nfp_lt_ord_of_isRegular /-
 theorem nfp_lt_ord_of_isRegular {f : Ordinal → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
     (hf : ∀ i < c.ord, f i < c.ord) {a} : a < c.ord → nfp f a < c.ord :=
   nfp_lt_ord (by rw [hc.cof_eq]; exact lt_of_le_of_ne hc.1 hc'.symm) hf
 #align cardinal.nfp_lt_ord_of_is_regular Cardinal.nfp_lt_ord_of_isRegular
+-/
 
+#print Cardinal.derivFamily_lt_ord_lift /-
 theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, v} f a < c.ord :=
@@ -1227,31 +1348,40 @@ theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc :
       bsup_lt_ord_of_is_regular hc (ord_lt_ord.1 ((ord_card_le b).trans_lt hb')) fun o' ho' =>
         H o' ho' (ho'.trans hb')
 #align cardinal.deriv_family_lt_ord_lift Cardinal.derivFamily_lt_ord_lift
+-/
 
+#print Cardinal.derivFamily_lt_ord /-
 theorem derivFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c)
     (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, u} f a < c.ord :=
   derivFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf
 #align cardinal.deriv_family_lt_ord Cardinal.derivFamily_lt_ord
+-/
 
+#print Cardinal.derivBFamily_lt_ord_lift /-
 theorem derivBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (hι : o.card.lift < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → derivBFamily.{u, v} o f a < c.ord :=
   derivFamily_lt_ord_lift hc (by rwa [mk_ordinal_out]) hc' fun i => hf _ _
 #align cardinal.deriv_bfamily_lt_ord_lift Cardinal.derivBFamily_lt_ord_lift
+-/
 
+#print Cardinal.derivBFamily_lt_ord /-
 theorem derivBFamily_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : o.card < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → derivBFamily.{u, u} o f a < c.ord :=
   derivBFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf
 #align cardinal.deriv_bfamily_lt_ord Cardinal.derivBFamily_lt_ord
+-/
 
+#print Cardinal.deriv_lt_ord /-
 theorem deriv_lt_ord {f : Ordinal.{u} → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
     (hf : ∀ i < c.ord, f i < c.ord) {a} : a < c.ord → deriv f a < c.ord :=
   derivFamily_lt_ord_lift hc
     (by simpa using cardinal.one_lt_aleph_0.trans (lt_of_le_of_ne hc.1 hc'.symm)) hc' fun _ => hf
 #align cardinal.deriv_lt_ord Cardinal.deriv_lt_ord
+-/
 
 #print Cardinal.IsInaccessible /-
 /-- A cardinal is inaccessible if it is an uncountable regular strong limit cardinal. -/
@@ -1276,6 +1406,7 @@ theorem univ_inaccessible : IsInaccessible univ.{u, v} :=
 #align cardinal.univ_inaccessible Cardinal.univ_inaccessible
 -/
 
+#print Cardinal.lt_power_cof /-
 theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
   Quotient.inductionOn c fun α h =>
     by
@@ -1295,7 +1426,9 @@ theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
     · have := typein_lt_type r i
       rwa [← re, lt_ord] at this
 #align cardinal.lt_power_cof Cardinal.lt_power_cof
+-/
 
+#print Cardinal.lt_cof_power /-
 theorem lt_cof_power {a b : Cardinal} (ha : ℵ₀ ≤ a) (b1 : 1 < b) : a < cof (b^a).ord :=
   by
   have b0 : b ≠ 0 := (zero_lt_one.trans b1).ne'
@@ -1303,6 +1436,7 @@ theorem lt_cof_power {a b : Cardinal} (ha : ℵ₀ ≤ a) (b1 : 1 < b) : a < cof
   rw [← power_mul, mul_eq_self ha]
   exact lt_power_cof (ha.trans <| (cantor' _ b1).le)
 #align cardinal.lt_cof_power Cardinal.lt_cof_power
+-/
 
 end Cardinal

7c2ce0c2

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -74,34 +74,16 @@ def cof (r : α → α → Prop) : Cardinal :=
 #align order.cof Order.cof
 -/
 
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-Case conversion may be inaccurate. Consider using '#align order.cof_nonempty Order.cof_nonemptyₓ'. -/
 /-- The set in the definition of `order.cof` is nonempty. -/
 theorem cof_nonempty (r : α → α → Prop) [IsRefl α r] :
     { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c }.Nonempty :=
   ⟨_, Set.univ, fun a => ⟨a, ⟨⟩, refl _⟩, rfl⟩
 #align order.cof_nonempty Order.cof_nonempty
 
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-Case conversion may be inaccurate. Consider using '#align order.cof_le Order.cof_leₓ'. -/
 theorem cof_le (r : α → α → Prop) {S : Set α} (h : ∀ a, ∃ b ∈ S, r a b) : cof r ≤ (#S) :=
   csInf_le' ⟨S, h, rfl⟩
 #align order.cof_le Order.cof_le
 
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 theorem le_cof {r : α → α → Prop} [IsRefl α r] (c : Cardinal) :
     c ≤ cof r ↔ ∀ {S : Set α}, (∀ a, ∃ b ∈ S, r a b) → c ≤ (#S) :=
   by
@@ -209,12 +191,6 @@ theorem cof_type_le [IsWellOrder α r] {S : Set α} (h : Unbounded r S) : cof (t
 #align ordinal.cof_type_le Ordinal.cof_type_le
 -/
 
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 theorem lt_cof_type [IsWellOrder α r] {S : Set α} : (#S) < cof (type r) → Bounded r S := by
   simpa using not_imp_not.2 cof_type_le
 #align ordinal.lt_cof_type Ordinal.lt_cof_type
@@ -275,12 +251,6 @@ theorem cof_lsub_def_nonempty (o) :
 #align ordinal.cof_lsub_def_nonempty Ordinal.cof_lsub_def_nonempty
 -/
 
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 theorem cof_eq_sInf_lsub (o : Ordinal.{u}) :
     cof o = sInf { a : Cardinal | ∃ (ι : Type u)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } :=
   by
@@ -314,12 +284,6 @@ theorem cof_eq_sInf_lsub (o : Ordinal.{u}) :
     exact hb'.trans_lt (lt_lsub.{u, u} f ⟨b, hb⟩)
 #align ordinal.cof_eq_Inf_lsub Ordinal.cof_eq_sInf_lsub
 
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 @[simp]
 theorem lift_cof (o) : (cof o).lift = cof o.lift :=
   by
@@ -356,12 +320,6 @@ theorem cof_ord_le (c : Cardinal) : c.ord.cof ≤ c := by simpa using cof_le_car
 #align ordinal.cof_ord_le Ordinal.cof_ord_le
 -/
 
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 theorem ord_cof_le (o : Ordinal.{u}) : o.cof.ord ≤ o :=
   (ord_le_ord.2 (cof_le_card o)).trans (ord_card_le o)
 #align ordinal.ord_cof_le Ordinal.ord_cof_le
@@ -401,76 +359,34 @@ theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
 #align ordinal.le_cof_iff_lsub Ordinal.le_cof_iff_lsub
 -/
 
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 theorem lsub_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : lsub.{u, v} f < c :=
   lt_of_le_of_ne (lsub_le hf) fun h => by subst h; exact (cof_lsub_le_lift f).not_lt hι
 #align ordinal.lsub_lt_ord_lift Ordinal.lsub_lt_ord_lift
 
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 theorem lsub_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
     (∀ i, f i < c) → lsub.{u, u} f < c :=
   lsub_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.lsub_lt_ord Ordinal.lsub_lt_ord
 
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 theorem cof_sup_le_lift {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup f) : cof (sup f) ≤ (#ι).lift := by
   rw [← sup_eq_lsub_iff_lt_sup] at H; rw [H]; exact cof_lsub_le_lift f
 #align ordinal.cof_sup_le_lift Ordinal.cof_sup_le_lift
 
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 theorem cof_sup_le {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup.{u, u} f) :
     cof (sup.{u, u} f) ≤ (#ι) := by rw [← (#ι).lift_id]; exact cof_sup_le_lift H
 #align ordinal.cof_sup_le Ordinal.cof_sup_le
 
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 theorem sup_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : sup.{u, v} f < c :=
   (sup_le_lsub.{u, v} f).trans_lt (lsub_lt_ord_lift hι hf)
 #align ordinal.sup_lt_ord_lift Ordinal.sup_lt_ord_lift
 
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 theorem sup_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
     (∀ i, f i < c) → sup.{u, u} f < c :=
   sup_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.sup_lt_ord Ordinal.sup_lt_ord
 
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 theorem iSup_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal} (hι : Cardinal.lift (#ι) < c.ord.cof)
     (hf : ∀ i, f i < c) : iSup f < c :=
   by
@@ -480,23 +396,11 @@ theorem iSup_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal} (hι : Cardinal.l
   apply hf
 #align ordinal.supr_lt_lift Ordinal.iSup_lt_lift
 
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 theorem iSup_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : (#ι) < c.ord.cof) :
     (∀ i, f i < c) → iSup f < c :=
   iSup_lt_lift (by rwa [(#ι).lift_id])
 #align ordinal.supr_lt Ordinal.iSup_lt
 
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 theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : (#ι).lift < cof c) (hf : ∀ (i), ∀ b < c, f i b < c) {a} (ha : a < c) :
     nfpFamily.{u, v} f a < c :=
@@ -510,58 +414,28 @@ theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : 
     · exact hf _ _ H
 #align ordinal.nfp_family_lt_ord_lift Ordinal.nfpFamily_lt_ord_lift
 
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 theorem nfpFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hc' : (#ι) < cof c)
     (hf : ∀ (i), ∀ b < c, f i b < c) {a} : a < c → nfpFamily.{u, u} f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [(#ι).lift_id]) hf
 #align ordinal.nfp_family_lt_ord Ordinal.nfpFamily_lt_ord
 
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 theorem nfpBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : o.card.lift < cof c) (hf : ∀ (i hi), ∀ b < c, f i hi b < c) {a} :
     a < c → nfpBFamily.{u, v} o f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [mk_ordinal_out]) fun i => hf _ _
 #align ordinal.nfp_bfamily_lt_ord_lift Ordinal.nfpBFamily_lt_ord_lift
 
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 theorem nfpBFamily_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : o.card < cof c) (hf : ∀ (i hi), ∀ b < c, f i hi b < c) {a} :
     a < c → nfpBFamily.{u, u} o f a < c :=
   nfpBFamily_lt_ord_lift hc (by rwa [o.card.lift_id]) hf
 #align ordinal.nfp_bfamily_lt_ord Ordinal.nfpBFamily_lt_ord
 
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 theorem nfp_lt_ord {f : Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hf : ∀ i < c, f i < c) {a} :
     a < c → nfp f a < c :=
   nfpFamily_lt_ord_lift hc (by simpa using cardinal.one_lt_aleph_0.trans hc) fun _ => hf
 #align ordinal.nfp_lt_ord Ordinal.nfp_lt_ord
 
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 theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, blsub.{u, u} _ f = o :=
   by
   rcases exists_lsub_cof o with ⟨ι, f, hf, hι⟩
@@ -571,12 +445,6 @@ theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, b
   exact ⟨_, hf⟩
 #align ordinal.exists_blsub_cof Ordinal.exists_blsub_cof
 
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 theorem le_cof_iff_blsub {b : Ordinal} {a : Cardinal} :
     a ≤ cof b ↔ ∀ {o} (f : ∀ a < o, Ordinal), blsub.{u, u} o f = b → a ≤ o.card :=
   le_cof_iff_lsub.trans
@@ -587,89 +455,41 @@ theorem le_cof_iff_blsub {b : Ordinal} {a : Cardinal} :
       simpa using H _ hf⟩
 #align ordinal.le_cof_iff_blsub Ordinal.le_cof_iff_blsub
 
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 theorem cof_blsub_le_lift {o} (f : ∀ a < o, Ordinal) :
     cof (blsub o f) ≤ Cardinal.lift.{v, u} o.card := by convert cof_lsub_le_lift _;
   exact (mk_ordinal_out o).symm
 #align ordinal.cof_blsub_le_lift Ordinal.cof_blsub_le_lift
 
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 theorem cof_blsub_le {o} (f : ∀ a < o, Ordinal) : cof (blsub.{u, u} o f) ≤ o.card := by
   rw [← o.card.lift_id]; exact cof_blsub_le_lift f
 #align ordinal.cof_blsub_le Ordinal.cof_blsub_le
 
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 theorem blsub_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : o.card.lift < c.cof) (hf : ∀ i hi, f i hi < c) : blsub.{u, v} o f < c :=
   lt_of_le_of_ne (blsub_le hf) fun h =>
     ho.not_le (by simpa [← supr_ord, hf, h] using cof_blsub_le_lift.{u} f)
 #align ordinal.blsub_lt_ord_lift Ordinal.blsub_lt_ord_lift
 
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 theorem blsub_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof)
     (hf : ∀ i hi, f i hi < c) : blsub.{u, u} o f < c :=
   blsub_lt_ord_lift (by rwa [o.card.lift_id]) hf
 #align ordinal.blsub_lt_ord Ordinal.blsub_lt_ord
 
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 theorem cof_bsup_le_lift {o : Ordinal} {f : ∀ a < o, Ordinal} (H : ∀ i h, f i h < bsup o f) :
     cof (bsup o f) ≤ o.card.lift := by rw [← bsup_eq_blsub_iff_lt_bsup] at H; rw [H];
   exact cof_blsub_le_lift f
 #align ordinal.cof_bsup_le_lift Ordinal.cof_bsup_le_lift
 
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 theorem cof_bsup_le {o : Ordinal} {f : ∀ a < o, Ordinal} :
     (∀ i h, f i h < bsup.{u, u} o f) → cof (bsup.{u, u} o f) ≤ o.card := by rw [← o.card.lift_id];
   exact cof_bsup_le_lift
 #align ordinal.cof_bsup_le Ordinal.cof_bsup_le
 
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 theorem bsup_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : o.card.lift < c.cof) (hf : ∀ i hi, f i hi < c) : bsup.{u, v} o f < c :=
   (bsup_le_blsub f).trans_lt (blsub_lt_ord_lift ho hf)
 #align ordinal.bsup_lt_ord_lift Ordinal.bsup_lt_ord_lift
 
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 theorem bsup_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof) :
     (∀ i hi, f i hi < c) → bsup.{u, u} o f < c :=
   bsup_lt_ord_lift (by rwa [o.card.lift_id])
@@ -750,12 +570,6 @@ theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
 #align ordinal.cof_eq_one_iff_is_succ Ordinal.cof_eq_one_iff_is_succ
 -/
 
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 /-- A fundamental sequence for `a` is an increasing sequence of length `o = cof a` that converges at
     `a`. We provide `o` explicitly in order to avoid type rewrites. -/
 def IsFundamentalSequence (a o : Ordinal.{u}) (f : ∀ b < o, Ordinal.{u}) : Prop :=
@@ -766,74 +580,32 @@ namespace IsFundamentalSequence
 
 variable {a o : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}}
 
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 protected theorem cof_eq (hf : IsFundamentalSequence a o f) : a.cof.ord = o :=
   hf.1.antisymm' <| by rw [← hf.2.2]; exact (ord_le_ord.2 (cof_blsub_le f)).trans (ord_card_le o)
 #align ordinal.is_fundamental_sequence.cof_eq Ordinal.IsFundamentalSequence.cof_eq
 
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 protected theorem strict_mono (hf : IsFundamentalSequence a o f) {i j} :
     ∀ hi hj, i < j → f i hi < f j hj :=
   hf.2.1
 #align ordinal.is_fundamental_sequence.strict_mono Ordinal.IsFundamentalSequence.strict_mono
 
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 theorem blsub_eq (hf : IsFundamentalSequence a o f) : blsub.{u, u} o f = a :=
   hf.2.2
 #align ordinal.is_fundamental_sequence.blsub_eq Ordinal.IsFundamentalSequence.blsub_eq
 
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 theorem ord_cof (hf : IsFundamentalSequence a o f) :
     IsFundamentalSequence a a.cof.ord fun i hi => f i (hi.trans_le (by rw [hf.cof_eq])) := by
   have H := hf.cof_eq; subst H; exact hf
 #align ordinal.is_fundamental_sequence.ord_cof Ordinal.IsFundamentalSequence.ord_cof
 
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 theorem id_of_le_cof (h : o ≤ o.cof.ord) : IsFundamentalSequence o o fun a _ => a :=
   ⟨h, fun _ _ _ _ => id, blsub_id o⟩
 #align ordinal.is_fundamental_sequence.id_of_le_cof Ordinal.IsFundamentalSequence.id_of_le_cof
 
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 protected theorem zero {f : ∀ b < (0 : Ordinal), Ordinal} : IsFundamentalSequence 0 0 f :=
   ⟨by rw [cof_zero, ord_zero], fun i j hi => (Ordinal.not_lt_zero i hi).elim, blsub_zero f⟩
 #align ordinal.is_fundamental_sequence.zero Ordinal.IsFundamentalSequence.zero
 
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 protected theorem succ : IsFundamentalSequence (succ o) 1 fun _ _ => o :=
   by
   refine' ⟨_, fun i j hi hj h => _, blsub_const Ordinal.one_ne_zero o⟩
@@ -843,12 +615,6 @@ protected theorem succ : IsFundamentalSequence (succ o) 1 fun _ _ => o :=
     exact h.false.elim
 #align ordinal.is_fundamental_sequence.succ Ordinal.IsFundamentalSequence.succ
 
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 protected theorem monotone (hf : IsFundamentalSequence a o f) {i j : Ordinal} (hi : i < o)
     (hj : j < o) (hij : i ≤ j) : f i hi ≤ f j hj :=
   by
@@ -857,9 +623,6 @@ protected theorem monotone (hf : IsFundamentalSequence a o f) {i j : Ordinal} (h
   · rfl
 #align ordinal.is_fundamental_sequence.monotone Ordinal.IsFundamentalSequence.monotone
 
-/- warning: ordinal.is_fundamental_sequence.trans -> Ordinal.IsFundamentalSequence.trans is a dubious translation:
-<too large>
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 theorem trans {a o o' : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}} (hf : IsFundamentalSequence a o f)
     {g : ∀ b < o', Ordinal.{u}} (hg : IsFundamentalSequence o o' g) :
     IsFundamentalSequence a o' fun i hi => f (g i hi) (by rw [← hg.2.2]; apply lt_blsub) :=
@@ -873,12 +636,6 @@ theorem trans {a o o' : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}} (hf : IsFundam
 
 end IsFundamentalSequence
 
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 /-- Every ordinal has a fundamental sequence. -/
 theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequence a a.cof.ord f :=
   by
@@ -922,12 +679,6 @@ theorem cof_cof (a : Ordinal.{u}) : cof (cof a).ord = cof a :=
 #align ordinal.cof_cof Ordinal.cof_cof
 -/
 
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 protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u}} (hf : IsNormal f)
     {a o} (ha : IsLimit a) {g} (hg : IsFundamentalSequence a o g) :
     IsFundamentalSequence (f a) o fun b hb => f (g b hb) :=
@@ -1028,12 +779,6 @@ theorem cof_omega : cof ω = ℵ₀ :=
 #align ordinal.cof_omega Ordinal.cof_omega
 -/
 
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 theorem cof_eq' (r : α → α → Prop) [IsWellOrder α r] (h : IsLimit (type r)) :
     ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = cof (type r) :=
   let ⟨S, H, e⟩ := cof_eq r
@@ -1073,12 +818,6 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ :=
 /-! ### Infinite pigeonhole principle -/
 
 
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 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
 theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder α r] {s : Set (Set α)}
@@ -1092,12 +831,6 @@ theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder
   exact ⟨f ⟨c, hc⟩, mem_range_self _, fun hxz => hxy (trans (wo.wf.lt_sup _ hy) hxz)⟩
 #align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_sUnion
 
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 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
 theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
@@ -1108,12 +841,6 @@ theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop)
   exact ⟨x, u⟩
 #align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_iUnion
 
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 /-- The infinite pigeonhole principle -/
 theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤ (#β)) (h₂ : (#α) < (#β).ord.cof) :
     ∃ a : α, (#f ⁻¹' {a}) = (#β) :=
@@ -1131,12 +858,6 @@ theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤
   exact ⟨_, rfl⟩
 #align ordinal.infinite_pigeonhole Ordinal.infinite_pigeonhole
 
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 /-- Pigeonhole principle for a cardinality below the cardinality of the domain -/
 theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal) (hθ : θ ≤ (#β))
     (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) : ∃ a : α, θ ≤ (#f ⁻¹' {a}) :=
@@ -1147,12 +868,6 @@ theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal
   exact mk_preimage_of_injective _ _ Subtype.val_injective
 #align ordinal.infinite_pigeonhole_card Ordinal.infinite_pigeonhole_card
 
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 theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ : Cardinal)
     (hθ : θ ≤ (#s)) (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) :
     ∃ (a : α)(t : Set β)(h : t ⊆ s), θ ≤ (#t) ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a :=
@@ -1194,12 +909,6 @@ theorem IsStrongLimit.ne_zero {c} (h : IsStrongLimit c) : c ≠ 0 :=
 #align cardinal.is_strong_limit.ne_zero Cardinal.IsStrongLimit.ne_zero
 -/
 
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 theorem IsStrongLimit.two_power_lt {x c} (h : IsStrongLimit c) : x < c → (2^x) < c :=
   h.2 x
 #align cardinal.is_strong_limit.two_power_lt Cardinal.IsStrongLimit.two_power_lt
@@ -1212,12 +921,6 @@ theorem isStrongLimit_aleph0 : IsStrongLimit ℵ₀ :=
 #align cardinal.is_strong_limit_aleph_0 Cardinal.isStrongLimit_aleph0
 -/
 
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 protected theorem IsStrongLimit.isSuccLimit {c} (H : IsStrongLimit c) : IsSuccLimit c :=
   isSuccLimit_of_succ_lt fun x h => (succ_le_of_lt <| cantor x).trans_lt (H.two_power_lt h)
 #align cardinal.is_strong_limit.is_succ_limit Cardinal.IsStrongLimit.isSuccLimit
@@ -1228,12 +931,6 @@ theorem IsStrongLimit.isLimit {c} (H : IsStrongLimit c) : IsLimit c :=
 #align cardinal.is_strong_limit.is_limit Cardinal.IsStrongLimit.isLimit
 -/
 
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 theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (beth o) :=
   by
   rcases eq_or_ne o 0 with (rfl | h)
@@ -1247,12 +944,6 @@ theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (be
     exact this.trans_lt (beth_lt.2 (H.succ_lt hi))
 #align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_beth
 
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 theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α → α → Prop}
     [IsWellOrder α r] (hr : (#α).ord = type r) : (#{ s : Set α // Bounded r s }) = (#α) :=
   by
@@ -1282,12 +973,6 @@ theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α
       simpa only [singleton_eq_singleton_iff] using hab
 #align cardinal.mk_bounded_subset Cardinal.mk_bounded_subset
 
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 theorem mk_subset_mk_lt_cof {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) :
     (#{ s : Set α // (#s) < cof (#α).ord }) = (#α) :=
   by
@@ -1328,22 +1013,10 @@ theorem IsRegular.cof_eq {c : Cardinal} (H : c.IsRegular) : c.ord.cof = c :=
 #align cardinal.is_regular.cof_eq Cardinal.IsRegular.cof_eq
 -/
 
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 theorem IsRegular.pos {c : Cardinal} (H : c.IsRegular) : 0 < c :=
   aleph0_pos.trans_le H.1
 #align cardinal.is_regular.pos Cardinal.IsRegular.pos
 
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 theorem IsRegular.ord_pos {c : Cardinal} (H : c.IsRegular) : 0 < c.ord := by rw [Cardinal.lt_ord];
   exact H.pos
 #align cardinal.is_regular.ord_pos Cardinal.IsRegular.ord_pos
@@ -1360,12 +1033,6 @@ theorem isRegular_aleph0 : IsRegular ℵ₀ :=
 #align cardinal.is_regular_aleph_0 Cardinal.isRegular_aleph0
 -/
 
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 theorem isRegular_succ {c : Cardinal.{u}} (h : ℵ₀ ≤ c) : IsRegular (succ c) :=
   ⟨h.trans (le_succ c),
     succ_le_of_lt
@@ -1388,22 +1055,10 @@ theorem isRegular_succ {c : Cardinal.{u}} (h : ℵ₀ ≤ c) : IsRegular (succ c
           apply typein_lt_type)⟩
 #align cardinal.is_regular_succ Cardinal.isRegular_succ
 
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 theorem isRegular_aleph_one : IsRegular (aleph 1) := by rw [← succ_aleph_0];
   exact is_regular_succ le_rfl
 #align cardinal.is_regular_aleph_one Cardinal.isRegular_aleph_one
 
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 theorem isRegular_aleph'_succ {o : Ordinal} (h : ω ≤ o) : IsRegular (aleph' (succ o)) := by
   rw [aleph'_succ]; exact is_regular_succ (aleph_0_le_aleph'.2 h)
 #align cardinal.is_regular_aleph'_succ Cardinal.isRegular_aleph'_succ
@@ -1414,12 +1069,6 @@ theorem isRegular_aleph_succ (o : Ordinal) : IsRegular (aleph (succ o)) := by rw
 #align cardinal.is_regular_aleph_succ Cardinal.isRegular_aleph_succ
 -/
 
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 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has a fiber with cardinality strictly great than the codomain.
 -/
@@ -1431,12 +1080,6 @@ theorem infinite_pigeonhole_card_lt {β α : Type u} (f : β → α) (w : (#α)
       ((lt_succ _).trans_le (is_regular_succ w').2.ge)
 #align cardinal.infinite_pigeonhole_card_lt Cardinal.infinite_pigeonhole_card_lt
 
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 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has an infinite fiber.
 -/
@@ -1448,12 +1091,6 @@ theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : (#α) < (#β
   exact ⟨a, w'.trans ha.le⟩
 #align cardinal.exists_infinite_fiber Cardinal.exists_infinite_fiber
 
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 /-- If an infinite type `β` can be expressed as a union of finite sets,
 then the cardinality of the collection of those finite sets
 must be at least the cardinality of `β`.
@@ -1480,168 +1117,78 @@ theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α 
   exact (@Infinite.of_injective _ _ p (inclusion (v' a)) (inclusion_injective _)).False
 #align cardinal.le_range_of_union_finset_eq_top Cardinal.le_range_of_union_finset_eq_top
 
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 theorem lsub_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_lift_of_is_regular Cardinal.lsub_lt_ord_lift_of_isRegular
 
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 theorem lsub_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_of_is_regular Cardinal.lsub_lt_ord_of_isRegular
 
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 theorem sup_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_lift_of_is_regular Cardinal.sup_lt_ord_lift_of_isRegular
 
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 theorem sup_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_of_is_regular Cardinal.sup_lt_ord_of_isRegular
 
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 theorem blsub_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (ho : Cardinal.lift o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.blsub o f < c.ord :=
   blsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.blsub_lt_ord_lift_of_is_regular Cardinal.blsub_lt_ord_lift_of_isRegular
 
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 theorem blsub_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (ho : o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.blsub o f < c.ord :=
   blsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.blsub_lt_ord_of_is_regular Cardinal.blsub_lt_ord_of_isRegular
 
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 theorem bsup_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.bsup o f < c.ord :=
   bsup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_lift_of_is_regular Cardinal.bsup_lt_ord_lift_of_isRegular
 
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 theorem bsup_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (hι : o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.bsup o f < c.ord :=
   bsup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_of_is_regular Cardinal.bsup_lt_ord_of_isRegular
 
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 theorem iSup_lt_lift_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c) → iSup f < c :=
   iSup_lt_lift (by rwa [hc.cof_eq])
 #align cardinal.supr_lt_lift_of_is_regular Cardinal.iSup_lt_lift_of_isRegular
 
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 theorem iSup_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c) → iSup f < c :=
   iSup_lt (by rwa [hc.cof_eq])
 #align cardinal.supr_lt_of_is_regular Cardinal.iSup_lt_of_isRegular
 
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 theorem sum_lt_lift_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : Cardinal.lift.{v, u} (#ι) < c) (hf : ∀ i, f i < c) : sum f < c :=
   (sum_le_iSup_lift _).trans_lt <| mul_lt_of_lt hc.1 hι (iSup_lt_lift_of_isRegular hc hι hf)
 #align cardinal.sum_lt_lift_of_is_regular Cardinal.sum_lt_lift_of_isRegular
 
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 theorem sum_lt_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : (#ι) < c) : (∀ i, f i < c) → sum f < c :=
   sum_lt_lift_of_isRegular.{u, u} hc (by rwa [lift_id])
 #align cardinal.sum_lt_of_is_regular Cardinal.sum_lt_of_isRegular
 
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 theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a}
     (ha : a < c.ord) : nfpFamily.{u, v} f a < c.ord := by
   apply nfp_family_lt_ord_lift _ _ hf ha <;> rwa [hc.cof_eq]; exact lt_of_le_of_ne hc.1 hc'.symm
 #align cardinal.nfp_family_lt_ord_lift_of_is_regular Cardinal.nfpFamily_lt_ord_lift_of_isRegular
 
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 theorem nfpFamily_lt_ord_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι) < c) (hc' : c ≠ ℵ₀) {a} (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) :
     a < c.ord → nfpFamily.{u, u} f a < c.ord :=
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_family_lt_ord_of_is_regular Cardinal.nfpFamily_lt_ord_of_isRegular
 
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 theorem nfpBFamily_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (ho : o.card.lift < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
@@ -1649,12 +1196,6 @@ theorem nfpBFamily_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordina
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [mk_ordinal_out]) hc' fun i => hf _ _
 #align cardinal.nfp_bfamily_lt_ord_lift_of_is_regular Cardinal.nfpBFamily_lt_ord_lift_of_isRegular
 
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 theorem nfpBFamily_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (ho : o.card < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
@@ -1662,23 +1203,11 @@ theorem nfpBFamily_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal →
   nfpBFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_bfamily_lt_ord_of_is_regular Cardinal.nfpBFamily_lt_ord_of_isRegular
 
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 theorem nfp_lt_ord_of_isRegular {f : Ordinal → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
     (hf : ∀ i < c.ord, f i < c.ord) {a} : a < c.ord → nfp f a < c.ord :=
   nfp_lt_ord (by rw [hc.cof_eq]; exact lt_of_le_of_ne hc.1 hc'.symm) hf
 #align cardinal.nfp_lt_ord_of_is_regular Cardinal.nfp_lt_ord_of_isRegular
 
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 theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, v} f a < c.ord :=
@@ -1699,24 +1228,12 @@ theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc :
         H o' ho' (ho'.trans hb')
 #align cardinal.deriv_family_lt_ord_lift Cardinal.derivFamily_lt_ord_lift
 
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 theorem derivFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c)
     (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, u} f a < c.ord :=
   derivFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf
 #align cardinal.deriv_family_lt_ord Cardinal.derivFamily_lt_ord
 
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 theorem derivBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (hι : o.card.lift < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
@@ -1724,24 +1241,12 @@ theorem derivBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordin
   derivFamily_lt_ord_lift hc (by rwa [mk_ordinal_out]) hc' fun i => hf _ _
 #align cardinal.deriv_bfamily_lt_ord_lift Cardinal.derivBFamily_lt_ord_lift
 
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 theorem derivBFamily_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : o.card < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → derivBFamily.{u, u} o f a < c.ord :=
   derivBFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf
 #align cardinal.deriv_bfamily_lt_ord Cardinal.derivBFamily_lt_ord
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.deriv_lt_ord Cardinal.deriv_lt_ordₓ'. -/
 theorem deriv_lt_ord {f : Ordinal.{u} → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
     (hf : ∀ i < c.ord, f i < c.ord) {a} : a < c.ord → deriv f a < c.ord :=
   derivFamily_lt_ord_lift hc
@@ -1755,12 +1260,6 @@ def IsInaccessible (c : Cardinal) :=
 #align cardinal.is_inaccessible Cardinal.IsInaccessible
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.is_inaccessible.mk Cardinal.IsInaccessible.mkₓ'. -/
 theorem IsInaccessible.mk {c} (h₁ : ℵ₀ < c) (h₂ : c ≤ c.ord.cof) (h₃ : ∀ x < c, (2^x) < c) :
     IsInaccessible c :=
   ⟨h₁, ⟨h₁.le, h₂⟩, (aleph0_pos.trans h₁).ne', h₃⟩
@@ -1777,12 +1276,6 @@ theorem univ_inaccessible : IsInaccessible univ.{u, v} :=
 #align cardinal.univ_inaccessible Cardinal.univ_inaccessible
 -/
 
-/- warning: cardinal.lt_power_cof -> Cardinal.lt_power_cof is a dubious translation:
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-  forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))))
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-  forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))))
-Case conversion may be inaccurate. Consider using '#align cardinal.lt_power_cof Cardinal.lt_power_cofₓ'. -/
 theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
   Quotient.inductionOn c fun α h =>
     by
@@ -1803,12 +1296,6 @@ theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
       rwa [← re, lt_ord] at this
 #align cardinal.lt_power_cof Cardinal.lt_power_cof
 
-/- warning: cardinal.lt_cof_power -> Cardinal.lt_cof_power is a dubious translation:
-lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (OfNat.mk.{succ u1} Cardinal.{u1} 1 (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1}))) b) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a (Ordinal.cof.{u1} (Cardinal.ord.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) b a))))
-but is expected to have type
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (One.toOfNat1.{succ u1} Cardinal.{u1} Cardinal.instOneCardinal.{u1})) b) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a (Ordinal.cof.{u1} (Cardinal.ord.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) b a))))
-Case conversion may be inaccurate. Consider using '#align cardinal.lt_cof_power Cardinal.lt_cof_powerₓ'. -/
 theorem lt_cof_power {a b : Cardinal} (ha : ℵ₀ ≤ a) (b1 : 1 < b) : a < cof (b^a).ord :=
   by
   have b0 : b ≠ 0 := (zero_lt_one.trans b1).ne'

7c2ce0c2

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -184,8 +184,7 @@ def cof (o : Ordinal.{u}) : Cardinal.{u} :=
       rintro ⟨α, r, wo₁⟩ ⟨β, s, wo₂⟩ ⟨⟨f, hf⟩⟩
       haveI := wo₁; haveI := wo₂
       apply @RelIso.cof_eq _ _ _ _ _ _
-      · constructor
-        exact fun a b => not_iff_not.2 hf
+      · constructor; exact fun a b => not_iff_not.2 hf
       · exact ⟨(IsWellOrder.isIrrefl r).1⟩
       · exact ⟨(IsWellOrder.isIrrefl s).1⟩)
 #align ordinal.cof Ordinal.cof
@@ -200,9 +199,7 @@ theorem cof_type (r : α → α → Prop) [IsWellOrder α r] : (type r).cof = St
 #print Ordinal.le_cof_type /-
 theorem le_cof_type [IsWellOrder α r] {c} : c ≤ cof (type r) ↔ ∀ S, Unbounded r S → c ≤ (#S) :=
   (le_csInf_iff'' (StrictOrder.cof_nonempty r)).trans
-    ⟨fun H S h => H _ ⟨S, h, rfl⟩, by
-      rintro H d ⟨S, h, rfl⟩
-      exact H _ h⟩
+    ⟨fun H S h => H _ ⟨S, h, rfl⟩, by rintro H d ⟨S, h, rfl⟩; exact H _ h⟩
 #align ordinal.le_cof_type Ordinal.le_cof_type
 -/
 
@@ -246,14 +243,11 @@ theorem ord_cof_eq (r : α → α → Prop) [IsWellOrder α r] :
                 aS⟩ :
               S))
           fun a b h => _).ordinal_type_le
-    rcases a with ⟨a, aS, ha⟩
-    rcases b with ⟨b, bS, hb⟩
+    rcases a with ⟨a, aS, ha⟩; rcases b with ⟨b, bS, hb⟩
     change s ⟨a, _⟩ ⟨b, _⟩
     refine' ((trichotomous_of s _ _).resolve_left fun hn => _).resolve_left _
     · exact asymm h (ha _ hn)
-    · intro e
-      injection e with e
-      subst b
+    · intro e; injection e with e; subst b
       exact irrefl _ h
   · intro a
     have : { b : S | ¬r b a }.Nonempty :=
@@ -306,10 +300,8 @@ theorem cof_eq_sInf_lsub (o : Ordinal.{u}) :
     simp_rw [← hf, lt_lsub_iff] at this
     cases' this with i hi
     refine' ⟨enum (· < ·) (f i) _, _, _⟩
-    · rw [type_lt, ← hf]
-      apply lt_lsub
-    · rw [mem_preimage, typein_enum]
-      exact mem_range_self i
+    · rw [type_lt, ← hf]; apply lt_lsub
+    · rw [mem_preimage, typein_enum]; exact mem_range_self i
     · rwa [← typein_le_typein, typein_enum]
   · rcases cof_eq (· < ·) with ⟨S, hS, hS'⟩
     let f : S → Ordinal := fun s => typein (· < ·) s.val
@@ -355,10 +347,7 @@ theorem lift_cof (o) : (cof o).lift = cof o.lift :=
 #align ordinal.lift_cof Ordinal.lift_cof
 
 #print Ordinal.cof_le_card /-
-theorem cof_le_card (o) : cof o ≤ card o :=
-  by
-  rw [cof_eq_Inf_lsub]
-  exact csInf_le' card_mem_cof
+theorem cof_le_card (o) : cof o ≤ card o := by rw [cof_eq_Inf_lsub]; exact csInf_le' card_mem_cof
 #align ordinal.cof_le_card Ordinal.cof_le_card
 -/
 
@@ -379,17 +368,13 @@ theorem ord_cof_le (o : Ordinal.{u}) : o.cof.ord ≤ o :=
 
 #print Ordinal.exists_lsub_cof /-
 theorem exists_lsub_cof (o : Ordinal) :
-    ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = cof o :=
-  by
-  rw [cof_eq_Inf_lsub]
+    ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = cof o := by rw [cof_eq_Inf_lsub];
   exact csInf_mem (cof_lsub_def_nonempty o)
 #align ordinal.exists_lsub_cof Ordinal.exists_lsub_cof
 -/
 
 #print Ordinal.cof_lsub_le /-
-theorem cof_lsub_le {ι} (f : ι → Ordinal) : cof (lsub.{u, u} f) ≤ (#ι) :=
-  by
-  rw [cof_eq_Inf_lsub]
+theorem cof_lsub_le {ι} (f : ι → Ordinal) : cof (lsub.{u, u} f) ≤ (#ι) := by rw [cof_eq_Inf_lsub];
   exact csInf_le' ⟨ι, f, rfl, rfl⟩
 #align ordinal.cof_lsub_le Ordinal.cof_lsub_le
 -/
@@ -412,10 +397,7 @@ theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
   rw [cof_eq_Inf_lsub]
   exact
     (le_csInf_iff'' (cof_lsub_def_nonempty o)).trans
-      ⟨fun H ι f hf => H _ ⟨ι, f, hf, rfl⟩, fun H b ⟨ι, f, hf, hb⟩ =>
-        by
-        rw [← hb]
-        exact H _ hf⟩
+      ⟨fun H ι f hf => H _ ⟨ι, f, hf, rfl⟩, fun H b ⟨ι, f, hf, hb⟩ => by rw [← hb]; exact H _ hf⟩
 #align ordinal.le_cof_iff_lsub Ordinal.le_cof_iff_lsub
 -/
 
@@ -427,9 +409,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align ordinal.lsub_lt_ord_lift Ordinal.lsub_lt_ord_liftₓ'. -/
 theorem lsub_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : lsub.{u, v} f < c :=
-  lt_of_le_of_ne (lsub_le hf) fun h => by
-    subst h
-    exact (cof_lsub_le_lift f).not_lt hι
+  lt_of_le_of_ne (lsub_le hf) fun h => by subst h; exact (cof_lsub_le_lift f).not_lt hι
 #align ordinal.lsub_lt_ord_lift Ordinal.lsub_lt_ord_lift
 
 /- warning: ordinal.lsub_lt_ord -> Ordinal.lsub_lt_ord is a dubious translation:
@@ -449,11 +429,8 @@ lean 3 declaration is
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2}}, (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) (Ordinal.sup.{u1, u2} ι f)) -> (LE.le.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instLECardinal.{max u1 u2} (Ordinal.cof.{max u1 u2} (Ordinal.sup.{u1, u2} ι f)) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)))
 Case conversion may be inaccurate. Consider using '#align ordinal.cof_sup_le_lift Ordinal.cof_sup_le_liftₓ'. -/
-theorem cof_sup_le_lift {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup f) : cof (sup f) ≤ (#ι).lift :=
-  by
-  rw [← sup_eq_lsub_iff_lt_sup] at H
-  rw [H]
-  exact cof_lsub_le_lift f
+theorem cof_sup_le_lift {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup f) : cof (sup f) ≤ (#ι).lift := by
+  rw [← sup_eq_lsub_iff_lt_sup] at H; rw [H]; exact cof_lsub_le_lift f
 #align ordinal.cof_sup_le_lift Ordinal.cof_sup_le_lift
 
 /- warning: ordinal.cof_sup_le -> Ordinal.cof_sup_le is a dubious translation:
@@ -463,9 +440,7 @@ but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Ordinal.{u1}}, (forall (i : ι), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i) (Ordinal.sup.{u1, u1} ι f)) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Ordinal.cof.{u1} (Ordinal.sup.{u1, u1} ι f)) (Cardinal.mk.{u1} ι))
 Case conversion may be inaccurate. Consider using '#align ordinal.cof_sup_le Ordinal.cof_sup_leₓ'. -/
 theorem cof_sup_le {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup.{u, u} f) :
-    cof (sup.{u, u} f) ≤ (#ι) := by
-  rw [← (#ι).lift_id]
-  exact cof_sup_le_lift H
+    cof (sup.{u, u} f) ≤ (#ι) := by rw [← (#ι).lift_id]; exact cof_sup_le_lift H
 #align ordinal.cof_sup_le Ordinal.cof_sup_le
 
 /- warning: ordinal.sup_lt_ord_lift -> Ordinal.sup_lt_ord_lift is a dubious translation:
@@ -619,9 +594,7 @@ but is expected to have type
   forall {o : Ordinal.{u1}} (f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{max u1 u2}), LE.le.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instLECardinal.{max u1 u2} (Ordinal.cof.{max u1 u2} (Ordinal.blsub.{u1, u2} o f)) (Cardinal.lift.{u2, u1} (Ordinal.card.{u1} o))
 Case conversion may be inaccurate. Consider using '#align ordinal.cof_blsub_le_lift Ordinal.cof_blsub_le_liftₓ'. -/
 theorem cof_blsub_le_lift {o} (f : ∀ a < o, Ordinal) :
-    cof (blsub o f) ≤ Cardinal.lift.{v, u} o.card :=
-  by
-  convert cof_lsub_le_lift _
+    cof (blsub o f) ≤ Cardinal.lift.{v, u} o.card := by convert cof_lsub_le_lift _;
   exact (mk_ordinal_out o).symm
 #align ordinal.cof_blsub_le_lift Ordinal.cof_blsub_le_lift
 
@@ -631,10 +604,8 @@ lean 3 declaration is
 but is expected to have type
   forall {o : Ordinal.{u1}} (f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Ordinal.cof.{u1} (Ordinal.blsub.{u1, u1} o f)) (Ordinal.card.{u1} o)
 Case conversion may be inaccurate. Consider using '#align ordinal.cof_blsub_le Ordinal.cof_blsub_leₓ'. -/
-theorem cof_blsub_le {o} (f : ∀ a < o, Ordinal) : cof (blsub.{u, u} o f) ≤ o.card :=
-  by
-  rw [← o.card.lift_id]
-  exact cof_blsub_le_lift f
+theorem cof_blsub_le {o} (f : ∀ a < o, Ordinal) : cof (blsub.{u, u} o f) ≤ o.card := by
+  rw [← o.card.lift_id]; exact cof_blsub_le_lift f
 #align ordinal.cof_blsub_le Ordinal.cof_blsub_le
 
 /- warning: ordinal.blsub_lt_ord_lift -> Ordinal.blsub_lt_ord_lift is a dubious translation:
@@ -667,10 +638,7 @@ but is expected to have type
   forall {o : Ordinal.{u1}} {f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{max u1 u2}}, (forall (i : Ordinal.{u1}) (h : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i h) (Ordinal.bsup.{u1, u2} o f)) -> (LE.le.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instLECardinal.{max u1 u2} (Ordinal.cof.{max u1 u2} (Ordinal.bsup.{u1, u2} o f)) (Cardinal.lift.{u2, u1} (Ordinal.card.{u1} o)))
 Case conversion may be inaccurate. Consider using '#align ordinal.cof_bsup_le_lift Ordinal.cof_bsup_le_liftₓ'. -/
 theorem cof_bsup_le_lift {o : Ordinal} {f : ∀ a < o, Ordinal} (H : ∀ i h, f i h < bsup o f) :
-    cof (bsup o f) ≤ o.card.lift :=
-  by
-  rw [← bsup_eq_blsub_iff_lt_bsup] at H
-  rw [H]
+    cof (bsup o f) ≤ o.card.lift := by rw [← bsup_eq_blsub_iff_lt_bsup] at H; rw [H];
   exact cof_blsub_le_lift f
 #align ordinal.cof_bsup_le_lift Ordinal.cof_bsup_le_lift
 
@@ -681,9 +649,7 @@ but is expected to have type
   forall {o : Ordinal.{u1}} {f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{u1}}, (forall (i : Ordinal.{u1}) (h : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i h) (Ordinal.bsup.{u1, u1} o f)) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Ordinal.cof.{u1} (Ordinal.bsup.{u1, u1} o f)) (Ordinal.card.{u1} o))
 Case conversion may be inaccurate. Consider using '#align ordinal.cof_bsup_le Ordinal.cof_bsup_leₓ'. -/
 theorem cof_bsup_le {o : Ordinal} {f : ∀ a < o, Ordinal} :
-    (∀ i h, f i h < bsup.{u, u} o f) → cof (bsup.{u, u} o f) ≤ o.card :=
-  by
-  rw [← o.card.lift_id]
+    (∀ i h, f i h < bsup.{u, u} o f) → cof (bsup.{u, u} o f) ≤ o.card := by rw [← o.card.lift_id];
   exact cof_bsup_le_lift
 #align ordinal.cof_bsup_le Ordinal.cof_bsup_le
 
@@ -745,12 +711,10 @@ theorem cof_succ (o) : cof (succ o) = 1 :=
   apply le_antisymm
   · refine' induction_on o fun α r _ => _
     change cof (type _) ≤ _
-    rw [← (_ : (#_) = 1)]
-    apply cof_type_le
+    rw [← (_ : (#_) = 1)]; apply cof_type_le
     · refine' fun a => ⟨Sum.inr PUnit.unit, Set.mem_singleton _, _⟩
       rcases a with (a | ⟨⟨⟨⟩⟩⟩) <;> simp [EmptyRelation]
-    · rw [Cardinal.mk_fintype, Set.card_singleton]
-      simp
+    · rw [Cardinal.mk_fintype, Set.card_singleton]; simp
   · rw [← Cardinal.succ_zero, succ_le_iff]
     simpa [lt_iff_le_and_ne, Cardinal.zero_le] using fun h =>
       succ_ne_zero o (cof_eq_zero.1 (Eq.symm h))
@@ -778,8 +742,7 @@ theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
         · exact Or.inl h
         · exact Or.inr ⟨PUnit.unit, h.symm⟩
         · rcases hl x with ⟨a', aS, hn⟩
-          rw [(_ : ↑a = a')] at h
-          · exact absurd h hn
+          rw [(_ : ↑a = a')] at h; · exact absurd h hn
           refine' congr_arg Subtype.val (_ : a = ⟨a', aS⟩)
           haveI := le_one_iff_subsingleton.1 (le_of_eq e)
           apply Subsingleton.elim,
@@ -810,9 +773,7 @@ but is expected to have type
   forall {a : Ordinal.{u1}} {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{u1}}, (Ordinal.IsFundamentalSequence.{u1} a o f) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o)
 Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.cof_eq Ordinal.IsFundamentalSequence.cof_eqₓ'. -/
 protected theorem cof_eq (hf : IsFundamentalSequence a o f) : a.cof.ord = o :=
-  hf.1.antisymm' <| by
-    rw [← hf.2.2]
-    exact (ord_le_ord.2 (cof_blsub_le f)).trans (ord_card_le o)
+  hf.1.antisymm' <| by rw [← hf.2.2]; exact (ord_le_ord.2 (cof_blsub_le f)).trans (ord_card_le o)
 #align ordinal.is_fundamental_sequence.cof_eq Ordinal.IsFundamentalSequence.cof_eq
 
 /- warning: ordinal.is_fundamental_sequence.strict_mono -> Ordinal.IsFundamentalSequence.strict_mono is a dubious translation:
@@ -843,11 +804,8 @@ but is expected to have type
   forall {a : Ordinal.{u1}} {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{u1}} (hf : Ordinal.IsFundamentalSequence.{u1} a o f), Ordinal.IsFundamentalSequence.{u1} a (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) (fun (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i (Cardinal.ord.{u1} (Ordinal.cof.{u1} a))) => f i (LT.lt.trans_le.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) i (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o hi (Eq.mpr.{0} (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o) (id.{0} (Eq.{1} Prop (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o)) (Eq.ndrec.{0, succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) (fun (_a : Ordinal.{u1}) => Eq.{1} Prop (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _a o)) (Eq.refl.{1} Prop (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o)) o (Ordinal.IsFundamentalSequence.cof_eq.{u1} a o f hf))) (le_refl.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o))))
 Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.ord_cof Ordinal.IsFundamentalSequence.ord_cofₓ'. -/
 theorem ord_cof (hf : IsFundamentalSequence a o f) :
-    IsFundamentalSequence a a.cof.ord fun i hi => f i (hi.trans_le (by rw [hf.cof_eq])) :=
-  by
-  have H := hf.cof_eq
-  subst H
-  exact hf
+    IsFundamentalSequence a a.cof.ord fun i hi => f i (hi.trans_le (by rw [hf.cof_eq])) := by
+  have H := hf.cof_eq; subst H; exact hf
 #align ordinal.is_fundamental_sequence.ord_cof Ordinal.IsFundamentalSequence.ord_cof
 
 /- warning: ordinal.is_fundamental_sequence.id_of_le_cof -> Ordinal.IsFundamentalSequence.id_of_le_cof is a dubious translation:
@@ -904,11 +862,7 @@ protected theorem monotone (hf : IsFundamentalSequence a o f) {i j : Ordinal} (h
 Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.trans Ordinal.IsFundamentalSequence.transₓ'. -/
 theorem trans {a o o' : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}} (hf : IsFundamentalSequence a o f)
     {g : ∀ b < o', Ordinal.{u}} (hg : IsFundamentalSequence o o' g) :
-    IsFundamentalSequence a o' fun i hi =>
-      f (g i hi)
-        (by
-          rw [← hg.2.2]
-          apply lt_blsub) :=
+    IsFundamentalSequence a o' fun i hi => f (g i hi) (by rw [← hg.2.2]; apply lt_blsub) :=
   by
   refine' ⟨_, fun i j _ _ h => hf.2.1 _ _ (hg.2.1 _ _ h), _⟩
   · rw [hf.cof_eq]
@@ -1040,14 +994,12 @@ theorem aleph0_le_cof {o} : ℵ₀ ≤ cof o ↔ IsLimit o :=
   rcases zero_or_succ_or_limit o with (rfl | ⟨o, rfl⟩ | l)
   · simp [not_zero_is_limit, Cardinal.aleph0_ne_zero]
   · simp [not_succ_is_limit, Cardinal.one_lt_aleph0]
-  · simp [l]
-    refine' le_of_not_lt fun h => _
+  · simp [l]; refine' le_of_not_lt fun h => _
     cases' Cardinal.lt_aleph0.1 h with n e
     have := cof_cof o
     rw [e, ord_nat] at this
     cases n
-    · simp at e
-      simpa [e, not_zero_is_limit] using l
+    · simp at e; simpa [e, not_zero_is_limit] using l
     · rw [nat_cast_succ, cof_succ] at this
       rw [← this, cof_eq_one_iff_is_succ] at e
       rcases e with ⟨a, rfl⟩
@@ -1072,10 +1024,7 @@ theorem aleph_cof {o : Ordinal} (ho : o.IsLimit) : (aleph o).ord.cof = o.cof :=
 #print Ordinal.cof_omega /-
 @[simp]
 theorem cof_omega : cof ω = ℵ₀ :=
-  (aleph0_le_cof.2 omega_isLimit).antisymm' <|
-    by
-    rw [← card_omega]
-    apply cof_le_card
+  (aleph0_le_cof.2 omega_isLimit).antisymm' <| by rw [← card_omega]; apply cof_le_card
 #align ordinal.cof_omega Ordinal.cof_omega
 -/
 
@@ -1093,10 +1042,7 @@ theorem cof_eq' (r : α → α → Prop) [IsWellOrder α r] (h : IsLimit (type r
     let ⟨b, h, ab⟩ := H a'
     ⟨b, h,
       (IsOrderConnected.conn a b a' <|
-            (typein_lt_typein r).1
-              (by
-                rw [typein_enum]
-                exact lt_succ (typein _ _))).resolve_right
+            (typein_lt_typein r).1 (by rw [typein_enum]; exact lt_succ (typein _ _))).resolve_right
         ab⟩,
     e⟩
 #align ordinal.cof_eq' Ordinal.cof_eq'
@@ -1213,8 +1159,7 @@ theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ
   by
   cases' infinite_pigeonhole_card f θ hθ h₁ h₂ with a ha
   refine' ⟨a, { x | ∃ h, f ⟨x, h⟩ = a }, _, _, _⟩
-  · rintro x ⟨hx, hx'⟩
-    exact hx
+  · rintro x ⟨hx, hx'⟩; exact hx
   · refine'
       ha.trans
         (ge_of_eq <|
@@ -1324,8 +1269,7 @@ theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α
   · have : { s : Set α | bounded r s } = ⋃ i, 𝒫{ j | r j i } := set_of_exists _
     rw [← coe_set_of, this]
     convert mk_Union_le_sum_mk.trans ((sum_le_supr _).trans (mul_le_max_of_aleph_0_le_left ha))
-    apply (max_eq_left _).symm
-    apply ciSup_le' fun i => _
+    apply (max_eq_left _).symm; apply ciSup_le' fun i => _
     rw [mk_powerset]
     apply (h'.two_power_lt _).le
     rw [coe_set_of, card_typein, ← lt_ord, hr]
@@ -1400,9 +1344,7 @@ lean 3 declaration is
 but is expected to have type
   forall {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) (Cardinal.ord.{u1} c))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_regular.ord_pos Cardinal.IsRegular.ord_posₓ'. -/
-theorem IsRegular.ord_pos {c : Cardinal} (H : c.IsRegular) : 0 < c.ord :=
-  by
-  rw [Cardinal.lt_ord]
+theorem IsRegular.ord_pos {c : Cardinal} (H : c.IsRegular) : 0 < c.ord := by rw [Cardinal.lt_ord];
   exact H.pos
 #align cardinal.is_regular.ord_pos Cardinal.IsRegular.ord_pos
 
@@ -1452,9 +1394,7 @@ lean 3 declaration is
 but is expected to have type
   Cardinal.IsRegular.{u1} (Cardinal.aleph.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_regular_aleph_one Cardinal.isRegular_aleph_oneₓ'. -/
-theorem isRegular_aleph_one : IsRegular (aleph 1) :=
-  by
-  rw [← succ_aleph_0]
+theorem isRegular_aleph_one : IsRegular (aleph 1) := by rw [← succ_aleph_0];
   exact is_regular_succ le_rfl
 #align cardinal.is_regular_aleph_one Cardinal.isRegular_aleph_one
 
@@ -1464,16 +1404,12 @@ lean 3 declaration is
 but is expected to have type
   forall {o : Ordinal.{u1}}, (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.omega.{u1} o) -> (Cardinal.IsRegular.{u1} (Cardinal.aleph'.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_regular_aleph'_succ Cardinal.isRegular_aleph'_succₓ'. -/
-theorem isRegular_aleph'_succ {o : Ordinal} (h : ω ≤ o) : IsRegular (aleph' (succ o)) :=
-  by
-  rw [aleph'_succ]
-  exact is_regular_succ (aleph_0_le_aleph'.2 h)
+theorem isRegular_aleph'_succ {o : Ordinal} (h : ω ≤ o) : IsRegular (aleph' (succ o)) := by
+  rw [aleph'_succ]; exact is_regular_succ (aleph_0_le_aleph'.2 h)
 #align cardinal.is_regular_aleph'_succ Cardinal.isRegular_aleph'_succ
 
 #print Cardinal.isRegular_aleph_succ /-
-theorem isRegular_aleph_succ (o : Ordinal) : IsRegular (aleph (succ o)) :=
-  by
-  rw [aleph_succ]
+theorem isRegular_aleph_succ (o : Ordinal) : IsRegular (aleph (succ o)) := by rw [aleph_succ];
   exact is_regular_succ (aleph_0_le_aleph o)
 #align cardinal.is_regular_aleph_succ Cardinal.isRegular_aleph_succ
 -/
@@ -1684,10 +1620,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align cardinal.nfp_family_lt_ord_lift_of_is_regular Cardinal.nfpFamily_lt_ord_lift_of_isRegularₓ'. -/
 theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a}
-    (ha : a < c.ord) : nfpFamily.{u, v} f a < c.ord :=
-  by
-  apply nfp_family_lt_ord_lift _ _ hf ha <;> rwa [hc.cof_eq]
-  exact lt_of_le_of_ne hc.1 hc'.symm
+    (ha : a < c.ord) : nfpFamily.{u, v} f a < c.ord := by
+  apply nfp_family_lt_ord_lift _ _ hf ha <;> rwa [hc.cof_eq]; exact lt_of_le_of_ne hc.1 hc'.symm
 #align cardinal.nfp_family_lt_ord_lift_of_is_regular Cardinal.nfpFamily_lt_ord_lift_of_isRegular
 
 /- warning: cardinal.nfp_family_lt_ord_of_is_regular -> Cardinal.nfpFamily_lt_ord_of_isRegular is a dubious translation:
@@ -1736,11 +1670,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align cardinal.nfp_lt_ord_of_is_regular Cardinal.nfp_lt_ord_of_isRegularₓ'. -/
 theorem nfp_lt_ord_of_isRegular {f : Ordinal → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
     (hf : ∀ i < c.ord, f i < c.ord) {a} : a < c.ord → nfp f a < c.ord :=
-  nfp_lt_ord
-    (by
-      rw [hc.cof_eq]
-      exact lt_of_le_of_ne hc.1 hc'.symm)
-    hf
+  nfp_lt_ord (by rw [hc.cof_eq]; exact lt_of_le_of_ne hc.1 hc'.symm) hf
 #align cardinal.nfp_lt_ord_of_is_regular Cardinal.nfp_lt_ord_of_isRegular
 
 /- warning: cardinal.deriv_family_lt_ord_lift -> Cardinal.derivFamily_lt_ord_lift is a dubious translation:
@@ -1753,9 +1683,7 @@ theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc :
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, v} f a < c.ord :=
   by
-  have hω : ℵ₀ < c.ord.cof := by
-    rw [hc.cof_eq]
-    exact lt_of_le_of_ne hc.1 hc'.symm
+  have hω : ℵ₀ < c.ord.cof := by rw [hc.cof_eq]; exact lt_of_le_of_ne hc.1 hc'.symm
   apply a.limit_rec_on
   · rw [deriv_family_zero]
     exact nfp_family_lt_ord_lift hω (by rwa [hc.cof_eq]) hf

7c2ce0c2

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -272,7 +272,6 @@ theorem ord_cof_eq (r : α → α → Prop) [IsWellOrder α r] :
 
 private theorem card_mem_cof {o} : ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = o.card :=
   ⟨_, _, lsub_typein o, mk_ordinal_out o⟩
-#align ordinal.card_mem_cof ordinal.card_mem_cof
 
 #print Ordinal.cof_lsub_def_nonempty /-
 /-- The set in the `lsub` characterization of `cof` is nonempty. -/
@@ -901,10 +900,7 @@ protected theorem monotone (hf : IsFundamentalSequence a o f) {i j : Ordinal} (h
 #align ordinal.is_fundamental_sequence.monotone Ordinal.IsFundamentalSequence.monotone
 
 /- warning: ordinal.is_fundamental_sequence.trans -> Ordinal.IsFundamentalSequence.trans is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.trans Ordinal.IsFundamentalSequence.transₓ'. -/
 theorem trans {a o o' : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}} (hf : IsFundamentalSequence a o f)
     {g : ∀ b < o', Ordinal.{u}} (hg : IsFundamentalSequence o o' g) :

7c2ce0c2

bump to nightly-2023-05-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

fbc7b476

Diff

@@ -770,7 +770,7 @@ theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
           Eq.symm <|
             Quotient.sound
               ⟨RelIso.ofSurjective (RelEmbedding.ofMonotone _ fun x y => _) fun x => _⟩⟩
-      · apply Sum.rec <;> [exact Subtype.val, exact fun _ => a]
+      · apply Sum.rec <;> [exact Subtype.val;exact fun _ => a]
       · rcases x with (x | ⟨⟨⟨⟩⟩⟩) <;> rcases y with (y | ⟨⟨⟨⟩⟩⟩) <;>
           simp [Subrel, Order.Preimage, EmptyRelation]
         exact x.2

7c2ce0c2

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -212,11 +212,15 @@ theorem cof_type_le [IsWellOrder α r] {S : Set α} (h : Unbounded r S) : cof (t
 #align ordinal.cof_type_le Ordinal.cof_type_le
 -/
 
-#print Ordinal.lt_cof_type /-
+/- warning: ordinal.lt_cof_type -> Ordinal.lt_cof_type is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r] {S : Set.{u1} α}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (Set.Elem.{u1} α S)) (Ordinal.cof.{u1} (Ordinal.type.{u1} α r _inst_1))) -> (Set.Bounded.{u1} α r S)
+Case conversion may be inaccurate. Consider using '#align ordinal.lt_cof_type Ordinal.lt_cof_typeₓ'. -/
 theorem lt_cof_type [IsWellOrder α r] {S : Set α} : (#S) < cof (type r) → Bounded r S := by
   simpa using not_imp_not.2 cof_type_le
 #align ordinal.lt_cof_type Ordinal.lt_cof_type
--/
 
 #print Ordinal.cof_eq /-
 theorem cof_eq (r : α → α → Prop) [IsWellOrder α r] : ∃ S, Unbounded r S ∧ (#S) = cof (type r) :=
@@ -364,11 +368,15 @@ theorem cof_ord_le (c : Cardinal) : c.ord.cof ≤ c := by simpa using cof_le_car
 #align ordinal.cof_ord_le Ordinal.cof_ord_le
 -/
 
-#print Ordinal.ord_cof_le /-
+/- warning: ordinal.ord_cof_le -> Ordinal.ord_cof_le is a dubious translation:
+lean 3 declaration is
+  forall (o : Ordinal.{u1}), LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} o)) o
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+Case conversion may be inaccurate. Consider using '#align ordinal.ord_cof_le Ordinal.ord_cof_leₓ'. -/
 theorem ord_cof_le (o : Ordinal.{u}) : o.cof.ord ≤ o :=
   (ord_le_ord.2 (cof_le_card o)).trans (ord_card_le o)
 #align ordinal.ord_cof_le Ordinal.ord_cof_le
--/
 
 #print Ordinal.exists_lsub_cof /-
 theorem exists_lsub_cof (o : Ordinal) :
@@ -412,56 +420,80 @@ theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
 #align ordinal.le_cof_iff_lsub Ordinal.le_cof_iff_lsub
 -/
 
-#print Ordinal.lsub_lt_ord_lift /-
+/- warning: ordinal.lsub_lt_ord_lift -> Ordinal.lsub_lt_ord_lift is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.lsub_lt_ord_lift Ordinal.lsub_lt_ord_liftₓ'. -/
 theorem lsub_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : lsub.{u, v} f < c :=
   lt_of_le_of_ne (lsub_le hf) fun h => by
     subst h
     exact (cof_lsub_le_lift f).not_lt hι
 #align ordinal.lsub_lt_ord_lift Ordinal.lsub_lt_ord_lift
--/
 
-#print Ordinal.lsub_lt_ord /-
+/- warning: ordinal.lsub_lt_ord -> Ordinal.lsub_lt_ord is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.lsub_lt_ord Ordinal.lsub_lt_ordₓ'. -/
 theorem lsub_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
     (∀ i, f i < c) → lsub.{u, u} f < c :=
   lsub_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.lsub_lt_ord Ordinal.lsub_lt_ord
--/
 
-#print Ordinal.cof_sup_le_lift /-
+/- warning: ordinal.cof_sup_le_lift -> Ordinal.cof_sup_le_lift is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2}}, (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) (Ordinal.sup.{u1, u2} ι f)) -> (LE.le.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instLECardinal.{max u1 u2} (Ordinal.cof.{max u1 u2} (Ordinal.sup.{u1, u2} ι f)) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)))
+Case conversion may be inaccurate. Consider using '#align ordinal.cof_sup_le_lift Ordinal.cof_sup_le_liftₓ'. -/
 theorem cof_sup_le_lift {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup f) : cof (sup f) ≤ (#ι).lift :=
   by
   rw [← sup_eq_lsub_iff_lt_sup] at H
   rw [H]
   exact cof_lsub_le_lift f
 #align ordinal.cof_sup_le_lift Ordinal.cof_sup_le_lift
--/
 
-#print Ordinal.cof_sup_le /-
+/- warning: ordinal.cof_sup_le -> Ordinal.cof_sup_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{u1}}, (forall (i : ι), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i) (Ordinal.sup.{u1, u1} ι f)) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Ordinal.cof.{u1} (Ordinal.sup.{u1, u1} ι f)) (Cardinal.mk.{u1} ι))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{u1}}, (forall (i : ι), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i) (Ordinal.sup.{u1, u1} ι f)) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Ordinal.cof.{u1} (Ordinal.sup.{u1, u1} ι f)) (Cardinal.mk.{u1} ι))
+Case conversion may be inaccurate. Consider using '#align ordinal.cof_sup_le Ordinal.cof_sup_leₓ'. -/
 theorem cof_sup_le {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup.{u, u} f) :
     cof (sup.{u, u} f) ≤ (#ι) := by
   rw [← (#ι).lift_id]
   exact cof_sup_le_lift H
 #align ordinal.cof_sup_le Ordinal.cof_sup_le
--/
 
-#print Ordinal.sup_lt_ord_lift /-
+/- warning: ordinal.sup_lt_ord_lift -> Ordinal.sup_lt_ord_lift is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.sup.{u1, u2} ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.sup.{u1, u2} ι f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.sup_lt_ord_lift Ordinal.sup_lt_ord_liftₓ'. -/
 theorem sup_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : sup.{u, v} f < c :=
   (sup_le_lsub.{u, v} f).trans_lt (lsub_lt_ord_lift hι hf)
 #align ordinal.sup_lt_ord_lift Ordinal.sup_lt_ord_lift
--/
 
-#print Ordinal.sup_lt_ord /-
+/- warning: ordinal.sup_lt_ord -> Ordinal.sup_lt_ord is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} c)) -> (forall (i : ι), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.sup.{u1, u1} ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} c)) -> (forall (i : ι), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.sup.{u1, u1} ι f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.sup_lt_ord Ordinal.sup_lt_ordₓ'. -/
 theorem sup_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
     (∀ i, f i < c) → sup.{u, u} f < c :=
   sup_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.sup_lt_ord Ordinal.sup_lt_ord
--/
 
 /- warning: ordinal.supr_lt_lift -> Ordinal.iSup_lt_lift is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (iSup.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (iSup.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (iSup.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toSupSet.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{max u1 u2}))) ι f) c)
 Case conversion may be inaccurate. Consider using '#align ordinal.supr_lt_lift Ordinal.iSup_lt_liftₓ'. -/
@@ -476,7 +508,7 @@ theorem iSup_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal} (hι : Cardinal.l
 
 /- warning: ordinal.supr_lt -> Ordinal.iSup_lt is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (iSup.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (iSup.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (iSup.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toSupSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) ι f) c)
 Case conversion may be inaccurate. Consider using '#align ordinal.supr_lt Ordinal.iSup_ltₓ'. -/
@@ -485,7 +517,12 @@ theorem iSup_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : (#ι) < c.ord.c
   iSup_lt_lift (by rwa [(#ι).lift_id])
 #align ordinal.supr_lt Ordinal.iSup_lt
 
-#print Ordinal.nfpFamily_lt_ord_lift /-
+/- warning: ordinal.nfp_family_lt_ord_lift -> Ordinal.nfpFamily_lt_ord_lift is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) Cardinal.aleph0.{max u1 u2} (Ordinal.cof.{max u1 u2} c)) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : ι) (b : Ordinal.{max u1 u2}), (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b c) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i b) c)) -> (forall {a : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) a c) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.nfpFamily.{u1, u2} ι f a) c))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) Cardinal.aleph0.{max u1 u2} (Ordinal.cof.{max u1 u2} c)) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : ι) (b : Ordinal.{max u1 u2}), (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b c) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i b) c)) -> (forall {a : Ordinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) a c) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u1 u2})) (Ordinal.nfpFamily.{u1, u2} ι f a) c))
+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_family_lt_ord_lift Ordinal.nfpFamily_lt_ord_liftₓ'. -/
 theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : (#ι).lift < cof c) (hf : ∀ (i), ∀ b < c, f i b < c) {a} (ha : a < c) :
     nfpFamily.{u, v} f a < c :=
@@ -498,39 +535,59 @@ theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : 
     · exact ha
     · exact hf _ _ H
 #align ordinal.nfp_family_lt_ord_lift Ordinal.nfpFamily_lt_ord_lift
--/
 
-#print Ordinal.nfpFamily_lt_ord /-
+/- warning: ordinal.nfp_family_lt_ord -> Ordinal.nfpFamily_lt_ord is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{u1} -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} (Ordinal.cof.{u1} c)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} c)) -> (forall (i : ι) (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i b) c)) -> (forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfpFamily.{u1, u1} ι f a) c))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_family_lt_ord Ordinal.nfpFamily_lt_ordₓ'. -/
 theorem nfpFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hc' : (#ι) < cof c)
     (hf : ∀ (i), ∀ b < c, f i b < c) {a} : a < c → nfpFamily.{u, u} f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [(#ι).lift_id]) hf
 #align ordinal.nfp_family_lt_ord Ordinal.nfpFamily_lt_ord
--/
 
-#print Ordinal.nfpBFamily_lt_ord_lift /-
+/- warning: ordinal.nfp_bfamily_lt_ord_lift -> Ordinal.nfpBFamily_lt_ord_lift is a dubious translation:
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+  forall {o : Ordinal.{u1}} {f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) Cardinal.aleph0.{max u1 u2} (Ordinal.cof.{max u1 u2} c)) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Ordinal.card.{u1} o)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o) (b : Ordinal.{max u1 u2}), (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b c) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i hi b) c)) -> (forall {a : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) a c) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.nfpBFamily.{u1, u2} o f a) c))
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_lt_ord_lift Ordinal.nfpBFamily_lt_ord_liftₓ'. -/
 theorem nfpBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : o.card.lift < cof c) (hf : ∀ (i hi), ∀ b < c, f i hi b < c) {a} :
     a < c → nfpBFamily.{u, v} o f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [mk_ordinal_out]) fun i => hf _ _
 #align ordinal.nfp_bfamily_lt_ord_lift Ordinal.nfpBFamily_lt_ord_lift
--/
 
-#print Ordinal.nfpBFamily_lt_ord /-
+/- warning: ordinal.nfp_bfamily_lt_ord -> Ordinal.nfpBFamily_lt_ord is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}} {f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{u1} -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} (Ordinal.cof.{u1} c)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} o) (Ordinal.cof.{u1} c)) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o) (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i hi b) c)) -> (forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfpBFamily.{u1, u1} o f a) c))
+but is expected to have type
+  forall {o : Ordinal.{u1}} {f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{u1} -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} (Ordinal.cof.{u1} c)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} o) (Ordinal.cof.{u1} c)) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o) (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i hi b) c)) -> (forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfpBFamily.{u1, u1} o f a) c))
+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_lt_ord Ordinal.nfpBFamily_lt_ordₓ'. -/
 theorem nfpBFamily_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : o.card < cof c) (hf : ∀ (i hi), ∀ b < c, f i hi b < c) {a} :
     a < c → nfpBFamily.{u, u} o f a < c :=
   nfpBFamily_lt_ord_lift hc (by rwa [o.card.lift_id]) hf
 #align ordinal.nfp_bfamily_lt_ord Ordinal.nfpBFamily_lt_ord
--/
 
-#print Ordinal.nfp_lt_ord /-
+/- warning: ordinal.nfp_lt_ord -> Ordinal.nfp_lt_ord is a dubious translation:
+lean 3 declaration is
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} (Ordinal.cof.{u1} c)) -> (forall (i : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i) c)) -> (forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfp.{u1} f a) c))
+but is expected to have type
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} (Ordinal.cof.{u1} c)) -> (forall (i : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i) c)) -> (forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfp.{u1} f a) c))
+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_lt_ord Ordinal.nfp_lt_ordₓ'. -/
 theorem nfp_lt_ord {f : Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hf : ∀ i < c, f i < c) {a} :
     a < c → nfp f a < c :=
   nfpFamily_lt_ord_lift hc (by simpa using cardinal.one_lt_aleph_0.trans hc) fun _ => hf
 #align ordinal.nfp_lt_ord Ordinal.nfp_lt_ord
--/
 
-#print Ordinal.exists_blsub_cof /-
+/- warning: ordinal.exists_blsub_cof -> Ordinal.exists_blsub_cof is a dubious translation:
+lean 3 declaration is
+  forall (o : Ordinal.{u1}), Exists.{succ (succ u1)} (forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (Cardinal.ord.{u1} (Ordinal.cof.{u1} o))) -> Ordinal.{u1}) (fun (f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (Cardinal.ord.{u1} (Ordinal.cof.{u1} o))) -> Ordinal.{u1}) => Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.blsub.{u1, u1} (Cardinal.ord.{u1} (Ordinal.cof.{u1} o)) f) o)
+but is expected to have type
+  forall (o : Ordinal.{u1}), Exists.{succ (succ u1)} (forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (Cardinal.ord.{u1} (Ordinal.cof.{u1} o))) -> Ordinal.{u1}) (fun (f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (Cardinal.ord.{u1} (Ordinal.cof.{u1} o))) -> Ordinal.{u1}) => Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.blsub.{u1, u1} (Cardinal.ord.{u1} (Ordinal.cof.{u1} o)) f) o)
+Case conversion may be inaccurate. Consider using '#align ordinal.exists_blsub_cof Ordinal.exists_blsub_cofₓ'. -/
 theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, blsub.{u, u} _ f = o :=
   by
   rcases exists_lsub_cof o with ⟨ι, f, hf, hι⟩
@@ -539,9 +596,13 @@ theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, b
   rw [← hι, hι']
   exact ⟨_, hf⟩
 #align ordinal.exists_blsub_cof Ordinal.exists_blsub_cof
--/
 
-#print Ordinal.le_cof_iff_blsub /-
+/- warning: ordinal.le_cof_iff_blsub -> Ordinal.le_cof_iff_blsub is a dubious translation:
+lean 3 declaration is
+  forall {b : Ordinal.{u1}} {a : Cardinal.{u1}}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} a (Ordinal.cof.{u1} b)) (forall {o : Ordinal.{u1}} (f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{u1}), (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.blsub.{u1, u1} o f) b) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} a (Ordinal.card.{u1} o)))
+but is expected to have type
+  forall {b : Ordinal.{u1}} {a : Cardinal.{u1}}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} a (Ordinal.cof.{u1} b)) (forall {o : Ordinal.{u1}} (f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{u1}), (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.blsub.{u1, u1} o f) b) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} a (Ordinal.card.{u1} o)))
+Case conversion may be inaccurate. Consider using '#align ordinal.le_cof_iff_blsub Ordinal.le_cof_iff_blsubₓ'. -/
 theorem le_cof_iff_blsub {b : Ordinal} {a : Cardinal} :
     a ≤ cof b ↔ ∀ {o} (f : ∀ a < o, Ordinal), blsub.{u, u} o f = b → a ≤ o.card :=
   le_cof_iff_lsub.trans
@@ -551,41 +612,61 @@ theorem le_cof_iff_blsub {b : Ordinal} {a : Cardinal} :
       rw [← @blsub_eq_lsub' ι r hr] at hf
       simpa using H _ hf⟩
 #align ordinal.le_cof_iff_blsub Ordinal.le_cof_iff_blsub
--/
 
-#print Ordinal.cof_blsub_le_lift /-
+/- warning: ordinal.cof_blsub_le_lift -> Ordinal.cof_blsub_le_lift is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ordinal.cof_blsub_le_lift Ordinal.cof_blsub_le_liftₓ'. -/
 theorem cof_blsub_le_lift {o} (f : ∀ a < o, Ordinal) :
     cof (blsub o f) ≤ Cardinal.lift.{v, u} o.card :=
   by
   convert cof_lsub_le_lift _
   exact (mk_ordinal_out o).symm
 #align ordinal.cof_blsub_le_lift Ordinal.cof_blsub_le_lift
--/
 
-#print Ordinal.cof_blsub_le /-
+/- warning: ordinal.cof_blsub_le -> Ordinal.cof_blsub_le is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}} (f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Ordinal.cof.{u1} (Ordinal.blsub.{u1, u1} o f)) (Ordinal.card.{u1} o)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.cof_blsub_le Ordinal.cof_blsub_leₓ'. -/
 theorem cof_blsub_le {o} (f : ∀ a < o, Ordinal) : cof (blsub.{u, u} o f) ≤ o.card :=
   by
   rw [← o.card.lift_id]
   exact cof_blsub_le_lift f
 #align ordinal.cof_blsub_le Ordinal.cof_blsub_le
--/
 
-#print Ordinal.blsub_lt_ord_lift /-
+/- warning: ordinal.blsub_lt_ord_lift -> Ordinal.blsub_lt_ord_lift is a dubious translation:
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+  forall {o : Ordinal.{u1}} {f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Ordinal.card.{u1} o)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i hi) c) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.blsub.{u1, u2} o f) c)
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+Case conversion may be inaccurate. Consider using '#align ordinal.blsub_lt_ord_lift Ordinal.blsub_lt_ord_liftₓ'. -/
 theorem blsub_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : o.card.lift < c.cof) (hf : ∀ i hi, f i hi < c) : blsub.{u, v} o f < c :=
   lt_of_le_of_ne (blsub_le hf) fun h =>
     ho.not_le (by simpa [← supr_ord, hf, h] using cof_blsub_le_lift.{u} f)
 #align ordinal.blsub_lt_ord_lift Ordinal.blsub_lt_ord_lift
--/
 
-#print Ordinal.blsub_lt_ord /-
+/- warning: ordinal.blsub_lt_ord -> Ordinal.blsub_lt_ord is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ordinal.blsub_lt_ord Ordinal.blsub_lt_ordₓ'. -/
 theorem blsub_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof)
     (hf : ∀ i hi, f i hi < c) : blsub.{u, u} o f < c :=
   blsub_lt_ord_lift (by rwa [o.card.lift_id]) hf
 #align ordinal.blsub_lt_ord Ordinal.blsub_lt_ord
--/
 
-#print Ordinal.cof_bsup_le_lift /-
+/- warning: ordinal.cof_bsup_le_lift -> Ordinal.cof_bsup_le_lift is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}} {f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{max u1 u2}}, (forall (i : Ordinal.{u1}) (h : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i h) (Ordinal.bsup.{u1, u2} o f)) -> (LE.le.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.hasLe.{max u1 u2} (Ordinal.cof.{max u1 u2} (Ordinal.bsup.{u1, u2} o f)) (Cardinal.lift.{u2, u1} (Ordinal.card.{u1} o)))
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+Case conversion may be inaccurate. Consider using '#align ordinal.cof_bsup_le_lift Ordinal.cof_bsup_le_liftₓ'. -/
 theorem cof_bsup_le_lift {o : Ordinal} {f : ∀ a < o, Ordinal} (H : ∀ i h, f i h < bsup o f) :
     cof (bsup o f) ≤ o.card.lift :=
   by
@@ -593,30 +674,41 @@ theorem cof_bsup_le_lift {o : Ordinal} {f : ∀ a < o, Ordinal} (H : ∀ i h, f
   rw [H]
   exact cof_blsub_le_lift f
 #align ordinal.cof_bsup_le_lift Ordinal.cof_bsup_le_lift
--/
 
-#print Ordinal.cof_bsup_le /-
+/- warning: ordinal.cof_bsup_le -> Ordinal.cof_bsup_le is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ordinal.cof_bsup_le Ordinal.cof_bsup_leₓ'. -/
 theorem cof_bsup_le {o : Ordinal} {f : ∀ a < o, Ordinal} :
     (∀ i h, f i h < bsup.{u, u} o f) → cof (bsup.{u, u} o f) ≤ o.card :=
   by
   rw [← o.card.lift_id]
   exact cof_bsup_le_lift
 #align ordinal.cof_bsup_le Ordinal.cof_bsup_le
--/
 
-#print Ordinal.bsup_lt_ord_lift /-
+/- warning: ordinal.bsup_lt_ord_lift -> Ordinal.bsup_lt_ord_lift is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ordinal.bsup_lt_ord_lift Ordinal.bsup_lt_ord_liftₓ'. -/
 theorem bsup_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : o.card.lift < c.cof) (hf : ∀ i hi, f i hi < c) : bsup.{u, v} o f < c :=
   (bsup_le_blsub f).trans_lt (blsub_lt_ord_lift ho hf)
 #align ordinal.bsup_lt_ord_lift Ordinal.bsup_lt_ord_lift
--/
 
-#print Ordinal.bsup_lt_ord /-
+/- warning: ordinal.bsup_lt_ord -> Ordinal.bsup_lt_ord is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.bsup_lt_ord Ordinal.bsup_lt_ordₓ'. -/
 theorem bsup_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof) :
     (∀ i hi, f i hi < c) → bsup.{u, u} o f < c :=
   bsup_lt_ord_lift (by rwa [o.card.lift_id])
 #align ordinal.bsup_lt_ord Ordinal.bsup_lt_ord
--/
 
 /-! ### Basic results -/
 
@@ -696,40 +788,61 @@ theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
 #align ordinal.cof_eq_one_iff_is_succ Ordinal.cof_eq_one_iff_is_succ
 -/
 
-#print Ordinal.IsFundamentalSequence /-
+/- warning: ordinal.is_fundamental_sequence -> Ordinal.IsFundamentalSequence is a dubious translation:
+lean 3 declaration is
+  Ordinal.{u1} -> (forall (o : Ordinal.{u1}), (forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{u1}) -> Prop)
+but is expected to have type
+  Ordinal.{u1} -> (forall (o : Ordinal.{u1}), (forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{u1}) -> Prop)
+Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence Ordinal.IsFundamentalSequenceₓ'. -/
 /-- A fundamental sequence for `a` is an increasing sequence of length `o = cof a` that converges at
     `a`. We provide `o` explicitly in order to avoid type rewrites. -/
 def IsFundamentalSequence (a o : Ordinal.{u}) (f : ∀ b < o, Ordinal.{u}) : Prop :=
   o ≤ a.cof.ord ∧ (∀ {i j} (hi hj), i < j → f i hi < f j hj) ∧ blsub.{u, u} o f = a
 #align ordinal.is_fundamental_sequence Ordinal.IsFundamentalSequence
--/
 
 namespace IsFundamentalSequence
 
 variable {a o : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}}
 
-#print Ordinal.IsFundamentalSequence.cof_eq /-
+/- warning: ordinal.is_fundamental_sequence.cof_eq -> Ordinal.IsFundamentalSequence.cof_eq is a dubious translation:
+lean 3 declaration is
+  forall {a : Ordinal.{u1}} {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{u1}}, (Ordinal.IsFundamentalSequence.{u1} a o f) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o)
+but is expected to have type
+  forall {a : Ordinal.{u1}} {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{u1}}, (Ordinal.IsFundamentalSequence.{u1} a o f) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o)
+Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.cof_eq Ordinal.IsFundamentalSequence.cof_eqₓ'. -/
 protected theorem cof_eq (hf : IsFundamentalSequence a o f) : a.cof.ord = o :=
   hf.1.antisymm' <| by
     rw [← hf.2.2]
     exact (ord_le_ord.2 (cof_blsub_le f)).trans (ord_card_le o)
 #align ordinal.is_fundamental_sequence.cof_eq Ordinal.IsFundamentalSequence.cof_eq
--/
 
-#print Ordinal.IsFundamentalSequence.strict_mono /-
+/- warning: ordinal.is_fundamental_sequence.strict_mono -> Ordinal.IsFundamentalSequence.strict_mono is a dubious translation:
+lean 3 declaration is
+  forall {a : Ordinal.{u1}} {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{u1}}, (Ordinal.IsFundamentalSequence.{u1} a o f) -> (forall {i : Ordinal.{u1}} {j : Ordinal.{u1}} (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o) (hj : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) j o), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i j) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i hi) (f j hj)))
+but is expected to have type
+  forall {a : Ordinal.{u1}} {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{u1}}, (Ordinal.IsFundamentalSequence.{u1} a o f) -> (forall {i : Ordinal.{u1}} {j : Ordinal.{u1}} (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o) (hj : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) j o), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i j) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i hi) (f j hj)))
+Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.strict_mono Ordinal.IsFundamentalSequence.strict_monoₓ'. -/
 protected theorem strict_mono (hf : IsFundamentalSequence a o f) {i j} :
     ∀ hi hj, i < j → f i hi < f j hj :=
   hf.2.1
 #align ordinal.is_fundamental_sequence.strict_mono Ordinal.IsFundamentalSequence.strict_mono
--/
 
-#print Ordinal.IsFundamentalSequence.blsub_eq /-
+/- warning: ordinal.is_fundamental_sequence.blsub_eq -> Ordinal.IsFundamentalSequence.blsub_eq is a dubious translation:
+lean 3 declaration is
+  forall {a : Ordinal.{u1}} {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{u1}}, (Ordinal.IsFundamentalSequence.{u1} a o f) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.blsub.{u1, u1} o f) a)
+but is expected to have type
+  forall {a : Ordinal.{u1}} {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{u1}}, (Ordinal.IsFundamentalSequence.{u1} a o f) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.blsub.{u1, u1} o f) a)
+Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.blsub_eq Ordinal.IsFundamentalSequence.blsub_eqₓ'. -/
 theorem blsub_eq (hf : IsFundamentalSequence a o f) : blsub.{u, u} o f = a :=
   hf.2.2
 #align ordinal.is_fundamental_sequence.blsub_eq Ordinal.IsFundamentalSequence.blsub_eq
--/
 
-#print Ordinal.IsFundamentalSequence.ord_cof /-
+/- warning: ordinal.is_fundamental_sequence.ord_cof -> Ordinal.IsFundamentalSequence.ord_cof is a dubious translation:
+lean 3 declaration is
+  forall {a : Ordinal.{u1}} {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{u1}} (hf : Ordinal.IsFundamentalSequence.{u1} a o f), Ordinal.IsFundamentalSequence.{u1} a (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) (fun (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i (Cardinal.ord.{u1} (Ordinal.cof.{u1} a))) => f i (LT.lt.trans_le.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) i (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o hi (Eq.mpr.{0} (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o)) (Eq.ndrec.{0, succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) (fun (_a : Ordinal.{u1}) => Eq.{1} Prop (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _a o)) (rfl.{1} Prop (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o)) o (Ordinal.IsFundamentalSequence.cof_eq.{u1} a o f hf))) (le_refl.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o))))
+but is expected to have type
+  forall {a : Ordinal.{u1}} {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{u1}} (hf : Ordinal.IsFundamentalSequence.{u1} a o f), Ordinal.IsFundamentalSequence.{u1} a (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) (fun (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i (Cardinal.ord.{u1} (Ordinal.cof.{u1} a))) => f i (LT.lt.trans_le.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) i (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o hi (Eq.mpr.{0} (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o) (id.{0} (Eq.{1} Prop (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o)) (Eq.ndrec.{0, succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) (fun (_a : Ordinal.{u1}) => Eq.{1} Prop (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _a o)) (Eq.refl.{1} Prop (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.cof.{u1} a)) o)) o (Ordinal.IsFundamentalSequence.cof_eq.{u1} a o f hf))) (le_refl.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o))))
+Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.ord_cof Ordinal.IsFundamentalSequence.ord_cofₓ'. -/
 theorem ord_cof (hf : IsFundamentalSequence a o f) :
     IsFundamentalSequence a a.cof.ord fun i hi => f i (hi.trans_le (by rw [hf.cof_eq])) :=
   by
@@ -737,23 +850,30 @@ theorem ord_cof (hf : IsFundamentalSequence a o f) :
   subst H
   exact hf
 #align ordinal.is_fundamental_sequence.ord_cof Ordinal.IsFundamentalSequence.ord_cof
--/
 
-#print Ordinal.IsFundamentalSequence.id_of_le_cof /-
+/- warning: ordinal.is_fundamental_sequence.id_of_le_cof -> Ordinal.IsFundamentalSequence.id_of_le_cof is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Cardinal.ord.{u1} (Ordinal.cof.{u1} o))) -> (Ordinal.IsFundamentalSequence.{u1} o o (fun (a : Ordinal.{u1}) (_x : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) => a))
+but is expected to have type
+  forall {o : Ordinal.{u1}}, (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Cardinal.ord.{u1} (Ordinal.cof.{u1} o))) -> (Ordinal.IsFundamentalSequence.{u1} o o (fun (a : Ordinal.{u1}) (_x : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) => a))
+Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.id_of_le_cof Ordinal.IsFundamentalSequence.id_of_le_cofₓ'. -/
 theorem id_of_le_cof (h : o ≤ o.cof.ord) : IsFundamentalSequence o o fun a _ => a :=
   ⟨h, fun _ _ _ _ => id, blsub_id o⟩
 #align ordinal.is_fundamental_sequence.id_of_le_cof Ordinal.IsFundamentalSequence.id_of_le_cof
--/
 
-#print Ordinal.IsFundamentalSequence.zero /-
+/- warning: ordinal.is_fundamental_sequence.zero -> Ordinal.IsFundamentalSequence.zero is a dubious translation:
+lean 3 declaration is
+  forall {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))) -> Ordinal.{u1}}, Ordinal.IsFundamentalSequence.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) f
+but is expected to have type
+  forall {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) -> Ordinal.{u1}}, Ordinal.IsFundamentalSequence.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) f
+Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.zero Ordinal.IsFundamentalSequence.zeroₓ'. -/
 protected theorem zero {f : ∀ b < (0 : Ordinal), Ordinal} : IsFundamentalSequence 0 0 f :=
   ⟨by rw [cof_zero, ord_zero], fun i j hi => (Ordinal.not_lt_zero i hi).elim, blsub_zero f⟩
 #align ordinal.is_fundamental_sequence.zero Ordinal.IsFundamentalSequence.zero
--/
 
 /- warning: ordinal.is_fundamental_sequence.succ -> Ordinal.IsFundamentalSequence.succ is a dubious translation:
 lean 3 declaration is
-  forall {o : Ordinal.{u1}}, Ordinal.IsFundamentalSequence.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))) (fun (_x : Ordinal.{u1}) (_x : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _x (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) => o)
+  forall {o : Ordinal.{u1}}, Ordinal.IsFundamentalSequence.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))) (fun (_x : Ordinal.{u1}) (_x : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _x (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) => o)
 but is expected to have type
   forall {o : Ordinal.{u1}}, Ordinal.IsFundamentalSequence.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})) (fun (_x : Ordinal.{u1}) (_x : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _x (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) => o)
 Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.succ Ordinal.IsFundamentalSequence.succₓ'. -/
@@ -766,7 +886,12 @@ protected theorem succ : IsFundamentalSequence (succ o) 1 fun _ _ => o :=
     exact h.false.elim
 #align ordinal.is_fundamental_sequence.succ Ordinal.IsFundamentalSequence.succ
 
-#print Ordinal.IsFundamentalSequence.monotone /-
+/- warning: ordinal.is_fundamental_sequence.monotone -> Ordinal.IsFundamentalSequence.monotone is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.monotone Ordinal.IsFundamentalSequence.monotoneₓ'. -/
 protected theorem monotone (hf : IsFundamentalSequence a o f) {i j : Ordinal} (hi : i < o)
     (hj : j < o) (hij : i ≤ j) : f i hi ≤ f j hj :=
   by
@@ -774,9 +899,13 @@ protected theorem monotone (hf : IsFundamentalSequence a o f) {i j : Ordinal} (h
   · exact (hf.2.1 hi hj hij).le
   · rfl
 #align ordinal.is_fundamental_sequence.monotone Ordinal.IsFundamentalSequence.monotone
--/
 
-#print Ordinal.IsFundamentalSequence.trans /-
+/- warning: ordinal.is_fundamental_sequence.trans -> Ordinal.IsFundamentalSequence.trans is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.trans Ordinal.IsFundamentalSequence.transₓ'. -/
 theorem trans {a o o' : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}} (hf : IsFundamentalSequence a o f)
     {g : ∀ b < o', Ordinal.{u}} (hg : IsFundamentalSequence o o' g) :
     IsFundamentalSequence a o' fun i hi =>
@@ -791,11 +920,15 @@ theorem trans {a o o' : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}} (hf : IsFundam
   · rw [@blsub_comp.{u, u, u} o _ f (@is_fundamental_sequence.monotone _ _ f hf)]
     exact hf.2.2
 #align ordinal.is_fundamental_sequence.trans Ordinal.IsFundamentalSequence.trans
--/
 
 end IsFundamentalSequence
 
-#print Ordinal.exists_fundamental_sequence /-
+/- warning: ordinal.exists_fundamental_sequence -> Ordinal.exists_fundamental_sequence is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.exists_fundamental_sequence Ordinal.exists_fundamental_sequenceₓ'. -/
 /-- Every ordinal has a fundamental sequence. -/
 theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequence a a.cof.ord f :=
   by
@@ -828,7 +961,6 @@ theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequ
         exact (wo.wf.not_lt_min _ h ⟨IsTrans.trans _ _ _ hkj hji, H⟩) hkj
       · rwa [bfamily_of_family'_typein]
 #align ordinal.exists_fundamental_sequence Ordinal.exists_fundamental_sequence
--/
 
 #print Ordinal.cof_cof /-
 @[simp]
@@ -840,7 +972,12 @@ theorem cof_cof (a : Ordinal.{u}) : cof (cof a).ord = cof a :=
 #align ordinal.cof_cof Ordinal.cof_cof
 -/
 
-#print Ordinal.IsNormal.isFundamentalSequence /-
+/- warning: ordinal.is_normal.is_fundamental_sequence -> Ordinal.IsNormal.isFundamentalSequence is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.is_normal.is_fundamental_sequence Ordinal.IsNormal.isFundamentalSequenceₓ'. -/
 protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u}} (hf : IsNormal f)
     {a o} (ha : IsLimit a) {g} (hg : IsFundamentalSequence a o g) :
     IsFundamentalSequence (f a) o fun b hb => f (g b hb) :=
@@ -870,7 +1007,6 @@ protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u
         hg.2.2]
     exact IsNormal.blsub_eq.{u, u} hf ha
 #align ordinal.is_normal.is_fundamental_sequence Ordinal.IsNormal.isFundamentalSequence
--/
 
 #print Ordinal.IsNormal.cof_eq /-
 theorem IsNormal.cof_eq {f} (hf : IsNormal f) {a} (ha : IsLimit a) : cof (f a) = cof a :=
@@ -997,7 +1133,7 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ :=
 
 /- warning: ordinal.unbounded_of_unbounded_sUnion -> Ordinal.unbounded_of_unbounded_sUnion is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.sUnion.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Set.{u1} α)) Type.{u1} (Set.hasCoeToSort.{u1} (Set.{u1} α)) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) => Set.Unbounded.{u1} α r x)))
 but is expected to have type
   forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.sUnion.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (Set.Elem.{u1} (Set.{u1} α) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) x s) (Set.Unbounded.{u1} α r x)))
 Case conversion may be inaccurate. Consider using '#align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_sUnionₓ'. -/
@@ -1014,7 +1150,12 @@ theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder
   exact ⟨f ⟨c, hc⟩, mem_range_self _, fun hxz => hxy (trans (wo.wf.lt_sup _ hy) hxz)⟩
 #align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_sUnion
 
-#print Ordinal.unbounded_of_unbounded_iUnion /-
+/- warning: ordinal.unbounded_of_unbounded_Union -> Ordinal.unbounded_of_unbounded_iUnion is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] (s : β -> (Set.{u1} α)), (Set.Unbounded.{u1} α r (Set.iUnion.{u1, succ u1} α β (fun (x : β) => s x))) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} β) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} β (fun (x : β) => Set.Unbounded.{u1} α r (s x)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] (s : β -> (Set.{u1} α)), (Set.Unbounded.{u1} α r (Set.iUnion.{u1, succ u1} α β (fun (x : β) => s x))) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} β) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} β (fun (x : β) => Set.Unbounded.{u1} α r (s x)))
+Case conversion may be inaccurate. Consider using '#align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_iUnionₓ'. -/
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
 theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
@@ -1024,9 +1165,13 @@ theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop)
   rcases unbounded_of_unbounded_sUnion r h₁ (mk_range_le.trans_lt h₂) with ⟨_, ⟨x, rfl⟩, u⟩
   exact ⟨x, u⟩
 #align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_iUnion
--/
 
-#print Ordinal.infinite_pigeonhole /-
+/- warning: ordinal.infinite_pigeonhole -> Ordinal.infinite_pigeonhole is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α), (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} (Cardinal.mk.{u1} β)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} β)))) -> (Exists.{succ u1} α (fun (a : α) => Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)))) (Cardinal.mk.{u1} β)))
+but is expected to have type
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α), (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} (Cardinal.mk.{u1} β)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} β)))) -> (Exists.{succ u1} α (fun (a : α) => Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Set.Elem.{u1} β (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)))) (Cardinal.mk.{u1} β)))
+Case conversion may be inaccurate. Consider using '#align ordinal.infinite_pigeonhole Ordinal.infinite_pigeonholeₓ'. -/
 /-- The infinite pigeonhole principle -/
 theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤ (#β)) (h₂ : (#α) < (#β).ord.cof) :
     ∃ a : α, (#f ⁻¹' {a}) = (#β) :=
@@ -1043,9 +1188,13 @@ theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤
   rw [le_mk_iff_exists_set]
   exact ⟨_, rfl⟩
 #align ordinal.infinite_pigeonhole Ordinal.infinite_pigeonhole
--/
 
-#print Ordinal.infinite_pigeonhole_card /-
+/- warning: ordinal.infinite_pigeonhole_card -> Ordinal.infinite_pigeonhole_card is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α) (θ : Cardinal.{u1}), (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} θ (Cardinal.mk.{u1} β)) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} θ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Ordinal.cof.{u1} (Cardinal.ord.{u1} θ))) -> (Exists.{succ u1} α (fun (a : α) => LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} θ (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a))))))
+but is expected to have type
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α) (θ : Cardinal.{u1}), (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} θ (Cardinal.mk.{u1} β)) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} θ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Ordinal.cof.{u1} (Cardinal.ord.{u1} θ))) -> (Exists.{succ u1} α (fun (a : α) => LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} θ (Cardinal.mk.{u1} (Set.Elem.{u1} β (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a))))))
+Case conversion may be inaccurate. Consider using '#align ordinal.infinite_pigeonhole_card Ordinal.infinite_pigeonhole_cardₓ'. -/
 /-- Pigeonhole principle for a cardinality below the cardinality of the domain -/
 theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal) (hθ : θ ≤ (#β))
     (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) : ∃ a : α, θ ≤ (#f ⁻¹' {a}) :=
@@ -1055,9 +1204,13 @@ theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal
   use a; rw [← ha, @preimage_comp _ _ _ Subtype.val f]
   exact mk_preimage_of_injective _ _ Subtype.val_injective
 #align ordinal.infinite_pigeonhole_card Ordinal.infinite_pigeonhole_card
--/
 
-#print Ordinal.infinite_pigeonhole_set /-
+/- warning: ordinal.infinite_pigeonhole_set -> Ordinal.infinite_pigeonhole_set is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {α : Type.{u1}} {s : Set.{u1} β} (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) s) -> α) (θ : Cardinal.{u1}), (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} θ (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) s))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} θ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Ordinal.cof.{u1} (Cardinal.ord.{u1} θ))) -> (Exists.{succ u1} α (fun (a : α) => Exists.{succ u1} (Set.{u1} β) (fun (t : Set.{u1} β) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} β) (Set.hasSubset.{u1} β) t s) (fun (h : HasSubset.Subset.{u1} (Set.{u1} β) (Set.hasSubset.{u1} β) t s) => And (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} θ (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) t))) (forall {{x : β}} (hx : Membership.Mem.{u1, u1} β (Set.{u1} β) (Set.hasMem.{u1} β) x t), Eq.{succ u1} α (f (Subtype.mk.{succ u1} β (fun (x : β) => Membership.Mem.{u1, u1} β (Set.{u1} β) (Set.hasMem.{u1} β) x s) x (h x hx))) a)))))
+but is expected to have type
+  forall {β : Type.{u1}} {α : Type.{u1}} {s : Set.{u1} β} (f : (Set.Elem.{u1} β s) -> α) (θ : Cardinal.{u1}), (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} θ (Cardinal.mk.{u1} (Set.Elem.{u1} β s))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} θ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Ordinal.cof.{u1} (Cardinal.ord.{u1} θ))) -> (Exists.{succ u1} α (fun (a : α) => Exists.{succ u1} (Set.{u1} β) (fun (t : Set.{u1} β) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} β) (Set.instHasSubsetSet.{u1} β) t s) (fun (h : HasSubset.Subset.{u1} (Set.{u1} β) (Set.instHasSubsetSet.{u1} β) t s) => And (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} θ (Cardinal.mk.{u1} (Set.Elem.{u1} β t))) (forall {{x : β}} (hx : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x t), Eq.{succ u1} α (f (Subtype.mk.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x s) x (h x hx))) a)))))
+Case conversion may be inaccurate. Consider using '#align ordinal.infinite_pigeonhole_set Ordinal.infinite_pigeonhole_setₓ'. -/
 theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ : Cardinal)
     (hθ : θ ≤ (#s)) (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) :
     ∃ (a : α)(t : Set β)(h : t ⊆ s), θ ≤ (#t) ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a :=
@@ -1073,7 +1226,6 @@ theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ
     simp only [coe_eq_subtype, mem_singleton_iff, mem_preimage, mem_set_of_eq]
   rintro x ⟨hx, hx'⟩; exact hx'
 #align ordinal.infinite_pigeonhole_set Ordinal.infinite_pigeonhole_set
--/
 
 end Ordinal
 
@@ -1103,7 +1255,7 @@ theorem IsStrongLimit.ne_zero {c} (h : IsStrongLimit c) : c ≠ 0 :=
 
 /- warning: cardinal.is_strong_limit.two_power_lt -> Cardinal.IsStrongLimit.two_power_lt is a dubious translation:
 lean 3 declaration is
-  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)
+  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)
 but is expected to have type
   forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.is_strong_limit.two_power_lt Cardinal.IsStrongLimit.two_power_ltₓ'. -/
@@ -1119,11 +1271,15 @@ theorem isStrongLimit_aleph0 : IsStrongLimit ℵ₀ :=
 #align cardinal.is_strong_limit_aleph_0 Cardinal.isStrongLimit_aleph0
 -/
 
-#print Cardinal.IsStrongLimit.isSuccLimit /-
+/- warning: cardinal.is_strong_limit.is_succ_limit -> Cardinal.IsStrongLimit.isSuccLimit is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (Order.IsSuccLimit.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c)
+but is expected to have type
+  forall {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (Order.IsSuccLimit.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.is_strong_limit.is_succ_limit Cardinal.IsStrongLimit.isSuccLimitₓ'. -/
 protected theorem IsStrongLimit.isSuccLimit {c} (H : IsStrongLimit c) : IsSuccLimit c :=
   isSuccLimit_of_succ_lt fun x h => (succ_le_of_lt <| cantor x).trans_lt (H.two_power_lt h)
 #align cardinal.is_strong_limit.is_succ_limit Cardinal.IsStrongLimit.isSuccLimit
--/
 
 #print Cardinal.IsStrongLimit.isLimit /-
 theorem IsStrongLimit.isLimit {c} (H : IsStrongLimit c) : IsLimit c :=
@@ -1131,7 +1287,12 @@ theorem IsStrongLimit.isLimit {c} (H : IsStrongLimit c) : IsLimit c :=
 #align cardinal.is_strong_limit.is_limit Cardinal.IsStrongLimit.isLimit
 -/
 
-#print Cardinal.isStrongLimit_beth /-
+/- warning: cardinal.is_strong_limit_beth -> Cardinal.isStrongLimit_beth is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, (Order.IsSuccLimit.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o) -> (Cardinal.IsStrongLimit.{u1} (Cardinal.beth.{u1} o))
+but is expected to have type
+  forall {o : Ordinal.{u1}}, (Order.IsSuccLimit.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o) -> (Cardinal.IsStrongLimit.{u1} (Cardinal.beth.{u1} o))
+Case conversion may be inaccurate. Consider using '#align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_bethₓ'. -/
 theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (beth o) :=
   by
   rcases eq_or_ne o 0 with (rfl | h)
@@ -1144,11 +1305,10 @@ theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (be
     rw [← beth_succ] at this
     exact this.trans_lt (beth_lt.2 (H.succ_lt hi))
 #align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_beth
--/
 
 /- warning: cardinal.mk_bounded_subset -> Cardinal.mk_bounded_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) (Cardinal.mk.{u1} α))) -> (forall {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r], (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => Set.Bounded.{u1} α r s))) (Cardinal.mk.{u1} α)))
+  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) (Cardinal.mk.{u1} α))) -> (forall {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r], (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => Set.Bounded.{u1} α r s))) (Cardinal.mk.{u1} α)))
 but is expected to have type
   forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) (Cardinal.mk.{u1} α))) -> (forall {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r], (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => Set.Bounded.{u1} α r s))) (Cardinal.mk.{u1} α)))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_bounded_subset Cardinal.mk_bounded_subsetₓ'. -/
@@ -1184,7 +1344,7 @@ theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α
 
 /- warning: cardinal.mk_subset_mk_lt_cof -> Cardinal.mk_subset_mk_lt_cof is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) (Cardinal.mk.{u1} α))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)))))) (Cardinal.mk.{u1} α))
+  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) (Cardinal.mk.{u1} α))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)))))) (Cardinal.mk.{u1} α))
 but is expected to have type
   forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) (Cardinal.mk.{u1} α))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (Set.Elem.{u1} α s)) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)))))) (Cardinal.mk.{u1} α))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_subset_mk_lt_cof Cardinal.mk_subset_mk_lt_cofₓ'. -/
@@ -1228,19 +1388,27 @@ theorem IsRegular.cof_eq {c : Cardinal} (H : c.IsRegular) : c.ord.cof = c :=
 #align cardinal.is_regular.cof_eq Cardinal.IsRegular.cof_eq
 -/
 
-#print Cardinal.IsRegular.pos /-
+/- warning: cardinal.is_regular.pos -> Cardinal.IsRegular.pos is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1}))) c)
+but is expected to have type
+  forall {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1})) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.is_regular.pos Cardinal.IsRegular.posₓ'. -/
 theorem IsRegular.pos {c : Cardinal} (H : c.IsRegular) : 0 < c :=
   aleph0_pos.trans_le H.1
 #align cardinal.is_regular.pos Cardinal.IsRegular.pos
--/
 
-#print Cardinal.IsRegular.ord_pos /-
+/- warning: cardinal.is_regular.ord_pos -> Cardinal.IsRegular.ord_pos is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (Cardinal.ord.{u1} c))
+but is expected to have type
+  forall {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) (Cardinal.ord.{u1} c))
+Case conversion may be inaccurate. Consider using '#align cardinal.is_regular.ord_pos Cardinal.IsRegular.ord_posₓ'. -/
 theorem IsRegular.ord_pos {c : Cardinal} (H : c.IsRegular) : 0 < c.ord :=
   by
   rw [Cardinal.lt_ord]
   exact H.pos
 #align cardinal.is_regular.ord_pos Cardinal.IsRegular.ord_pos
--/
 
 #print Cardinal.isRegular_cof /-
 theorem isRegular_cof {o : Ordinal} (h : o.IsLimit) : IsRegular o.cof :=
@@ -1294,13 +1462,17 @@ theorem isRegular_aleph_one : IsRegular (aleph 1) :=
   exact is_regular_succ le_rfl
 #align cardinal.is_regular_aleph_one Cardinal.isRegular_aleph_one
 
-#print Cardinal.isRegular_aleph'_succ /-
+/- warning: cardinal.is_regular_aleph'_succ -> Cardinal.isRegular_aleph'_succ is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.omega.{u1} o) -> (Cardinal.IsRegular.{u1} (Cardinal.aleph'.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)))
+but is expected to have type
+  forall {o : Ordinal.{u1}}, (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.omega.{u1} o) -> (Cardinal.IsRegular.{u1} (Cardinal.aleph'.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)))
+Case conversion may be inaccurate. Consider using '#align cardinal.is_regular_aleph'_succ Cardinal.isRegular_aleph'_succₓ'. -/
 theorem isRegular_aleph'_succ {o : Ordinal} (h : ω ≤ o) : IsRegular (aleph' (succ o)) :=
   by
   rw [aleph'_succ]
   exact is_regular_succ (aleph_0_le_aleph'.2 h)
 #align cardinal.is_regular_aleph'_succ Cardinal.isRegular_aleph'_succ
--/
 
 #print Cardinal.isRegular_aleph_succ /-
 theorem isRegular_aleph_succ (o : Ordinal) : IsRegular (aleph (succ o)) :=
@@ -1310,7 +1482,12 @@ theorem isRegular_aleph_succ (o : Ordinal) : IsRegular (aleph (succ o)) :=
 #align cardinal.is_regular_aleph_succ Cardinal.isRegular_aleph_succ
 -/
 
-#print Cardinal.infinite_pigeonhole_card_lt /-
+/- warning: cardinal.infinite_pigeonhole_card_lt -> Cardinal.infinite_pigeonhole_card_lt is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} (Cardinal.mk.{u1} α)) -> (Exists.{succ u1} α (fun (a : α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a))))))
+but is expected to have type
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} (Cardinal.mk.{u1} α)) -> (Exists.{succ u1} α (fun (a : α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} (Set.Elem.{u1} β (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a))))))
+Case conversion may be inaccurate. Consider using '#align cardinal.infinite_pigeonhole_card_lt Cardinal.infinite_pigeonhole_card_ltₓ'. -/
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has a fiber with cardinality strictly great than the codomain.
 -/
@@ -1321,9 +1498,13 @@ theorem infinite_pigeonhole_card_lt {β α : Type u} (f : β → α) (w : (#α)
     Ordinal.infinite_pigeonhole_card f (succ (#α)) (succ_le_of_lt w) (w'.trans (lt_succ _).le)
       ((lt_succ _).trans_le (is_regular_succ w').2.ge)
 #align cardinal.infinite_pigeonhole_card_lt Cardinal.infinite_pigeonhole_card_lt
--/
 
-#print Cardinal.exists_infinite_fiber /-
+/- warning: cardinal.exists_infinite_fiber -> Cardinal.exists_infinite_fiber is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) -> (Infinite.{succ u1} α) -> (Exists.{succ u1} α (fun (a : α) => Infinite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)))))
+but is expected to have type
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) -> (Infinite.{succ u1} α) -> (Exists.{succ u1} α (fun (a : α) => Infinite.{succ u1} (Set.Elem.{u1} β (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)))))
+Case conversion may be inaccurate. Consider using '#align cardinal.exists_infinite_fiber Cardinal.exists_infinite_fiberₓ'. -/
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has an infinite fiber.
 -/
@@ -1334,7 +1515,6 @@ theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : (#α) < (#β
   cases' infinite_pigeonhole_card_lt f w w' with a ha
   exact ⟨a, w'.trans ha.le⟩
 #align cardinal.exists_infinite_fiber Cardinal.exists_infinite_fiber
--/
 
 /- warning: cardinal.le_range_of_union_finset_eq_top -> Cardinal.le_range_of_union_finset_eq_top is a dubious translation:
 lean 3 declaration is
@@ -1368,65 +1548,97 @@ theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α 
   exact (@Infinite.of_injective _ _ p (inclusion (v' a)) (inclusion_injective _)).False
 #align cardinal.le_range_of_union_finset_eq_top Cardinal.le_range_of_union_finset_eq_top
 
-#print Cardinal.lsub_lt_ord_lift_of_isRegular /-
+/- warning: cardinal.lsub_lt_ord_lift_of_is_regular -> Cardinal.lsub_lt_ord_lift_of_isRegular is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) (Cardinal.ord.{max u1 u2} c)) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.lsub.{u1, u2} ι f) (Cardinal.ord.{max u1 u2} c))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) (Cardinal.ord.{max u1 u2} c)) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u1 u2})) (Ordinal.lsub.{u1, u2} ι f) (Cardinal.ord.{max u1 u2} c))
+Case conversion may be inaccurate. Consider using '#align cardinal.lsub_lt_ord_lift_of_is_regular Cardinal.lsub_lt_ord_lift_of_isRegularₓ'. -/
 theorem lsub_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_lift_of_is_regular Cardinal.lsub_lt_ord_lift_of_isRegular
--/
 
-#print Cardinal.lsub_lt_ord_of_isRegular /-
+/- warning: cardinal.lsub_lt_ord_of_is_regular -> Cardinal.lsub_lt_ord_of_isRegular is a dubious translation:
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+  forall {ι : Type.{max u1 u2}} {f : ι -> Ordinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.mk.{max u1 u2} ι) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) (Cardinal.ord.{max u1 u2} c)) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.lsub.{max u1 u2, u1} ι f) (Cardinal.ord.{max u1 u2} c))
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+Case conversion may be inaccurate. Consider using '#align cardinal.lsub_lt_ord_of_is_regular Cardinal.lsub_lt_ord_of_isRegularₓ'. -/
 theorem lsub_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_of_is_regular Cardinal.lsub_lt_ord_of_isRegular
--/
 
-#print Cardinal.sup_lt_ord_lift_of_isRegular /-
+/- warning: cardinal.sup_lt_ord_lift_of_is_regular -> Cardinal.sup_lt_ord_lift_of_isRegular is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.sup_lt_ord_lift_of_is_regular Cardinal.sup_lt_ord_lift_of_isRegularₓ'. -/
 theorem sup_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_lift_of_is_regular Cardinal.sup_lt_ord_lift_of_isRegular
--/
 
-#print Cardinal.sup_lt_ord_of_isRegular /-
+/- warning: cardinal.sup_lt_ord_of_is_regular -> Cardinal.sup_lt_ord_of_isRegular is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.sup_lt_ord_of_is_regular Cardinal.sup_lt_ord_of_isRegularₓ'. -/
 theorem sup_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_of_is_regular Cardinal.sup_lt_ord_of_isRegular
--/
 
-#print Cardinal.blsub_lt_ord_lift_of_isRegular /-
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+Case conversion may be inaccurate. Consider using '#align cardinal.blsub_lt_ord_lift_of_is_regular Cardinal.blsub_lt_ord_lift_of_isRegularₓ'. -/
 theorem blsub_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (ho : Cardinal.lift o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.blsub o f < c.ord :=
   blsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.blsub_lt_ord_lift_of_is_regular Cardinal.blsub_lt_ord_lift_of_isRegular
--/
 
-#print Cardinal.blsub_lt_ord_of_isRegular /-
+/- warning: cardinal.blsub_lt_ord_of_is_regular -> Cardinal.blsub_lt_ord_of_isRegular is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.blsub_lt_ord_of_is_regular Cardinal.blsub_lt_ord_of_isRegularₓ'. -/
 theorem blsub_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (ho : o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.blsub o f < c.ord :=
   blsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.blsub_lt_ord_of_is_regular Cardinal.blsub_lt_ord_of_isRegular
--/
 
-#print Cardinal.bsup_lt_ord_lift_of_isRegular /-
+/- warning: cardinal.bsup_lt_ord_lift_of_is_regular -> Cardinal.bsup_lt_ord_lift_of_isRegular is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.bsup_lt_ord_lift_of_is_regular Cardinal.bsup_lt_ord_lift_of_isRegularₓ'. -/
 theorem bsup_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.bsup o f < c.ord :=
   bsup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_lift_of_is_regular Cardinal.bsup_lt_ord_lift_of_isRegular
--/
 
-#print Cardinal.bsup_lt_ord_of_isRegular /-
+/- warning: cardinal.bsup_lt_ord_of_is_regular -> Cardinal.bsup_lt_ord_of_isRegular is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{max u1 u2}} {f : forall (a : Ordinal.{max u1 u2}), (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) a o) -> Ordinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Ordinal.card.{max u1 u2} o) c) -> (forall (i : Ordinal.{max u1 u2}) (hi : LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) i o), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i hi) (Cardinal.ord.{max u1 u2} c)) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.bsup.{max u1 u2, u1} o f) (Cardinal.ord.{max u1 u2} c))
+but is expected to have type
+  forall {o : Ordinal.{max u2 u1}} {f : forall (a : Ordinal.{max u2 u1}), (LT.lt.{succ (max u2 u1)} Ordinal.{max u2 u1} (Preorder.toLT.{succ (max u2 u1)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{succ (max u2 u1)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u2 u1})) a o) -> Ordinal.{max u2 u1}} {c : Cardinal.{max u2 u1}}, (Cardinal.IsRegular.{max u2 u1} c) -> (LT.lt.{succ (max u2 u1)} Cardinal.{max u2 u1} (Preorder.toLT.{succ (max u2 u1)} Cardinal.{max u2 u1} (PartialOrder.toPreorder.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.partialOrder.{max u2 u1})) (Ordinal.card.{max u2 u1} o) c) -> (forall (i : Ordinal.{max u2 u1}) (hi : LT.lt.{succ (max u2 u1)} Ordinal.{max u2 u1} (Preorder.toLT.{succ (max u2 u1)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{succ (max u2 u1)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u2 u1})) i o), LT.lt.{succ (max u2 u1)} Ordinal.{max u2 u1} (Preorder.toLT.{succ (max u2 u1)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{succ (max u2 u1)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u2 u1})) (f i hi) (Cardinal.ord.{max u2 u1} c)) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u1 u2})) (Ordinal.bsup.{max u2 u1, u1} o f) (Cardinal.ord.{max u1 u2} c))
+Case conversion may be inaccurate. Consider using '#align cardinal.bsup_lt_ord_of_is_regular Cardinal.bsup_lt_ord_of_isRegularₓ'. -/
 theorem bsup_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (hι : o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.bsup o f < c.ord :=
   bsup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_of_is_regular Cardinal.bsup_lt_ord_of_isRegular
--/
 
 /- warning: cardinal.supr_lt_lift_of_is_regular -> Cardinal.iSup_lt_lift_of_isRegular is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (iSup.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (iSup.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (iSup.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toSupSet.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{max u1 u2}))) ι f) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.supr_lt_lift_of_is_regular Cardinal.iSup_lt_lift_of_isRegularₓ'. -/
@@ -1437,7 +1649,7 @@ theorem iSup_lt_lift_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular
 
 /- warning: cardinal.supr_lt_of_is_regular -> Cardinal.iSup_lt_of_isRegular is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (iSup.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (iSup.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (iSup.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toSupSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) ι f) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.supr_lt_of_is_regular Cardinal.iSup_lt_of_isRegularₓ'. -/
@@ -1446,21 +1658,34 @@ theorem iSup_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c) (
   iSup_lt (by rwa [hc.cof_eq])
 #align cardinal.supr_lt_of_is_regular Cardinal.iSup_lt_of_isRegular
 
-#print Cardinal.sum_lt_lift_of_isRegular /-
+/- warning: cardinal.sum_lt_lift_of_is_regular -> Cardinal.sum_lt_lift_of_isRegular is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.sum.{u1, max u1 u2} ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.sum.{u1, max u1 u2} ι f) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.sum_lt_lift_of_is_regular Cardinal.sum_lt_lift_of_isRegularₓ'. -/
 theorem sum_lt_lift_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : Cardinal.lift.{v, u} (#ι) < c) (hf : ∀ i, f i < c) : sum f < c :=
   (sum_le_iSup_lift _).trans_lt <| mul_lt_of_lt hc.1 hι (iSup_lt_lift_of_isRegular hc hι hf)
 #align cardinal.sum_lt_lift_of_is_regular Cardinal.sum_lt_lift_of_isRegular
--/
 
-#print Cardinal.sum_lt_of_isRegular /-
+/- warning: cardinal.sum_lt_of_is_regular -> Cardinal.sum_lt_of_isRegular is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.sum.{u1, u1} ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.sum.{u1, u1} ι f) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.sum_lt_of_is_regular Cardinal.sum_lt_of_isRegularₓ'. -/
 theorem sum_lt_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : (#ι) < c) : (∀ i, f i < c) → sum f < c :=
   sum_lt_lift_of_isRegular.{u, u} hc (by rwa [lift_id])
 #align cardinal.sum_lt_of_is_regular Cardinal.sum_lt_of_isRegular
--/
 
-#print Cardinal.nfpFamily_lt_ord_lift_of_isRegular /-
+/- warning: cardinal.nfp_family_lt_ord_lift_of_is_regular -> Cardinal.nfpFamily_lt_ord_lift_of_isRegular is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (Ne.{succ (succ (max u1 u2))} Cardinal.{max u1 u2} c Cardinal.aleph0.{max u1 u2}) -> (forall (i : ι) (b : Ordinal.{max u1 u2}), (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b (Cardinal.ord.{max u1 u2} c)) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i b) (Cardinal.ord.{max u1 u2} c))) -> (forall {a : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) a (Cardinal.ord.{max u1 u2} c)) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.nfpFamily.{u1, u2} ι f a) (Cardinal.ord.{max u1 u2} c)))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (Ne.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u1 u2} c Cardinal.aleph0.{max u1 u2}) -> (forall (i : ι) (b : Ordinal.{max u1 u2}), (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b (Cardinal.ord.{max u1 u2} c)) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i b) (Cardinal.ord.{max u1 u2} c))) -> (forall {a : Ordinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) a (Cardinal.ord.{max u1 u2} c)) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u1 u2})) (Ordinal.nfpFamily.{u1, u2} ι f a) (Cardinal.ord.{max u1 u2} c)))
+Case conversion may be inaccurate. Consider using '#align cardinal.nfp_family_lt_ord_lift_of_is_regular Cardinal.nfpFamily_lt_ord_lift_of_isRegularₓ'. -/
 theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a}
     (ha : a < c.ord) : nfpFamily.{u, v} f a < c.ord :=
@@ -1468,35 +1693,51 @@ theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal}
   apply nfp_family_lt_ord_lift _ _ hf ha <;> rwa [hc.cof_eq]
   exact lt_of_le_of_ne hc.1 hc'.symm
 #align cardinal.nfp_family_lt_ord_lift_of_is_regular Cardinal.nfpFamily_lt_ord_lift_of_isRegular
--/
 
-#print Cardinal.nfpFamily_lt_ord_of_isRegular /-
+/- warning: cardinal.nfp_family_lt_ord_of_is_regular -> Cardinal.nfpFamily_lt_ord_of_isRegular is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align cardinal.nfp_family_lt_ord_of_is_regular Cardinal.nfpFamily_lt_ord_of_isRegularₓ'. -/
 theorem nfpFamily_lt_ord_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι) < c) (hc' : c ≠ ℵ₀) {a} (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) :
     a < c.ord → nfpFamily.{u, u} f a < c.ord :=
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_family_lt_ord_of_is_regular Cardinal.nfpFamily_lt_ord_of_isRegular
--/
 
-#print Cardinal.nfpBFamily_lt_ord_lift_of_isRegular /-
+/- warning: cardinal.nfp_bfamily_lt_ord_lift_of_is_regular -> Cardinal.nfpBFamily_lt_ord_lift_of_isRegular is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.nfp_bfamily_lt_ord_lift_of_is_regular Cardinal.nfpBFamily_lt_ord_lift_of_isRegularₓ'. -/
 theorem nfpBFamily_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (ho : o.card.lift < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → nfpBFamily.{u, v} o f a < c.ord :=
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [mk_ordinal_out]) hc' fun i => hf _ _
 #align cardinal.nfp_bfamily_lt_ord_lift_of_is_regular Cardinal.nfpBFamily_lt_ord_lift_of_isRegular
--/
 
-#print Cardinal.nfpBFamily_lt_ord_of_isRegular /-
+/- warning: cardinal.nfp_bfamily_lt_ord_of_is_regular -> Cardinal.nfpBFamily_lt_ord_of_isRegular is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.nfp_bfamily_lt_ord_of_is_regular Cardinal.nfpBFamily_lt_ord_of_isRegularₓ'. -/
 theorem nfpBFamily_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (ho : o.card < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → nfpBFamily.{u, u} o f a < c.ord :=
   nfpBFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_bfamily_lt_ord_of_is_regular Cardinal.nfpBFamily_lt_ord_of_isRegular
--/
 
-#print Cardinal.nfp_lt_ord_of_isRegular /-
+/- warning: cardinal.nfp_lt_ord_of_is_regular -> Cardinal.nfp_lt_ord_of_isRegular is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align cardinal.nfp_lt_ord_of_is_regular Cardinal.nfp_lt_ord_of_isRegularₓ'. -/
 theorem nfp_lt_ord_of_isRegular {f : Ordinal → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
     (hf : ∀ i < c.ord, f i < c.ord) {a} : a < c.ord → nfp f a < c.ord :=
   nfp_lt_ord
@@ -1505,9 +1746,13 @@ theorem nfp_lt_ord_of_isRegular {f : Ordinal → Ordinal} {c} (hc : IsRegular c)
       exact lt_of_le_of_ne hc.1 hc'.symm)
     hf
 #align cardinal.nfp_lt_ord_of_is_regular Cardinal.nfp_lt_ord_of_isRegular
--/
 
-#print Cardinal.derivFamily_lt_ord_lift /-
+/- warning: cardinal.deriv_family_lt_ord_lift -> Cardinal.derivFamily_lt_ord_lift is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.deriv_family_lt_ord_lift Cardinal.derivFamily_lt_ord_liftₓ'. -/
 theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, v} f a < c.ord :=
@@ -1529,40 +1774,55 @@ theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc :
       bsup_lt_ord_of_is_regular hc (ord_lt_ord.1 ((ord_card_le b).trans_lt hb')) fun o' ho' =>
         H o' ho' (ho'.trans hb')
 #align cardinal.deriv_family_lt_ord_lift Cardinal.derivFamily_lt_ord_lift
--/
 
-#print Cardinal.derivFamily_lt_ord /-
+/- warning: cardinal.deriv_family_lt_ord -> Cardinal.derivFamily_lt_ord is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.deriv_family_lt_ord Cardinal.derivFamily_lt_ordₓ'. -/
 theorem derivFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c)
     (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, u} f a < c.ord :=
   derivFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf
 #align cardinal.deriv_family_lt_ord Cardinal.derivFamily_lt_ord
--/
 
-#print Cardinal.derivBFamily_lt_ord_lift /-
+/- warning: cardinal.deriv_bfamily_lt_ord_lift -> Cardinal.derivBFamily_lt_ord_lift is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.deriv_bfamily_lt_ord_lift Cardinal.derivBFamily_lt_ord_liftₓ'. -/
 theorem derivBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (hι : o.card.lift < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → derivBFamily.{u, v} o f a < c.ord :=
   derivFamily_lt_ord_lift hc (by rwa [mk_ordinal_out]) hc' fun i => hf _ _
 #align cardinal.deriv_bfamily_lt_ord_lift Cardinal.derivBFamily_lt_ord_lift
--/
 
-#print Cardinal.derivBFamily_lt_ord /-
+/- warning: cardinal.deriv_bfamily_lt_ord -> Cardinal.derivBFamily_lt_ord is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.deriv_bfamily_lt_ord Cardinal.derivBFamily_lt_ordₓ'. -/
 theorem derivBFamily_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : o.card < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → derivBFamily.{u, u} o f a < c.ord :=
   derivBFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf
 #align cardinal.deriv_bfamily_lt_ord Cardinal.derivBFamily_lt_ord
--/
 
-#print Cardinal.deriv_lt_ord /-
+/- warning: cardinal.deriv_lt_ord -> Cardinal.deriv_lt_ord is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.deriv_lt_ord Cardinal.deriv_lt_ordₓ'. -/
 theorem deriv_lt_ord {f : Ordinal.{u} → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
     (hf : ∀ i < c.ord, f i < c.ord) {a} : a < c.ord → deriv f a < c.ord :=
   derivFamily_lt_ord_lift hc
     (by simpa using cardinal.one_lt_aleph_0.trans (lt_of_le_of_ne hc.1 hc'.symm)) hc' fun _ => hf
 #align cardinal.deriv_lt_ord Cardinal.deriv_lt_ord
--/
 
 #print Cardinal.IsInaccessible /-
 /-- A cardinal is inaccessible if it is an uncountable regular strong limit cardinal. -/
@@ -1573,7 +1833,7 @@ def IsInaccessible (c : Cardinal) :=
 
 /- warning: cardinal.is_inaccessible.mk -> Cardinal.IsInaccessible.mk is a dubious translation:
 lean 3 declaration is
-  forall {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)) -> (Cardinal.IsInaccessible.{u1} c)
+  forall {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)) -> (Cardinal.IsInaccessible.{u1} c)
 but is expected to have type
   forall {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) c)) -> (Cardinal.IsInaccessible.{u1} c)
 Case conversion may be inaccurate. Consider using '#align cardinal.is_inaccessible.mk Cardinal.IsInaccessible.mkₓ'. -/
@@ -1593,7 +1853,12 @@ theorem univ_inaccessible : IsInaccessible univ.{u, v} :=
 #align cardinal.univ_inaccessible Cardinal.univ_inaccessible
 -/
 
-#print Cardinal.lt_power_cof /-
+/- warning: cardinal.lt_power_cof -> Cardinal.lt_power_cof is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))))
+but is expected to have type
+  forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))))
+Case conversion may be inaccurate. Consider using '#align cardinal.lt_power_cof Cardinal.lt_power_cofₓ'. -/
 theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
   Quotient.inductionOn c fun α h =>
     by
@@ -1613,9 +1878,13 @@ theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
     · have := typein_lt_type r i
       rwa [← re, lt_ord] at this
 #align cardinal.lt_power_cof Cardinal.lt_power_cof
--/
 
-#print Cardinal.lt_cof_power /-
+/- warning: cardinal.lt_cof_power -> Cardinal.lt_cof_power is a dubious translation:
+lean 3 declaration is
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (OfNat.mk.{succ u1} Cardinal.{u1} 1 (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1}))) b) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a (Ordinal.cof.{u1} (Cardinal.ord.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) b a))))
+but is expected to have type
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (One.toOfNat1.{succ u1} Cardinal.{u1} Cardinal.instOneCardinal.{u1})) b) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a (Ordinal.cof.{u1} (Cardinal.ord.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) b a))))
+Case conversion may be inaccurate. Consider using '#align cardinal.lt_cof_power Cardinal.lt_cof_powerₓ'. -/
 theorem lt_cof_power {a b : Cardinal} (ha : ℵ₀ ≤ a) (b1 : 1 < b) : a < cof (b^a).ord :=
   by
   have b0 : b ≠ 0 := (zero_lt_one.trans b1).ne'
@@ -1623,7 +1892,6 @@ theorem lt_cof_power {a b : Cardinal} (ha : ℵ₀ ≤ a) (b1 : 1 < b) : a < cof
   rw [← power_mul, mul_eq_self ha]
   exact lt_power_cof (ha.trans <| (cantor' _ b1).le)
 #align cardinal.lt_cof_power Cardinal.lt_cof_power
--/
 
 end Cardinal

7c2ce0c2

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -70,7 +70,7 @@ namespace Order
 /-- Cofinality of a reflexive order `≼`. This is the smallest cardinality
   of a subset `S : set α` such that `∀ a, ∃ b ∈ S, a ≼ b`. -/
 def cof (r : α → α → Prop) : Cardinal :=
-  infₛ { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c }
+  sInf { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c }
 #align order.cof Order.cof
 -/
 
@@ -93,7 +93,7 @@ but is expected to have type
   forall {α : Type.{u1}} (r : α -> α -> Prop) {S : Set.{u1} α}, (forall (a : α), Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b S) (r a b))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Order.cof.{u1} α r) (Cardinal.mk.{u1} (Set.Elem.{u1} α S)))
 Case conversion may be inaccurate. Consider using '#align order.cof_le Order.cof_leₓ'. -/
 theorem cof_le (r : α → α → Prop) {S : Set α} (h : ∀ a, ∃ b ∈ S, r a b) : cof r ≤ (#S) :=
-  cinfₛ_le' ⟨S, h, rfl⟩
+  csInf_le' ⟨S, h, rfl⟩
 #align order.cof_le Order.cof_le
 
 /- warning: order.le_cof -> Order.le_cof is a dubious translation:
@@ -105,7 +105,7 @@ Case conversion may be inaccurate. Consider using '#align order.le_cof Order.le_
 theorem le_cof {r : α → α → Prop} [IsRefl α r] (c : Cardinal) :
     c ≤ cof r ↔ ∀ {S : Set α}, (∀ a, ∃ b ∈ S, r a b) → c ≤ (#S) :=
   by
-  rw [cof, le_cinfₛ_iff'' (cof_nonempty r)]
+  rw [cof, le_csInf_iff'' (cof_nonempty r)]
   use fun H S h => H _ ⟨S, h, rfl⟩
   rintro H d ⟨S, h, rfl⟩
   exact H h
@@ -118,9 +118,9 @@ theorem RelIso.cof_le_lift {α : Type u} {β : Type v} {r : α → α → Prop}
     (f : r ≃r s) : Cardinal.lift.{max u v} (Order.cof r) ≤ Cardinal.lift.{max u v} (Order.cof s) :=
   by
   rw [Order.cof, Order.cof, lift_Inf, lift_Inf,
-    le_cinfₛ_iff'' (nonempty_image_iff.2 (Order.cof_nonempty s))]
+    le_csInf_iff'' (nonempty_image_iff.2 (Order.cof_nonempty s))]
   rintro - ⟨-, ⟨u, H, rfl⟩, rfl⟩
-  apply cinfₛ_le'
+  apply csInf_le'
   refine'
     ⟨_, ⟨f.symm '' u, fun a => _, rfl⟩,
       lift_mk_eq.{u, v, max u v}.2 ⟨(f.symm.toEquiv.image u).symm⟩⟩
@@ -199,7 +199,7 @@ theorem cof_type (r : α → α → Prop) [IsWellOrder α r] : (type r).cof = St
 
 #print Ordinal.le_cof_type /-
 theorem le_cof_type [IsWellOrder α r] {c} : c ≤ cof (type r) ↔ ∀ S, Unbounded r S → c ≤ (#S) :=
-  (le_cinfₛ_iff'' (StrictOrder.cof_nonempty r)).trans
+  (le_csInf_iff'' (StrictOrder.cof_nonempty r)).trans
     ⟨fun H S h => H _ ⟨S, h, rfl⟩, by
       rintro H d ⟨S, h, rfl⟩
       exact H _ h⟩
@@ -220,7 +220,7 @@ theorem lt_cof_type [IsWellOrder α r] {S : Set α} : (#S) < cof (type r) → Bo
 
 #print Ordinal.cof_eq /-
 theorem cof_eq (r : α → α → Prop) [IsWellOrder α r] : ∃ S, Unbounded r S ∧ (#S) = cof (type r) :=
-  cinfₛ_mem (StrictOrder.cof_nonempty r)
+  csInf_mem (StrictOrder.cof_nonempty r)
 #align ordinal.cof_eq Ordinal.cof_eq
 -/
 
@@ -278,16 +278,16 @@ theorem cof_lsub_def_nonempty (o) :
 #align ordinal.cof_lsub_def_nonempty Ordinal.cof_lsub_def_nonempty
 -/
 
-/- warning: ordinal.cof_eq_Inf_lsub -> Ordinal.cof_eq_infₛ_lsub is a dubious translation:
+/- warning: ordinal.cof_eq_Inf_lsub -> Ordinal.cof_eq_sInf_lsub is a dubious translation:
 lean 3 declaration is
-  forall (o : Ordinal.{u1}), Eq.{succ (succ u1)} Cardinal.{u1} (Ordinal.cof.{u1} o) (InfSet.infₛ.{succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasInf.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) (setOf.{succ u1} Cardinal.{u1} (fun (a : Cardinal.{u1}) => Exists.{succ (succ u1)} Type.{u1} (fun {ι : Type.{u1}} => Exists.{succ (succ u1)} (ι -> Ordinal.{u1}) (fun (f : ι -> Ordinal.{u1}) => And (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.lsub.{u1, u1} ι f) o) (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} ι) a))))))
+  forall (o : Ordinal.{u1}), Eq.{succ (succ u1)} Cardinal.{u1} (Ordinal.cof.{u1} o) (InfSet.sInf.{succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasInf.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) (setOf.{succ u1} Cardinal.{u1} (fun (a : Cardinal.{u1}) => Exists.{succ (succ u1)} Type.{u1} (fun {ι : Type.{u1}} => Exists.{succ (succ u1)} (ι -> Ordinal.{u1}) (fun (f : ι -> Ordinal.{u1}) => And (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.lsub.{u1, u1} ι f) o) (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} ι) a))))))
 but is expected to have type
-  forall (o : Ordinal.{u1}), Eq.{succ (succ u1)} Cardinal.{u1} (Ordinal.cof.{u1} o) (InfSet.infₛ.{succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toInfSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) (setOf.{succ u1} Cardinal.{u1} (fun (a : Cardinal.{u1}) => Exists.{succ (succ u1)} Type.{u1} (fun (ι : Type.{u1}) => Exists.{succ (succ u1)} (ι -> Ordinal.{u1}) (fun (f : ι -> Ordinal.{u1}) => And (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.lsub.{u1, u1} ι f) o) (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} ι) a))))))
-Case conversion may be inaccurate. Consider using '#align ordinal.cof_eq_Inf_lsub Ordinal.cof_eq_infₛ_lsubₓ'. -/
-theorem cof_eq_infₛ_lsub (o : Ordinal.{u}) :
-    cof o = infₛ { a : Cardinal | ∃ (ι : Type u)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } :=
+  forall (o : Ordinal.{u1}), Eq.{succ (succ u1)} Cardinal.{u1} (Ordinal.cof.{u1} o) (InfSet.sInf.{succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toInfSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) (setOf.{succ u1} Cardinal.{u1} (fun (a : Cardinal.{u1}) => Exists.{succ (succ u1)} Type.{u1} (fun (ι : Type.{u1}) => Exists.{succ (succ u1)} (ι -> Ordinal.{u1}) (fun (f : ι -> Ordinal.{u1}) => And (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.lsub.{u1, u1} ι f) o) (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} ι) a))))))
+Case conversion may be inaccurate. Consider using '#align ordinal.cof_eq_Inf_lsub Ordinal.cof_eq_sInf_lsubₓ'. -/
+theorem cof_eq_sInf_lsub (o : Ordinal.{u}) :
+    cof o = sInf { a : Cardinal | ∃ (ι : Type u)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } :=
   by
-  refine' le_antisymm (le_cinfₛ (cof_lsub_def_nonempty o) _) (cinfₛ_le' _)
+  refine' le_antisymm (le_csInf (cof_lsub_def_nonempty o) _) (csInf_le' _)
   · rintro a ⟨ι, f, hf, rfl⟩
     rw [← type_lt o]
     refine'
@@ -317,7 +317,7 @@ theorem cof_eq_infₛ_lsub (o : Ordinal.{u}) :
     rcases hS (enum (· < ·) a ha) with ⟨b, hb, hb'⟩
     rw [← typein_le_typein, typein_enum] at hb'
     exact hb'.trans_lt (lt_lsub.{u, u} f ⟨b, hb⟩)
-#align ordinal.cof_eq_Inf_lsub Ordinal.cof_eq_infₛ_lsub
+#align ordinal.cof_eq_Inf_lsub Ordinal.cof_eq_sInf_lsub
 
 /- warning: ordinal.lift_cof -> Ordinal.lift_cof is a dubious translation:
 lean 3 declaration is
@@ -355,7 +355,7 @@ theorem lift_cof (o) : (cof o).lift = cof o.lift :=
 theorem cof_le_card (o) : cof o ≤ card o :=
   by
   rw [cof_eq_Inf_lsub]
-  exact cinfₛ_le' card_mem_cof
+  exact csInf_le' card_mem_cof
 #align ordinal.cof_le_card Ordinal.cof_le_card
 -/
 
@@ -375,7 +375,7 @@ theorem exists_lsub_cof (o : Ordinal) :
     ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = cof o :=
   by
   rw [cof_eq_Inf_lsub]
-  exact cinfₛ_mem (cof_lsub_def_nonempty o)
+  exact csInf_mem (cof_lsub_def_nonempty o)
 #align ordinal.exists_lsub_cof Ordinal.exists_lsub_cof
 -/
 
@@ -383,7 +383,7 @@ theorem exists_lsub_cof (o : Ordinal) :
 theorem cof_lsub_le {ι} (f : ι → Ordinal) : cof (lsub.{u, u} f) ≤ (#ι) :=
   by
   rw [cof_eq_Inf_lsub]
-  exact cinfₛ_le' ⟨ι, f, rfl, rfl⟩
+  exact csInf_le' ⟨ι, f, rfl, rfl⟩
 #align ordinal.cof_lsub_le Ordinal.cof_lsub_le
 -/
 
@@ -404,7 +404,7 @@ theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
   by
   rw [cof_eq_Inf_lsub]
   exact
-    (le_cinfₛ_iff'' (cof_lsub_def_nonempty o)).trans
+    (le_csInf_iff'' (cof_lsub_def_nonempty o)).trans
       ⟨fun H ι f hf => H _ ⟨ι, f, hf, rfl⟩, fun H b ⟨ι, f, hf, hb⟩ =>
         by
         rw [← hb]
@@ -459,31 +459,31 @@ theorem sup_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof)
 #align ordinal.sup_lt_ord Ordinal.sup_lt_ord
 -/
 
-/- warning: ordinal.supr_lt_lift -> Ordinal.supᵢ_lt_lift is a dubious translation:
+/- warning: ordinal.supr_lt_lift -> Ordinal.iSup_lt_lift is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (iSup.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
 but is expected to have type
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toSupSet.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{max u1 u2}))) ι f) c)
-Case conversion may be inaccurate. Consider using '#align ordinal.supr_lt_lift Ordinal.supᵢ_lt_liftₓ'. -/
-theorem supᵢ_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal} (hι : Cardinal.lift (#ι) < c.ord.cof)
-    (hf : ∀ i, f i < c) : supᵢ f < c :=
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (iSup.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toSupSet.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{max u1 u2}))) ι f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.supr_lt_lift Ordinal.iSup_lt_liftₓ'. -/
+theorem iSup_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal} (hι : Cardinal.lift (#ι) < c.ord.cof)
+    (hf : ∀ i, f i < c) : iSup f < c :=
   by
   rw [← ord_lt_ord, supr_ord (Cardinal.bddAbove_range _)]
   refine' sup_lt_ord_lift hι fun i => _
   rw [ord_lt_ord]
   apply hf
-#align ordinal.supr_lt_lift Ordinal.supᵢ_lt_lift
+#align ordinal.supr_lt_lift Ordinal.iSup_lt_lift
 
-/- warning: ordinal.supr_lt -> Ordinal.supᵢ_lt is a dubious translation:
+/- warning: ordinal.supr_lt -> Ordinal.iSup_lt is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (iSup.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
 but is expected to have type
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toSupSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) ι f) c)
-Case conversion may be inaccurate. Consider using '#align ordinal.supr_lt Ordinal.supᵢ_ltₓ'. -/
-theorem supᵢ_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : (#ι) < c.ord.cof) :
-    (∀ i, f i < c) → supᵢ f < c :=
-  supᵢ_lt_lift (by rwa [(#ι).lift_id])
-#align ordinal.supr_lt Ordinal.supᵢ_lt
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (iSup.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toSupSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) ι f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.supr_lt Ordinal.iSup_ltₓ'. -/
+theorem iSup_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : (#ι) < c.ord.cof) :
+    (∀ i, f i < c) → iSup f < c :=
+  iSup_lt_lift (by rwa [(#ι).lift_id])
+#align ordinal.supr_lt Ordinal.iSup_lt
 
 #print Ordinal.nfpFamily_lt_ord_lift /-
 theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
@@ -858,13 +858,13 @@ protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u
       rwa [hf', ← IsNormal.blsub_eq.{u, u} hf ha, lt_blsub_iff] at this
     refine' (lsub_le fun i => _).antisymm (le_of_forall_lt fun b hb => _)
     · rcases H i with ⟨b, hb, hb'⟩
-      exact lt_of_le_of_lt (cinfₛ_le' hb') hb
+      exact lt_of_le_of_lt (csInf_le' hb') hb
     · have := hf.strict_mono hb
       rw [← hf', lt_lsub_iff] at this
       cases' this with i hi
       rcases H i with ⟨b, _, hb⟩
       exact
-        ((le_cinfₛ_iff'' ⟨b, hb⟩).2 fun c hc => hf.strict_mono.le_iff_le.1 (hi.trans hc)).trans_lt
+        ((le_csInf_iff'' ⟨b, hb⟩).2 fun c hc => hf.strict_mono.le_iff_le.1 (hi.trans hc)).trans_lt
           (lt_lsub _ i)
   · rw [@blsub_comp.{u, u, u} a _ (fun b _ => f b) (fun i j hi hj h => hf.strict_mono.monotone h) g
         hg.2.2]
@@ -995,35 +995,35 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ :=
 /-! ### Infinite pigeonhole principle -/
 
 
-/- warning: ordinal.unbounded_of_unbounded_sUnion -> Ordinal.unbounded_of_unbounded_unionₛ is a dubious translation:
+/- warning: ordinal.unbounded_of_unbounded_sUnion -> Ordinal.unbounded_of_unbounded_sUnion is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.unionₛ.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Set.{u1} α)) Type.{u1} (Set.hasCoeToSort.{u1} (Set.{u1} α)) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) => Set.Unbounded.{u1} α r x)))
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.sUnion.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Set.{u1} α)) Type.{u1} (Set.hasCoeToSort.{u1} (Set.{u1} α)) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) => Set.Unbounded.{u1} α r x)))
 but is expected to have type
-  forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.unionₛ.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (Set.Elem.{u1} (Set.{u1} α) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) x s) (Set.Unbounded.{u1} α r x)))
-Case conversion may be inaccurate. Consider using '#align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_unionₛₓ'. -/
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.sUnion.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (Set.Elem.{u1} (Set.{u1} α) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) x s) (Set.Unbounded.{u1} α r x)))
+Case conversion may be inaccurate. Consider using '#align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_sUnionₓ'. -/
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
-theorem unbounded_of_unbounded_unionₛ (r : α → α → Prop) [wo : IsWellOrder α r] {s : Set (Set α)}
+theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder α r] {s : Set (Set α)}
     (h₁ : Unbounded r <| ⋃₀ s) (h₂ : (#s) < StrictOrder.cof r) : ∃ x ∈ s, Unbounded r x :=
   by
   by_contra' h
   simp_rw [not_unbounded_iff] at h
   let f : s → α := fun x : s => wo.wf.sup x (h x.1 x.2)
-  refine' h₂.not_le (le_trans (cinfₛ_le' ⟨range f, fun x => _, rfl⟩) mk_range_le)
+  refine' h₂.not_le (le_trans (csInf_le' ⟨range f, fun x => _, rfl⟩) mk_range_le)
   rcases h₁ x with ⟨y, ⟨c, hc, hy⟩, hxy⟩
   exact ⟨f ⟨c, hc⟩, mem_range_self _, fun hxz => hxy (trans (wo.wf.lt_sup _ hy) hxz)⟩
-#align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_unionₛ
+#align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_sUnion
 
-#print Ordinal.unbounded_of_unbounded_unionᵢ /-
+#print Ordinal.unbounded_of_unbounded_iUnion /-
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
-theorem unbounded_of_unbounded_unionᵢ {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
+theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
     (s : β → Set α) (h₁ : Unbounded r <| ⋃ x, s x) (h₂ : (#β) < StrictOrder.cof r) :
     ∃ x : β, Unbounded r (s x) := by
   rw [← sUnion_range] at h₁
   rcases unbounded_of_unbounded_sUnion r h₁ (mk_range_le.trans_lt h₂) with ⟨_, ⟨x, rfl⟩, u⟩
   exact ⟨x, u⟩
-#align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_unionᵢ
+#align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_iUnion
 -/
 
 #print Ordinal.infinite_pigeonhole /-
@@ -1139,7 +1139,7 @@ theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (be
     exact is_strong_limit_aleph_0
   · refine' ⟨beth_ne_zero o, fun a ha => _⟩
     rw [beth_limit ⟨h, is_succ_limit_iff_succ_lt.1 H⟩] at ha
-    rcases exists_lt_of_lt_csupᵢ' ha with ⟨⟨i, hi⟩, ha⟩
+    rcases exists_lt_of_lt_ciSup' ha with ⟨⟨i, hi⟩, ha⟩
     have := power_le_power_left two_ne_zero ha.le
     rw [← beth_succ] at this
     exact this.trans_lt (beth_lt.2 (H.succ_lt hi))
@@ -1169,7 +1169,7 @@ theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α
     rw [← coe_set_of, this]
     convert mk_Union_le_sum_mk.trans ((sum_le_supr _).trans (mul_le_max_of_aleph_0_le_left ha))
     apply (max_eq_left _).symm
-    apply csupᵢ_le' fun i => _
+    apply ciSup_le' fun i => _
     rw [mk_powerset]
     apply (h'.two_power_lt _).le
     rw [coe_set_of, card_typein, ← lt_ord, hr]
@@ -1338,9 +1338,9 @@ theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : (#α) < (#β
 
 /- warning: cardinal.le_range_of_union_finset_eq_top -> Cardinal.le_range_of_union_finset_eq_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Infinite.{succ u2} β] (f : α -> (Finset.{u2} β)), (Eq.{succ u2} (Set.{u2} β) (Set.unionᵢ.{u2, succ u1} β α (fun (a : α) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f a))) (Top.top.{u2} (Set.{u2} β) (CompleteLattice.toHasTop.{u2} (Set.{u2} β) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} β) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} β) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} β) (Set.completeBooleanAlgebra.{u2} β))))))) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Cardinal.mk.{u2} β) (Cardinal.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} (Finset.{u2} β)) Type.{u2} (Set.hasCoeToSort.{u2} (Finset.{u2} β)) (Set.range.{u2, succ u1} (Finset.{u2} β) α f))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Infinite.{succ u2} β] (f : α -> (Finset.{u2} β)), (Eq.{succ u2} (Set.{u2} β) (Set.iUnion.{u2, succ u1} β α (fun (a : α) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f a))) (Top.top.{u2} (Set.{u2} β) (CompleteLattice.toHasTop.{u2} (Set.{u2} β) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} β) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} β) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} β) (Set.completeBooleanAlgebra.{u2} β))))))) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Cardinal.mk.{u2} β) (Cardinal.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} (Finset.{u2} β)) Type.{u2} (Set.hasCoeToSort.{u2} (Finset.{u2} β)) (Set.range.{u2, succ u1} (Finset.{u2} β) α f))))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Infinite.{succ u1} β] (f : α -> (Finset.{u1} β)), (Eq.{succ u1} (Set.{u1} β) (Set.unionᵢ.{u1, succ u2} β α (fun (a : α) => Finset.toSet.{u1} β (f a))) (Top.top.{u1} (Set.{u1} β) (CompleteLattice.toTop.{u1} (Set.{u1} β) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} β) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} β) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} β) (Set.instCompleteBooleanAlgebraSet.{u1} β))))))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} β) (Cardinal.mk.{u1} (Set.Elem.{u1} (Finset.{u1} β) (Set.range.{u1, succ u2} (Finset.{u1} β) α f))))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Infinite.{succ u1} β] (f : α -> (Finset.{u1} β)), (Eq.{succ u1} (Set.{u1} β) (Set.iUnion.{u1, succ u2} β α (fun (a : α) => Finset.toSet.{u1} β (f a))) (Top.top.{u1} (Set.{u1} β) (CompleteLattice.toTop.{u1} (Set.{u1} β) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} β) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} β) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} β) (Set.instCompleteBooleanAlgebraSet.{u1} β))))))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} β) (Cardinal.mk.{u1} (Set.Elem.{u1} (Finset.{u1} β) (Set.range.{u1, succ u2} (Finset.{u1} β) α f))))
 Case conversion may be inaccurate. Consider using '#align cardinal.le_range_of_union_finset_eq_top Cardinal.le_range_of_union_finset_eq_topₓ'. -/
 /-- If an infinite type `β` can be expressed as a union of finite sets,
 then the cardinality of the collection of those finite sets
@@ -1424,32 +1424,32 @@ theorem bsup_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc
 #align cardinal.bsup_lt_ord_of_is_regular Cardinal.bsup_lt_ord_of_isRegular
 -/
 
-/- warning: cardinal.supr_lt_lift_of_is_regular -> Cardinal.supᵢ_lt_lift_of_isRegular is a dubious translation:
+/- warning: cardinal.supr_lt_lift_of_is_regular -> Cardinal.iSup_lt_lift_of_isRegular is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (iSup.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
 but is expected to have type
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toSupSet.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{max u1 u2}))) ι f) c)
-Case conversion may be inaccurate. Consider using '#align cardinal.supr_lt_lift_of_is_regular Cardinal.supᵢ_lt_lift_of_isRegularₓ'. -/
-theorem supᵢ_lt_lift_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c)
-    (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c) → supᵢ f < c :=
-  supᵢ_lt_lift (by rwa [hc.cof_eq])
-#align cardinal.supr_lt_lift_of_is_regular Cardinal.supᵢ_lt_lift_of_isRegular
-
-/- warning: cardinal.supr_lt_of_is_regular -> Cardinal.supᵢ_lt_of_isRegular is a dubious translation:
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (iSup.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toSupSet.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{max u1 u2}))) ι f) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.supr_lt_lift_of_is_regular Cardinal.iSup_lt_lift_of_isRegularₓ'. -/
+theorem iSup_lt_lift_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c)
+    (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c) → iSup f < c :=
+  iSup_lt_lift (by rwa [hc.cof_eq])
+#align cardinal.supr_lt_lift_of_is_regular Cardinal.iSup_lt_lift_of_isRegular
+
+/- warning: cardinal.supr_lt_of_is_regular -> Cardinal.iSup_lt_of_isRegular is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (iSup.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
 but is expected to have type
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toSupSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) ι f) c)
-Case conversion may be inaccurate. Consider using '#align cardinal.supr_lt_of_is_regular Cardinal.supᵢ_lt_of_isRegularₓ'. -/
-theorem supᵢ_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
-    (∀ i, f i < c) → supᵢ f < c :=
-  supᵢ_lt (by rwa [hc.cof_eq])
-#align cardinal.supr_lt_of_is_regular Cardinal.supᵢ_lt_of_isRegular
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (iSup.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toSupSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) ι f) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.supr_lt_of_is_regular Cardinal.iSup_lt_of_isRegularₓ'. -/
+theorem iSup_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
+    (∀ i, f i < c) → iSup f < c :=
+  iSup_lt (by rwa [hc.cof_eq])
+#align cardinal.supr_lt_of_is_regular Cardinal.iSup_lt_of_isRegular
 
 #print Cardinal.sum_lt_lift_of_isRegular /-
 theorem sum_lt_lift_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : Cardinal.lift.{v, u} (#ι) < c) (hf : ∀ i, f i < c) : sum f < c :=
-  (sum_le_supᵢ_lift _).trans_lt <| mul_lt_of_lt hc.1 hι (supᵢ_lt_lift_of_isRegular hc hι hf)
+  (sum_le_iSup_lift _).trans_lt <| mul_lt_of_lt hc.1 hι (iSup_lt_lift_of_isRegular hc hι hf)
 #align cardinal.sum_lt_lift_of_is_regular Cardinal.sum_lt_lift_of_isRegular
 -/

7c2ce0c2

bump to nightly-2023-04-13-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a

bd75793a

Diff

@@ -461,7 +461,7 @@ theorem sup_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof)
 
 /- warning: ordinal.supr_lt_lift -> Ordinal.supᵢ_lt_lift is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toSupSet.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{max u1 u2}))) ι f) c)
 Case conversion may be inaccurate. Consider using '#align ordinal.supr_lt_lift Ordinal.supᵢ_lt_liftₓ'. -/
@@ -476,7 +476,7 @@ theorem supᵢ_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal} (hι : Cardinal
 
 /- warning: ordinal.supr_lt -> Ordinal.supᵢ_lt is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toSupSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) ι f) c)
 Case conversion may be inaccurate. Consider using '#align ordinal.supr_lt Ordinal.supᵢ_ltₓ'. -/
@@ -997,7 +997,7 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ :=
 
 /- warning: ordinal.unbounded_of_unbounded_sUnion -> Ordinal.unbounded_of_unbounded_unionₛ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.unionₛ.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Set.{u1} α)) Type.{u1} (Set.hasCoeToSort.{u1} (Set.{u1} α)) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) => Set.Unbounded.{u1} α r x)))
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.unionₛ.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Set.{u1} α)) Type.{u1} (Set.hasCoeToSort.{u1} (Set.{u1} α)) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) => Set.Unbounded.{u1} α r x)))
 but is expected to have type
   forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.unionₛ.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (Set.Elem.{u1} (Set.{u1} α) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) x s) (Set.Unbounded.{u1} α r x)))
 Case conversion may be inaccurate. Consider using '#align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_unionₛₓ'. -/
@@ -1103,7 +1103,7 @@ theorem IsStrongLimit.ne_zero {c} (h : IsStrongLimit c) : c ≠ 0 :=
 
 /- warning: cardinal.is_strong_limit.two_power_lt -> Cardinal.IsStrongLimit.two_power_lt is a dubious translation:
 lean 3 declaration is
-  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)
+  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)
 but is expected to have type
   forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.is_strong_limit.two_power_lt Cardinal.IsStrongLimit.two_power_ltₓ'. -/
@@ -1148,7 +1148,7 @@ theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (be
 
 /- warning: cardinal.mk_bounded_subset -> Cardinal.mk_bounded_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) (Cardinal.mk.{u1} α))) -> (forall {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r], (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => Set.Bounded.{u1} α r s))) (Cardinal.mk.{u1} α)))
+  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) (Cardinal.mk.{u1} α))) -> (forall {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r], (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => Set.Bounded.{u1} α r s))) (Cardinal.mk.{u1} α)))
 but is expected to have type
   forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) (Cardinal.mk.{u1} α))) -> (forall {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r], (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => Set.Bounded.{u1} α r s))) (Cardinal.mk.{u1} α)))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_bounded_subset Cardinal.mk_bounded_subsetₓ'. -/
@@ -1184,7 +1184,7 @@ theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α
 
 /- warning: cardinal.mk_subset_mk_lt_cof -> Cardinal.mk_subset_mk_lt_cof is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) (Cardinal.mk.{u1} α))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)))))) (Cardinal.mk.{u1} α))
+  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) (Cardinal.mk.{u1} α))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)))))) (Cardinal.mk.{u1} α))
 but is expected to have type
   forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) (Cardinal.mk.{u1} α))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (Set.Elem.{u1} α s)) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)))))) (Cardinal.mk.{u1} α))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_subset_mk_lt_cof Cardinal.mk_subset_mk_lt_cofₓ'. -/
@@ -1256,7 +1256,7 @@ theorem isRegular_aleph0 : IsRegular ℵ₀ :=
 
 /- warning: cardinal.is_regular_succ -> Cardinal.isRegular_succ is a dubious translation:
 lean 3 declaration is
-  forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (Cardinal.IsRegular.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1}))))) Cardinal.succOrder.{u1} c))
+  forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (Cardinal.IsRegular.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.succOrder.{u1} c))
 but is expected to have type
   forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} c) -> (Cardinal.IsRegular.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} c))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_regular_succ Cardinal.isRegular_succₓ'. -/
@@ -1426,7 +1426,7 @@ theorem bsup_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc
 
 /- warning: cardinal.supr_lt_lift_of_is_regular -> Cardinal.supᵢ_lt_lift_of_isRegular is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toSupSet.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{max u1 u2}))) ι f) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.supr_lt_lift_of_is_regular Cardinal.supᵢ_lt_lift_of_isRegularₓ'. -/
@@ -1437,7 +1437,7 @@ theorem supᵢ_lt_lift_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegul
 
 /- warning: cardinal.supr_lt_of_is_regular -> Cardinal.supᵢ_lt_of_isRegular is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toSupSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) ι f) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.supr_lt_of_is_regular Cardinal.supᵢ_lt_of_isRegularₓ'. -/
@@ -1573,7 +1573,7 @@ def IsInaccessible (c : Cardinal) :=
 
 /- warning: cardinal.is_inaccessible.mk -> Cardinal.IsInaccessible.mk is a dubious translation:
 lean 3 declaration is
-  forall {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) Cardinal.aleph0.{u1} c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)) -> (Cardinal.IsInaccessible.{u1} c)
+  forall {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)) -> (Cardinal.IsInaccessible.{u1} c)
 but is expected to have type
   forall {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) c)) -> (Cardinal.IsInaccessible.{u1} c)
 Case conversion may be inaccurate. Consider using '#align cardinal.is_inaccessible.mk Cardinal.IsInaccessible.mkₓ'. -/

7c2ce0c2

bump to nightly-2023-04-10-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/284fdd2962e67d2932fa3a79ce19fcf92d38e228

542f5cb1

Diff

@@ -212,15 +212,11 @@ theorem cof_type_le [IsWellOrder α r] {S : Set α} (h : Unbounded r S) : cof (t
 #align ordinal.cof_type_le Ordinal.cof_type_le
 -/
 
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-Case conversion may be inaccurate. Consider using '#align ordinal.lt_cof_type Ordinal.lt_cof_typeₓ'. -/
+#print Ordinal.lt_cof_type /-
 theorem lt_cof_type [IsWellOrder α r] {S : Set α} : (#S) < cof (type r) → Bounded r S := by
   simpa using not_imp_not.2 cof_type_le
 #align ordinal.lt_cof_type Ordinal.lt_cof_type
+-/
 
 #print Ordinal.cof_eq /-
 theorem cof_eq (r : α → α → Prop) [IsWellOrder α r] : ∃ S, Unbounded r S ∧ (#S) = cof (type r) :=
@@ -416,29 +412,21 @@ theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
 #align ordinal.le_cof_iff_lsub Ordinal.le_cof_iff_lsub
 -/
 
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-Case conversion may be inaccurate. Consider using '#align ordinal.lsub_lt_ord_lift Ordinal.lsub_lt_ord_liftₓ'. -/
+#print Ordinal.lsub_lt_ord_lift /-
 theorem lsub_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : lsub.{u, v} f < c :=
   lt_of_le_of_ne (lsub_le hf) fun h => by
     subst h
     exact (cof_lsub_le_lift f).not_lt hι
 #align ordinal.lsub_lt_ord_lift Ordinal.lsub_lt_ord_lift
+-/
 
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-Case conversion may be inaccurate. Consider using '#align ordinal.lsub_lt_ord Ordinal.lsub_lt_ordₓ'. -/
+#print Ordinal.lsub_lt_ord /-
 theorem lsub_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
     (∀ i, f i < c) → lsub.{u, u} f < c :=
   lsub_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.lsub_lt_ord Ordinal.lsub_lt_ord
+-/
 
 #print Ordinal.cof_sup_le_lift /-
 theorem cof_sup_le_lift {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup f) : cof (sup f) ≤ (#ι).lift :=
@@ -457,27 +445,19 @@ theorem cof_sup_le {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup.{u, u} f) :
 #align ordinal.cof_sup_le Ordinal.cof_sup_le
 -/
 
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-Case conversion may be inaccurate. Consider using '#align ordinal.sup_lt_ord_lift Ordinal.sup_lt_ord_liftₓ'. -/
+#print Ordinal.sup_lt_ord_lift /-
 theorem sup_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : sup.{u, v} f < c :=
   (sup_le_lsub.{u, v} f).trans_lt (lsub_lt_ord_lift hι hf)
 #align ordinal.sup_lt_ord_lift Ordinal.sup_lt_ord_lift
+-/
 
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-Case conversion may be inaccurate. Consider using '#align ordinal.sup_lt_ord Ordinal.sup_lt_ordₓ'. -/
+#print Ordinal.sup_lt_ord /-
 theorem sup_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
     (∀ i, f i < c) → sup.{u, u} f < c :=
   sup_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.sup_lt_ord Ordinal.sup_lt_ord
+-/
 
 /- warning: ordinal.supr_lt_lift -> Ordinal.supᵢ_lt_lift is a dubious translation:
 lean 3 declaration is
@@ -505,12 +485,7 @@ theorem supᵢ_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : (#ι) < c.ord
   supᵢ_lt_lift (by rwa [(#ι).lift_id])
 #align ordinal.supr_lt Ordinal.supᵢ_lt
 
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+#print Ordinal.nfpFamily_lt_ord_lift /-
 theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : (#ι).lift < cof c) (hf : ∀ (i), ∀ b < c, f i b < c) {a} (ha : a < c) :
     nfpFamily.{u, v} f a < c :=
@@ -523,52 +498,37 @@ theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : 
     · exact ha
     · exact hf _ _ H
 #align ordinal.nfp_family_lt_ord_lift Ordinal.nfpFamily_lt_ord_lift
+-/
 
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+#print Ordinal.nfpFamily_lt_ord /-
 theorem nfpFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hc' : (#ι) < cof c)
     (hf : ∀ (i), ∀ b < c, f i b < c) {a} : a < c → nfpFamily.{u, u} f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [(#ι).lift_id]) hf
 #align ordinal.nfp_family_lt_ord Ordinal.nfpFamily_lt_ord
+-/
 
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+#print Ordinal.nfpBFamily_lt_ord_lift /-
 theorem nfpBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : o.card.lift < cof c) (hf : ∀ (i hi), ∀ b < c, f i hi b < c) {a} :
     a < c → nfpBFamily.{u, v} o f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [mk_ordinal_out]) fun i => hf _ _
 #align ordinal.nfp_bfamily_lt_ord_lift Ordinal.nfpBFamily_lt_ord_lift
+-/
 
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+#print Ordinal.nfpBFamily_lt_ord /-
 theorem nfpBFamily_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : o.card < cof c) (hf : ∀ (i hi), ∀ b < c, f i hi b < c) {a} :
     a < c → nfpBFamily.{u, u} o f a < c :=
   nfpBFamily_lt_ord_lift hc (by rwa [o.card.lift_id]) hf
 #align ordinal.nfp_bfamily_lt_ord Ordinal.nfpBFamily_lt_ord
+-/
 
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-Case conversion may be inaccurate. Consider using '#align ordinal.nfp_lt_ord Ordinal.nfp_lt_ordₓ'. -/
+#print Ordinal.nfp_lt_ord /-
 theorem nfp_lt_ord {f : Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hf : ∀ i < c, f i < c) {a} :
     a < c → nfp f a < c :=
   nfpFamily_lt_ord_lift hc (by simpa using cardinal.one_lt_aleph_0.trans hc) fun _ => hf
 #align ordinal.nfp_lt_ord Ordinal.nfp_lt_ord
+-/
 
 #print Ordinal.exists_blsub_cof /-
 theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, blsub.{u, u} _ f = o :=
@@ -610,28 +570,20 @@ theorem cof_blsub_le {o} (f : ∀ a < o, Ordinal) : cof (blsub.{u, u} o f) ≤ o
 #align ordinal.cof_blsub_le Ordinal.cof_blsub_le
 -/
 
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+#print Ordinal.blsub_lt_ord_lift /-
 theorem blsub_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : o.card.lift < c.cof) (hf : ∀ i hi, f i hi < c) : blsub.{u, v} o f < c :=
   lt_of_le_of_ne (blsub_le hf) fun h =>
     ho.not_le (by simpa [← supr_ord, hf, h] using cof_blsub_le_lift.{u} f)
 #align ordinal.blsub_lt_ord_lift Ordinal.blsub_lt_ord_lift
+-/
 
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+#print Ordinal.blsub_lt_ord /-
 theorem blsub_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof)
     (hf : ∀ i hi, f i hi < c) : blsub.{u, u} o f < c :=
   blsub_lt_ord_lift (by rwa [o.card.lift_id]) hf
 #align ordinal.blsub_lt_ord Ordinal.blsub_lt_ord
+-/
 
 #print Ordinal.cof_bsup_le_lift /-
 theorem cof_bsup_le_lift {o : Ordinal} {f : ∀ a < o, Ordinal} (H : ∀ i h, f i h < bsup o f) :
@@ -652,27 +604,19 @@ theorem cof_bsup_le {o : Ordinal} {f : ∀ a < o, Ordinal} :
 #align ordinal.cof_bsup_le Ordinal.cof_bsup_le
 -/
 
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+#print Ordinal.bsup_lt_ord_lift /-
 theorem bsup_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : o.card.lift < c.cof) (hf : ∀ i hi, f i hi < c) : bsup.{u, v} o f < c :=
   (bsup_le_blsub f).trans_lt (blsub_lt_ord_lift ho hf)
 #align ordinal.bsup_lt_ord_lift Ordinal.bsup_lt_ord_lift
+-/
 
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+#print Ordinal.bsup_lt_ord /-
 theorem bsup_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof) :
     (∀ i hi, f i hi < c) → bsup.{u, u} o f < c :=
   bsup_lt_ord_lift (by rwa [o.card.lift_id])
 #align ordinal.bsup_lt_ord Ordinal.bsup_lt_ord
+-/
 
 /-! ### Basic results -/
 
@@ -1070,12 +1014,7 @@ theorem unbounded_of_unbounded_unionₛ (r : α → α → Prop) [wo : IsWellOrd
   exact ⟨f ⟨c, hc⟩, mem_range_self _, fun hxz => hxy (trans (wo.wf.lt_sup _ hy) hxz)⟩
 #align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_unionₛ
 
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+#print Ordinal.unbounded_of_unbounded_unionᵢ /-
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
 theorem unbounded_of_unbounded_unionᵢ {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
@@ -1085,13 +1024,9 @@ theorem unbounded_of_unbounded_unionᵢ {α β : Type u} (r : α → α → Prop
   rcases unbounded_of_unbounded_sUnion r h₁ (mk_range_le.trans_lt h₂) with ⟨_, ⟨x, rfl⟩, u⟩
   exact ⟨x, u⟩
 #align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_unionᵢ
+-/
 
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+#print Ordinal.infinite_pigeonhole /-
 /-- The infinite pigeonhole principle -/
 theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤ (#β)) (h₂ : (#α) < (#β).ord.cof) :
     ∃ a : α, (#f ⁻¹' {a}) = (#β) :=
@@ -1108,13 +1043,9 @@ theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤
   rw [le_mk_iff_exists_set]
   exact ⟨_, rfl⟩
 #align ordinal.infinite_pigeonhole Ordinal.infinite_pigeonhole
+-/
 
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+#print Ordinal.infinite_pigeonhole_card /-
 /-- Pigeonhole principle for a cardinality below the cardinality of the domain -/
 theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal) (hθ : θ ≤ (#β))
     (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) : ∃ a : α, θ ≤ (#f ⁻¹' {a}) :=
@@ -1124,13 +1055,9 @@ theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal
   use a; rw [← ha, @preimage_comp _ _ _ Subtype.val f]
   exact mk_preimage_of_injective _ _ Subtype.val_injective
 #align ordinal.infinite_pigeonhole_card Ordinal.infinite_pigeonhole_card
+-/
 
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+#print Ordinal.infinite_pigeonhole_set /-
 theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ : Cardinal)
     (hθ : θ ≤ (#s)) (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) :
     ∃ (a : α)(t : Set β)(h : t ⊆ s), θ ≤ (#t) ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a :=
@@ -1146,6 +1073,7 @@ theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ
     simp only [coe_eq_subtype, mem_singleton_iff, mem_preimage, mem_set_of_eq]
   rintro x ⟨hx, hx'⟩; exact hx'
 #align ordinal.infinite_pigeonhole_set Ordinal.infinite_pigeonhole_set
+-/
 
 end Ordinal
 
@@ -1191,9 +1119,11 @@ theorem isStrongLimit_aleph0 : IsStrongLimit ℵ₀ :=
 #align cardinal.is_strong_limit_aleph_0 Cardinal.isStrongLimit_aleph0
 -/
 
+#print Cardinal.IsStrongLimit.isSuccLimit /-
 protected theorem IsStrongLimit.isSuccLimit {c} (H : IsStrongLimit c) : IsSuccLimit c :=
   isSuccLimit_of_succ_lt fun x h => (succ_le_of_lt <| cantor x).trans_lt (H.two_power_lt h)
 #align cardinal.is_strong_limit.is_succ_limit Cardinal.IsStrongLimit.isSuccLimit
+-/
 
 #print Cardinal.IsStrongLimit.isLimit /-
 theorem IsStrongLimit.isLimit {c} (H : IsStrongLimit c) : IsLimit c :=
@@ -1201,12 +1131,7 @@ theorem IsStrongLimit.isLimit {c} (H : IsStrongLimit c) : IsLimit c :=
 #align cardinal.is_strong_limit.is_limit Cardinal.IsStrongLimit.isLimit
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_bethₓ'. -/
+#print Cardinal.isStrongLimit_beth /-
 theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (beth o) :=
   by
   rcases eq_or_ne o 0 with (rfl | h)
@@ -1219,6 +1144,7 @@ theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (be
     rw [← beth_succ] at this
     exact this.trans_lt (beth_lt.2 (H.succ_lt hi))
 #align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_beth
+-/
 
 /- warning: cardinal.mk_bounded_subset -> Cardinal.mk_bounded_subset is a dubious translation:
 lean 3 declaration is
@@ -1302,15 +1228,11 @@ theorem IsRegular.cof_eq {c : Cardinal} (H : c.IsRegular) : c.ord.cof = c :=
 #align cardinal.is_regular.cof_eq Cardinal.IsRegular.cof_eq
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.is_regular.pos Cardinal.IsRegular.posₓ'. -/
+#print Cardinal.IsRegular.pos /-
 theorem IsRegular.pos {c : Cardinal} (H : c.IsRegular) : 0 < c :=
   aleph0_pos.trans_le H.1
 #align cardinal.is_regular.pos Cardinal.IsRegular.pos
+-/
 
 #print Cardinal.IsRegular.ord_pos /-
 theorem IsRegular.ord_pos {c : Cardinal} (H : c.IsRegular) : 0 < c.ord :=
@@ -1388,12 +1310,7 @@ theorem isRegular_aleph_succ (o : Ordinal) : IsRegular (aleph (succ o)) :=
 #align cardinal.is_regular_aleph_succ Cardinal.isRegular_aleph_succ
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.infinite_pigeonhole_card_lt Cardinal.infinite_pigeonhole_card_ltₓ'. -/
+#print Cardinal.infinite_pigeonhole_card_lt /-
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has a fiber with cardinality strictly great than the codomain.
 -/
@@ -1404,13 +1321,9 @@ theorem infinite_pigeonhole_card_lt {β α : Type u} (f : β → α) (w : (#α)
     Ordinal.infinite_pigeonhole_card f (succ (#α)) (succ_le_of_lt w) (w'.trans (lt_succ _).le)
       ((lt_succ _).trans_le (is_regular_succ w').2.ge)
 #align cardinal.infinite_pigeonhole_card_lt Cardinal.infinite_pigeonhole_card_lt
+-/
 
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+#print Cardinal.exists_infinite_fiber /-
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has an infinite fiber.
 -/
@@ -1421,6 +1334,7 @@ theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : (#α) < (#β
   cases' infinite_pigeonhole_card_lt f w w' with a ha
   exact ⟨a, w'.trans ha.le⟩
 #align cardinal.exists_infinite_fiber Cardinal.exists_infinite_fiber
+-/
 
 /- warning: cardinal.le_range_of_union_finset_eq_top -> Cardinal.le_range_of_union_finset_eq_top is a dubious translation:
 lean 3 declaration is
@@ -1454,93 +1368,61 @@ theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α 
   exact (@Infinite.of_injective _ _ p (inclusion (v' a)) (inclusion_injective _)).False
 #align cardinal.le_range_of_union_finset_eq_top Cardinal.le_range_of_union_finset_eq_top
 
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+#print Cardinal.lsub_lt_ord_lift_of_isRegular /-
 theorem lsub_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_lift_of_is_regular Cardinal.lsub_lt_ord_lift_of_isRegular
+-/
 
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+#print Cardinal.lsub_lt_ord_of_isRegular /-
 theorem lsub_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_of_is_regular Cardinal.lsub_lt_ord_of_isRegular
+-/
 
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+#print Cardinal.sup_lt_ord_lift_of_isRegular /-
 theorem sup_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_lift_of_is_regular Cardinal.sup_lt_ord_lift_of_isRegular
+-/
 
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+#print Cardinal.sup_lt_ord_of_isRegular /-
 theorem sup_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_of_is_regular Cardinal.sup_lt_ord_of_isRegular
+-/
 
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+#print Cardinal.blsub_lt_ord_lift_of_isRegular /-
 theorem blsub_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (ho : Cardinal.lift o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.blsub o f < c.ord :=
   blsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.blsub_lt_ord_lift_of_is_regular Cardinal.blsub_lt_ord_lift_of_isRegular
+-/
 
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+#print Cardinal.blsub_lt_ord_of_isRegular /-
 theorem blsub_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (ho : o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.blsub o f < c.ord :=
   blsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.blsub_lt_ord_of_is_regular Cardinal.blsub_lt_ord_of_isRegular
+-/
 
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+#print Cardinal.bsup_lt_ord_lift_of_isRegular /-
 theorem bsup_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.bsup o f < c.ord :=
   bsup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_lift_of_is_regular Cardinal.bsup_lt_ord_lift_of_isRegular
+-/
 
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+#print Cardinal.bsup_lt_ord_of_isRegular /-
 theorem bsup_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (hι : o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.bsup o f < c.ord :=
   bsup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_of_is_regular Cardinal.bsup_lt_ord_of_isRegular
+-/
 
 /- warning: cardinal.supr_lt_lift_of_is_regular -> Cardinal.supᵢ_lt_lift_of_isRegular is a dubious translation:
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@@ -1564,34 +1446,21 @@ theorem supᵢ_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c)
   supᵢ_lt (by rwa [hc.cof_eq])
 #align cardinal.supr_lt_of_is_regular Cardinal.supᵢ_lt_of_isRegular
 
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+#print Cardinal.sum_lt_lift_of_isRegular /-
 theorem sum_lt_lift_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : Cardinal.lift.{v, u} (#ι) < c) (hf : ∀ i, f i < c) : sum f < c :=
   (sum_le_supᵢ_lift _).trans_lt <| mul_lt_of_lt hc.1 hι (supᵢ_lt_lift_of_isRegular hc hι hf)
 #align cardinal.sum_lt_lift_of_is_regular Cardinal.sum_lt_lift_of_isRegular
+-/
 
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+#print Cardinal.sum_lt_of_isRegular /-
 theorem sum_lt_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : (#ι) < c) : (∀ i, f i < c) → sum f < c :=
   sum_lt_lift_of_isRegular.{u, u} hc (by rwa [lift_id])
 #align cardinal.sum_lt_of_is_regular Cardinal.sum_lt_of_isRegular
+-/
 
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+#print Cardinal.nfpFamily_lt_ord_lift_of_isRegular /-
 theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a}
     (ha : a < c.ord) : nfpFamily.{u, v} f a < c.ord :=
@@ -1599,44 +1468,33 @@ theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal}
   apply nfp_family_lt_ord_lift _ _ hf ha <;> rwa [hc.cof_eq]
   exact lt_of_le_of_ne hc.1 hc'.symm
 #align cardinal.nfp_family_lt_ord_lift_of_is_regular Cardinal.nfpFamily_lt_ord_lift_of_isRegular
+-/
 
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+#print Cardinal.nfpFamily_lt_ord_of_isRegular /-
 theorem nfpFamily_lt_ord_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι) < c) (hc' : c ≠ ℵ₀) {a} (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) :
     a < c.ord → nfpFamily.{u, u} f a < c.ord :=
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_family_lt_ord_of_is_regular Cardinal.nfpFamily_lt_ord_of_isRegular
+-/
 
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+#print Cardinal.nfpBFamily_lt_ord_lift_of_isRegular /-
 theorem nfpBFamily_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (ho : o.card.lift < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → nfpBFamily.{u, v} o f a < c.ord :=
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [mk_ordinal_out]) hc' fun i => hf _ _
 #align cardinal.nfp_bfamily_lt_ord_lift_of_is_regular Cardinal.nfpBFamily_lt_ord_lift_of_isRegular
+-/
 
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+#print Cardinal.nfpBFamily_lt_ord_of_isRegular /-
 theorem nfpBFamily_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (ho : o.card < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → nfpBFamily.{u, u} o f a < c.ord :=
   nfpBFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_bfamily_lt_ord_of_is_regular Cardinal.nfpBFamily_lt_ord_of_isRegular
+-/
 
 #print Cardinal.nfp_lt_ord_of_isRegular /-
 theorem nfp_lt_ord_of_isRegular {f : Ordinal → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
@@ -1649,12 +1507,7 @@ theorem nfp_lt_ord_of_isRegular {f : Ordinal → Ordinal} {c} (hc : IsRegular c)
 #align cardinal.nfp_lt_ord_of_is_regular Cardinal.nfp_lt_ord_of_isRegular
 -/
 
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+#print Cardinal.derivFamily_lt_ord_lift /-
 theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, v} f a < c.ord :=
@@ -1676,43 +1529,32 @@ theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc :
       bsup_lt_ord_of_is_regular hc (ord_lt_ord.1 ((ord_card_le b).trans_lt hb')) fun o' ho' =>
         H o' ho' (ho'.trans hb')
 #align cardinal.deriv_family_lt_ord_lift Cardinal.derivFamily_lt_ord_lift
+-/
 
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+#print Cardinal.derivFamily_lt_ord /-
 theorem derivFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c)
     (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, u} f a < c.ord :=
   derivFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf
 #align cardinal.deriv_family_lt_ord Cardinal.derivFamily_lt_ord
+-/
 
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+#print Cardinal.derivBFamily_lt_ord_lift /-
 theorem derivBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (hι : o.card.lift < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → derivBFamily.{u, v} o f a < c.ord :=
   derivFamily_lt_ord_lift hc (by rwa [mk_ordinal_out]) hc' fun i => hf _ _
 #align cardinal.deriv_bfamily_lt_ord_lift Cardinal.derivBFamily_lt_ord_lift
+-/
 
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+#print Cardinal.derivBFamily_lt_ord /-
 theorem derivBFamily_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : o.card < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → derivBFamily.{u, u} o f a < c.ord :=
   derivBFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf
 #align cardinal.deriv_bfamily_lt_ord Cardinal.derivBFamily_lt_ord
+-/
 
 #print Cardinal.deriv_lt_ord /-
 theorem deriv_lt_ord {f : Ordinal.{u} → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
@@ -1751,12 +1593,7 @@ theorem univ_inaccessible : IsInaccessible univ.{u, v} :=
 #align cardinal.univ_inaccessible Cardinal.univ_inaccessible
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.lt_power_cof Cardinal.lt_power_cofₓ'. -/
+#print Cardinal.lt_power_cof /-
 theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
   Quotient.inductionOn c fun α h =>
     by
@@ -1776,13 +1613,9 @@ theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
     · have := typein_lt_type r i
       rwa [← re, lt_ord] at this
 #align cardinal.lt_power_cof Cardinal.lt_power_cof
+-/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.lt_cof_power Cardinal.lt_cof_powerₓ'. -/
+#print Cardinal.lt_cof_power /-
 theorem lt_cof_power {a b : Cardinal} (ha : ℵ₀ ≤ a) (b1 : 1 < b) : a < cof (b^a).ord :=
   by
   have b0 : b ≠ 0 := (zero_lt_one.trans b1).ne'
@@ -1790,6 +1623,7 @@ theorem lt_cof_power {a b : Cardinal} (ha : ℵ₀ ≤ a) (b1 : 1 < b) : a < cof
   rw [← power_mul, mul_eq_self ha]
   exact lt_power_cof (ha.trans <| (cantor' _ b1).le)
 #align cardinal.lt_cof_power Cardinal.lt_cof_power
+-/
 
 end Cardinal

7c2ce0c2

bump to nightly-2023-04-04-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/3cacc945118c8c637d89950af01da78307f59325

2ee17135

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.cofinality
-! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
+! leanprover-community/mathlib commit 7c2ce0c2da15516b4e65d0c9e254bb6dc93abd1f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -24,7 +24,6 @@ This file contains the definition of cofinality of an ordinal number and regular
 * `ordinal.cof o` is the cofinality of the ordinal `o`.
   If `o` is the order type of the relation `<` on `α`, then `o.cof` is the smallest cardinality of a
   subset `s` of α that is *cofinal* in `α`, i.e. `∀ x : α, ∃ y ∈ s, ¬ y < x`.
-* `cardinal.is_limit c` means that `c` is a (weak) limit cardinal: `c ≠ 0 ∧ ∀ x < c, succ x < c`.
 * `cardinal.is_strong_limit c` means that `c` is a strong limit cardinal:
   `c ≠ 0 ∧ ∀ x < c, 2 ^ x < c`.
 * `cardinal.is_regular c` means that `c` is a regular cardinal: `ℵ₀ ≤ c ∧ c.ord.cof = c`.
@@ -1160,40 +1159,6 @@ open Ordinal
 -- mathport name: cardinal.pow
 local infixr:0 "^" => @pow Cardinal.{u} Cardinal Cardinal.hasPow
 
-#print Cardinal.IsLimit /-
-/-- A cardinal is a limit if it is not zero or a successor
-  cardinal. Note that `ℵ₀` is a limit cardinal by this definition. -/
-def IsLimit (c : Cardinal) : Prop :=
-  c ≠ 0 ∧ ∀ x < c, succ x < c
-#align cardinal.is_limit Cardinal.IsLimit
--/
-
-#print Cardinal.IsLimit.ne_zero /-
-theorem IsLimit.ne_zero {c} (h : IsLimit c) : c ≠ 0 :=
-  h.1
-#align cardinal.is_limit.ne_zero Cardinal.IsLimit.ne_zero
--/
-
-/- warning: cardinal.is_limit.succ_lt -> Cardinal.IsLimit.succ_lt is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} x) c)
-Case conversion may be inaccurate. Consider using '#align cardinal.is_limit.succ_lt Cardinal.IsLimit.succ_ltₓ'. -/
-theorem IsLimit.succ_lt {x c} (h : IsLimit c) : x < c → succ x < c :=
-  h.2 x
-#align cardinal.is_limit.succ_lt Cardinal.IsLimit.succ_lt
-
-#print Cardinal.IsLimit.aleph0_le /-
-theorem IsLimit.aleph0_le {c} (h : IsLimit c) : ℵ₀ ≤ c :=
-  by
-  by_contra' h'
-  rcases lt_aleph_0.1 h' with ⟨_ | n, rfl⟩
-  · exact h.1.irrefl
-  · simpa using h.2 n
-#align cardinal.is_limit.aleph_0_le Cardinal.IsLimit.aleph0_le
--/
-
 #print Cardinal.IsStrongLimit /-
 /-- A cardinal is a strong limit if it is not zero and it is
   closed under powersets. Note that `ℵ₀` is a strong limit by this definition. -/
@@ -1226,32 +1191,34 @@ theorem isStrongLimit_aleph0 : IsStrongLimit ℵ₀ :=
 #align cardinal.is_strong_limit_aleph_0 Cardinal.isStrongLimit_aleph0
 -/
 
+protected theorem IsStrongLimit.isSuccLimit {c} (H : IsStrongLimit c) : IsSuccLimit c :=
+  isSuccLimit_of_succ_lt fun x h => (succ_le_of_lt <| cantor x).trans_lt (H.two_power_lt h)
+#align cardinal.is_strong_limit.is_succ_limit Cardinal.IsStrongLimit.isSuccLimit
+
 #print Cardinal.IsStrongLimit.isLimit /-
 theorem IsStrongLimit.isLimit {c} (H : IsStrongLimit c) : IsLimit c :=
-  ⟨H.1, fun x h => (succ_le_of_lt <| cantor x).trans_lt (H.2 _ h)⟩
+  ⟨H.NeZero, H.IsSuccLimit⟩
 #align cardinal.is_strong_limit.is_limit Cardinal.IsStrongLimit.isLimit
 -/
 
-#print Cardinal.isLimit_aleph0 /-
-theorem isLimit_aleph0 : IsLimit ℵ₀ :=
-  isStrongLimit_aleph0.IsLimit
-#align cardinal.is_limit_aleph_0 Cardinal.isLimit_aleph0
--/
-
-#print Cardinal.isStrongLimit_beth /-
-theorem isStrongLimit_beth {o : Ordinal} (H : ∀ a < o, succ a < o) : IsStrongLimit (beth o) :=
+/- warning: cardinal.is_strong_limit_beth -> Cardinal.isStrongLimit_beth is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, (Order.IsSuccLimit.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o) -> (Cardinal.IsStrongLimit.{u1} (Cardinal.beth.{u1} o))
+but is expected to have type
+  forall {o : Ordinal.{u1}}, (forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} a) o)) -> (Cardinal.IsStrongLimit.{u1} (Cardinal.beth.{u1} o))
+Case conversion may be inaccurate. Consider using '#align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_bethₓ'. -/
+theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (beth o) :=
   by
   rcases eq_or_ne o 0 with (rfl | h)
   · rw [beth_zero]
     exact is_strong_limit_aleph_0
   · refine' ⟨beth_ne_zero o, fun a ha => _⟩
-    rw [beth_limit ⟨h, H⟩] at ha
+    rw [beth_limit ⟨h, is_succ_limit_iff_succ_lt.1 H⟩] at ha
     rcases exists_lt_of_lt_csupᵢ' ha with ⟨⟨i, hi⟩, ha⟩
     have := power_le_power_left two_ne_zero ha.le
     rw [← beth_succ] at this
-    exact this.trans_lt (beth_lt.2 (H i hi))
+    exact this.trans_lt (beth_lt.2 (H.succ_lt hi))
 #align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_beth
--/
 
 /- warning: cardinal.mk_bounded_subset -> Cardinal.mk_bounded_subset is a dubious translation:
 lean 3 declaration is

ee05e9ce

bump to nightly-2023-04-03-02

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

8477bcac

Diff

@@ -213,11 +213,15 @@ theorem cof_type_le [IsWellOrder α r] {S : Set α} (h : Unbounded r S) : cof (t
 #align ordinal.cof_type_le Ordinal.cof_type_le
 -/
 
-#print Ordinal.lt_cof_type /-
+/- warning: ordinal.lt_cof_type -> Ordinal.lt_cof_type is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r] {S : Set.{u1} α}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) S)) (Ordinal.cof.{u1} (Ordinal.type.{u1} α r _inst_1))) -> (Set.Bounded.{u1} α r S)
+but is expected to have type
+  forall {α : Type.{u1}} {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r] {S : Set.{u1} α}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (Set.Elem.{u1} α S)) (Ordinal.cof.{u1} (Ordinal.type.{u1} α r _inst_1))) -> (Set.Bounded.{u1} α r S)
+Case conversion may be inaccurate. Consider using '#align ordinal.lt_cof_type Ordinal.lt_cof_typeₓ'. -/
 theorem lt_cof_type [IsWellOrder α r] {S : Set α} : (#S) < cof (type r) → Bounded r S := by
   simpa using not_imp_not.2 cof_type_le
 #align ordinal.lt_cof_type Ordinal.lt_cof_type
--/
 
 #print Ordinal.cof_eq /-
 theorem cof_eq (r : α → α → Prop) [IsWellOrder α r] : ∃ S, Unbounded r S ∧ (#S) = cof (type r) :=
@@ -413,21 +417,29 @@ theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
 #align ordinal.le_cof_iff_lsub Ordinal.le_cof_iff_lsub
 -/
 
-#print Ordinal.lsub_lt_ord_lift /-
+/- warning: ordinal.lsub_lt_ord_lift -> Ordinal.lsub_lt_ord_lift is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.lsub.{u1, u2} ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u1 u2})) (Ordinal.lsub.{u1, u2} ι f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.lsub_lt_ord_lift Ordinal.lsub_lt_ord_liftₓ'. -/
 theorem lsub_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : lsub.{u, v} f < c :=
   lt_of_le_of_ne (lsub_le hf) fun h => by
     subst h
     exact (cof_lsub_le_lift f).not_lt hι
 #align ordinal.lsub_lt_ord_lift Ordinal.lsub_lt_ord_lift
--/
 
-#print Ordinal.lsub_lt_ord /-
+/- warning: ordinal.lsub_lt_ord -> Ordinal.lsub_lt_ord is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} c)) -> (forall (i : ι), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.lsub.{u1, u1} ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} c)) -> (forall (i : ι), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.lsub.{u1, u1} ι f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.lsub_lt_ord Ordinal.lsub_lt_ordₓ'. -/
 theorem lsub_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
     (∀ i, f i < c) → lsub.{u, u} f < c :=
   lsub_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.lsub_lt_ord Ordinal.lsub_lt_ord
--/
 
 #print Ordinal.cof_sup_le_lift /-
 theorem cof_sup_le_lift {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup f) : cof (sup f) ≤ (#ι).lift :=
@@ -446,23 +458,31 @@ theorem cof_sup_le {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup.{u, u} f) :
 #align ordinal.cof_sup_le Ordinal.cof_sup_le
 -/
 
-#print Ordinal.sup_lt_ord_lift /-
+/- warning: ordinal.sup_lt_ord_lift -> Ordinal.sup_lt_ord_lift is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.sup.{u1, u2} ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.sup.{u1, u2} ι f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.sup_lt_ord_lift Ordinal.sup_lt_ord_liftₓ'. -/
 theorem sup_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : sup.{u, v} f < c :=
   (sup_le_lsub.{u, v} f).trans_lt (lsub_lt_ord_lift hι hf)
 #align ordinal.sup_lt_ord_lift Ordinal.sup_lt_ord_lift
--/
 
-#print Ordinal.sup_lt_ord /-
+/- warning: ordinal.sup_lt_ord -> Ordinal.sup_lt_ord is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} c)) -> (forall (i : ι), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.sup.{u1, u1} ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} c)) -> (forall (i : ι), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.sup.{u1, u1} ι f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.sup_lt_ord Ordinal.sup_lt_ordₓ'. -/
 theorem sup_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
     (∀ i, f i < c) → sup.{u, u} f < c :=
   sup_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.sup_lt_ord Ordinal.sup_lt_ord
--/
 
 /- warning: ordinal.supr_lt_lift -> Ordinal.supᵢ_lt_lift is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toSupSet.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{max u1 u2}))) ι f) c)
 Case conversion may be inaccurate. Consider using '#align ordinal.supr_lt_lift Ordinal.supᵢ_lt_liftₓ'. -/
@@ -477,7 +497,7 @@ theorem supᵢ_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal} (hι : Cardinal
 
 /- warning: ordinal.supr_lt -> Ordinal.supᵢ_lt is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toSupSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) ι f) c)
 Case conversion may be inaccurate. Consider using '#align ordinal.supr_lt Ordinal.supᵢ_ltₓ'. -/
@@ -486,7 +506,12 @@ theorem supᵢ_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : (#ι) < c.ord
   supᵢ_lt_lift (by rwa [(#ι).lift_id])
 #align ordinal.supr_lt Ordinal.supᵢ_lt
 
-#print Ordinal.nfpFamily_lt_ord_lift /-
+/- warning: ordinal.nfp_family_lt_ord_lift -> Ordinal.nfpFamily_lt_ord_lift is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) Cardinal.aleph0.{max u1 u2} (Ordinal.cof.{max u1 u2} c)) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : ι) (b : Ordinal.{max u1 u2}), (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b c) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i b) c)) -> (forall {a : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) a c) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.nfpFamily.{u1, u2} ι f a) c))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) Cardinal.aleph0.{max u1 u2} (Ordinal.cof.{max u1 u2} c)) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : ι) (b : Ordinal.{max u1 u2}), (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b c) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i b) c)) -> (forall {a : Ordinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) a c) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u1 u2})) (Ordinal.nfpFamily.{u1, u2} ι f a) c))
+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_family_lt_ord_lift Ordinal.nfpFamily_lt_ord_liftₓ'. -/
 theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : (#ι).lift < cof c) (hf : ∀ (i), ∀ b < c, f i b < c) {a} (ha : a < c) :
     nfpFamily.{u, v} f a < c :=
@@ -499,37 +524,52 @@ theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : 
     · exact ha
     · exact hf _ _ H
 #align ordinal.nfp_family_lt_ord_lift Ordinal.nfpFamily_lt_ord_lift
--/
 
-#print Ordinal.nfpFamily_lt_ord /-
+/- warning: ordinal.nfp_family_lt_ord -> Ordinal.nfpFamily_lt_ord is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{u1} -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) Cardinal.aleph0.{u1} (Ordinal.cof.{u1} c)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} c)) -> (forall (i : ι) (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i b) c)) -> (forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfpFamily.{u1, u1} ι f a) c))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{u1} -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} (Ordinal.cof.{u1} c)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} c)) -> (forall (i : ι) (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i b) c)) -> (forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfpFamily.{u1, u1} ι f a) c))
+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_family_lt_ord Ordinal.nfpFamily_lt_ordₓ'. -/
 theorem nfpFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hc' : (#ι) < cof c)
     (hf : ∀ (i), ∀ b < c, f i b < c) {a} : a < c → nfpFamily.{u, u} f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [(#ι).lift_id]) hf
 #align ordinal.nfp_family_lt_ord Ordinal.nfpFamily_lt_ord
--/
 
-#print Ordinal.nfpBFamily_lt_ord_lift /-
+/- warning: ordinal.nfp_bfamily_lt_ord_lift -> Ordinal.nfpBFamily_lt_ord_lift is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_lt_ord_lift Ordinal.nfpBFamily_lt_ord_liftₓ'. -/
 theorem nfpBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : o.card.lift < cof c) (hf : ∀ (i hi), ∀ b < c, f i hi b < c) {a} :
     a < c → nfpBFamily.{u, v} o f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [mk_ordinal_out]) fun i => hf _ _
 #align ordinal.nfp_bfamily_lt_ord_lift Ordinal.nfpBFamily_lt_ord_lift
--/
 
-#print Ordinal.nfpBFamily_lt_ord /-
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_lt_ord Ordinal.nfpBFamily_lt_ordₓ'. -/
 theorem nfpBFamily_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : o.card < cof c) (hf : ∀ (i hi), ∀ b < c, f i hi b < c) {a} :
     a < c → nfpBFamily.{u, u} o f a < c :=
   nfpBFamily_lt_ord_lift hc (by rwa [o.card.lift_id]) hf
 #align ordinal.nfp_bfamily_lt_ord Ordinal.nfpBFamily_lt_ord
--/
 
-#print Ordinal.nfp_lt_ord /-
+/- warning: ordinal.nfp_lt_ord -> Ordinal.nfp_lt_ord is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_lt_ord Ordinal.nfp_lt_ordₓ'. -/
 theorem nfp_lt_ord {f : Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hf : ∀ i < c, f i < c) {a} :
     a < c → nfp f a < c :=
   nfpFamily_lt_ord_lift hc (by simpa using cardinal.one_lt_aleph_0.trans hc) fun _ => hf
 #align ordinal.nfp_lt_ord Ordinal.nfp_lt_ord
--/
 
 #print Ordinal.exists_blsub_cof /-
 theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, blsub.{u, u} _ f = o :=
@@ -571,20 +611,28 @@ theorem cof_blsub_le {o} (f : ∀ a < o, Ordinal) : cof (blsub.{u, u} o f) ≤ o
 #align ordinal.cof_blsub_le Ordinal.cof_blsub_le
 -/
 
-#print Ordinal.blsub_lt_ord_lift /-
+/- warning: ordinal.blsub_lt_ord_lift -> Ordinal.blsub_lt_ord_lift is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.blsub_lt_ord_lift Ordinal.blsub_lt_ord_liftₓ'. -/
 theorem blsub_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : o.card.lift < c.cof) (hf : ∀ i hi, f i hi < c) : blsub.{u, v} o f < c :=
   lt_of_le_of_ne (blsub_le hf) fun h =>
     ho.not_le (by simpa [← supr_ord, hf, h] using cof_blsub_le_lift.{u} f)
 #align ordinal.blsub_lt_ord_lift Ordinal.blsub_lt_ord_lift
--/
 
-#print Ordinal.blsub_lt_ord /-
+/- warning: ordinal.blsub_lt_ord -> Ordinal.blsub_lt_ord is a dubious translation:
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+  forall {o : Ordinal.{u1}} {f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} o) (Ordinal.cof.{u1} c)) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i hi) c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.blsub.{u1, u1} o f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.blsub_lt_ord Ordinal.blsub_lt_ordₓ'. -/
 theorem blsub_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof)
     (hf : ∀ i hi, f i hi < c) : blsub.{u, u} o f < c :=
   blsub_lt_ord_lift (by rwa [o.card.lift_id]) hf
 #align ordinal.blsub_lt_ord Ordinal.blsub_lt_ord
--/
 
 #print Ordinal.cof_bsup_le_lift /-
 theorem cof_bsup_le_lift {o : Ordinal} {f : ∀ a < o, Ordinal} (H : ∀ i h, f i h < bsup o f) :
@@ -605,19 +653,27 @@ theorem cof_bsup_le {o : Ordinal} {f : ∀ a < o, Ordinal} :
 #align ordinal.cof_bsup_le Ordinal.cof_bsup_le
 -/
 
-#print Ordinal.bsup_lt_ord_lift /-
+/- warning: ordinal.bsup_lt_ord_lift -> Ordinal.bsup_lt_ord_lift is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}} {f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (Cardinal.lift.{u2, u1} (Ordinal.card.{u1} o)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i hi) c) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.bsup.{u1, u2} o f) c)
+but is expected to have type
+  forall {o : Ordinal.{u1}} {f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{max u1 u2}} {c : Ordinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Ordinal.card.{u1} o)) (Ordinal.cof.{max u1 u2} c)) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i hi) c) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.bsup.{u1, u2} o f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.bsup_lt_ord_lift Ordinal.bsup_lt_ord_liftₓ'. -/
 theorem bsup_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : o.card.lift < c.cof) (hf : ∀ i hi, f i hi < c) : bsup.{u, v} o f < c :=
   (bsup_le_blsub f).trans_lt (blsub_lt_ord_lift ho hf)
 #align ordinal.bsup_lt_ord_lift Ordinal.bsup_lt_ord_lift
--/
 
-#print Ordinal.bsup_lt_ord /-
+/- warning: ordinal.bsup_lt_ord -> Ordinal.bsup_lt_ord is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}} {f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Ordinal.card.{u1} o) (Ordinal.cof.{u1} c)) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i hi) c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.bsup.{u1, u1} o f) c)
+but is expected to have type
+  forall {o : Ordinal.{u1}} {f : forall (a : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a o) -> Ordinal.{u1}} {c : Ordinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} o) (Ordinal.cof.{u1} c)) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f i hi) c) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.bsup.{u1, u1} o f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.bsup_lt_ord Ordinal.bsup_lt_ordₓ'. -/
 theorem bsup_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof) :
     (∀ i hi, f i hi < c) → bsup.{u, u} o f < c :=
   bsup_lt_ord_lift (by rwa [o.card.lift_id])
 #align ordinal.bsup_lt_ord Ordinal.bsup_lt_ord
--/
 
 /-! ### Basic results -/
 
@@ -998,7 +1054,7 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ :=
 
 /- warning: ordinal.unbounded_of_unbounded_sUnion -> Ordinal.unbounded_of_unbounded_unionₛ is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.unionₛ.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Set.{u1} α)) Type.{u1} (Set.hasCoeToSort.{u1} (Set.{u1} α)) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) => Set.Unbounded.{u1} α r x)))
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.unionₛ.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Set.{u1} α)) Type.{u1} (Set.hasCoeToSort.{u1} (Set.{u1} α)) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) => Set.Unbounded.{u1} α r x)))
 but is expected to have type
   forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.unionₛ.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (Set.Elem.{u1} (Set.{u1} α) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) x s) (Set.Unbounded.{u1} α r x)))
 Case conversion may be inaccurate. Consider using '#align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_unionₛₓ'. -/
@@ -1015,7 +1071,12 @@ theorem unbounded_of_unbounded_unionₛ (r : α → α → Prop) [wo : IsWellOrd
   exact ⟨f ⟨c, hc⟩, mem_range_self _, fun hxz => hxy (trans (wo.wf.lt_sup _ hy) hxz)⟩
 #align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_unionₛ
 
-#print Ordinal.unbounded_of_unbounded_unionᵢ /-
+/- warning: ordinal.unbounded_of_unbounded_Union -> Ordinal.unbounded_of_unbounded_unionᵢ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] (s : β -> (Set.{u1} α)), (Set.Unbounded.{u1} α r (Set.unionᵢ.{u1, succ u1} α β (fun (x : β) => s x))) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} β) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} β (fun (x : β) => Set.Unbounded.{u1} α r (s x)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] (s : β -> (Set.{u1} α)), (Set.Unbounded.{u1} α r (Set.unionᵢ.{u1, succ u1} α β (fun (x : β) => s x))) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} β) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} β (fun (x : β) => Set.Unbounded.{u1} α r (s x)))
+Case conversion may be inaccurate. Consider using '#align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_unionᵢₓ'. -/
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
 theorem unbounded_of_unbounded_unionᵢ {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
@@ -1025,9 +1086,13 @@ theorem unbounded_of_unbounded_unionᵢ {α β : Type u} (r : α → α → Prop
   rcases unbounded_of_unbounded_sUnion r h₁ (mk_range_le.trans_lt h₂) with ⟨_, ⟨x, rfl⟩, u⟩
   exact ⟨x, u⟩
 #align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_unionᵢ
--/
 
-#print Ordinal.infinite_pigeonhole /-
+/- warning: ordinal.infinite_pigeonhole -> Ordinal.infinite_pigeonhole is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α), (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} (Cardinal.mk.{u1} β)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} α) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} β)))) -> (Exists.{succ u1} α (fun (a : α) => Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)))) (Cardinal.mk.{u1} β)))
+but is expected to have type
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α), (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} (Cardinal.mk.{u1} β)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} β)))) -> (Exists.{succ u1} α (fun (a : α) => Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Set.Elem.{u1} β (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)))) (Cardinal.mk.{u1} β)))
+Case conversion may be inaccurate. Consider using '#align ordinal.infinite_pigeonhole Ordinal.infinite_pigeonholeₓ'. -/
 /-- The infinite pigeonhole principle -/
 theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤ (#β)) (h₂ : (#α) < (#β).ord.cof) :
     ∃ a : α, (#f ⁻¹' {a}) = (#β) :=
@@ -1044,9 +1109,13 @@ theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤
   rw [le_mk_iff_exists_set]
   exact ⟨_, rfl⟩
 #align ordinal.infinite_pigeonhole Ordinal.infinite_pigeonhole
--/
 
-#print Ordinal.infinite_pigeonhole_card /-
+/- warning: ordinal.infinite_pigeonhole_card -> Ordinal.infinite_pigeonhole_card is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α) (θ : Cardinal.{u1}), (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} θ (Cardinal.mk.{u1} β)) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} θ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} α) (Ordinal.cof.{u1} (Cardinal.ord.{u1} θ))) -> (Exists.{succ u1} α (fun (a : α) => LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} θ (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a))))))
+but is expected to have type
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α) (θ : Cardinal.{u1}), (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} θ (Cardinal.mk.{u1} β)) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} θ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Ordinal.cof.{u1} (Cardinal.ord.{u1} θ))) -> (Exists.{succ u1} α (fun (a : α) => LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} θ (Cardinal.mk.{u1} (Set.Elem.{u1} β (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a))))))
+Case conversion may be inaccurate. Consider using '#align ordinal.infinite_pigeonhole_card Ordinal.infinite_pigeonhole_cardₓ'. -/
 /-- Pigeonhole principle for a cardinality below the cardinality of the domain -/
 theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal) (hθ : θ ≤ (#β))
     (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) : ∃ a : α, θ ≤ (#f ⁻¹' {a}) :=
@@ -1056,9 +1125,13 @@ theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal
   use a; rw [← ha, @preimage_comp _ _ _ Subtype.val f]
   exact mk_preimage_of_injective _ _ Subtype.val_injective
 #align ordinal.infinite_pigeonhole_card Ordinal.infinite_pigeonhole_card
--/
 
-#print Ordinal.infinite_pigeonhole_set /-
+/- warning: ordinal.infinite_pigeonhole_set -> Ordinal.infinite_pigeonhole_set is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {α : Type.{u1}} {s : Set.{u1} β} (f : (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) s) -> α) (θ : Cardinal.{u1}), (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} θ (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) s))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} θ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} α) (Ordinal.cof.{u1} (Cardinal.ord.{u1} θ))) -> (Exists.{succ u1} α (fun (a : α) => Exists.{succ u1} (Set.{u1} β) (fun (t : Set.{u1} β) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} β) (Set.hasSubset.{u1} β) t s) (fun (h : HasSubset.Subset.{u1} (Set.{u1} β) (Set.hasSubset.{u1} β) t s) => And (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} θ (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) t))) (forall {{x : β}} (hx : Membership.Mem.{u1, u1} β (Set.{u1} β) (Set.hasMem.{u1} β) x t), Eq.{succ u1} α (f (Subtype.mk.{succ u1} β (fun (x : β) => Membership.Mem.{u1, u1} β (Set.{u1} β) (Set.hasMem.{u1} β) x s) x (h x hx))) a)))))
+but is expected to have type
+  forall {β : Type.{u1}} {α : Type.{u1}} {s : Set.{u1} β} (f : (Set.Elem.{u1} β s) -> α) (θ : Cardinal.{u1}), (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} θ (Cardinal.mk.{u1} (Set.Elem.{u1} β s))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} θ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Ordinal.cof.{u1} (Cardinal.ord.{u1} θ))) -> (Exists.{succ u1} α (fun (a : α) => Exists.{succ u1} (Set.{u1} β) (fun (t : Set.{u1} β) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} β) (Set.instHasSubsetSet.{u1} β) t s) (fun (h : HasSubset.Subset.{u1} (Set.{u1} β) (Set.instHasSubsetSet.{u1} β) t s) => And (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} θ (Cardinal.mk.{u1} (Set.Elem.{u1} β t))) (forall {{x : β}} (hx : Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x t), Eq.{succ u1} α (f (Subtype.mk.{succ u1} β (fun (x : β) => Membership.mem.{u1, u1} β (Set.{u1} β) (Set.instMembershipSet.{u1} β) x s) x (h x hx))) a)))))
+Case conversion may be inaccurate. Consider using '#align ordinal.infinite_pigeonhole_set Ordinal.infinite_pigeonhole_setₓ'. -/
 theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ : Cardinal)
     (hθ : θ ≤ (#s)) (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) :
     ∃ (a : α)(t : Set β)(h : t ⊆ s), θ ≤ (#t) ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a :=
@@ -1074,7 +1147,6 @@ theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ
     simp only [coe_eq_subtype, mem_singleton_iff, mem_preimage, mem_set_of_eq]
   rintro x ⟨hx, hx'⟩; exact hx'
 #align ordinal.infinite_pigeonhole_set Ordinal.infinite_pigeonhole_set
--/
 
 end Ordinal
 
@@ -1104,7 +1176,7 @@ theorem IsLimit.ne_zero {c} (h : IsLimit c) : c ≠ 0 :=
 
 /- warning: cardinal.is_limit.succ_lt -> Cardinal.IsLimit.succ_lt is a dubious translation:
 lean 3 declaration is
-  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.succOrder.{u1} x) c)
+  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1}))))) Cardinal.succOrder.{u1} x) c)
 but is expected to have type
   forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} x) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.is_limit.succ_lt Cardinal.IsLimit.succ_ltₓ'. -/
@@ -1138,7 +1210,7 @@ theorem IsStrongLimit.ne_zero {c} (h : IsStrongLimit c) : c ≠ 0 :=
 
 /- warning: cardinal.is_strong_limit.two_power_lt -> Cardinal.IsStrongLimit.two_power_lt is a dubious translation:
 lean 3 declaration is
-  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)
+  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)
 but is expected to have type
   forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.is_strong_limit.two_power_lt Cardinal.IsStrongLimit.two_power_ltₓ'. -/
@@ -1183,7 +1255,7 @@ theorem isStrongLimit_beth {o : Ordinal} (H : ∀ a < o, succ a < o) : IsStrongL
 
 /- warning: cardinal.mk_bounded_subset -> Cardinal.mk_bounded_subset is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) (Cardinal.mk.{u1} α))) -> (forall {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r], (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => Set.Bounded.{u1} α r s))) (Cardinal.mk.{u1} α)))
 but is expected to have type
   forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) (Cardinal.mk.{u1} α))) -> (forall {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r], (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => Set.Bounded.{u1} α r s))) (Cardinal.mk.{u1} α)))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_bounded_subset Cardinal.mk_bounded_subsetₓ'. -/
@@ -1219,7 +1291,7 @@ theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α
 
 /- warning: cardinal.mk_subset_mk_lt_cof -> Cardinal.mk_subset_mk_lt_cof is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) (Cardinal.mk.{u1} α))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)))))) (Cardinal.mk.{u1} α))
 but is expected to have type
   forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) (Cardinal.mk.{u1} α))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (Set.Elem.{u1} α s)) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)))))) (Cardinal.mk.{u1} α))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_subset_mk_lt_cof Cardinal.mk_subset_mk_lt_cofₓ'. -/
@@ -1263,11 +1335,15 @@ theorem IsRegular.cof_eq {c : Cardinal} (H : c.IsRegular) : c.ord.cof = c :=
 #align cardinal.is_regular.cof_eq Cardinal.IsRegular.cof_eq
 -/
 
-#print Cardinal.IsRegular.pos /-
+/- warning: cardinal.is_regular.pos -> Cardinal.IsRegular.pos is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1}))) c)
+but is expected to have type
+  forall {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1})) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.is_regular.pos Cardinal.IsRegular.posₓ'. -/
 theorem IsRegular.pos {c : Cardinal} (H : c.IsRegular) : 0 < c :=
   aleph0_pos.trans_le H.1
 #align cardinal.is_regular.pos Cardinal.IsRegular.pos
--/
 
 #print Cardinal.IsRegular.ord_pos /-
 theorem IsRegular.ord_pos {c : Cardinal} (H : c.IsRegular) : 0 < c.ord :=
@@ -1291,7 +1367,7 @@ theorem isRegular_aleph0 : IsRegular ℵ₀ :=
 
 /- warning: cardinal.is_regular_succ -> Cardinal.isRegular_succ is a dubious translation:
 lean 3 declaration is
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+  forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (Cardinal.IsRegular.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1}))))) Cardinal.succOrder.{u1} c))
 but is expected to have type
   forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} c) -> (Cardinal.IsRegular.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} c))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_regular_succ Cardinal.isRegular_succₓ'. -/
@@ -1345,7 +1421,12 @@ theorem isRegular_aleph_succ (o : Ordinal) : IsRegular (aleph (succ o)) :=
 #align cardinal.is_regular_aleph_succ Cardinal.isRegular_aleph_succ
 -/
 
-#print Cardinal.infinite_pigeonhole_card_lt /-
+/- warning: cardinal.infinite_pigeonhole_card_lt -> Cardinal.infinite_pigeonhole_card_lt is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} (Cardinal.mk.{u1} α)) -> (Exists.{succ u1} α (fun (a : α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a))))))
+but is expected to have type
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} (Cardinal.mk.{u1} α)) -> (Exists.{succ u1} α (fun (a : α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} (Set.Elem.{u1} β (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a))))))
+Case conversion may be inaccurate. Consider using '#align cardinal.infinite_pigeonhole_card_lt Cardinal.infinite_pigeonhole_card_ltₓ'. -/
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has a fiber with cardinality strictly great than the codomain.
 -/
@@ -1356,9 +1437,13 @@ theorem infinite_pigeonhole_card_lt {β α : Type u} (f : β → α) (w : (#α)
     Ordinal.infinite_pigeonhole_card f (succ (#α)) (succ_le_of_lt w) (w'.trans (lt_succ _).le)
       ((lt_succ _).trans_le (is_regular_succ w').2.ge)
 #align cardinal.infinite_pigeonhole_card_lt Cardinal.infinite_pigeonhole_card_lt
--/
 
-#print Cardinal.exists_infinite_fiber /-
+/- warning: cardinal.exists_infinite_fiber -> Cardinal.exists_infinite_fiber is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) -> (Infinite.{succ u1} α) -> (Exists.{succ u1} α (fun (a : α) => Infinite.{succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} β) Type.{u1} (Set.hasCoeToSort.{u1} β) (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) a)))))
+but is expected to have type
+  forall {β : Type.{u1}} {α : Type.{u1}} (f : β -> α), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) -> (Infinite.{succ u1} α) -> (Exists.{succ u1} α (fun (a : α) => Infinite.{succ u1} (Set.Elem.{u1} β (Set.preimage.{u1, u1} β α f (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) a)))))
+Case conversion may be inaccurate. Consider using '#align cardinal.exists_infinite_fiber Cardinal.exists_infinite_fiberₓ'. -/
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has an infinite fiber.
 -/
@@ -1369,7 +1454,6 @@ theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : (#α) < (#β
   cases' infinite_pigeonhole_card_lt f w w' with a ha
   exact ⟨a, w'.trans ha.le⟩
 #align cardinal.exists_infinite_fiber Cardinal.exists_infinite_fiber
--/
 
 /- warning: cardinal.le_range_of_union_finset_eq_top -> Cardinal.le_range_of_union_finset_eq_top is a dubious translation:
 lean 3 declaration is
@@ -1403,65 +1487,97 @@ theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α 
   exact (@Infinite.of_injective _ _ p (inclusion (v' a)) (inclusion_injective _)).False
 #align cardinal.le_range_of_union_finset_eq_top Cardinal.le_range_of_union_finset_eq_top
 
-#print Cardinal.lsub_lt_ord_lift_of_isRegular /-
+/- warning: cardinal.lsub_lt_ord_lift_of_is_regular -> Cardinal.lsub_lt_ord_lift_of_isRegular is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) (Cardinal.ord.{max u1 u2} c)) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.lsub.{u1, u2} ι f) (Cardinal.ord.{max u1 u2} c))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) (Cardinal.ord.{max u1 u2} c)) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u1 u2})) (Ordinal.lsub.{u1, u2} ι f) (Cardinal.ord.{max u1 u2} c))
+Case conversion may be inaccurate. Consider using '#align cardinal.lsub_lt_ord_lift_of_is_regular Cardinal.lsub_lt_ord_lift_of_isRegularₓ'. -/
 theorem lsub_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_lift_of_is_regular Cardinal.lsub_lt_ord_lift_of_isRegular
--/
 
-#print Cardinal.lsub_lt_ord_of_isRegular /-
+/- warning: cardinal.lsub_lt_ord_of_is_regular -> Cardinal.lsub_lt_ord_of_isRegular is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{max u1 u2}} {f : ι -> Ordinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (Cardinal.mk.{max u1 u2} ι) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i) (Cardinal.ord.{max u1 u2} c)) -> (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.lsub.{max u1 u2, u1} ι f) (Cardinal.ord.{max u1 u2} c))
+but is expected to have type
+  forall {ι : Type.{max u2 u1}} {f : ι -> Ordinal.{max u2 u1}} {c : Cardinal.{max u2 u1}}, (Cardinal.IsRegular.{max u2 u1} c) -> (LT.lt.{succ (max u2 u1)} Cardinal.{max u2 u1} (Preorder.toLT.{succ (max u2 u1)} Cardinal.{max u2 u1} (PartialOrder.toPreorder.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.partialOrder.{max u2 u1})) (Cardinal.mk.{max u2 u1} ι) c) -> (forall (i : ι), LT.lt.{succ (max u2 u1)} Ordinal.{max u2 u1} (Preorder.toLT.{succ (max u2 u1)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{succ (max u2 u1)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u2 u1})) (f i) (Cardinal.ord.{max u2 u1} c)) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u1 u2})) (Ordinal.lsub.{max u2 u1, u1} ι f) (Cardinal.ord.{max u1 u2} c))
+Case conversion may be inaccurate. Consider using '#align cardinal.lsub_lt_ord_of_is_regular Cardinal.lsub_lt_ord_of_isRegularₓ'. -/
 theorem lsub_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_of_is_regular Cardinal.lsub_lt_ord_of_isRegular
--/
 
-#print Cardinal.sup_lt_ord_lift_of_isRegular /-
+/- warning: cardinal.sup_lt_ord_lift_of_is_regular -> Cardinal.sup_lt_ord_lift_of_isRegular is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.sup_lt_ord_lift_of_is_regular Cardinal.sup_lt_ord_lift_of_isRegularₓ'. -/
 theorem sup_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_lift_of_is_regular Cardinal.sup_lt_ord_lift_of_isRegular
--/
 
-#print Cardinal.sup_lt_ord_of_isRegular /-
+/- warning: cardinal.sup_lt_ord_of_is_regular -> Cardinal.sup_lt_ord_of_isRegular is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.sup_lt_ord_of_is_regular Cardinal.sup_lt_ord_of_isRegularₓ'. -/
 theorem sup_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_of_is_regular Cardinal.sup_lt_ord_of_isRegular
--/
 
-#print Cardinal.blsub_lt_ord_lift_of_isRegular /-
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+Case conversion may be inaccurate. Consider using '#align cardinal.blsub_lt_ord_lift_of_is_regular Cardinal.blsub_lt_ord_lift_of_isRegularₓ'. -/
 theorem blsub_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (ho : Cardinal.lift o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.blsub o f < c.ord :=
   blsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.blsub_lt_ord_lift_of_is_regular Cardinal.blsub_lt_ord_lift_of_isRegular
--/
 
-#print Cardinal.blsub_lt_ord_of_isRegular /-
+/- warning: cardinal.blsub_lt_ord_of_is_regular -> Cardinal.blsub_lt_ord_of_isRegular is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.blsub_lt_ord_of_is_regular Cardinal.blsub_lt_ord_of_isRegularₓ'. -/
 theorem blsub_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (ho : o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.blsub o f < c.ord :=
   blsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.blsub_lt_ord_of_is_regular Cardinal.blsub_lt_ord_of_isRegular
--/
 
-#print Cardinal.bsup_lt_ord_lift_of_isRegular /-
+/- warning: cardinal.bsup_lt_ord_lift_of_is_regular -> Cardinal.bsup_lt_ord_lift_of_isRegular is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.bsup_lt_ord_lift_of_is_regular Cardinal.bsup_lt_ord_lift_of_isRegularₓ'. -/
 theorem bsup_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.bsup o f < c.ord :=
   bsup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_lift_of_is_regular Cardinal.bsup_lt_ord_lift_of_isRegular
--/
 
-#print Cardinal.bsup_lt_ord_of_isRegular /-
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+  forall {o : Ordinal.{max u2 u1}} {f : forall (a : Ordinal.{max u2 u1}), (LT.lt.{succ (max u2 u1)} Ordinal.{max u2 u1} (Preorder.toLT.{succ (max u2 u1)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{succ (max u2 u1)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u2 u1})) a o) -> Ordinal.{max u2 u1}} {c : Cardinal.{max u2 u1}}, (Cardinal.IsRegular.{max u2 u1} c) -> (LT.lt.{succ (max u2 u1)} Cardinal.{max u2 u1} (Preorder.toLT.{succ (max u2 u1)} Cardinal.{max u2 u1} (PartialOrder.toPreorder.{succ (max u2 u1)} Cardinal.{max u2 u1} Cardinal.partialOrder.{max u2 u1})) (Ordinal.card.{max u2 u1} o) c) -> (forall (i : Ordinal.{max u2 u1}) (hi : LT.lt.{succ (max u2 u1)} Ordinal.{max u2 u1} (Preorder.toLT.{succ (max u2 u1)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{succ (max u2 u1)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u2 u1})) i o), LT.lt.{succ (max u2 u1)} Ordinal.{max u2 u1} (Preorder.toLT.{succ (max u2 u1)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{succ (max u2 u1)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u2 u1})) (f i hi) (Cardinal.ord.{max u2 u1} c)) -> (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u1 u2})) (Ordinal.bsup.{max u2 u1, u1} o f) (Cardinal.ord.{max u1 u2} c))
+Case conversion may be inaccurate. Consider using '#align cardinal.bsup_lt_ord_of_is_regular Cardinal.bsup_lt_ord_of_isRegularₓ'. -/
 theorem bsup_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (hι : o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.bsup o f < c.ord :=
   bsup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_of_is_regular Cardinal.bsup_lt_ord_of_isRegular
--/
 
 /- warning: cardinal.supr_lt_lift_of_is_regular -> Cardinal.supᵢ_lt_lift_of_isRegular is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toSupSet.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{max u1 u2}))) ι f) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.supr_lt_lift_of_is_regular Cardinal.supᵢ_lt_lift_of_isRegularₓ'. -/
@@ -1472,7 +1588,7 @@ theorem supᵢ_lt_lift_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegul
 
 /- warning: cardinal.supr_lt_of_is_regular -> Cardinal.supᵢ_lt_of_isRegular is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
 but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toSupSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) ι f) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.supr_lt_of_is_regular Cardinal.supᵢ_lt_of_isRegularₓ'. -/
@@ -1481,21 +1597,34 @@ theorem supᵢ_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c)
   supᵢ_lt (by rwa [hc.cof_eq])
 #align cardinal.supr_lt_of_is_regular Cardinal.supᵢ_lt_of_isRegular
 
-#print Cardinal.sum_lt_lift_of_isRegular /-
+/- warning: cardinal.sum_lt_lift_of_is_regular -> Cardinal.sum_lt_lift_of_isRegular is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 u2)} Cardinal.{max u1 u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyOrderedCommSemiring.{max u1 u2})))))) (Cardinal.sum.{u1, max u1 u2} ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.sum.{u1, max u1 u2} ι f) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.sum_lt_lift_of_is_regular Cardinal.sum_lt_lift_of_isRegularₓ'. -/
 theorem sum_lt_lift_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : Cardinal.lift.{v, u} (#ι) < c) (hf : ∀ i, f i < c) : sum f < c :=
   (sum_le_supᵢ_lift _).trans_lt <| mul_lt_of_lt hc.1 hι (supᵢ_lt_lift_of_isRegular hc hι hf)
 #align cardinal.sum_lt_lift_of_is_regular Cardinal.sum_lt_lift_of_isRegular
--/
 
-#print Cardinal.sum_lt_of_isRegular /-
+/- warning: cardinal.sum_lt_of_is_regular -> Cardinal.sum_lt_of_isRegular is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (Cardinal.sum.{u1, u1} ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.sum.{u1, u1} ι f) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.sum_lt_of_is_regular Cardinal.sum_lt_of_isRegularₓ'. -/
 theorem sum_lt_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : (#ι) < c) : (∀ i, f i < c) → sum f < c :=
   sum_lt_lift_of_isRegular.{u, u} hc (by rwa [lift_id])
 #align cardinal.sum_lt_of_is_regular Cardinal.sum_lt_of_isRegular
--/
 
-#print Cardinal.nfpFamily_lt_ord_lift_of_isRegular /-
+/- warning: cardinal.nfp_family_lt_ord_lift_of_is_regular -> Cardinal.nfpFamily_lt_ord_lift_of_isRegular is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align cardinal.nfp_family_lt_ord_lift_of_is_regular Cardinal.nfpFamily_lt_ord_lift_of_isRegularₓ'. -/
 theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a}
     (ha : a < c.ord) : nfpFamily.{u, v} f a < c.ord :=
@@ -1503,33 +1632,44 @@ theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal}
   apply nfp_family_lt_ord_lift _ _ hf ha <;> rwa [hc.cof_eq]
   exact lt_of_le_of_ne hc.1 hc'.symm
 #align cardinal.nfp_family_lt_ord_lift_of_is_regular Cardinal.nfpFamily_lt_ord_lift_of_isRegular
--/
 
-#print Cardinal.nfpFamily_lt_ord_of_isRegular /-
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+Case conversion may be inaccurate. Consider using '#align cardinal.nfp_family_lt_ord_of_is_regular Cardinal.nfpFamily_lt_ord_of_isRegularₓ'. -/
 theorem nfpFamily_lt_ord_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι) < c) (hc' : c ≠ ℵ₀) {a} (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) :
     a < c.ord → nfpFamily.{u, u} f a < c.ord :=
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_family_lt_ord_of_is_regular Cardinal.nfpFamily_lt_ord_of_isRegular
--/
 
-#print Cardinal.nfpBFamily_lt_ord_lift_of_isRegular /-
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+Case conversion may be inaccurate. Consider using '#align cardinal.nfp_bfamily_lt_ord_lift_of_is_regular Cardinal.nfpBFamily_lt_ord_lift_of_isRegularₓ'. -/
 theorem nfpBFamily_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (ho : o.card.lift < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → nfpBFamily.{u, v} o f a < c.ord :=
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [mk_ordinal_out]) hc' fun i => hf _ _
 #align cardinal.nfp_bfamily_lt_ord_lift_of_is_regular Cardinal.nfpBFamily_lt_ord_lift_of_isRegular
--/
 
-#print Cardinal.nfpBFamily_lt_ord_of_isRegular /-
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+Case conversion may be inaccurate. Consider using '#align cardinal.nfp_bfamily_lt_ord_of_is_regular Cardinal.nfpBFamily_lt_ord_of_isRegularₓ'. -/
 theorem nfpBFamily_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (ho : o.card < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → nfpBFamily.{u, u} o f a < c.ord :=
   nfpBFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_bfamily_lt_ord_of_is_regular Cardinal.nfpBFamily_lt_ord_of_isRegular
--/
 
 #print Cardinal.nfp_lt_ord_of_isRegular /-
 theorem nfp_lt_ord_of_isRegular {f : Ordinal → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
@@ -1542,7 +1682,12 @@ theorem nfp_lt_ord_of_isRegular {f : Ordinal → Ordinal} {c} (hc : IsRegular c)
 #align cardinal.nfp_lt_ord_of_is_regular Cardinal.nfp_lt_ord_of_isRegular
 -/
 
-#print Cardinal.derivFamily_lt_ord_lift /-
+/- warning: cardinal.deriv_family_lt_ord_lift -> Cardinal.derivFamily_lt_ord_lift is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.deriv_family_lt_ord_lift Cardinal.derivFamily_lt_ord_liftₓ'. -/
 theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, v} f a < c.ord :=
@@ -1564,32 +1709,43 @@ theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc :
       bsup_lt_ord_of_is_regular hc (ord_lt_ord.1 ((ord_card_le b).trans_lt hb')) fun o' ho' =>
         H o' ho' (ho'.trans hb')
 #align cardinal.deriv_family_lt_ord_lift Cardinal.derivFamily_lt_ord_lift
--/
 
-#print Cardinal.derivFamily_lt_ord /-
+/- warning: cardinal.deriv_family_lt_ord -> Cardinal.derivFamily_lt_ord is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.deriv_family_lt_ord Cardinal.derivFamily_lt_ordₓ'. -/
 theorem derivFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c)
     (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, u} f a < c.ord :=
   derivFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf
 #align cardinal.deriv_family_lt_ord Cardinal.derivFamily_lt_ord
--/
 
-#print Cardinal.derivBFamily_lt_ord_lift /-
+/- warning: cardinal.deriv_bfamily_lt_ord_lift -> Cardinal.derivBFamily_lt_ord_lift is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.deriv_bfamily_lt_ord_lift Cardinal.derivBFamily_lt_ord_liftₓ'. -/
 theorem derivBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (hι : o.card.lift < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → derivBFamily.{u, v} o f a < c.ord :=
   derivFamily_lt_ord_lift hc (by rwa [mk_ordinal_out]) hc' fun i => hf _ _
 #align cardinal.deriv_bfamily_lt_ord_lift Cardinal.derivBFamily_lt_ord_lift
--/
 
-#print Cardinal.derivBFamily_lt_ord /-
+/- warning: cardinal.deriv_bfamily_lt_ord -> Cardinal.derivBFamily_lt_ord is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.deriv_bfamily_lt_ord Cardinal.derivBFamily_lt_ordₓ'. -/
 theorem derivBFamily_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : o.card < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → derivBFamily.{u, u} o f a < c.ord :=
   derivBFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf
 #align cardinal.deriv_bfamily_lt_ord Cardinal.derivBFamily_lt_ord
--/
 
 #print Cardinal.deriv_lt_ord /-
 theorem deriv_lt_ord {f : Ordinal.{u} → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
@@ -1608,7 +1764,7 @@ def IsInaccessible (c : Cardinal) :=
 
 /- warning: cardinal.is_inaccessible.mk -> Cardinal.IsInaccessible.mk is a dubious translation:
 lean 3 declaration is
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+  forall {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) Cardinal.aleph0.{u1} c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)) -> (Cardinal.IsInaccessible.{u1} c)
 but is expected to have type
   forall {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) c)) -> (Cardinal.IsInaccessible.{u1} c)
 Case conversion may be inaccurate. Consider using '#align cardinal.is_inaccessible.mk Cardinal.IsInaccessible.mkₓ'. -/
@@ -1628,7 +1784,12 @@ theorem univ_inaccessible : IsInaccessible univ.{u, v} :=
 #align cardinal.univ_inaccessible Cardinal.univ_inaccessible
 -/
 
-#print Cardinal.lt_power_cof /-
+/- warning: cardinal.lt_power_cof -> Cardinal.lt_power_cof is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) c (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))))
+but is expected to have type
+  forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))))
+Case conversion may be inaccurate. Consider using '#align cardinal.lt_power_cof Cardinal.lt_power_cofₓ'. -/
 theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
   Quotient.inductionOn c fun α h =>
     by
@@ -1648,9 +1809,13 @@ theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
     · have := typein_lt_type r i
       rwa [← re, lt_ord] at this
 #align cardinal.lt_power_cof Cardinal.lt_power_cof
--/
 
-#print Cardinal.lt_cof_power /-
+/- warning: cardinal.lt_cof_power -> Cardinal.lt_cof_power is a dubious translation:
+lean 3 declaration is
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (OfNat.mk.{succ u1} Cardinal.{u1} 1 (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1}))) b) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) a (Ordinal.cof.{u1} (Cardinal.ord.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) b a))))
+but is expected to have type
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (One.toOfNat1.{succ u1} Cardinal.{u1} Cardinal.instOneCardinal.{u1})) b) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a (Ordinal.cof.{u1} (Cardinal.ord.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) b a))))
+Case conversion may be inaccurate. Consider using '#align cardinal.lt_cof_power Cardinal.lt_cof_powerₓ'. -/
 theorem lt_cof_power {a b : Cardinal} (ha : ℵ₀ ≤ a) (b1 : 1 < b) : a < cof (b^a).ord :=
   by
   have b0 : b ≠ 0 := (zero_lt_one.trans b1).ne'
@@ -1658,7 +1823,6 @@ theorem lt_cof_power {a b : Cardinal} (ha : ℵ₀ ≤ a) (b1 : 1 < b) : a < cof
   rw [← power_mul, mul_eq_self ha]
   exact lt_power_cof (ha.trans <| (cantor' _ b1).le)
 #align cardinal.lt_cof_power Cardinal.lt_cof_power
--/
 
 end Cardinal

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: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.cofinality
-! leanprover-community/mathlib commit bb168510ef455e9280a152e7f31673cabd3d7496
+! 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.Ordinal.FixedPoint
 /-!
 # Cofinality
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains the definition of cofinality of an ordinal number and regular cardinals
 
 ## Main Definitions

bb168510

bump to nightly-2023-02-25-00

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

aca219f8

Diff

@@ -64,22 +64,42 @@ variable {α : Type _} {r : α → α → Prop}
 
 namespace Order
 
+#print Order.cof /-
 /-- Cofinality of a reflexive order `≼`. This is the smallest cardinality
   of a subset `S : set α` such that `∀ a, ∃ b ∈ S, a ≼ b`. -/
 def cof (r : α → α → Prop) : Cardinal :=
   infₛ { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c }
 #align order.cof Order.cof
+-/
 
+/- warning: order.cof_nonempty -> Order.cof_nonempty is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsRefl.{u1} α r], Set.Nonempty.{succ u1} Cardinal.{u1} (setOf.{succ u1} Cardinal.{u1} (fun (c : Cardinal.{u1}) => Exists.{succ u1} (Set.{u1} α) (fun (S : Set.{u1} α) => And (forall (a : α), Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b S) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b S) => r a b))) (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) S)) c))))
+but is expected to have type
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsRefl.{u1} α r], Set.Nonempty.{succ u1} Cardinal.{u1} (setOf.{succ u1} Cardinal.{u1} (fun (c : Cardinal.{u1}) => Exists.{succ u1} (Set.{u1} α) (fun (S : Set.{u1} α) => And (forall (a : α), Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b S) (r a b))) (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Set.Elem.{u1} α S)) c))))
+Case conversion may be inaccurate. Consider using '#align order.cof_nonempty Order.cof_nonemptyₓ'. -/
 /-- The set in the definition of `order.cof` is nonempty. -/
 theorem cof_nonempty (r : α → α → Prop) [IsRefl α r] :
     { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c }.Nonempty :=
   ⟨_, Set.univ, fun a => ⟨a, ⟨⟩, refl _⟩, rfl⟩
 #align order.cof_nonempty Order.cof_nonempty
 
+/- warning: order.cof_le -> Order.cof_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) {S : Set.{u1} α}, (forall (a : α), Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b S) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b S) => r a b))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Order.cof.{u1} α r) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) S)))
+but is expected to have type
+  forall {α : Type.{u1}} (r : α -> α -> Prop) {S : Set.{u1} α}, (forall (a : α), Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b S) (r a b))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Order.cof.{u1} α r) (Cardinal.mk.{u1} (Set.Elem.{u1} α S)))
+Case conversion may be inaccurate. Consider using '#align order.cof_le Order.cof_leₓ'. -/
 theorem cof_le (r : α → α → Prop) {S : Set α} (h : ∀ a, ∃ b ∈ S, r a b) : cof r ≤ (#S) :=
   cinfₛ_le' ⟨S, h, rfl⟩
 #align order.cof_le Order.cof_le
 
+/- warning: order.le_cof -> Order.le_cof is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {r : α -> α -> Prop} [_inst_1 : IsRefl.{u1} α r] (c : Cardinal.{u1}), Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} c (Order.cof.{u1} α r)) (forall {S : Set.{u1} α}, (forall (a : α), Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b S) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b S) => r a b))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} c (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) S))))
+but is expected to have type
+  forall {α : Type.{u1}} {r : α -> α -> Prop} [_inst_1 : IsRefl.{u1} α r] (c : Cardinal.{u1}), Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} c (Order.cof.{u1} α r)) (forall {S : Set.{u1} α}, (forall (a : α), Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b S) (r a b))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} c (Cardinal.mk.{u1} (Set.Elem.{u1} α S))))
+Case conversion may be inaccurate. Consider using '#align order.le_cof Order.le_cofₓ'. -/
 theorem le_cof {r : α → α → Prop} [IsRefl α r] (c : Cardinal) :
     c ≤ cof r ↔ ∀ {S : Set α}, (∀ a, ∃ b ∈ S, r a b) → c ≤ (#S) :=
   by
@@ -91,6 +111,7 @@ theorem le_cof {r : α → α → Prop} [IsRefl α r] (c : Cardinal) :
 
 end Order
 
+#print RelIso.cof_le_lift /-
 theorem RelIso.cof_le_lift {α : Type u} {β : Type v} {r : α → α → Prop} {s} [IsRefl β s]
     (f : r ≃r s) : Cardinal.lift.{max u v} (Order.cof r) ≤ Cardinal.lift.{max u v} (Order.cof s) :=
   by
@@ -105,39 +126,51 @@ theorem RelIso.cof_le_lift {α : Type u} {β : Type v} {r : α → α → Prop}
   refine' ⟨f.symm b, mem_image_of_mem _ hb, f.map_rel_iff.1 _⟩
   rwa [RelIso.apply_symm_apply]
 #align rel_iso.cof_le_lift RelIso.cof_le_lift
+-/
 
+#print RelIso.cof_eq_lift /-
 theorem RelIso.cof_eq_lift {α : Type u} {β : Type v} {r s} [IsRefl α r] [IsRefl β s] (f : r ≃r s) :
     Cardinal.lift.{max u v} (Order.cof r) = Cardinal.lift.{max u v} (Order.cof s) :=
   (RelIso.cof_le_lift f).antisymm (RelIso.cof_le_lift f.symm)
 #align rel_iso.cof_eq_lift RelIso.cof_eq_lift
+-/
 
+#print RelIso.cof_le /-
 theorem RelIso.cof_le {α β : Type u} {r : α → α → Prop} {s} [IsRefl β s] (f : r ≃r s) :
     Order.cof r ≤ Order.cof s :=
   lift_le.1 (RelIso.cof_le_lift f)
 #align rel_iso.cof_le RelIso.cof_le
+-/
 
+#print RelIso.cof_eq /-
 theorem RelIso.cof_eq {α β : Type u} {r s} [IsRefl α r] [IsRefl β s] (f : r ≃r s) :
     Order.cof r = Order.cof s :=
   lift_inj.1 (RelIso.cof_eq_lift f)
 #align rel_iso.cof_eq RelIso.cof_eq
+-/
 
+#print StrictOrder.cof /-
 /-- Cofinality of a strict order `≺`. This is the smallest cardinality of a set `S : set α` such
 that `∀ a, ∃ b ∈ S, ¬ b ≺ a`. -/
 def StrictOrder.cof (r : α → α → Prop) : Cardinal :=
   Order.cof (swap rᶜ)
 #align strict_order.cof StrictOrder.cof
+-/
 
+#print StrictOrder.cof_nonempty /-
 /-- The set in the definition of `order.strict_order.cof` is nonempty. -/
 theorem StrictOrder.cof_nonempty (r : α → α → Prop) [IsIrrefl α r] :
     { c | ∃ S : Set α, Unbounded r S ∧ (#S) = c }.Nonempty :=
   @Order.cof_nonempty α _ (IsRefl.swap (rᶜ))
 #align strict_order.cof_nonempty StrictOrder.cof_nonempty
+-/
 
 /-! ### Cofinality of ordinals -/
 
 
 namespace Ordinal
 
+#print Ordinal.cof /-
 /-- Cofinality of an ordinal. This is the smallest cardinal of a
   subset `S` of the ordinal which is unbounded, in the sense
   `∀ a, ∃ b ∈ S, a ≤ b`. It is defined for all ordinals, but
@@ -154,30 +187,42 @@ def cof (o : Ordinal.{u}) : Cardinal.{u} :=
       · exact ⟨(IsWellOrder.isIrrefl r).1⟩
       · exact ⟨(IsWellOrder.isIrrefl s).1⟩)
 #align ordinal.cof Ordinal.cof
+-/
 
+#print Ordinal.cof_type /-
 theorem cof_type (r : α → α → Prop) [IsWellOrder α r] : (type r).cof = StrictOrder.cof r :=
   rfl
 #align ordinal.cof_type Ordinal.cof_type
+-/
 
+#print Ordinal.le_cof_type /-
 theorem le_cof_type [IsWellOrder α r] {c} : c ≤ cof (type r) ↔ ∀ S, Unbounded r S → c ≤ (#S) :=
   (le_cinfₛ_iff'' (StrictOrder.cof_nonempty r)).trans
     ⟨fun H S h => H _ ⟨S, h, rfl⟩, by
       rintro H d ⟨S, h, rfl⟩
       exact H _ h⟩
 #align ordinal.le_cof_type Ordinal.le_cof_type
+-/
 
+#print Ordinal.cof_type_le /-
 theorem cof_type_le [IsWellOrder α r] {S : Set α} (h : Unbounded r S) : cof (type r) ≤ (#S) :=
   le_cof_type.1 le_rfl S h
 #align ordinal.cof_type_le Ordinal.cof_type_le
+-/
 
+#print Ordinal.lt_cof_type /-
 theorem lt_cof_type [IsWellOrder α r] {S : Set α} : (#S) < cof (type r) → Bounded r S := by
   simpa using not_imp_not.2 cof_type_le
 #align ordinal.lt_cof_type Ordinal.lt_cof_type
+-/
 
+#print Ordinal.cof_eq /-
 theorem cof_eq (r : α → α → Prop) [IsWellOrder α r] : ∃ S, Unbounded r S ∧ (#S) = cof (type r) :=
   cinfₛ_mem (StrictOrder.cof_nonempty r)
 #align ordinal.cof_eq Ordinal.cof_eq
+-/
 
+#print Ordinal.ord_cof_eq /-
 theorem ord_cof_eq (r : α → α → Prop) [IsWellOrder α r] :
     ∃ S, Unbounded r S ∧ type (Subrel r S) = (cof (type r)).ord :=
   by
@@ -214,6 +259,7 @@ theorem ord_cof_eq (r : α → α → Prop) [IsWellOrder α r] :
     rw [show ∀ b : S, (⟨b, b.2⟩ : S) = b by intro b <;> cases b <;> rfl]
     exact IsWellFounded.wf.not_lt_min _ this (IsOrderConnected.neg_trans h ba)
 #align ordinal.ord_cof_eq Ordinal.ord_cof_eq
+-/
 
 /-! ### Cofinality of suprema and least strict upper bounds -/
 
@@ -222,12 +268,20 @@ private theorem card_mem_cof {o} : ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u}
   ⟨_, _, lsub_typein o, mk_ordinal_out o⟩
 #align ordinal.card_mem_cof ordinal.card_mem_cof
 
+#print Ordinal.cof_lsub_def_nonempty /-
 /-- The set in the `lsub` characterization of `cof` is nonempty. -/
 theorem cof_lsub_def_nonempty (o) :
     { a : Cardinal | ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a }.Nonempty :=
   ⟨_, card_mem_cof⟩
 #align ordinal.cof_lsub_def_nonempty Ordinal.cof_lsub_def_nonempty
+-/
 
+/- warning: ordinal.cof_eq_Inf_lsub -> Ordinal.cof_eq_infₛ_lsub is a dubious translation:
+lean 3 declaration is
+  forall (o : Ordinal.{u1}), Eq.{succ (succ u1)} Cardinal.{u1} (Ordinal.cof.{u1} o) (InfSet.infₛ.{succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasInf.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) (setOf.{succ u1} Cardinal.{u1} (fun (a : Cardinal.{u1}) => Exists.{succ (succ u1)} Type.{u1} (fun {ι : Type.{u1}} => Exists.{succ (succ u1)} (ι -> Ordinal.{u1}) (fun (f : ι -> Ordinal.{u1}) => And (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.lsub.{u1, u1} ι f) o) (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} ι) a))))))
+but is expected to have type
+  forall (o : Ordinal.{u1}), Eq.{succ (succ u1)} Cardinal.{u1} (Ordinal.cof.{u1} o) (InfSet.infₛ.{succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toInfSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) (setOf.{succ u1} Cardinal.{u1} (fun (a : Cardinal.{u1}) => Exists.{succ (succ u1)} Type.{u1} (fun (ι : Type.{u1}) => Exists.{succ (succ u1)} (ι -> Ordinal.{u1}) (fun (f : ι -> Ordinal.{u1}) => And (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.lsub.{u1, u1} ι f) o) (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} ι) a))))))
+Case conversion may be inaccurate. Consider using '#align ordinal.cof_eq_Inf_lsub Ordinal.cof_eq_infₛ_lsubₓ'. -/
 theorem cof_eq_infₛ_lsub (o : Ordinal.{u}) :
     cof o = infₛ { a : Cardinal | ∃ (ι : Type u)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } :=
   by
@@ -263,6 +317,12 @@ theorem cof_eq_infₛ_lsub (o : Ordinal.{u}) :
     exact hb'.trans_lt (lt_lsub.{u, u} f ⟨b, hb⟩)
 #align ordinal.cof_eq_Inf_lsub Ordinal.cof_eq_infₛ_lsub
 
+/- warning: ordinal.lift_cof -> Ordinal.lift_cof is a dubious translation:
+lean 3 declaration is
+  forall (o : Ordinal.{u1}), Eq.{succ (succ (max u1 u2))} Cardinal.{max u1 u2} (Cardinal.lift.{u2, u1} (Ordinal.cof.{u1} o)) (Ordinal.cof.{max u1 u2} (Ordinal.lift.{u2, u1} o))
+but is expected to have type
+  forall (o : Ordinal.{u2}), Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u2 u1} (Cardinal.lift.{u1, u2} (Ordinal.cof.{u2} o)) (Ordinal.cof.{max u1 u2} (Ordinal.lift.{u1, u2} o))
+Case conversion may be inaccurate. Consider using '#align ordinal.lift_cof Ordinal.lift_cofₓ'. -/
 @[simp]
 theorem lift_cof (o) : (cof o).lift = cof o.lift :=
   by
@@ -289,32 +349,43 @@ theorem lift_cof (o) : (cof o).lift = cof o.lift :=
       ⟨⟨b⟩, bs, br⟩
 #align ordinal.lift_cof Ordinal.lift_cof
 
+#print Ordinal.cof_le_card /-
 theorem cof_le_card (o) : cof o ≤ card o :=
   by
   rw [cof_eq_Inf_lsub]
   exact cinfₛ_le' card_mem_cof
 #align ordinal.cof_le_card Ordinal.cof_le_card
+-/
 
+#print Ordinal.cof_ord_le /-
 theorem cof_ord_le (c : Cardinal) : c.ord.cof ≤ c := by simpa using cof_le_card c.ord
 #align ordinal.cof_ord_le Ordinal.cof_ord_le
+-/
 
+#print Ordinal.ord_cof_le /-
 theorem ord_cof_le (o : Ordinal.{u}) : o.cof.ord ≤ o :=
   (ord_le_ord.2 (cof_le_card o)).trans (ord_card_le o)
 #align ordinal.ord_cof_le Ordinal.ord_cof_le
+-/
 
+#print Ordinal.exists_lsub_cof /-
 theorem exists_lsub_cof (o : Ordinal) :
     ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = cof o :=
   by
   rw [cof_eq_Inf_lsub]
   exact cinfₛ_mem (cof_lsub_def_nonempty o)
 #align ordinal.exists_lsub_cof Ordinal.exists_lsub_cof
+-/
 
+#print Ordinal.cof_lsub_le /-
 theorem cof_lsub_le {ι} (f : ι → Ordinal) : cof (lsub.{u, u} f) ≤ (#ι) :=
   by
   rw [cof_eq_Inf_lsub]
   exact cinfₛ_le' ⟨ι, f, rfl, rfl⟩
 #align ordinal.cof_lsub_le Ordinal.cof_lsub_le
+-/
 
+#print Ordinal.cof_lsub_le_lift /-
 theorem cof_lsub_le_lift {ι} (f : ι → Ordinal) : cof (lsub f) ≤ Cardinal.lift.{v, u} (#ι) :=
   by
   rw [← mk_ulift]
@@ -323,7 +394,9 @@ theorem cof_lsub_le_lift {ι} (f : ι → Ordinal) : cof (lsub f) ≤ Cardinal.l
     lsub_eq_of_range_eq.{u, max u v, max u v}
       (Set.ext fun x => ⟨fun ⟨i, hi⟩ => ⟨ULift.up i, hi⟩, fun ⟨i, hi⟩ => ⟨_, hi⟩⟩)
 #align ordinal.cof_lsub_le_lift Ordinal.cof_lsub_le_lift
+-/
 
+#print Ordinal.le_cof_iff_lsub /-
 theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
     a ≤ cof o ↔ ∀ {ι} (f : ι → Ordinal), lsub.{u, u} f = o → a ≤ (#ι) :=
   by
@@ -335,42 +408,61 @@ theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
         rw [← hb]
         exact H _ hf⟩
 #align ordinal.le_cof_iff_lsub Ordinal.le_cof_iff_lsub
+-/
 
+#print Ordinal.lsub_lt_ord_lift /-
 theorem lsub_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : lsub.{u, v} f < c :=
   lt_of_le_of_ne (lsub_le hf) fun h => by
     subst h
     exact (cof_lsub_le_lift f).not_lt hι
 #align ordinal.lsub_lt_ord_lift Ordinal.lsub_lt_ord_lift
+-/
 
+#print Ordinal.lsub_lt_ord /-
 theorem lsub_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
     (∀ i, f i < c) → lsub.{u, u} f < c :=
   lsub_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.lsub_lt_ord Ordinal.lsub_lt_ord
+-/
 
+#print Ordinal.cof_sup_le_lift /-
 theorem cof_sup_le_lift {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup f) : cof (sup f) ≤ (#ι).lift :=
   by
   rw [← sup_eq_lsub_iff_lt_sup] at H
   rw [H]
   exact cof_lsub_le_lift f
 #align ordinal.cof_sup_le_lift Ordinal.cof_sup_le_lift
+-/
 
+#print Ordinal.cof_sup_le /-
 theorem cof_sup_le {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup.{u, u} f) :
     cof (sup.{u, u} f) ≤ (#ι) := by
   rw [← (#ι).lift_id]
   exact cof_sup_le_lift H
 #align ordinal.cof_sup_le Ordinal.cof_sup_le
+-/
 
+#print Ordinal.sup_lt_ord_lift /-
 theorem sup_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift (#ι) < c.cof)
     (hf : ∀ i, f i < c) : sup.{u, v} f < c :=
   (sup_le_lsub.{u, v} f).trans_lt (lsub_lt_ord_lift hι hf)
 #align ordinal.sup_lt_ord_lift Ordinal.sup_lt_ord_lift
+-/
 
+#print Ordinal.sup_lt_ord /-
 theorem sup_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
     (∀ i, f i < c) → sup.{u, u} f < c :=
   sup_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.sup_lt_ord Ordinal.sup_lt_ord
+-/
 
+/- warning: ordinal.supr_lt_lift -> Ordinal.supᵢ_lt_lift is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) (Ordinal.cof.{max u1 u2} (Cardinal.ord.{max u1 u2} c))) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toSupSet.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{max u1 u2}))) ι f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.supr_lt_lift Ordinal.supᵢ_lt_liftₓ'. -/
 theorem supᵢ_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal} (hι : Cardinal.lift (#ι) < c.ord.cof)
     (hf : ∀ i, f i < c) : supᵢ f < c :=
   by
@@ -380,11 +472,18 @@ theorem supᵢ_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal} (hι : Cardinal
   apply hf
 #align ordinal.supr_lt_lift Ordinal.supᵢ_lt_lift
 
+/- warning: ordinal.supr_lt -> Ordinal.supᵢ_lt is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toSupSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) ι f) c)
+Case conversion may be inaccurate. Consider using '#align ordinal.supr_lt Ordinal.supᵢ_ltₓ'. -/
 theorem supᵢ_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : (#ι) < c.ord.cof) :
     (∀ i, f i < c) → supᵢ f < c :=
   supᵢ_lt_lift (by rwa [(#ι).lift_id])
 #align ordinal.supr_lt Ordinal.supᵢ_lt
 
+#print Ordinal.nfpFamily_lt_ord_lift /-
 theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : (#ι).lift < cof c) (hf : ∀ (i), ∀ b < c, f i b < c) {a} (ha : a < c) :
     nfpFamily.{u, v} f a < c :=
@@ -397,29 +496,39 @@ theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : 
     · exact ha
     · exact hf _ _ H
 #align ordinal.nfp_family_lt_ord_lift Ordinal.nfpFamily_lt_ord_lift
+-/
 
+#print Ordinal.nfpFamily_lt_ord /-
 theorem nfpFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hc' : (#ι) < cof c)
     (hf : ∀ (i), ∀ b < c, f i b < c) {a} : a < c → nfpFamily.{u, u} f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [(#ι).lift_id]) hf
 #align ordinal.nfp_family_lt_ord Ordinal.nfpFamily_lt_ord
+-/
 
+#print Ordinal.nfpBFamily_lt_ord_lift /-
 theorem nfpBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : o.card.lift < cof c) (hf : ∀ (i hi), ∀ b < c, f i hi b < c) {a} :
     a < c → nfpBFamily.{u, v} o f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [mk_ordinal_out]) fun i => hf _ _
 #align ordinal.nfp_bfamily_lt_ord_lift Ordinal.nfpBFamily_lt_ord_lift
+-/
 
+#print Ordinal.nfpBFamily_lt_ord /-
 theorem nfpBFamily_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : o.card < cof c) (hf : ∀ (i hi), ∀ b < c, f i hi b < c) {a} :
     a < c → nfpBFamily.{u, u} o f a < c :=
   nfpBFamily_lt_ord_lift hc (by rwa [o.card.lift_id]) hf
 #align ordinal.nfp_bfamily_lt_ord Ordinal.nfpBFamily_lt_ord
+-/
 
+#print Ordinal.nfp_lt_ord /-
 theorem nfp_lt_ord {f : Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hf : ∀ i < c, f i < c) {a} :
     a < c → nfp f a < c :=
   nfpFamily_lt_ord_lift hc (by simpa using cardinal.one_lt_aleph_0.trans hc) fun _ => hf
 #align ordinal.nfp_lt_ord Ordinal.nfp_lt_ord
+-/
 
+#print Ordinal.exists_blsub_cof /-
 theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, blsub.{u, u} _ f = o :=
   by
   rcases exists_lsub_cof o with ⟨ι, f, hf, hι⟩
@@ -428,7 +537,9 @@ theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, b
   rw [← hι, hι']
   exact ⟨_, hf⟩
 #align ordinal.exists_blsub_cof Ordinal.exists_blsub_cof
+-/
 
+#print Ordinal.le_cof_iff_blsub /-
 theorem le_cof_iff_blsub {b : Ordinal} {a : Cardinal} :
     a ≤ cof b ↔ ∀ {o} (f : ∀ a < o, Ordinal), blsub.{u, u} o f = b → a ≤ o.card :=
   le_cof_iff_lsub.trans
@@ -438,31 +549,41 @@ theorem le_cof_iff_blsub {b : Ordinal} {a : Cardinal} :
       rw [← @blsub_eq_lsub' ι r hr] at hf
       simpa using H _ hf⟩
 #align ordinal.le_cof_iff_blsub Ordinal.le_cof_iff_blsub
+-/
 
+#print Ordinal.cof_blsub_le_lift /-
 theorem cof_blsub_le_lift {o} (f : ∀ a < o, Ordinal) :
     cof (blsub o f) ≤ Cardinal.lift.{v, u} o.card :=
   by
   convert cof_lsub_le_lift _
   exact (mk_ordinal_out o).symm
 #align ordinal.cof_blsub_le_lift Ordinal.cof_blsub_le_lift
+-/
 
+#print Ordinal.cof_blsub_le /-
 theorem cof_blsub_le {o} (f : ∀ a < o, Ordinal) : cof (blsub.{u, u} o f) ≤ o.card :=
   by
   rw [← o.card.lift_id]
   exact cof_blsub_le_lift f
 #align ordinal.cof_blsub_le Ordinal.cof_blsub_le
+-/
 
+#print Ordinal.blsub_lt_ord_lift /-
 theorem blsub_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : o.card.lift < c.cof) (hf : ∀ i hi, f i hi < c) : blsub.{u, v} o f < c :=
   lt_of_le_of_ne (blsub_le hf) fun h =>
     ho.not_le (by simpa [← supr_ord, hf, h] using cof_blsub_le_lift.{u} f)
 #align ordinal.blsub_lt_ord_lift Ordinal.blsub_lt_ord_lift
+-/
 
+#print Ordinal.blsub_lt_ord /-
 theorem blsub_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof)
     (hf : ∀ i hi, f i hi < c) : blsub.{u, u} o f < c :=
   blsub_lt_ord_lift (by rwa [o.card.lift_id]) hf
 #align ordinal.blsub_lt_ord Ordinal.blsub_lt_ord
+-/
 
+#print Ordinal.cof_bsup_le_lift /-
 theorem cof_bsup_le_lift {o : Ordinal} {f : ∀ a < o, Ordinal} (H : ∀ i h, f i h < bsup o f) :
     cof (bsup o f) ≤ o.card.lift :=
   by
@@ -470,32 +591,42 @@ theorem cof_bsup_le_lift {o : Ordinal} {f : ∀ a < o, Ordinal} (H : ∀ i h, f
   rw [H]
   exact cof_blsub_le_lift f
 #align ordinal.cof_bsup_le_lift Ordinal.cof_bsup_le_lift
+-/
 
+#print Ordinal.cof_bsup_le /-
 theorem cof_bsup_le {o : Ordinal} {f : ∀ a < o, Ordinal} :
     (∀ i h, f i h < bsup.{u, u} o f) → cof (bsup.{u, u} o f) ≤ o.card :=
   by
   rw [← o.card.lift_id]
   exact cof_bsup_le_lift
 #align ordinal.cof_bsup_le Ordinal.cof_bsup_le
+-/
 
+#print Ordinal.bsup_lt_ord_lift /-
 theorem bsup_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : o.card.lift < c.cof) (hf : ∀ i hi, f i hi < c) : bsup.{u, v} o f < c :=
   (bsup_le_blsub f).trans_lt (blsub_lt_ord_lift ho hf)
 #align ordinal.bsup_lt_ord_lift Ordinal.bsup_lt_ord_lift
+-/
 
+#print Ordinal.bsup_lt_ord /-
 theorem bsup_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof) :
     (∀ i hi, f i hi < c) → bsup.{u, u} o f < c :=
   bsup_lt_ord_lift (by rwa [o.card.lift_id])
 #align ordinal.bsup_lt_ord Ordinal.bsup_lt_ord
+-/
 
 /-! ### Basic results -/
 
 
+#print Ordinal.cof_zero /-
 @[simp]
 theorem cof_zero : cof 0 = 0 :=
   (cof_le_card 0).antisymm (Cardinal.zero_le _)
 #align ordinal.cof_zero Ordinal.cof_zero
+-/
 
+#print Ordinal.cof_eq_zero /-
 @[simp]
 theorem cof_eq_zero {o} : cof o = 0 ↔ o = 0 :=
   ⟨inductionOn o fun α r _ z =>
@@ -506,11 +637,15 @@ theorem cof_eq_zero {o} : cof o = 0 ↔ o = 0 :=
           (mk_eq_zero_iff.1 (e.trans z)).elim' ⟨_, h⟩⟩,
     fun e => by simp [e]⟩
 #align ordinal.cof_eq_zero Ordinal.cof_eq_zero
+-/
 
+#print Ordinal.cof_ne_zero /-
 theorem cof_ne_zero {o} : cof o ≠ 0 ↔ o ≠ 0 :=
   cof_eq_zero.Not
 #align ordinal.cof_ne_zero Ordinal.cof_ne_zero
+-/
 
+#print Ordinal.cof_succ /-
 @[simp]
 theorem cof_succ (o) : cof (succ o) = 1 :=
   by
@@ -527,7 +662,9 @@ theorem cof_succ (o) : cof (succ o) = 1 :=
     simpa [lt_iff_le_and_ne, Cardinal.zero_le] using fun h =>
       succ_ne_zero o (cof_eq_zero.1 (Eq.symm h))
 #align ordinal.cof_succ Ordinal.cof_succ
+-/
 
+#print Ordinal.cof_eq_one_iff_is_succ /-
 @[simp]
 theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
   ⟨inductionOn o fun α r _ z => by
@@ -555,32 +692,42 @@ theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
           apply Subsingleton.elim,
     fun ⟨a, e⟩ => by simp [e]⟩
 #align ordinal.cof_eq_one_iff_is_succ Ordinal.cof_eq_one_iff_is_succ
+-/
 
+#print Ordinal.IsFundamentalSequence /-
 /-- A fundamental sequence for `a` is an increasing sequence of length `o = cof a` that converges at
     `a`. We provide `o` explicitly in order to avoid type rewrites. -/
 def IsFundamentalSequence (a o : Ordinal.{u}) (f : ∀ b < o, Ordinal.{u}) : Prop :=
   o ≤ a.cof.ord ∧ (∀ {i j} (hi hj), i < j → f i hi < f j hj) ∧ blsub.{u, u} o f = a
 #align ordinal.is_fundamental_sequence Ordinal.IsFundamentalSequence
+-/
 
 namespace IsFundamentalSequence
 
 variable {a o : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}}
 
+#print Ordinal.IsFundamentalSequence.cof_eq /-
 protected theorem cof_eq (hf : IsFundamentalSequence a o f) : a.cof.ord = o :=
   hf.1.antisymm' <| by
     rw [← hf.2.2]
     exact (ord_le_ord.2 (cof_blsub_le f)).trans (ord_card_le o)
 #align ordinal.is_fundamental_sequence.cof_eq Ordinal.IsFundamentalSequence.cof_eq
+-/
 
+#print Ordinal.IsFundamentalSequence.strict_mono /-
 protected theorem strict_mono (hf : IsFundamentalSequence a o f) {i j} :
     ∀ hi hj, i < j → f i hi < f j hj :=
   hf.2.1
 #align ordinal.is_fundamental_sequence.strict_mono Ordinal.IsFundamentalSequence.strict_mono
+-/
 
+#print Ordinal.IsFundamentalSequence.blsub_eq /-
 theorem blsub_eq (hf : IsFundamentalSequence a o f) : blsub.{u, u} o f = a :=
   hf.2.2
 #align ordinal.is_fundamental_sequence.blsub_eq Ordinal.IsFundamentalSequence.blsub_eq
+-/
 
+#print Ordinal.IsFundamentalSequence.ord_cof /-
 theorem ord_cof (hf : IsFundamentalSequence a o f) :
     IsFundamentalSequence a a.cof.ord fun i hi => f i (hi.trans_le (by rw [hf.cof_eq])) :=
   by
@@ -588,15 +735,26 @@ theorem ord_cof (hf : IsFundamentalSequence a o f) :
   subst H
   exact hf
 #align ordinal.is_fundamental_sequence.ord_cof Ordinal.IsFundamentalSequence.ord_cof
+-/
 
+#print Ordinal.IsFundamentalSequence.id_of_le_cof /-
 theorem id_of_le_cof (h : o ≤ o.cof.ord) : IsFundamentalSequence o o fun a _ => a :=
   ⟨h, fun _ _ _ _ => id, blsub_id o⟩
 #align ordinal.is_fundamental_sequence.id_of_le_cof Ordinal.IsFundamentalSequence.id_of_le_cof
+-/
 
+#print Ordinal.IsFundamentalSequence.zero /-
 protected theorem zero {f : ∀ b < (0 : Ordinal), Ordinal} : IsFundamentalSequence 0 0 f :=
   ⟨by rw [cof_zero, ord_zero], fun i j hi => (Ordinal.not_lt_zero i hi).elim, blsub_zero f⟩
 #align ordinal.is_fundamental_sequence.zero Ordinal.IsFundamentalSequence.zero
+-/
 
+/- warning: ordinal.is_fundamental_sequence.succ -> Ordinal.IsFundamentalSequence.succ is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, Ordinal.IsFundamentalSequence.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))) (fun (_x : Ordinal.{u1}) (_x : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _x (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) => o)
+but is expected to have type
+  forall {o : Ordinal.{u1}}, Ordinal.IsFundamentalSequence.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})) (fun (_x : Ordinal.{u1}) (_x : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _x (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) => o)
+Case conversion may be inaccurate. Consider using '#align ordinal.is_fundamental_sequence.succ Ordinal.IsFundamentalSequence.succₓ'. -/
 protected theorem succ : IsFundamentalSequence (succ o) 1 fun _ _ => o :=
   by
   refine' ⟨_, fun i j hi hj h => _, blsub_const Ordinal.one_ne_zero o⟩
@@ -606,6 +764,7 @@ protected theorem succ : IsFundamentalSequence (succ o) 1 fun _ _ => o :=
     exact h.false.elim
 #align ordinal.is_fundamental_sequence.succ Ordinal.IsFundamentalSequence.succ
 
+#print Ordinal.IsFundamentalSequence.monotone /-
 protected theorem monotone (hf : IsFundamentalSequence a o f) {i j : Ordinal} (hi : i < o)
     (hj : j < o) (hij : i ≤ j) : f i hi ≤ f j hj :=
   by
@@ -613,7 +772,9 @@ protected theorem monotone (hf : IsFundamentalSequence a o f) {i j : Ordinal} (h
   · exact (hf.2.1 hi hj hij).le
   · rfl
 #align ordinal.is_fundamental_sequence.monotone Ordinal.IsFundamentalSequence.monotone
+-/
 
+#print Ordinal.IsFundamentalSequence.trans /-
 theorem trans {a o o' : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}} (hf : IsFundamentalSequence a o f)
     {g : ∀ b < o', Ordinal.{u}} (hg : IsFundamentalSequence o o' g) :
     IsFundamentalSequence a o' fun i hi =>
@@ -628,9 +789,11 @@ theorem trans {a o o' : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}} (hf : IsFundam
   · rw [@blsub_comp.{u, u, u} o _ f (@is_fundamental_sequence.monotone _ _ f hf)]
     exact hf.2.2
 #align ordinal.is_fundamental_sequence.trans Ordinal.IsFundamentalSequence.trans
+-/
 
 end IsFundamentalSequence
 
+#print Ordinal.exists_fundamental_sequence /-
 /-- Every ordinal has a fundamental sequence. -/
 theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequence a a.cof.ord f :=
   by
@@ -663,7 +826,9 @@ theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequ
         exact (wo.wf.not_lt_min _ h ⟨IsTrans.trans _ _ _ hkj hji, H⟩) hkj
       · rwa [bfamily_of_family'_typein]
 #align ordinal.exists_fundamental_sequence Ordinal.exists_fundamental_sequence
+-/
 
+#print Ordinal.cof_cof /-
 @[simp]
 theorem cof_cof (a : Ordinal.{u}) : cof (cof a).ord = cof a :=
   by
@@ -671,7 +836,9 @@ theorem cof_cof (a : Ordinal.{u}) : cof (cof a).ord = cof a :=
   cases' exists_fundamental_sequence a.cof.ord with g hg
   exact ord_injective (hf.trans hg).cof_eq.symm
 #align ordinal.cof_cof Ordinal.cof_cof
+-/
 
+#print Ordinal.IsNormal.isFundamentalSequence /-
 protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u}} (hf : IsNormal f)
     {a o} (ha : IsLimit a) {g} (hg : IsFundamentalSequence a o g) :
     IsFundamentalSequence (f a) o fun b hb => f (g b hb) :=
@@ -701,12 +868,16 @@ protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u
         hg.2.2]
     exact IsNormal.blsub_eq.{u, u} hf ha
 #align ordinal.is_normal.is_fundamental_sequence Ordinal.IsNormal.isFundamentalSequence
+-/
 
+#print Ordinal.IsNormal.cof_eq /-
 theorem IsNormal.cof_eq {f} (hf : IsNormal f) {a} (ha : IsLimit a) : cof (f a) = cof a :=
   let ⟨g, hg⟩ := exists_fundamental_sequence a
   ord_injective (hf.IsFundamentalSequence ha hg).cof_eq
 #align ordinal.is_normal.cof_eq Ordinal.IsNormal.cof_eq
+-/
 
+#print Ordinal.IsNormal.cof_le /-
 theorem IsNormal.cof_le {f} (hf : IsNormal f) (a) : cof a ≤ cof (f a) :=
   by
   rcases zero_or_succ_or_limit a with (rfl | ⟨b, rfl⟩ | ha)
@@ -716,7 +887,9 @@ theorem IsNormal.cof_le {f} (hf : IsNormal f) (a) : cof a ≤ cof (f a) :=
     exact (Ordinal.zero_le (f b)).trans_lt (hf.1 b)
   · rw [hf.cof_eq ha]
 #align ordinal.is_normal.cof_le Ordinal.IsNormal.cof_le
+-/
 
+#print Ordinal.cof_add /-
 @[simp]
 theorem cof_add (a b : Ordinal) : b ≠ 0 → cof (a + b) = cof b := fun h =>
   by
@@ -725,7 +898,9 @@ theorem cof_add (a b : Ordinal) : b ≠ 0 → cof (a + b) = cof b := fun h =>
   · rw [add_succ, cof_succ, cof_succ]
   · exact (add_is_normal a).cof_eq hb
 #align ordinal.cof_add Ordinal.cof_add
+-/
 
+#print Ordinal.aleph0_le_cof /-
 theorem aleph0_le_cof {o} : ℵ₀ ≤ cof o ↔ IsLimit o :=
   by
   rcases zero_or_succ_or_limit o with (rfl | ⟨o, rfl⟩ | l)
@@ -744,17 +919,23 @@ theorem aleph0_le_cof {o} : ℵ₀ ≤ cof o ↔ IsLimit o :=
       rcases e with ⟨a, rfl⟩
       exact not_succ_is_limit _ l
 #align ordinal.aleph_0_le_cof Ordinal.aleph0_le_cof
+-/
 
+#print Ordinal.aleph'_cof /-
 @[simp]
 theorem aleph'_cof {o : Ordinal} (ho : o.IsLimit) : (aleph' o).ord.cof = o.cof :=
   aleph'_isNormal.cof_eq ho
 #align ordinal.aleph'_cof Ordinal.aleph'_cof
+-/
 
+#print Ordinal.aleph_cof /-
 @[simp]
 theorem aleph_cof {o : Ordinal} (ho : o.IsLimit) : (aleph o).ord.cof = o.cof :=
   aleph_isNormal.cof_eq ho
 #align ordinal.aleph_cof Ordinal.aleph_cof
+-/
 
+#print Ordinal.cof_omega /-
 @[simp]
 theorem cof_omega : cof ω = ℵ₀ :=
   (aleph0_le_cof.2 omega_isLimit).antisymm' <|
@@ -762,7 +943,14 @@ theorem cof_omega : cof ω = ℵ₀ :=
     rw [← card_omega]
     apply cof_le_card
 #align ordinal.cof_omega Ordinal.cof_omega
+-/
 
+/- warning: ordinal.cof_eq' -> Ordinal.cof_eq' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], (Ordinal.IsLimit.{u1} (Ordinal.type.{u1} α r _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (S : Set.{u1} α) => And (forall (a : α), Exists.{succ u1} α (fun (b : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b S) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b S) => r a b))) (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) S)) (Ordinal.cof.{u1} (Ordinal.type.{u1} α r _inst_1)))))
+but is expected to have type
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], (Ordinal.IsLimit.{u1} (Ordinal.type.{u1} α r _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (S : Set.{u1} α) => And (forall (a : α), Exists.{succ u1} α (fun (b : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b S) (r a b))) (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Set.Elem.{u1} α S)) (Ordinal.cof.{u1} (Ordinal.type.{u1} α r _inst_1)))))
+Case conversion may be inaccurate. Consider using '#align ordinal.cof_eq' Ordinal.cof_eq'ₓ'. -/
 theorem cof_eq' (r : α → α → Prop) [IsWellOrder α r] (h : IsLimit (type r)) :
     ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = cof (type r) :=
   let ⟨S, H, e⟩ := cof_eq r
@@ -779,6 +967,7 @@ theorem cof_eq' (r : α → α → Prop) [IsWellOrder α r] (h : IsLimit (type r
     e⟩
 #align ordinal.cof_eq' Ordinal.cof_eq'
 
+#print Ordinal.cof_univ /-
 @[simp]
 theorem cof_univ : cof univ.{u, v} = Cardinal.univ :=
   le_antisymm (cof_le_card _)
@@ -799,10 +988,17 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ :=
       rw [← show g (f.symm ⟨b, h⟩) = b by dsimp [g] <;> simp]
       apply le_sup)
 #align ordinal.cof_univ Ordinal.cof_univ
+-/
 
 /-! ### Infinite pigeonhole principle -/
 
 
+/- warning: ordinal.unbounded_of_unbounded_sUnion -> Ordinal.unbounded_of_unbounded_unionₛ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.unionₛ.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} (Set.{u1} α)) Type.{u1} (Set.hasCoeToSort.{u1} (Set.{u1} α)) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.hasMem.{u1} (Set.{u1} α)) x s) => Set.Unbounded.{u1} α r x)))
+but is expected to have type
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [wo : IsWellOrder.{u1} α r] {s : Set.{u1} (Set.{u1} α)}, (Set.Unbounded.{u1} α r (Set.unionₛ.{u1} α s)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (Set.Elem.{u1} (Set.{u1} α) s)) (StrictOrder.cof.{u1} α r)) -> (Exists.{succ u1} (Set.{u1} α) (fun (x : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Set.{u1} (Set.{u1} α)) (Set.instMembershipSet.{u1} (Set.{u1} α)) x s) (Set.Unbounded.{u1} α r x)))
+Case conversion may be inaccurate. Consider using '#align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_unionₛₓ'. -/
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
 theorem unbounded_of_unbounded_unionₛ (r : α → α → Prop) [wo : IsWellOrder α r] {s : Set (Set α)}
@@ -816,6 +1012,7 @@ theorem unbounded_of_unbounded_unionₛ (r : α → α → Prop) [wo : IsWellOrd
   exact ⟨f ⟨c, hc⟩, mem_range_self _, fun hxz => hxy (trans (wo.wf.lt_sup _ hy) hxz)⟩
 #align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_unionₛ
 
+#print Ordinal.unbounded_of_unbounded_unionᵢ /-
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
 theorem unbounded_of_unbounded_unionᵢ {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
@@ -825,7 +1022,9 @@ theorem unbounded_of_unbounded_unionᵢ {α β : Type u} (r : α → α → Prop
   rcases unbounded_of_unbounded_sUnion r h₁ (mk_range_le.trans_lt h₂) with ⟨_, ⟨x, rfl⟩, u⟩
   exact ⟨x, u⟩
 #align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_unionᵢ
+-/
 
+#print Ordinal.infinite_pigeonhole /-
 /-- The infinite pigeonhole principle -/
 theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤ (#β)) (h₂ : (#α) < (#β).ord.cof) :
     ∃ a : α, (#f ⁻¹' {a}) = (#β) :=
@@ -842,7 +1041,9 @@ theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤
   rw [le_mk_iff_exists_set]
   exact ⟨_, rfl⟩
 #align ordinal.infinite_pigeonhole Ordinal.infinite_pigeonhole
+-/
 
+#print Ordinal.infinite_pigeonhole_card /-
 /-- Pigeonhole principle for a cardinality below the cardinality of the domain -/
 theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal) (hθ : θ ≤ (#β))
     (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) : ∃ a : α, θ ≤ (#f ⁻¹' {a}) :=
@@ -852,7 +1053,9 @@ theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal
   use a; rw [← ha, @preimage_comp _ _ _ Subtype.val f]
   exact mk_preimage_of_injective _ _ Subtype.val_injective
 #align ordinal.infinite_pigeonhole_card Ordinal.infinite_pigeonhole_card
+-/
 
+#print Ordinal.infinite_pigeonhole_set /-
 theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ : Cardinal)
     (hθ : θ ≤ (#s)) (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) :
     ∃ (a : α)(t : Set β)(h : t ⊆ s), θ ≤ (#t) ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a :=
@@ -868,6 +1071,7 @@ theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ
     simp only [coe_eq_subtype, mem_singleton_iff, mem_preimage, mem_set_of_eq]
   rintro x ⟨hx, hx'⟩; exact hx'
 #align ordinal.infinite_pigeonhole_set Ordinal.infinite_pigeonhole_set
+-/
 
 end Ordinal
 
@@ -881,20 +1085,31 @@ open Ordinal
 -- mathport name: cardinal.pow
 local infixr:0 "^" => @pow Cardinal.{u} Cardinal Cardinal.hasPow
 
+#print Cardinal.IsLimit /-
 /-- A cardinal is a limit if it is not zero or a successor
   cardinal. Note that `ℵ₀` is a limit cardinal by this definition. -/
 def IsLimit (c : Cardinal) : Prop :=
   c ≠ 0 ∧ ∀ x < c, succ x < c
 #align cardinal.is_limit Cardinal.IsLimit
+-/
 
+#print Cardinal.IsLimit.ne_zero /-
 theorem IsLimit.ne_zero {c} (h : IsLimit c) : c ≠ 0 :=
   h.1
 #align cardinal.is_limit.ne_zero Cardinal.IsLimit.ne_zero
+-/
 
+/- warning: cardinal.is_limit.succ_lt -> Cardinal.IsLimit.succ_lt is a dubious translation:
+lean 3 declaration is
+  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.succOrder.{u1} x) c)
+but is expected to have type
+  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} x) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.is_limit.succ_lt Cardinal.IsLimit.succ_ltₓ'. -/
 theorem IsLimit.succ_lt {x c} (h : IsLimit c) : x < c → succ x < c :=
   h.2 x
 #align cardinal.is_limit.succ_lt Cardinal.IsLimit.succ_lt
 
+#print Cardinal.IsLimit.aleph0_le /-
 theorem IsLimit.aleph0_le {c} (h : IsLimit c) : ℵ₀ ≤ c :=
   by
   by_contra' h'
@@ -902,35 +1117,53 @@ theorem IsLimit.aleph0_le {c} (h : IsLimit c) : ℵ₀ ≤ c :=
   · exact h.1.irrefl
   · simpa using h.2 n
 #align cardinal.is_limit.aleph_0_le Cardinal.IsLimit.aleph0_le
+-/
 
+#print Cardinal.IsStrongLimit /-
 /-- A cardinal is a strong limit if it is not zero and it is
   closed under powersets. Note that `ℵ₀` is a strong limit by this definition. -/
 def IsStrongLimit (c : Cardinal) : Prop :=
   c ≠ 0 ∧ ∀ x < c, (2^x) < c
 #align cardinal.is_strong_limit Cardinal.IsStrongLimit
+-/
 
+#print Cardinal.IsStrongLimit.ne_zero /-
 theorem IsStrongLimit.ne_zero {c} (h : IsStrongLimit c) : c ≠ 0 :=
   h.1
 #align cardinal.is_strong_limit.ne_zero Cardinal.IsStrongLimit.ne_zero
+-/
 
+/- warning: cardinal.is_strong_limit.two_power_lt -> Cardinal.IsStrongLimit.two_power_lt is a dubious translation:
+lean 3 declaration is
+  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)
+but is expected to have type
+  forall {x : Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsStrongLimit.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.is_strong_limit.two_power_lt Cardinal.IsStrongLimit.two_power_ltₓ'. -/
 theorem IsStrongLimit.two_power_lt {x c} (h : IsStrongLimit c) : x < c → (2^x) < c :=
   h.2 x
 #align cardinal.is_strong_limit.two_power_lt Cardinal.IsStrongLimit.two_power_lt
 
+#print Cardinal.isStrongLimit_aleph0 /-
 theorem isStrongLimit_aleph0 : IsStrongLimit ℵ₀ :=
   ⟨aleph0_ne_zero, fun x hx => by
     rcases lt_aleph_0.1 hx with ⟨n, rfl⟩
     exact_mod_cast nat_lt_aleph_0 (pow 2 n)⟩
 #align cardinal.is_strong_limit_aleph_0 Cardinal.isStrongLimit_aleph0
+-/
 
+#print Cardinal.IsStrongLimit.isLimit /-
 theorem IsStrongLimit.isLimit {c} (H : IsStrongLimit c) : IsLimit c :=
   ⟨H.1, fun x h => (succ_le_of_lt <| cantor x).trans_lt (H.2 _ h)⟩
 #align cardinal.is_strong_limit.is_limit Cardinal.IsStrongLimit.isLimit
+-/
 
+#print Cardinal.isLimit_aleph0 /-
 theorem isLimit_aleph0 : IsLimit ℵ₀ :=
   isStrongLimit_aleph0.IsLimit
 #align cardinal.is_limit_aleph_0 Cardinal.isLimit_aleph0
+-/
 
+#print Cardinal.isStrongLimit_beth /-
 theorem isStrongLimit_beth {o : Ordinal} (H : ∀ a < o, succ a < o) : IsStrongLimit (beth o) :=
   by
   rcases eq_or_ne o 0 with (rfl | h)
@@ -943,7 +1176,14 @@ theorem isStrongLimit_beth {o : Ordinal} (H : ∀ a < o, succ a < o) : IsStrongL
     rw [← beth_succ] at this
     exact this.trans_lt (beth_lt.2 (H i hi))
 #align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_beth
+-/
 
+/- warning: cardinal.mk_bounded_subset -> Cardinal.mk_bounded_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) (Cardinal.mk.{u1} α))) -> (forall {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r], (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => Set.Bounded.{u1} α r s))) (Cardinal.mk.{u1} α)))
+but is expected to have type
+  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) (Cardinal.mk.{u1} α))) -> (forall {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r], (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => Set.Bounded.{u1} α r s))) (Cardinal.mk.{u1} α)))
+Case conversion may be inaccurate. Consider using '#align cardinal.mk_bounded_subset Cardinal.mk_bounded_subsetₓ'. -/
 theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α → α → Prop}
     [IsWellOrder α r] (hr : (#α).ord = type r) : (#{ s : Set α // Bounded r s }) = (#α) :=
   by
@@ -974,6 +1214,12 @@ theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α
       simpa only [singleton_eq_singleton_iff] using hab
 #align cardinal.mk_bounded_subset Cardinal.mk_bounded_subset
 
+/- warning: cardinal.mk_subset_mk_lt_cof -> Cardinal.mk_subset_mk_lt_cof is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}}, (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x (Cardinal.mk.{u1} α)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) (Cardinal.mk.{u1} α))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Ordinal.cof.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)))))) (Cardinal.mk.{u1} α))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align cardinal.mk_subset_mk_lt_cof Cardinal.mk_subset_mk_lt_cofₓ'. -/
 theorem mk_subset_mk_lt_cof {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) :
     (#{ s : Set α // (#s) < cof (#α).ord }) = (#α) :=
   by
@@ -995,37 +1241,57 @@ theorem mk_subset_mk_lt_cof {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) :
       simpa only [singleton_eq_singleton_iff] using hab
 #align cardinal.mk_subset_mk_lt_cof Cardinal.mk_subset_mk_lt_cof
 
+#print Cardinal.IsRegular /-
 /-- A cardinal is regular if it is infinite and it equals its own cofinality. -/
 def IsRegular (c : Cardinal) : Prop :=
   ℵ₀ ≤ c ∧ c ≤ c.ord.cof
 #align cardinal.is_regular Cardinal.IsRegular
+-/
 
+#print Cardinal.IsRegular.aleph0_le /-
 theorem IsRegular.aleph0_le {c : Cardinal} (H : c.IsRegular) : ℵ₀ ≤ c :=
   H.1
 #align cardinal.is_regular.aleph_0_le Cardinal.IsRegular.aleph0_le
+-/
 
+#print Cardinal.IsRegular.cof_eq /-
 theorem IsRegular.cof_eq {c : Cardinal} (H : c.IsRegular) : c.ord.cof = c :=
   (cof_ord_le c).antisymm H.2
 #align cardinal.is_regular.cof_eq Cardinal.IsRegular.cof_eq
+-/
 
+#print Cardinal.IsRegular.pos /-
 theorem IsRegular.pos {c : Cardinal} (H : c.IsRegular) : 0 < c :=
   aleph0_pos.trans_le H.1
 #align cardinal.is_regular.pos Cardinal.IsRegular.pos
+-/
 
+#print Cardinal.IsRegular.ord_pos /-
 theorem IsRegular.ord_pos {c : Cardinal} (H : c.IsRegular) : 0 < c.ord :=
   by
   rw [Cardinal.lt_ord]
   exact H.pos
 #align cardinal.is_regular.ord_pos Cardinal.IsRegular.ord_pos
+-/
 
+#print Cardinal.isRegular_cof /-
 theorem isRegular_cof {o : Ordinal} (h : o.IsLimit) : IsRegular o.cof :=
   ⟨aleph0_le_cof.2 h, (cof_cof o).ge⟩
 #align cardinal.is_regular_cof Cardinal.isRegular_cof
+-/
 
+#print Cardinal.isRegular_aleph0 /-
 theorem isRegular_aleph0 : IsRegular ℵ₀ :=
   ⟨le_rfl, by simp⟩
 #align cardinal.is_regular_aleph_0 Cardinal.isRegular_aleph0
+-/
 
+/- warning: cardinal.is_regular_succ -> Cardinal.isRegular_succ is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (Cardinal.IsRegular.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.succOrder.{u1} c))
+but is expected to have type
+  forall {c : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} c) -> (Cardinal.IsRegular.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} c))
+Case conversion may be inaccurate. Consider using '#align cardinal.is_regular_succ Cardinal.isRegular_succₓ'. -/
 theorem isRegular_succ {c : Cardinal.{u}} (h : ℵ₀ ≤ c) : IsRegular (succ c) :=
   ⟨h.trans (le_succ c),
     succ_le_of_lt
@@ -1048,24 +1314,35 @@ theorem isRegular_succ {c : Cardinal.{u}} (h : ℵ₀ ≤ c) : IsRegular (succ c
           apply typein_lt_type)⟩
 #align cardinal.is_regular_succ Cardinal.isRegular_succ
 
+/- warning: cardinal.is_regular_aleph_one -> Cardinal.isRegular_aleph_one is a dubious translation:
+lean 3 declaration is
+  Cardinal.IsRegular.{u1} (Cardinal.aleph.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))
+but is expected to have type
+  Cardinal.IsRegular.{u1} (Cardinal.aleph.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))
+Case conversion may be inaccurate. Consider using '#align cardinal.is_regular_aleph_one Cardinal.isRegular_aleph_oneₓ'. -/
 theorem isRegular_aleph_one : IsRegular (aleph 1) :=
   by
   rw [← succ_aleph_0]
   exact is_regular_succ le_rfl
 #align cardinal.is_regular_aleph_one Cardinal.isRegular_aleph_one
 
+#print Cardinal.isRegular_aleph'_succ /-
 theorem isRegular_aleph'_succ {o : Ordinal} (h : ω ≤ o) : IsRegular (aleph' (succ o)) :=
   by
   rw [aleph'_succ]
   exact is_regular_succ (aleph_0_le_aleph'.2 h)
 #align cardinal.is_regular_aleph'_succ Cardinal.isRegular_aleph'_succ
+-/
 
+#print Cardinal.isRegular_aleph_succ /-
 theorem isRegular_aleph_succ (o : Ordinal) : IsRegular (aleph (succ o)) :=
   by
   rw [aleph_succ]
   exact is_regular_succ (aleph_0_le_aleph o)
 #align cardinal.is_regular_aleph_succ Cardinal.isRegular_aleph_succ
+-/
 
+#print Cardinal.infinite_pigeonhole_card_lt /-
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has a fiber with cardinality strictly great than the codomain.
 -/
@@ -1076,7 +1353,9 @@ theorem infinite_pigeonhole_card_lt {β α : Type u} (f : β → α) (w : (#α)
     Ordinal.infinite_pigeonhole_card f (succ (#α)) (succ_le_of_lt w) (w'.trans (lt_succ _).le)
       ((lt_succ _).trans_le (is_regular_succ w').2.ge)
 #align cardinal.infinite_pigeonhole_card_lt Cardinal.infinite_pigeonhole_card_lt
+-/
 
+#print Cardinal.exists_infinite_fiber /-
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has an infinite fiber.
 -/
@@ -1087,7 +1366,14 @@ theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : (#α) < (#β
   cases' infinite_pigeonhole_card_lt f w w' with a ha
   exact ⟨a, w'.trans ha.le⟩
 #align cardinal.exists_infinite_fiber Cardinal.exists_infinite_fiber
+-/
 
+/- warning: cardinal.le_range_of_union_finset_eq_top -> Cardinal.le_range_of_union_finset_eq_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : Infinite.{succ u2} β] (f : α -> (Finset.{u2} β)), (Eq.{succ u2} (Set.{u2} β) (Set.unionᵢ.{u2, succ u1} β α (fun (a : α) => (fun (a : Type.{u2}) (b : Type.{u2}) [self : HasLiftT.{succ u2, succ u2} a b] => self.0) (Finset.{u2} β) (Set.{u2} β) (HasLiftT.mk.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (CoeTCₓ.coe.{succ u2, succ u2} (Finset.{u2} β) (Set.{u2} β) (Finset.Set.hasCoeT.{u2} β))) (f a))) (Top.top.{u2} (Set.{u2} β) (CompleteLattice.toHasTop.{u2} (Set.{u2} β) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} β) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} β) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} β) (Set.completeBooleanAlgebra.{u2} β))))))) -> (LE.le.{succ u2} Cardinal.{u2} Cardinal.hasLe.{u2} (Cardinal.mk.{u2} β) (Cardinal.mk.{u2} (coeSort.{succ u2, succ (succ u2)} (Set.{u2} (Finset.{u2} β)) Type.{u2} (Set.hasCoeToSort.{u2} (Finset.{u2} β)) (Set.range.{u2, succ u1} (Finset.{u2} β) α f))))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : Infinite.{succ u1} β] (f : α -> (Finset.{u1} β)), (Eq.{succ u1} (Set.{u1} β) (Set.unionᵢ.{u1, succ u2} β α (fun (a : α) => Finset.toSet.{u1} β (f a))) (Top.top.{u1} (Set.{u1} β) (CompleteLattice.toTop.{u1} (Set.{u1} β) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} β) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} β) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} β) (Set.instCompleteBooleanAlgebraSet.{u1} β))))))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} β) (Cardinal.mk.{u1} (Set.Elem.{u1} (Finset.{u1} β) (Set.range.{u1, succ u2} (Finset.{u1} β) α f))))
+Case conversion may be inaccurate. Consider using '#align cardinal.le_range_of_union_finset_eq_top Cardinal.le_range_of_union_finset_eq_topₓ'. -/
 /-- If an infinite type `β` can be expressed as a union of finite sets,
 then the cardinality of the collection of those finite sets
 must be at least the cardinality of `β`.
@@ -1114,66 +1400,99 @@ theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α 
   exact (@Infinite.of_injective _ _ p (inclusion (v' a)) (inclusion_injective _)).False
 #align cardinal.le_range_of_union_finset_eq_top Cardinal.le_range_of_union_finset_eq_top
 
+#print Cardinal.lsub_lt_ord_lift_of_isRegular /-
 theorem lsub_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_lift_of_is_regular Cardinal.lsub_lt_ord_lift_of_isRegular
+-/
 
+#print Cardinal.lsub_lt_ord_of_isRegular /-
 theorem lsub_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_of_is_regular Cardinal.lsub_lt_ord_of_isRegular
+-/
 
+#print Cardinal.sup_lt_ord_lift_of_isRegular /-
 theorem sup_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_lift_of_is_regular Cardinal.sup_lt_ord_lift_of_isRegular
+-/
 
+#print Cardinal.sup_lt_ord_of_isRegular /-
 theorem sup_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_of_is_regular Cardinal.sup_lt_ord_of_isRegular
+-/
 
+#print Cardinal.blsub_lt_ord_lift_of_isRegular /-
 theorem blsub_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (ho : Cardinal.lift o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.blsub o f < c.ord :=
   blsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.blsub_lt_ord_lift_of_is_regular Cardinal.blsub_lt_ord_lift_of_isRegular
+-/
 
+#print Cardinal.blsub_lt_ord_of_isRegular /-
 theorem blsub_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (ho : o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.blsub o f < c.ord :=
   blsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.blsub_lt_ord_of_is_regular Cardinal.blsub_lt_ord_of_isRegular
+-/
 
+#print Cardinal.bsup_lt_ord_lift_of_isRegular /-
 theorem bsup_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.bsup o f < c.ord :=
   bsup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_lift_of_is_regular Cardinal.bsup_lt_ord_lift_of_isRegular
+-/
 
+#print Cardinal.bsup_lt_ord_of_isRegular /-
 theorem bsup_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc : IsRegular c)
     (hι : o.card < c) : (∀ i hi, f i hi < c.ord) → Ordinal.bsup o f < c.ord :=
   bsup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_of_is_regular Cardinal.bsup_lt_ord_of_isRegular
+-/
 
+/- warning: cardinal.supr_lt_lift_of_is_regular -> Cardinal.supᵢ_lt_lift_of_isRegular is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toHasSup.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ (max u1 u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.conditionallyCompleteLinearOrderBot.{max u1 u2}))) ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{max u1 u2}} {c : Cardinal.{max u1 u2}}, (Cardinal.IsRegular.{max u1 u2} c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} ι)) c) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (f i) c) -> (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (supᵢ.{succ (max u1 u2), succ u1} Cardinal.{max u1 u2} (ConditionallyCompleteLattice.toSupSet.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{max u1 u2}))) ι f) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.supr_lt_lift_of_is_regular Cardinal.supᵢ_lt_lift_of_isRegularₓ'. -/
 theorem supᵢ_lt_lift_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift (#ι) < c) : (∀ i, f i < c) → supᵢ f < c :=
   supᵢ_lt_lift (by rwa [hc.cof_eq])
 #align cardinal.supr_lt_lift_of_is_regular Cardinal.supᵢ_lt_lift_of_isRegular
 
+/- warning: cardinal.supr_lt_of_is_regular -> Cardinal.supᵢ_lt_of_isRegular is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toHasSup.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.conditionallyCompleteLinearOrderBot.{u1}))) ι f) c)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Cardinal.{u1}} {c : Cardinal.{u1}}, (Cardinal.IsRegular.{u1} c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.mk.{u1} ι) c) -> (forall (i : ι), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (f i) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (supᵢ.{succ u1, succ u1} Cardinal.{u1} (ConditionallyCompleteLattice.toSupSet.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Cardinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Cardinal.{u1} Cardinal.instConditionallyCompleteLinearOrderBotCardinal.{u1}))) ι f) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.supr_lt_of_is_regular Cardinal.supᵢ_lt_of_isRegularₓ'. -/
 theorem supᵢ_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
     (∀ i, f i < c) → supᵢ f < c :=
   supᵢ_lt (by rwa [hc.cof_eq])
 #align cardinal.supr_lt_of_is_regular Cardinal.supᵢ_lt_of_isRegular
 
+#print Cardinal.sum_lt_lift_of_isRegular /-
 theorem sum_lt_lift_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : Cardinal.lift.{v, u} (#ι) < c) (hf : ∀ i, f i < c) : sum f < c :=
   (sum_le_supᵢ_lift _).trans_lt <| mul_lt_of_lt hc.1 hι (supᵢ_lt_lift_of_isRegular hc hι hf)
 #align cardinal.sum_lt_lift_of_is_regular Cardinal.sum_lt_lift_of_isRegular
+-/
 
+#print Cardinal.sum_lt_of_isRegular /-
 theorem sum_lt_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : (#ι) < c) : (∀ i, f i < c) → sum f < c :=
   sum_lt_lift_of_isRegular.{u, u} hc (by rwa [lift_id])
 #align cardinal.sum_lt_of_is_regular Cardinal.sum_lt_of_isRegular
+-/
 
+#print Cardinal.nfpFamily_lt_ord_lift_of_isRegular /-
 theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a}
     (ha : a < c.ord) : nfpFamily.{u, v} f a < c.ord :=
@@ -1181,27 +1500,35 @@ theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal}
   apply nfp_family_lt_ord_lift _ _ hf ha <;> rwa [hc.cof_eq]
   exact lt_of_le_of_ne hc.1 hc'.symm
 #align cardinal.nfp_family_lt_ord_lift_of_is_regular Cardinal.nfpFamily_lt_ord_lift_of_isRegular
+-/
 
+#print Cardinal.nfpFamily_lt_ord_of_isRegular /-
 theorem nfpFamily_lt_ord_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι) < c) (hc' : c ≠ ℵ₀) {a} (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) :
     a < c.ord → nfpFamily.{u, u} f a < c.ord :=
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_family_lt_ord_of_is_regular Cardinal.nfpFamily_lt_ord_of_isRegular
+-/
 
+#print Cardinal.nfpBFamily_lt_ord_lift_of_isRegular /-
 theorem nfpBFamily_lt_ord_lift_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (ho : o.card.lift < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → nfpBFamily.{u, v} o f a < c.ord :=
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [mk_ordinal_out]) hc' fun i => hf _ _
 #align cardinal.nfp_bfamily_lt_ord_lift_of_is_regular Cardinal.nfpBFamily_lt_ord_lift_of_isRegular
+-/
 
+#print Cardinal.nfpBFamily_lt_ord_of_isRegular /-
 theorem nfpBFamily_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (ho : o.card < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → nfpBFamily.{u, u} o f a < c.ord :=
   nfpBFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_bfamily_lt_ord_of_is_regular Cardinal.nfpBFamily_lt_ord_of_isRegular
+-/
 
+#print Cardinal.nfp_lt_ord_of_isRegular /-
 theorem nfp_lt_ord_of_isRegular {f : Ordinal → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
     (hf : ∀ i < c.ord, f i < c.ord) {a} : a < c.ord → nfp f a < c.ord :=
   nfp_lt_ord
@@ -1210,7 +1537,9 @@ theorem nfp_lt_ord_of_isRegular {f : Ordinal → Ordinal} {c} (hc : IsRegular c)
       exact lt_of_le_of_ne hc.1 hc'.symm)
     hf
 #align cardinal.nfp_lt_ord_of_is_regular Cardinal.nfp_lt_ord_of_isRegular
+-/
 
+#print Cardinal.derivFamily_lt_ord_lift /-
 theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : (#ι).lift < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, v} f a < c.ord :=
@@ -1232,42 +1561,60 @@ theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc :
       bsup_lt_ord_of_is_regular hc (ord_lt_ord.1 ((ord_card_le b).trans_lt hb')) fun o' ho' =>
         H o' ho' (ho'.trans hb')
 #align cardinal.deriv_family_lt_ord_lift Cardinal.derivFamily_lt_ord_lift
+-/
 
+#print Cardinal.derivFamily_lt_ord /-
 theorem derivFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c)
     (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, u} f a < c.ord :=
   derivFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf
 #align cardinal.deriv_family_lt_ord Cardinal.derivFamily_lt_ord
+-/
 
+#print Cardinal.derivBFamily_lt_ord_lift /-
 theorem derivBFamily_lt_ord_lift {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c}
     (hc : IsRegular c) (hι : o.card.lift < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → derivBFamily.{u, v} o f a < c.ord :=
   derivFamily_lt_ord_lift hc (by rwa [mk_ordinal_out]) hc' fun i => hf _ _
 #align cardinal.deriv_bfamily_lt_ord_lift Cardinal.derivBFamily_lt_ord_lift
+-/
 
+#print Cardinal.derivBFamily_lt_ord /-
 theorem derivBFamily_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : o.card < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i hi), ∀ b < c.ord, f i hi b < c.ord) {a} :
     a < c.ord → derivBFamily.{u, u} o f a < c.ord :=
   derivBFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf
 #align cardinal.deriv_bfamily_lt_ord Cardinal.derivBFamily_lt_ord
+-/
 
+#print Cardinal.deriv_lt_ord /-
 theorem deriv_lt_ord {f : Ordinal.{u} → Ordinal} {c} (hc : IsRegular c) (hc' : c ≠ ℵ₀)
     (hf : ∀ i < c.ord, f i < c.ord) {a} : a < c.ord → deriv f a < c.ord :=
   derivFamily_lt_ord_lift hc
     (by simpa using cardinal.one_lt_aleph_0.trans (lt_of_le_of_ne hc.1 hc'.symm)) hc' fun _ => hf
 #align cardinal.deriv_lt_ord Cardinal.deriv_lt_ord
+-/
 
+#print Cardinal.IsInaccessible /-
 /-- A cardinal is inaccessible if it is an uncountable regular strong limit cardinal. -/
 def IsInaccessible (c : Cardinal) :=
   ℵ₀ < c ∧ IsRegular c ∧ IsStrongLimit c
 #align cardinal.is_inaccessible Cardinal.IsInaccessible
+-/
 
+/- warning: cardinal.is_inaccessible.mk -> Cardinal.IsInaccessible.mk is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) x) c)) -> (Cardinal.IsInaccessible.{u1} c)
+but is expected to have type
+  forall {c : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} c (Ordinal.cof.{u1} (Cardinal.ord.{u1} c))) -> (forall (x : Cardinal.{u1}), (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) x) c)) -> (Cardinal.IsInaccessible.{u1} c)
+Case conversion may be inaccurate. Consider using '#align cardinal.is_inaccessible.mk Cardinal.IsInaccessible.mkₓ'. -/
 theorem IsInaccessible.mk {c} (h₁ : ℵ₀ < c) (h₂ : c ≤ c.ord.cof) (h₃ : ∀ x < c, (2^x) < c) :
     IsInaccessible c :=
   ⟨h₁, ⟨h₁.le, h₂⟩, (aleph0_pos.trans h₁).ne', h₃⟩
 #align cardinal.is_inaccessible.mk Cardinal.IsInaccessible.mk
 
+#print Cardinal.univ_inaccessible /-
 -- Lean's foundations prove the existence of ℵ₀ many inaccessible cardinals
 theorem univ_inaccessible : IsInaccessible univ.{u, v} :=
   IsInaccessible.mk (by simpa using lift_lt_univ' ℵ₀) (by simp) fun c h =>
@@ -1276,7 +1623,9 @@ theorem univ_inaccessible : IsInaccessible univ.{u, v} :=
     rw [← lift_two_power.{u, max (u + 1) v}]
     apply lift_lt_univ'
 #align cardinal.univ_inaccessible Cardinal.univ_inaccessible
+-/
 
+#print Cardinal.lt_power_cof /-
 theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
   Quotient.inductionOn c fun α h =>
     by
@@ -1296,7 +1645,9 @@ theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
     · have := typein_lt_type r i
       rwa [← re, lt_ord] at this
 #align cardinal.lt_power_cof Cardinal.lt_power_cof
+-/
 
+#print Cardinal.lt_cof_power /-
 theorem lt_cof_power {a b : Cardinal} (ha : ℵ₀ ≤ a) (b1 : 1 < b) : a < cof (b^a).ord :=
   by
   have b0 : b ≠ 0 := (zero_lt_one.trans b1).ne'
@@ -1304,6 +1655,7 @@ theorem lt_cof_power {a b : Cardinal} (ha : ℵ₀ ≤ a) (b1 : 1 < b) : a < cof
   rw [← power_mul, mul_eq_self ha]
   exact lt_power_cof (ha.trans <| (cantor' _ b1).le)
 #align cardinal.lt_cof_power Cardinal.lt_cof_power
+-/
 
 end Cardinal

bb168510

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

7c2ce0c2

chore: Rename nat_cast/int_cast/rat_cast to natCast/intCast/ratCast (#11486)

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

145460b9

Diff

@@ -714,7 +714,7 @@ theorem aleph0_le_cof {o} : ℵ₀ ≤ cof o ↔ IsLimit o := by
     cases n
     · simp at e
       simp [e, not_zero_isLimit] at l
-    · rw [nat_cast_succ, cof_succ] at this
+    · rw [natCast_succ, cof_succ] at this
       rw [← this, cof_eq_one_iff_is_succ] at e
       rcases e with ⟨a, rfl⟩
       exact not_succ_isLimit _ l

7c2ce0c2

feat : new properties of the CardinalInterFilter (#11758)

extend more of the API from CountableInterFilter to CardinalInterFilter

Co-authored-by: Oliver Nash <github@olivernash.org>

beeea28f

Diff

@@ -957,6 +957,9 @@ theorem IsRegular.pos {c : Cardinal} (H : c.IsRegular) : 0 < c :=
   aleph0_pos.trans_le H.1
 #align cardinal.is_regular.pos Cardinal.IsRegular.pos
 
+theorem IsRegular.nat_lt {c : Cardinal} (H : c.IsRegular) (n : ℕ) : n < c :=
+  lt_of_lt_of_le (nat_lt_aleph0 n) H.aleph0_le
+
 theorem IsRegular.ord_pos {c : Cardinal} (H : c.IsRegular) : 0 < c.ord := by
   rw [Cardinal.lt_ord, card_zero]
   exact H.pos
@@ -1114,6 +1117,33 @@ theorem sum_lt_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (
   sum_lt_lift_of_isRegular.{u, u} hc (by rwa [lift_id])
 #align cardinal.sum_lt_of_is_regular Cardinal.sum_lt_of_isRegular
 
+@[simp]
+theorem card_lt_of_card_iUnion_lt {ι : Type u} {α : Type u} {t : ι → Set α} {c : Cardinal}
+    (h : #(⋃ i, t i) < c) (i : ι) : #(t i) < c :=
+  lt_of_le_of_lt (Cardinal.mk_le_mk_of_subset <| subset_iUnion _ _) h
+
+@[simp]
+theorem card_iUnion_lt_iff_forall_of_isRegular {ι : Type u} {α : Type u} {t : ι → Set α}
+    {c : Cardinal} (hc : c.IsRegular) (hι : #ι < c) : #(⋃ i, t i) < c ↔ ∀ i, #(t i) < c := by
+  refine ⟨card_lt_of_card_iUnion_lt, fun h ↦ ?_⟩
+  apply lt_of_le_of_lt (Cardinal.mk_sUnion_le _)
+  apply Cardinal.mul_lt_of_lt hc.aleph0_le
+    (lt_of_le_of_lt Cardinal.mk_range_le hι)
+  apply Cardinal.iSup_lt_of_isRegular hc (lt_of_le_of_lt Cardinal.mk_range_le hι)
+  simpa
+
+theorem card_lt_of_card_biUnion_lt {α β : Type u} {s : Set α} {t : ∀ a ∈ s, Set β} {c : Cardinal}
+    (h : #(⋃ a ∈ s, t a ‹_›) < c) (a : α) (ha : a ∈ s) : # (t a ha) < c := by
+  rw [biUnion_eq_iUnion] at h
+  have := card_lt_of_card_iUnion_lt h
+  simp_all only [iUnion_coe_set,
+    Subtype.forall]
+
+theorem card_biUnion_lt_iff_forall_of_isRegular {α β : Type u} {s : Set α} {t : ∀ a ∈ s, Set β}
+    {c : Cardinal} (hc : c.IsRegular) (hs : #s < c) :
+    #(⋃ a ∈ s, t a ‹_›) < c ↔ ∀ a (ha : a ∈ s), # (t a ha) < c := by
+  rw [biUnion_eq_iUnion, card_iUnion_lt_iff_forall_of_isRegular hc hs, SetCoe.forall']
+
 theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
     (hι : Cardinal.lift.{v, u} #ι < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a}
     (ha : a < c.ord) : nfpFamily.{u, v} f a < c.ord := by

7c2ce0c2

chore: remove useless tactics (#11333)

The removal of some pointless tactics flagged by #11308.

ee18bf38

Diff

@@ -516,7 +516,6 @@ theorem cof_succ (o) : cof (succ o) = 1 := by
 @[simp]
 theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
   ⟨inductionOn o fun α r _ z => by
-      skip
       rcases cof_eq r with ⟨S, hl, e⟩; rw [z] at e
       cases' mk_ne_zero_iff.1 (by rw [e]; exact one_ne_zero) with a
       refine'
@@ -976,7 +975,7 @@ theorem isRegular_succ {c : Cardinal.{u}} (h : ℵ₀ ≤ c) : IsRegular (succ c
     succ_le_of_lt
       (by
         cases' Quotient.exists_rep (@succ Cardinal _ _ c) with α αe; simp at αe
-        rcases ord_eq α with ⟨r, wo, re⟩; skip
+        rcases ord_eq α with ⟨r, wo, re⟩
         have := ord_isLimit (h.trans (le_succ _))
         rw [← αe, re] at this ⊢
         rcases cof_eq' r this with ⟨S, H, Se⟩
@@ -1222,7 +1221,7 @@ theorem univ_inaccessible : IsInaccessible univ.{u, v} :=
 
 theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
   Quotient.inductionOn c fun α h => by
-    rcases ord_eq α with ⟨r, wo, re⟩; skip
+    rcases ord_eq α with ⟨r, wo, re⟩
     have := ord_isLimit h
     rw [mk'_def, re] at this ⊢
     rcases cof_eq' r this with ⟨S, H, Se⟩

7c2ce0c2

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

@@ -49,7 +49,8 @@ noncomputable section
 
 open Function Cardinal Set Order
 
-open Classical Cardinal Ordinal
+open scoped Classical
+open Cardinal Ordinal
 
 universe u v w

7c2ce0c2

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -770,7 +770,7 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ.{u, v} :=
       let o := succ (sup.{u, u} g)
       rcases H o with ⟨b, h, l⟩
       refine' l (lt_succ_iff.2 _)
-      rw [← show g (f.symm ⟨b, h⟩) = b by simp]
+      rw [← show g (f.symm ⟨b, h⟩) = b by simp [g]]
       apply le_sup)
 #align ordinal.cof_univ Ordinal.cof_univ
 
@@ -1045,7 +1045,7 @@ theorem le_range_of_union_finset_eq_top {α β : Type*} [Infinite β] (f : α 
   let u' : β → range f := fun b => ⟨f (u b).choose, by simp⟩
   have v' : ∀ a, u' ⁻¹' {⟨f a, by simp⟩} ≤ f a := by
     rintro a p m
-    simp? at m says simp only [mem_preimage, mem_singleton_iff, Subtype.mk.injEq] at m
+    simp? [u']  at m says simp only [mem_preimage, mem_singleton_iff, Subtype.mk.injEq, u'] at m
     rw [← m]
     apply fun b => (u b).choose_spec
   obtain ⟨⟨-, ⟨a, rfl⟩⟩, p⟩ := exists_infinite_fiber u' h k

7c2ce0c2

chore: remove terminal, terminal refines (#10762)

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

ea36aa7d

Diff

@@ -266,7 +266,7 @@ theorem lift_cof (o) : Cardinal.lift.{u, v} (cof o) = cof (Ordinal.lift.{u, v} o
   · refine' le_cof_type.2 fun S H => _
     have : Cardinal.lift.{u, v} #(ULift.up ⁻¹' S) ≤ #(S : Type (max u v)) := by
       rw [← Cardinal.lift_umax.{v, u}, ← Cardinal.lift_id'.{v, u} #S]
-      refine mk_preimage_of_injective_lift.{v, max u v} ULift.up S (ULift.up_injective.{u, v})
+      exact mk_preimage_of_injective_lift.{v, max u v} ULift.up S (ULift.up_injective.{u, v})
     refine' (Cardinal.lift_le.2 <| cof_type_le _).trans this
     exact fun a =>
       let ⟨⟨b⟩, bs, br⟩ := H ⟨a⟩

7c2ce0c2

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -181,8 +181,8 @@ theorem ord_cof_eq (r : α → α → Prop) [IsWellOrder α r] :
   let ⟨S, hS, e⟩ := cof_eq r
   let ⟨s, _, e'⟩ := Cardinal.ord_eq S
   let T : Set α := { a | ∃ aS : a ∈ S, ∀ b : S, s b ⟨_, aS⟩ → r b a }
-  suffices : Unbounded r T
-  · refine' ⟨T, this, le_antisymm _ (Cardinal.ord_le.2 <| cof_type_le this)⟩
+  suffices Unbounded r T by
+    refine' ⟨T, this, le_antisymm _ (Cardinal.ord_le.2 <| cof_type_le this)⟩
     rw [← e, e']
     refine'
       (RelEmbedding.ofMonotone
@@ -527,8 +527,8 @@ theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
       · rcases x with (x | ⟨⟨⟨⟩⟩⟩) <;> rcases y with (y | ⟨⟨⟨⟩⟩⟩) <;>
           simp [Subrel, Order.Preimage, EmptyRelation]
         exact x.2
-      · suffices : r x a ∨ ∃ _ : PUnit.{u}, ↑a = x
-        · convert this
+      · suffices r x a ∨ ∃ _ : PUnit.{u}, ↑a = x by
+          convert this
           dsimp [RelEmbedding.ofMonotone]; simp
         rcases trichotomous_of r x a with (h | h | h)
         · exact Or.inl h
@@ -614,8 +614,8 @@ end IsFundamentalSequence
 /-- Every ordinal has a fundamental sequence. -/
 theorem exists_fundamental_sequence (a : Ordinal.{u}) :
     ∃ f, IsFundamentalSequence a a.cof.ord f := by
-  suffices h : ∃ o f, IsFundamentalSequence a o f
-  · rcases h with ⟨o, f, hf⟩
+  suffices h : ∃ o f, IsFundamentalSequence a o f by
+    rcases h with ⟨o, f, hf⟩
     exact ⟨_, hf.ord_cof⟩
   rcases exists_lsub_cof a with ⟨ι, f, hf, hι⟩
   rcases ord_eq ι with ⟨r, wo, hr⟩
@@ -631,8 +631,8 @@ theorem exists_fundamental_sequence (a : Ordinal.{u}) :
     rwa [hrr'.2, @enum_lt_enum _ r']
   · rw [← hf, lsub_le_iff]
     intro i
-    suffices h : ∃ i' hi', f i ≤ bfamilyOfFamily' r' (fun i => f i) i' hi'
-    · rcases h with ⟨i', hi', hfg⟩
+    suffices h : ∃ i' hi', f i ≤ bfamilyOfFamily' r' (fun i => f i) i' hi' by
+      rcases h with ⟨i', hi', hfg⟩
       exact hfg.trans_lt (lt_blsub _ _ _)
     by_cases h : ∀ j, r j i → f j < f i
     · refine' ⟨typein r' ⟨i, h⟩, typein_lt_type _ _, _⟩

7c2ce0c2

chore(Data/Finset): drop some Nonempty arguments (#9377)

rename Finset.Nonempty.image_iff to Finset.image_nonempty, deprecate the old version;
rename Set.nonempty_image_iff to Set.image_nonempty, deprecate the old version;
drop unneeded Finset.Nonempty arguments here and there;
add versions of some lemmas that assume Nonempty s instead of Nonempty (s.image f) or Nonempty (s.map f).

4bd6aa25

Diff

@@ -90,7 +90,7 @@ theorem RelIso.cof_le_lift {α : Type u} {β : Type v} {r : α → α → Prop}
     (f : r ≃r s) : Cardinal.lift.{max u v} (Order.cof r) ≤
     Cardinal.lift.{max u v} (Order.cof s) := by
   rw [Order.cof, Order.cof, lift_sInf, lift_sInf,
-    le_csInf_iff'' (nonempty_image_iff.2 (Order.cof_nonempty s))]
+    le_csInf_iff'' ((Order.cof_nonempty s).image _)]
   rintro - ⟨-, ⟨u, H, rfl⟩, rfl⟩
   apply csInf_le'
   refine'

7c2ce0c2

feat: demote the instance Fintype.ofIsEmpty to a def (#8816)

Rationale: this instance creates (empty) data out of nothing, which may conflict with other data. If you have in the context [Fintype i] and case on whether i is empty or not, then this gave two non-defeq instances of [Fintype i] around.

8eef7faf

Diff

@@ -923,8 +923,7 @@ theorem mk_bounded_subset {α : Type*} (h : ∀ x < #α, (2^x) < #α) {r : α 
 theorem mk_subset_mk_lt_cof {α : Type*} (h : ∀ x < #α, (2^x) < #α) :
     #{ s : Set α // #s < cof (#α).ord } = #α := by
   rcases eq_or_ne #α 0 with (ha | ha)
-  · rw [ha]
-    simp [fun s => (Cardinal.zero_le s).not_lt]
+  · simp [ha]
   have h' : IsStrongLimit #α := ⟨ha, h⟩
   rcases ord_eq α with ⟨r, wo, hr⟩
   haveI := wo

7c2ce0c2

chore: Remove nonterminal simp at (#7795)

Removes nonterminal uses of simp at. Replaces most of these with instances of simp? ... says.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

4160b2aa

Diff

@@ -1046,7 +1046,7 @@ theorem le_range_of_union_finset_eq_top {α β : Type*} [Infinite β] (f : α 
   let u' : β → range f := fun b => ⟨f (u b).choose, by simp⟩
   have v' : ∀ a, u' ⁻¹' {⟨f a, by simp⟩} ≤ f a := by
     rintro a p m
-    simp at m
+    simp? at m says simp only [mem_preimage, mem_singleton_iff, Subtype.mk.injEq] at m
     rw [← m]
     apply fun b => (u b).choose_spec
   obtain ⟨⟨-, ⟨a, rfl⟩⟩, p⟩ := exists_infinite_fiber u' h k

7c2ce0c2

chore: rename by_contra' to by_contra! (#8797)

To fit with the "please try harder" convention of ! tactics.

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

738b1a97

Diff

@@ -640,7 +640,7 @@ theorem exists_fundamental_sequence (a : Ordinal.{u}) :
     · push_neg at h
       cases' wo.wf.min_mem _ h with hji hij
       refine' ⟨typein r' ⟨_, fun k hkj => lt_of_lt_of_le _ hij⟩, typein_lt_type _ _, _⟩
-      · by_contra' H
+      · by_contra! H
         exact (wo.wf.not_lt_min _ h ⟨IsTrans.trans _ _ _ hkj hji, H⟩) hkj
       · rwa [bfamilyOfFamily'_typein]
 #align ordinal.exists_fundamental_sequence Ordinal.exists_fundamental_sequence
@@ -781,7 +781,7 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ.{u, v} :=
   then s has an unbounded member -/
 theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder α r] {s : Set (Set α)}
     (h₁ : Unbounded r <| ⋃₀ s) (h₂ : #s < StrictOrder.cof r) : ∃ x ∈ s, Unbounded r x := by
-  by_contra' h
+  by_contra! h
   simp_rw [not_unbounded_iff] at h
   let f : s → α := fun x : s => wo.wf.sup x (h x.1 x.2)
   refine' h₂.not_le (le_trans (csInf_le' ⟨range f, fun x => _, rfl⟩) mk_range_le)
@@ -803,7 +803,7 @@ theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop)
 theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤ #β) (h₂ : #α < (#β).ord.cof) :
     ∃ a : α, #(f ⁻¹' {a}) = #β := by
   have : ∃ a, #β ≤ #(f ⁻¹' {a}) := by
-    by_contra' h
+    by_contra! h
     apply mk_univ.not_lt
     rw [← preimage_univ, ← iUnion_of_singleton, preimage_iUnion]
     exact

7c2ce0c2

chore: replace exact_mod_cast tactic with mod_cast elaborator where possible (#8404)

We still have the exact_mod_cast tactic, used in a few places, which somehow (?) works a little bit harder to prevent the expected type influencing the elaboration of the term. I would like to get to the bottom of this, and it will be easier once the only usages of exact_mod_cast are the ones that don't work using the term elaborator by itself.

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

693fd795

Diff

@@ -866,7 +866,7 @@ theorem IsStrongLimit.two_power_lt {x c} (h : IsStrongLimit c) : x < c → (2^x)
 theorem isStrongLimit_aleph0 : IsStrongLimit ℵ₀ :=
   ⟨aleph0_ne_zero, fun x hx => by
     rcases lt_aleph0.1 hx with ⟨n, rfl⟩
-    exact_mod_cast nat_lt_aleph0 (2 ^ n)⟩
+    exact mod_cast nat_lt_aleph0 (2 ^ n)⟩
 #align cardinal.is_strong_limit_aleph_0 Cardinal.isStrongLimit_aleph0
 
 protected theorem IsStrongLimit.isSuccLimit {c} (H : IsStrongLimit c) : IsSuccLimit c :=

7c2ce0c2

fix: remove remaining ^ fixes (#8463)

b0e957dd

Diff

@@ -849,10 +849,6 @@ namespace Cardinal
 
 open Ordinal
 
---Porting note: commented out, doesn't seem necessary
--- mathport name: cardinal.pow
---local infixr:0 "^" => @HPow.hPow Cardinal Cardinal Cardinal instHPow
-
 /-- A cardinal is a strong limit if it is not zero and it is
   closed under powersets. Note that `ℵ₀` is a strong limit by this definition. -/
 def IsStrongLimit (c : Cardinal) : Prop :=

7c2ce0c2

chore: remove many Type _ before the colon (#7718)

We have turned to Type* instead of Type _, but many of them remained in mathlib because the straight replacement did not work. In general, having Type _ before the colon is a code smell, though, as it hides which types should be in the same universe and which shouldn't, and is not very robust.

This PR replaces most of the remaining Type _ before the colon (except those in category theory) by Type* or Type u. This has uncovered a few bugs (where declarations were not as polymorphic as they should be).

I had to increase heartbeats at two places when replacing Type _ by Type*, but I think it's worth it as it's really more robust.

fe9572d2

Diff

@@ -1026,7 +1026,7 @@ theorem infinite_pigeonhole_card_lt {β α : Type u} (f : β → α) (w : #α <
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has an infinite fiber.
 -/
-theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : #α < #β) (w' : Infinite α) :
+theorem exists_infinite_fiber {β α : Type u} (f : β → α) (w : #α < #β) (w' : Infinite α) :
     ∃ a : α, Infinite (f ⁻¹' {a}) := by
   simp_rw [Cardinal.infinite_iff] at w' ⊢
   cases' infinite_pigeonhole_card_lt f w w' with a ha

7c2ce0c2

feat(SetTheory): definition of initial ordinals, ω₁ as an ordinal, ordinal-indexed unions (#6404)

I setup notation for the first ordinal in each cardinality.
ω₁ is defined as an ordinal, not as an out (cf. MeasureTheory.CardMeasurableSpace).
Lemma using the cofinality of ω₁.
Lemma on the cardinality of ordinal-indexed iUnions in preparation for material on the Borel hierarchy.

Co-authored-by: Pedro Sánchez Terraf <sterraf@users.noreply.github.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

58a5282e

Diff

@@ -1250,3 +1250,20 @@ theorem lt_cof_power {a b : Cardinal} (ha : ℵ₀ ≤ a) (b1 : 1 < b) : a < cof
 #align cardinal.lt_cof_power Cardinal.lt_cof_power
 
 end Cardinal
+
+section Omega1
+
+namespace Ordinal
+
+open Cardinal
+open scoped Ordinal
+
+lemma sup_sequence_lt_omega1 {α} [Countable α] (o : α → Ordinal) (ho : ∀ n, o n < ω₁) :
+    sup o < ω₁ := by
+  apply sup_lt_ord_lift _ ho
+  rw [Cardinal.isRegular_aleph_one.cof_eq]
+  exact lt_of_le_of_lt mk_le_aleph0 aleph0_lt_aleph_one
+
+end Ordinal
+
+end Omega1

7c2ce0c2

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

@@ -53,7 +53,7 @@ open Classical Cardinal Ordinal
 
 universe u v w
 
-variable {α : Type _} {r : α → α → Prop}
+variable {α : Type*} {r : α → α → Prop}
 
 /-! ### Cofinality of orders -/
 
@@ -893,7 +893,7 @@ theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (be
     exact this.trans_lt (beth_lt.2 (H.succ_lt hi))
 #align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_beth
 
-theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < #α) {r : α → α → Prop}
+theorem mk_bounded_subset {α : Type*} (h : ∀ x < #α, (2^x) < #α) {r : α → α → Prop}
     [IsWellOrder α r] (hr : (#α).ord = type r) : #{ s : Set α // Bounded r s } = #α := by
   rcases eq_or_ne #α 0 with (ha | ha)
   · rw [ha]
@@ -924,7 +924,7 @@ theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < #α) {r : α 
       simpa [singleton_eq_singleton_iff] using hab
 #align cardinal.mk_bounded_subset Cardinal.mk_bounded_subset
 
-theorem mk_subset_mk_lt_cof {α : Type _} (h : ∀ x < #α, (2^x) < #α) :
+theorem mk_subset_mk_lt_cof {α : Type*} (h : ∀ x < #α, (2^x) < #α) :
     #{ s : Set α // #s < cof (#α).ord } = #α := by
   rcases eq_or_ne #α 0 with (ha | ha)
   · rw [ha]
@@ -1037,7 +1037,7 @@ theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : #α < #β) (
 then the cardinality of the collection of those finite sets
 must be at least the cardinality of `β`.
 -/
-theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α → Finset β)
+theorem le_range_of_union_finset_eq_top {α β : Type*} [Infinite β] (f : α → Finset β)
     (w : ⋃ a, (f a : Set β) = ⊤) : #β ≤ #(range f) := by
   have k : _root_.Infinite (range f) := by
     rw [infinite_coe_iff]

7c2ce0c2

feat: change definition of natCast in Cardinal to lift #(Fin n) (#6384)

The new definition is conceptually more satisfactory.

By also changing the definition of the Zero and One instances, we get ((0 : ℕ) : Cardinal) = 0 and ((1 : ℕ) : Cardinal) = 1 definitionally (which wasn't true before), which is in practice more convenient than definitional equality with PEmpty or PUnit.

dc0a7a96

Diff

@@ -475,8 +475,10 @@ theorem bsup_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o
 
 
 @[simp]
-theorem cof_zero : cof 0 = 0 :=
-  (cof_le_card 0).antisymm (Cardinal.zero_le _)
+theorem cof_zero : cof 0 = 0 := by
+  refine LE.le.antisymm  ?_ (Cardinal.zero_le _)
+  rw [← card_zero]
+  exact cof_le_card 0
 #align ordinal.cof_zero Ordinal.cof_zero
 
 @[simp]
@@ -961,7 +963,7 @@ theorem IsRegular.pos {c : Cardinal} (H : c.IsRegular) : 0 < c :=
 #align cardinal.is_regular.pos Cardinal.IsRegular.pos
 
 theorem IsRegular.ord_pos {c : Cardinal} (H : c.IsRegular) : 0 < c.ord := by
-  rw [Cardinal.lt_ord]
+  rw [Cardinal.lt_ord, card_zero]
   exact H.pos
 #align cardinal.is_regular.ord_pos Cardinal.IsRegular.ord_pos

7c2ce0c2

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 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios
-
-! This file was ported from Lean 3 source module set_theory.cardinal.cofinality
-! leanprover-community/mathlib commit 7c2ce0c2da15516b4e65d0c9e254bb6dc93abd1f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.SetTheory.Cardinal.Ordinal
 import Mathlib.SetTheory.Ordinal.FixedPoint
 
+#align_import set_theory.cardinal.cofinality from "leanprover-community/mathlib"@"7c2ce0c2da15516b4e65d0c9e254bb6dc93abd1f"
+
 /-!
 # Cofinality

7c2ce0c2

chore: bump to nightly-2023-07-01 (#5409)

depends on: https://github.com/leanprover/std4/pull/163
depends on: #5584
depends on: #5715
depends on: #5729
depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

906f7221

Diff

@@ -1164,15 +1164,18 @@ theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc :
   have hω : ℵ₀ < c.ord.cof := by
     rw [hc.cof_eq]
     exact lt_of_le_of_ne hc.1 hc'.symm
-  apply a.limitRecOn
-  · rw [derivFamily_zero]
+  induction a using limitRecOn with
+  | H₁ =>
+    rw [derivFamily_zero]
     exact nfpFamily_lt_ord_lift hω (by rwa [hc.cof_eq]) hf
-  · intro b hb hb'
+  | H₂ b hb =>
+    intro hb'
     rw [derivFamily_succ]
     exact
       nfpFamily_lt_ord_lift hω (by rwa [hc.cof_eq]) hf
         ((ord_isLimit hc.1).2 _ (hb ((lt_succ b).trans hb')))
-  · intro b hb H hb'
+  | H₃ b hb H =>
+    intro hb'
     rw [derivFamily_limit f hb]
     exact
       bsup_lt_ord_of_isRegular.{u, v} hc (ord_lt_ord.1 ((ord_card_le b).trans_lt hb')) fun o' ho' =>

7c2ce0c2

chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

cb02d09e

Diff

@@ -529,7 +529,7 @@ theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
           simp [Subrel, Order.Preimage, EmptyRelation]
         exact x.2
       · suffices : r x a ∨ ∃ _ : PUnit.{u}, ↑a = x
-        . convert this
+        · convert this
           dsimp [RelEmbedding.ofMonotone]; simp
         rcases trichotomous_of r x a with (h | h | h)
         · exact Or.inl h

7c2ce0c2

fix: precedence of # (#5623)

d450fcd7

Diff

@@ -66,21 +66,21 @@ namespace Order
 /-- Cofinality of a reflexive order `≼`. This is the smallest cardinality
   of a subset `S : Set α` such that `∀ a, ∃ b ∈ S, a ≼ b`. -/
 def cof (r : α → α → Prop) : Cardinal :=
-  sInf { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c }
+  sInf { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ #S = c }
 #align order.cof Order.cof
 
 /-- The set in the definition of `Order.cof` is nonempty. -/
 theorem cof_nonempty (r : α → α → Prop) [IsRefl α r] :
-    { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c }.Nonempty :=
+    { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ #S = c }.Nonempty :=
   ⟨_, Set.univ, fun a => ⟨a, ⟨⟩, refl _⟩, rfl⟩
 #align order.cof_nonempty Order.cof_nonempty
 
-theorem cof_le (r : α → α → Prop) {S : Set α} (h : ∀ a, ∃ b ∈ S, r a b) : cof r ≤ (#S) :=
+theorem cof_le (r : α → α → Prop) {S : Set α} (h : ∀ a, ∃ b ∈ S, r a b) : cof r ≤ #S :=
   csInf_le' ⟨S, h, rfl⟩
 #align order.cof_le Order.cof_le
 
 theorem le_cof {r : α → α → Prop} [IsRefl α r] (c : Cardinal) :
-    c ≤ cof r ↔ ∀ {S : Set α}, (∀ a, ∃ b ∈ S, r a b) → c ≤ (#S) := by
+    c ≤ cof r ↔ ∀ {S : Set α}, (∀ a, ∃ b ∈ S, r a b) → c ≤ #S := by
   rw [cof, le_csInf_iff'' (cof_nonempty r)]
   use fun H S h => H _ ⟨S, h, rfl⟩
   rintro H d ⟨S, h, rfl⟩
@@ -127,7 +127,7 @@ def StrictOrder.cof (r : α → α → Prop) : Cardinal :=
 
 /-- The set in the definition of `Order.StrictOrder.cof` is nonempty. -/
 theorem StrictOrder.cof_nonempty (r : α → α → Prop) [IsIrrefl α r] :
-    { c | ∃ S : Set α, Unbounded r S ∧ (#S) = c }.Nonempty :=
+    { c | ∃ S : Set α, Unbounded r S ∧ #S = c }.Nonempty :=
   @Order.cof_nonempty α _ (IsRefl.swap rᶜ)
 #align strict_order.cof_nonempty StrictOrder.cof_nonempty
 
@@ -160,22 +160,22 @@ theorem cof_type (r : α → α → Prop) [IsWellOrder α r] : (type r).cof = St
   rfl
 #align ordinal.cof_type Ordinal.cof_type
 
-theorem le_cof_type [IsWellOrder α r] {c} : c ≤ cof (type r) ↔ ∀ S, Unbounded r S → c ≤ (#S) :=
+theorem le_cof_type [IsWellOrder α r] {c} : c ≤ cof (type r) ↔ ∀ S, Unbounded r S → c ≤ #S :=
   (le_csInf_iff'' (StrictOrder.cof_nonempty r)).trans
     ⟨fun H S h => H _ ⟨S, h, rfl⟩, by
       rintro H d ⟨S, h, rfl⟩
       exact H _ h⟩
 #align ordinal.le_cof_type Ordinal.le_cof_type
 
-theorem cof_type_le [IsWellOrder α r] {S : Set α} (h : Unbounded r S) : cof (type r) ≤ (#S) :=
+theorem cof_type_le [IsWellOrder α r] {S : Set α} (h : Unbounded r S) : cof (type r) ≤ #S :=
   le_cof_type.1 le_rfl S h
 #align ordinal.cof_type_le Ordinal.cof_type_le
 
-theorem lt_cof_type [IsWellOrder α r] {S : Set α} : (#S) < cof (type r) → Bounded r S := by
+theorem lt_cof_type [IsWellOrder α r] {S : Set α} : #S < cof (type r) → Bounded r S := by
   simpa using not_imp_not.2 cof_type_le
 #align ordinal.lt_cof_type Ordinal.lt_cof_type
 
-theorem cof_eq (r : α → α → Prop) [IsWellOrder α r] : ∃ S, Unbounded r S ∧ (#S) = cof (type r) :=
+theorem cof_eq (r : α → α → Prop) [IsWellOrder α r] : ∃ S, Unbounded r S ∧ #S = cof (type r) :=
   csInf_mem (StrictOrder.cof_nonempty r)
 #align ordinal.cof_eq Ordinal.cof_eq
 
@@ -218,17 +218,17 @@ theorem ord_cof_eq (r : α → α → Prop) [IsWellOrder α r] :
 /-! ### Cofinality of suprema and least strict upper bounds -/
 
 
-private theorem card_mem_cof {o} : ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = o.card :=
+private theorem card_mem_cof {o} : ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ #ι = o.card :=
   ⟨_, _, lsub_typein o, mk_ordinal_out o⟩
 
 /-- The set in the `lsub` characterization of `cof` is nonempty. -/
 theorem cof_lsub_def_nonempty (o) :
-    { a : Cardinal | ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a }.Nonempty :=
+    { a : Cardinal | ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ #ι = a }.Nonempty :=
   ⟨_, card_mem_cof⟩
 #align ordinal.cof_lsub_def_nonempty Ordinal.cof_lsub_def_nonempty
 
 theorem cof_eq_sInf_lsub (o : Ordinal.{u}) : cof o =
-    sInf { a : Cardinal | ∃ (ι : Type u) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } := by
+    sInf { a : Cardinal | ∃ (ι : Type u) (f : ι → Ordinal), lsub.{u, u} f = o ∧ #ι = a } := by
   refine' le_antisymm (le_csInf (cof_lsub_def_nonempty o) _) (csInf_le' _)
   · rintro a ⟨ι, f, hf, rfl⟩
     rw [← type_lt o]
@@ -267,15 +267,15 @@ theorem lift_cof (o) : Cardinal.lift.{u, v} (cof o) = cof (Ordinal.lift.{u, v} o
   intro α r _
   apply le_antisymm
   · refine' le_cof_type.2 fun S H => _
-    have : Cardinal.lift.{u, v} (#(ULift.up ⁻¹' S)) ≤ (#(S : Type (max u v))) := by
-      rw [← Cardinal.lift_umax.{v, u}, ← Cardinal.lift_id'.{v, u} (#S)]
+    have : Cardinal.lift.{u, v} #(ULift.up ⁻¹' S) ≤ #(S : Type (max u v)) := by
+      rw [← Cardinal.lift_umax.{v, u}, ← Cardinal.lift_id'.{v, u} #S]
       refine mk_preimage_of_injective_lift.{v, max u v} ULift.up S (ULift.up_injective.{u, v})
     refine' (Cardinal.lift_le.2 <| cof_type_le _).trans this
     exact fun a =>
       let ⟨⟨b⟩, bs, br⟩ := H ⟨a⟩
       ⟨b, bs, br⟩
   · rcases cof_eq r with ⟨S, H, e'⟩
-    have : (#ULift.down.{u, v} ⁻¹' S) ≤ Cardinal.lift.{u, v} (#S) :=
+    have : #(ULift.down.{u, v} ⁻¹' S) ≤ Cardinal.lift.{u, v} #S :=
       ⟨⟨fun ⟨⟨x⟩, h⟩ => ⟨⟨x, h⟩⟩, fun ⟨⟨x⟩, h₁⟩ ⟨⟨y⟩, h₂⟩ e => by
           simp at e; congr⟩⟩
     rw [e'] at this
@@ -298,18 +298,18 @@ theorem ord_cof_le (o : Ordinal.{u}) : o.cof.ord ≤ o :=
 #align ordinal.ord_cof_le Ordinal.ord_cof_le
 
 theorem exists_lsub_cof (o : Ordinal) :
-    ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = cof o := by
+    ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ #ι = cof o := by
   rw [cof_eq_sInf_lsub]
   exact csInf_mem (cof_lsub_def_nonempty o)
 #align ordinal.exists_lsub_cof Ordinal.exists_lsub_cof
 
-theorem cof_lsub_le {ι} (f : ι → Ordinal) : cof (lsub.{u, u} f) ≤ (#ι) := by
+theorem cof_lsub_le {ι} (f : ι → Ordinal) : cof (lsub.{u, u} f) ≤ #ι := by
   rw [cof_eq_sInf_lsub]
   exact csInf_le' ⟨ι, f, rfl, rfl⟩
 #align ordinal.cof_lsub_le Ordinal.cof_lsub_le
 
 theorem cof_lsub_le_lift {ι} (f : ι → Ordinal) :
-    cof (lsub.{u, v} f) ≤ Cardinal.lift.{v, u} (#ι) := by
+    cof (lsub.{u, v} f) ≤ Cardinal.lift.{v, u} #ι := by
   rw [← mk_uLift.{u, v}]
   convert cof_lsub_le.{max u v} fun i : ULift.{v, u} ι => f i.down
   exact
@@ -318,7 +318,7 @@ theorem cof_lsub_le_lift {ι} (f : ι → Ordinal) :
 #align ordinal.cof_lsub_le_lift Ordinal.cof_lsub_le_lift
 
 theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
-    a ≤ cof o ↔ ∀ {ι} (f : ι → Ordinal), lsub.{u, u} f = o → a ≤ (#ι) := by
+    a ≤ cof o ↔ ∀ {ι} (f : ι → Ordinal), lsub.{u, u} f = o → a ≤ #ι := by
   rw [cof_eq_sInf_lsub]
   exact
     (le_csInf_iff'' (cof_lsub_def_nonempty o)).trans
@@ -328,43 +328,43 @@ theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
 #align ordinal.le_cof_iff_lsub Ordinal.le_cof_iff_lsub
 
 theorem lsub_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal}
-    (hι : Cardinal.lift.{v, u} (#ι) < c.cof)
+    (hι : Cardinal.lift.{v, u} #ι < c.cof)
     (hf : ∀ i, f i < c) : lsub.{u, v} f < c :=
   lt_of_le_of_ne (lsub_le.{v, u} hf) fun h => by
     subst h
     exact (cof_lsub_le_lift.{u, v} f).not_lt hι
 #align ordinal.lsub_lt_ord_lift Ordinal.lsub_lt_ord_lift
 
-theorem lsub_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
+theorem lsub_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : #ι < c.cof) :
     (∀ i, f i < c) → lsub.{u, u} f < c :=
   lsub_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.lsub_lt_ord Ordinal.lsub_lt_ord
 
 theorem cof_sup_le_lift {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup.{u, v} f) :
-    cof (sup.{u, v} f) ≤ Cardinal.lift.{v, u} (#ι) := by
+    cof (sup.{u, v} f) ≤ Cardinal.lift.{v, u} #ι := by
   rw [← sup_eq_lsub_iff_lt_sup.{u, v}] at H
   rw [H]
   exact cof_lsub_le_lift f
 #align ordinal.cof_sup_le_lift Ordinal.cof_sup_le_lift
 
 theorem cof_sup_le {ι} {f : ι → Ordinal} (H : ∀ i, f i < sup.{u, u} f) :
-    cof (sup.{u, u} f) ≤ (#ι) := by
+    cof (sup.{u, u} f) ≤ #ι := by
   rw [← (#ι).lift_id]
   exact cof_sup_le_lift H
 #align ordinal.cof_sup_le Ordinal.cof_sup_le
 
-theorem sup_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift.{v, u} (#ι) < c.cof)
+theorem sup_lt_ord_lift {ι} {f : ι → Ordinal} {c : Ordinal} (hι : Cardinal.lift.{v, u} #ι < c.cof)
     (hf : ∀ i, f i < c) : sup.{u, v} f < c :=
   (sup_le_lsub.{u, v} f).trans_lt (lsub_lt_ord_lift hι hf)
 #align ordinal.sup_lt_ord_lift Ordinal.sup_lt_ord_lift
 
-theorem sup_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof) :
+theorem sup_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : #ι < c.cof) :
     (∀ i, f i < c) → sup.{u, u} f < c :=
   sup_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.sup_lt_ord Ordinal.sup_lt_ord
 
 theorem iSup_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal}
-    (hι : Cardinal.lift.{v, u} (#ι) < c.ord.cof)
+    (hι : Cardinal.lift.{v, u} #ι < c.ord.cof)
     (hf : ∀ i, f i < c) : iSup.{max u v + 1, u + 1} f < c := by
   rw [← ord_lt_ord, iSup_ord (Cardinal.bddAbove_range.{u, v} _)]
   refine' sup_lt_ord_lift hι fun i => _
@@ -372,13 +372,13 @@ theorem iSup_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal}
   apply hf
 #align ordinal.supr_lt_lift Ordinal.iSup_lt_lift
 
-theorem iSup_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : (#ι) < c.ord.cof) :
+theorem iSup_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : #ι < c.ord.cof) :
     (∀ i, f i < c) → iSup f < c :=
   iSup_lt_lift (by rwa [(#ι).lift_id])
 #align ordinal.supr_lt Ordinal.iSup_lt
 
 theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
-    (hc' : Cardinal.lift.{v, u} (#ι) < cof c) (hf : ∀ (i), ∀ b < c, f i b < c) {a} (ha : a < c) :
+    (hc' : Cardinal.lift.{v, u} #ι < cof c) (hf : ∀ (i), ∀ b < c, f i b < c) {a} (ha : a < c) :
     nfpFamily.{u, v} f a < c := by
   refine' sup_lt_ord_lift ((Cardinal.lift_le.2 (mk_list_le_max ι)).trans_lt _) fun l => _
   · rw [lift_max]
@@ -389,7 +389,7 @@ theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : 
     · exact hf _ _ H
 #align ordinal.nfp_family_lt_ord_lift Ordinal.nfpFamily_lt_ord_lift
 
-theorem nfpFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hc' : (#ι) < cof c)
+theorem nfpFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hc' : #ι < cof c)
     (hf : ∀ (i), ∀ b < c, f i b < c) {a} : a < c → nfpFamily.{u, u} f a < c :=
   nfpFamily_lt_ord_lift hc (by rwa [(#ι).lift_id]) hf
 #align ordinal.nfp_family_lt_ord Ordinal.nfpFamily_lt_ord
@@ -502,7 +502,7 @@ theorem cof_succ (o) : cof (succ o) = 1 := by
   apply le_antisymm
   · refine' inductionOn o fun α r _ => _
     change cof (type _) ≤ _
-    rw [← (_ : (#_) = 1)]
+    rw [← (_ : #_ = 1)]
     apply cof_type_le
     · refine' fun a => ⟨Sum.inr PUnit.unit, Set.mem_singleton _, _⟩
       rcases a with (a | ⟨⟨⟨⟩⟩⟩) <;> simp [EmptyRelation]
@@ -739,7 +739,7 @@ theorem cof_omega : cof ω = ℵ₀ :=
 #align ordinal.cof_omega Ordinal.cof_omega
 
 theorem cof_eq' (r : α → α → Prop) [IsWellOrder α r] (h : IsLimit (type r)) :
-    ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = cof (type r) :=
+    ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ #S = cof (type r) :=
   let ⟨S, H, e⟩ := cof_eq r
   ⟨S, fun a =>
     let a' := enum r _ (h.2 _ (typein_lt_type r a))
@@ -781,7 +781,7 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ.{u, v} :=
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
 theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder α r] {s : Set (Set α)}
-    (h₁ : Unbounded r <| ⋃₀ s) (h₂ : (#s) < StrictOrder.cof r) : ∃ x ∈ s, Unbounded r x := by
+    (h₁ : Unbounded r <| ⋃₀ s) (h₂ : #s < StrictOrder.cof r) : ∃ x ∈ s, Unbounded r x := by
   by_contra' h
   simp_rw [not_unbounded_iff] at h
   let f : s → α := fun x : s => wo.wf.sup x (h x.1 x.2)
@@ -793,7 +793,7 @@ theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
 theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
-    (s : β → Set α) (h₁ : Unbounded r <| ⋃ x, s x) (h₂ : (#β) < StrictOrder.cof r) :
+    (s : β → Set α) (h₁ : Unbounded r <| ⋃ x, s x) (h₂ : #β < StrictOrder.cof r) :
     ∃ x : β, Unbounded r (s x) := by
   rw [← sUnion_range] at h₁
   rcases unbounded_of_unbounded_sUnion r h₁ (mk_range_le.trans_lt h₂) with ⟨_, ⟨x, rfl⟩, u⟩
@@ -801,9 +801,9 @@ theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop)
 #align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_iUnion
 
 /-- The infinite pigeonhole principle -/
-theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤ (#β)) (h₂ : (#α) < (#β).ord.cof) :
-    ∃ a : α, (#f ⁻¹' {a}) = (#β) := by
-  have : ∃ a, (#β) ≤ (#f ⁻¹' {a}) := by
+theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤ #β) (h₂ : #α < (#β).ord.cof) :
+    ∃ a : α, #(f ⁻¹' {a}) = #β := by
+  have : ∃ a, #β ≤ #(f ⁻¹' {a}) := by
     by_contra' h
     apply mk_univ.not_lt
     rw [← preimage_univ, ← iUnion_of_singleton, preimage_iUnion]
@@ -817,8 +817,8 @@ theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤
 #align ordinal.infinite_pigeonhole Ordinal.infinite_pigeonhole
 
 /-- Pigeonhole principle for a cardinality below the cardinality of the domain -/
-theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal) (hθ : θ ≤ (#β))
-    (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) : ∃ a : α, θ ≤ (#f ⁻¹' {a}) := by
+theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal) (hθ : θ ≤ #β)
+    (h₁ : ℵ₀ ≤ θ) (h₂ : #α < θ.ord.cof) : ∃ a : α, θ ≤ #(f ⁻¹' {a}) := by
   rcases le_mk_iff_exists_set.1 hθ with ⟨s, rfl⟩
   cases' infinite_pigeonhole (f ∘ Subtype.val : s → α) h₁ h₂ with a ha
   use a; rw [← ha, @preimage_comp _ _ _ Subtype.val f]
@@ -826,8 +826,8 @@ theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal
 #align ordinal.infinite_pigeonhole_card Ordinal.infinite_pigeonhole_card
 
 theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ : Cardinal)
-    (hθ : θ ≤ (#s)) (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) :
-    ∃ (a : α) (t : Set β) (h : t ⊆ s), θ ≤ (#t) ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a := by
+    (hθ : θ ≤ #s) (h₁ : ℵ₀ ≤ θ) (h₂ : #α < θ.ord.cof) :
+    ∃ (a : α) (t : Set β) (h : t ⊆ s), θ ≤ #t ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a := by
   cases' infinite_pigeonhole_card f θ hθ h₁ h₂ with a ha
   refine' ⟨a, { x | ∃ h, f ⟨x, h⟩ = a }, _, _, _⟩
   · rintro x ⟨hx, _⟩
@@ -894,16 +894,16 @@ theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (be
     exact this.trans_lt (beth_lt.2 (H.succ_lt hi))
 #align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_beth
 
-theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α → α → Prop}
-    [IsWellOrder α r] (hr : (#α).ord = type r) : (#{ s : Set α // Bounded r s }) = (#α) := by
-  rcases eq_or_ne (#α) 0 with (ha | ha)
+theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < #α) {r : α → α → Prop}
+    [IsWellOrder α r] (hr : (#α).ord = type r) : #{ s : Set α // Bounded r s } = #α := by
+  rcases eq_or_ne #α 0 with (ha | ha)
   · rw [ha]
     haveI := mk_eq_zero_iff.1 ha
     rw [mk_eq_zero_iff]
     constructor
     rintro ⟨s, hs⟩
     exact (not_unbounded_iff s).2 hs (unbounded_of_isEmpty s)
-  have h' : IsStrongLimit (#α) := ⟨ha, h⟩
+  have h' : IsStrongLimit #α := ⟨ha, h⟩
   have ha := h'.isLimit.aleph0_le
   apply le_antisymm
   · have : { s : Set α | Bounded r s } = ⋃ i, 𝒫{ j | r j i } := setOf_exists _
@@ -925,12 +925,12 @@ theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α
       simpa [singleton_eq_singleton_iff] using hab
 #align cardinal.mk_bounded_subset Cardinal.mk_bounded_subset
 
-theorem mk_subset_mk_lt_cof {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) :
-    (#{ s : Set α // (#s) < cof (#α).ord }) = (#α) := by
-  rcases eq_or_ne (#α) 0 with (ha | ha)
+theorem mk_subset_mk_lt_cof {α : Type _} (h : ∀ x < #α, (2^x) < #α) :
+    #{ s : Set α // #s < cof (#α).ord } = #α := by
+  rcases eq_or_ne #α 0 with (ha | ha)
   · rw [ha]
     simp [fun s => (Cardinal.zero_le s).not_lt]
-  have h' : IsStrongLimit (#α) := ⟨ha, h⟩
+  have h' : IsStrongLimit #α := ⟨ha, h⟩
   rcases ord_eq α with ⟨r, wo, hr⟩
   haveI := wo
   apply le_antisymm
@@ -1016,18 +1016,18 @@ theorem isRegular_aleph_succ (o : Ordinal) : IsRegular (aleph (succ o)) := by
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has a fiber with cardinality strictly great than the codomain.
 -/
-theorem infinite_pigeonhole_card_lt {β α : Type u} (f : β → α) (w : (#α) < (#β)) (w' : ℵ₀ ≤ (#α)) :
-    ∃ a : α, (#α) < (#f ⁻¹' {a}) := by
+theorem infinite_pigeonhole_card_lt {β α : Type u} (f : β → α) (w : #α < #β) (w' : ℵ₀ ≤ #α) :
+    ∃ a : α, #α < #(f ⁻¹' {a}) := by
   simp_rw [← succ_le_iff]
   exact
-    Ordinal.infinite_pigeonhole_card f (succ (#α)) (succ_le_of_lt w) (w'.trans (lt_succ _).le)
+    Ordinal.infinite_pigeonhole_card f (succ #α) (succ_le_of_lt w) (w'.trans (lt_succ _).le)
       ((lt_succ _).trans_le (isRegular_succ w').2.ge)
 #align cardinal.infinite_pigeonhole_card_lt Cardinal.infinite_pigeonhole_card_lt
 
 /-- A function whose codomain's cardinality is infinite but strictly smaller than its domain's
 has an infinite fiber.
 -/
-theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : (#α) < (#β)) (w' : Infinite α) :
+theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : #α < #β) (w' : Infinite α) :
     ∃ a : α, Infinite (f ⁻¹' {a}) := by
   simp_rw [Cardinal.infinite_iff] at w' ⊢
   cases' infinite_pigeonhole_card_lt f w w' with a ha
@@ -1039,7 +1039,7 @@ then the cardinality of the collection of those finite sets
 must be at least the cardinality of `β`.
 -/
 theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α → Finset β)
-    (w : ⋃ a, (f a : Set β) = ⊤) : (#β) ≤ (#range f) := by
+    (w : ⋃ a, (f a : Set β) = ⊤) : #β ≤ #(range f) := by
   have k : _root_.Infinite (range f) := by
     rw [infinite_coe_iff]
     apply mt (union_finset_finite_of_range_finite f)
@@ -1059,21 +1059,21 @@ theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α 
 #align cardinal.le_range_of_union_finset_eq_top Cardinal.le_range_of_union_finset_eq_top
 
 theorem lsub_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
-    (hι : Cardinal.lift.{v, u} (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.lsub.{u, v} f < c.ord :=
+    (hι : Cardinal.lift.{v, u} #ι < c) : (∀ i, f i < c.ord) → Ordinal.lsub.{u, v} f < c.ord :=
   lsub_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_lift_of_is_regular Cardinal.lsub_lt_ord_lift_of_isRegular
 
-theorem lsub_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
+theorem lsub_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : #ι < c) :
     (∀ i, f i < c.ord) → Ordinal.lsub f < c.ord :=
   lsub_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.lsub_lt_ord_of_is_regular Cardinal.lsub_lt_ord_of_isRegular
 
 theorem sup_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c)
-    (hι : Cardinal.lift.{v, u} (#ι) < c) : (∀ i, f i < c.ord) → Ordinal.sup.{u, v} f < c.ord :=
+    (hι : Cardinal.lift.{v, u} #ι < c) : (∀ i, f i < c.ord) → Ordinal.sup.{u, v} f < c.ord :=
   sup_lt_ord_lift (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_lift_of_is_regular Cardinal.sup_lt_ord_lift_of_isRegular
 
-theorem sup_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
+theorem sup_lt_ord_of_isRegular {ι} {f : ι → Ordinal} {c} (hc : IsRegular c) (hι : #ι < c) :
     (∀ i, f i < c.ord) → Ordinal.sup f < c.ord :=
   sup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.sup_lt_ord_of_is_regular Cardinal.sup_lt_ord_of_isRegular
@@ -1101,27 +1101,27 @@ theorem bsup_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc
 #align cardinal.bsup_lt_ord_of_is_regular Cardinal.bsup_lt_ord_of_isRegular
 
 theorem iSup_lt_lift_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c)
-    (hι : Cardinal.lift.{v, u} (#ι) < c) : (∀ i, f i < c) → iSup.{max u v + 1, u + 1} f < c :=
+    (hι : Cardinal.lift.{v, u} #ι < c) : (∀ i, f i < c) → iSup.{max u v + 1, u + 1} f < c :=
   iSup_lt_lift.{u, v} (by rwa [hc.cof_eq])
 #align cardinal.supr_lt_lift_of_is_regular Cardinal.iSup_lt_lift_of_isRegular
 
-theorem iSup_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
+theorem iSup_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c) (hι : #ι < c) :
     (∀ i, f i < c) → iSup f < c :=
   iSup_lt (by rwa [hc.cof_eq])
 #align cardinal.supr_lt_of_is_regular Cardinal.iSup_lt_of_isRegular
 
 theorem sum_lt_lift_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
-    (hι : Cardinal.lift.{v, u} (#ι) < c) (hf : ∀ i, f i < c) : sum f < c :=
+    (hι : Cardinal.lift.{v, u} #ι < c) (hf : ∀ i, f i < c) : sum f < c :=
   (sum_le_iSup_lift _).trans_lt <| mul_lt_of_lt hc.1 hι (iSup_lt_lift_of_isRegular hc hι hf)
 #align cardinal.sum_lt_lift_of_is_regular Cardinal.sum_lt_lift_of_isRegular
 
 theorem sum_lt_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
-    (hι : (#ι) < c) : (∀ i, f i < c) → sum f < c :=
+    (hι : #ι < c) : (∀ i, f i < c) → sum f < c :=
   sum_lt_lift_of_isRegular.{u, u} hc (by rwa [lift_id])
 #align cardinal.sum_lt_of_is_regular Cardinal.sum_lt_of_isRegular
 
 theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
-    (hι : Cardinal.lift.{v, u} (#ι) < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a}
+    (hι : Cardinal.lift.{v, u} #ι < c) (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a}
     (ha : a < c.ord) : nfpFamily.{u, v} f a < c.ord := by
   apply nfpFamily_lt_ord_lift.{u, v} _ _ hf ha <;> rw [hc.cof_eq]
   exact lt_of_le_of_ne hc.1 hc'.symm
@@ -1129,7 +1129,7 @@ theorem nfpFamily_lt_ord_lift_of_isRegular {ι} {f : ι → Ordinal → Ordinal}
 #align cardinal.nfp_family_lt_ord_lift_of_is_regular Cardinal.nfpFamily_lt_ord_lift_of_isRegular
 
 theorem nfpFamily_lt_ord_of_isRegular {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
-    (hι : (#ι) < c) (hc' : c ≠ ℵ₀) {a} (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) :
+    (hι : #ι < c) (hc' : c ≠ ℵ₀) {a} (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) :
     a < c.ord → nfpFamily.{u, u} f a < c.ord :=
   nfpFamily_lt_ord_lift_of_isRegular hc (by rwa [lift_id]) hc' hf
 #align cardinal.nfp_family_lt_ord_of_is_regular Cardinal.nfpFamily_lt_ord_of_isRegular
@@ -1158,7 +1158,7 @@ theorem nfp_lt_ord_of_isRegular {f : Ordinal → Ordinal} {c} (hc : IsRegular c)
 #align cardinal.nfp_lt_ord_of_is_regular Cardinal.nfp_lt_ord_of_isRegular
 
 theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c)
-    (hι : Cardinal.lift.{v, u} (#ι) < c) (hc' : c ≠ ℵ₀)
+    (hι : Cardinal.lift.{v, u} #ι < c) (hc' : c ≠ ℵ₀)
     (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, v} f a < c.ord := by
   have hω : ℵ₀ < c.ord.cof := by
@@ -1179,7 +1179,7 @@ theorem derivFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc :
         H o' ho' (ho'.trans hb')
 #align cardinal.deriv_family_lt_ord_lift Cardinal.derivFamily_lt_ord_lift
 
-theorem derivFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c) (hι : (#ι) < c)
+theorem derivFamily_lt_ord {ι} {f : ι → Ordinal → Ordinal} {c} (hc : IsRegular c) (hι : #ι < c)
     (hc' : c ≠ ℵ₀) (hf : ∀ (i), ∀ b < c.ord, f i b < c.ord) {a} :
     a < c.ord → derivFamily.{u, u} f a < c.ord :=
   derivFamily_lt_ord_lift hc (by rwa [lift_id]) hc' hf

7c2ce0c2

fix: precedences of ⨆⋃⋂⨅ (#5614)

e3c8f983

Diff

@@ -1039,7 +1039,7 @@ then the cardinality of the collection of those finite sets
 must be at least the cardinality of `β`.
 -/
 theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α → Finset β)
-    (w : (⋃ a, (f a : Set β)) = ⊤) : (#β) ≤ (#range f) := by
+    (w : ⋃ a, (f a : Set β) = ⊤) : (#β) ≤ (#range f) := by
   have k : _root_.Infinite (range f) := by
     rw [infinite_coe_iff]
     apply mt (union_finset_finite_of_range_finite f)

7c2ce0c2

fix: change compl precedence (#5586)

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

4d4f0f25

Diff

@@ -128,7 +128,7 @@ def StrictOrder.cof (r : α → α → Prop) : Cardinal :=
 /-- The set in the definition of `Order.StrictOrder.cof` is nonempty. -/
 theorem StrictOrder.cof_nonempty (r : α → α → Prop) [IsIrrefl α r] :
     { c | ∃ S : Set α, Unbounded r S ∧ (#S) = c }.Nonempty :=
-  @Order.cof_nonempty α _ (IsRefl.swap (rᶜ))
+  @Order.cof_nonempty α _ (IsRefl.swap rᶜ)
 #align strict_order.cof_nonempty StrictOrder.cof_nonempty
 
 /-! ### Cofinality of ordinals -/

7c2ce0c2

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -638,7 +638,7 @@ theorem exists_fundamental_sequence (a : Ordinal.{u}) :
     by_cases h : ∀ j, r j i → f j < f i
     · refine' ⟨typein r' ⟨i, h⟩, typein_lt_type _ _, _⟩
       rw [bfamilyOfFamily'_typein]
-    · push_neg  at h
+    · push_neg at h
       cases' wo.wf.min_mem _ h with hji hij
       refine' ⟨typein r' ⟨_, fun k hkj => lt_of_lt_of_le _ hij⟩, typein_lt_type _ _, _⟩
       · by_contra' H
@@ -983,7 +983,7 @@ theorem isRegular_succ {c : Cardinal.{u}} (h : ℵ₀ ≤ c) : IsRegular (succ c
         cases' Quotient.exists_rep (@succ Cardinal _ _ c) with α αe; simp at αe
         rcases ord_eq α with ⟨r, wo, re⟩; skip
         have := ord_isLimit (h.trans (le_succ _))
-        rw [← αe, re] at this⊢
+        rw [← αe, re] at this ⊢
         rcases cof_eq' r this with ⟨S, H, Se⟩
         rw [← Se]
         apply lt_imp_lt_of_le_imp_le fun h => mul_le_mul_right' h c
@@ -1029,7 +1029,7 @@ has an infinite fiber.
 -/
 theorem exists_infinite_fiber {β α : Type _} (f : β → α) (w : (#α) < (#β)) (w' : Infinite α) :
     ∃ a : α, Infinite (f ⁻¹' {a}) := by
-  simp_rw [Cardinal.infinite_iff] at w'⊢
+  simp_rw [Cardinal.infinite_iff] at w' ⊢
   cases' infinite_pigeonhole_card_lt f w w' with a ha
   exact ⟨a, w'.trans ha.le⟩
 #align cardinal.exists_infinite_fiber Cardinal.exists_infinite_fiber
@@ -1226,7 +1226,7 @@ theorem lt_power_cof {c : Cardinal.{u}} : ℵ₀ ≤ c → c < (c^cof c.ord) :=
   Quotient.inductionOn c fun α h => by
     rcases ord_eq α with ⟨r, wo, re⟩; skip
     have := ord_isLimit h
-    rw [mk'_def, re] at this⊢
+    rw [mk'_def, re] at this ⊢
     rcases cof_eq' r this with ⟨S, H, Se⟩
     have := sum_lt_prod (fun a : S => #{ x // r x a }) (fun _ => #α) fun i => ?_
     · simp only [Cardinal.prod_const, Cardinal.lift_id, ← Se, ← mk_sigma, power_def] at this ⊢

7c2ce0c2

chore: formatting issues (#4947)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

5068808d

Diff

@@ -218,17 +218,17 @@ theorem ord_cof_eq (r : α → α → Prop) [IsWellOrder α r] :
 /-! ### Cofinality of suprema and least strict upper bounds -/
 
 
-private theorem card_mem_cof {o} : ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = o.card :=
+private theorem card_mem_cof {o} : ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = o.card :=
   ⟨_, _, lsub_typein o, mk_ordinal_out o⟩
 
 /-- The set in the `lsub` characterization of `cof` is nonempty. -/
 theorem cof_lsub_def_nonempty (o) :
-    { a : Cardinal | ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a }.Nonempty :=
+    { a : Cardinal | ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a }.Nonempty :=
   ⟨_, card_mem_cof⟩
 #align ordinal.cof_lsub_def_nonempty Ordinal.cof_lsub_def_nonempty
 
 theorem cof_eq_sInf_lsub (o : Ordinal.{u}) : cof o =
-    sInf { a : Cardinal | ∃ (ι : Type u)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } := by
+    sInf { a : Cardinal | ∃ (ι : Type u) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } := by
   refine' le_antisymm (le_csInf (cof_lsub_def_nonempty o) _) (csInf_le' _)
   · rintro a ⟨ι, f, hf, rfl⟩
     rw [← type_lt o]
@@ -298,7 +298,7 @@ theorem ord_cof_le (o : Ordinal.{u}) : o.cof.ord ≤ o :=
 #align ordinal.ord_cof_le Ordinal.ord_cof_le
 
 theorem exists_lsub_cof (o : Ordinal) :
-    ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = cof o := by
+    ∃ (ι : _) (f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = cof o := by
   rw [cof_eq_sInf_lsub]
   exact csInf_mem (cof_lsub_def_nonempty o)
 #align ordinal.exists_lsub_cof Ordinal.exists_lsub_cof
@@ -827,7 +827,7 @@ theorem infinite_pigeonhole_card {β α : Type u} (f : β → α) (θ : Cardinal
 
 theorem infinite_pigeonhole_set {β α : Type u} {s : Set β} (f : s → α) (θ : Cardinal)
     (hθ : θ ≤ (#s)) (h₁ : ℵ₀ ≤ θ) (h₂ : (#α) < θ.ord.cof) :
-    ∃ (a : α)(t : Set β)(h : t ⊆ s), θ ≤ (#t) ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a := by
+    ∃ (a : α) (t : Set β) (h : t ⊆ s), θ ≤ (#t) ∧ ∀ ⦃x⦄ (hx : x ∈ t), f ⟨x, h hx⟩ = a := by
   cases' infinite_pigeonhole_card f θ hθ h₁ h₂ with a ha
   refine' ⟨a, { x | ∃ h, f ⟨x, h⟩ = a }, _, _, _⟩
   · rintro x ⟨hx, _⟩

7c2ce0c2

chore: update std 05-22 (#4248)

The main breaking change is that tac <;> [t1, t2] is now written tac <;> [t1; t2], to avoid clashing with tactics like cases and use that take comma-separated lists.

ac36b28e

Diff

@@ -524,7 +524,7 @@ theorem cof_eq_one_iff_is_succ {o} : cof.{u} o = 1 ↔ ∃ a, o = succ a :=
           Eq.symm <|
             Quotient.sound
               ⟨RelIso.ofSurjective (RelEmbedding.ofMonotone _ fun x y => _) fun x => _⟩⟩
-      · apply Sum.rec <;> [exact Subtype.val, exact fun _ => a]
+      · apply Sum.rec <;> [exact Subtype.val; exact fun _ => a]
       · rcases x with (x | ⟨⟨⟨⟩⟩⟩) <;> rcases y with (y | ⟨⟨⟨⟩⟩⟩) <;>
           simp [Subrel, Order.Preimage, EmptyRelation]
         exact x.2

7c2ce0c2

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

@@ -66,7 +66,7 @@ namespace Order
 /-- Cofinality of a reflexive order `≼`. This is the smallest cardinality
   of a subset `S : Set α` such that `∀ a, ∃ b ∈ S, a ≼ b`. -/
 def cof (r : α → α → Prop) : Cardinal :=
-  infₛ { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c }
+  sInf { c | ∃ S : Set α, (∀ a, ∃ b ∈ S, r a b) ∧ (#S) = c }
 #align order.cof Order.cof
 
 /-- The set in the definition of `Order.cof` is nonempty. -/
@@ -76,12 +76,12 @@ theorem cof_nonempty (r : α → α → Prop) [IsRefl α r] :
 #align order.cof_nonempty Order.cof_nonempty
 
 theorem cof_le (r : α → α → Prop) {S : Set α} (h : ∀ a, ∃ b ∈ S, r a b) : cof r ≤ (#S) :=
-  cinfₛ_le' ⟨S, h, rfl⟩
+  csInf_le' ⟨S, h, rfl⟩
 #align order.cof_le Order.cof_le
 
 theorem le_cof {r : α → α → Prop} [IsRefl α r] (c : Cardinal) :
     c ≤ cof r ↔ ∀ {S : Set α}, (∀ a, ∃ b ∈ S, r a b) → c ≤ (#S) := by
-  rw [cof, le_cinfₛ_iff'' (cof_nonempty r)]
+  rw [cof, le_csInf_iff'' (cof_nonempty r)]
   use fun H S h => H _ ⟨S, h, rfl⟩
   rintro H d ⟨S, h, rfl⟩
   exact H h
@@ -92,10 +92,10 @@ end Order
 theorem RelIso.cof_le_lift {α : Type u} {β : Type v} {r : α → α → Prop} {s} [IsRefl β s]
     (f : r ≃r s) : Cardinal.lift.{max u v} (Order.cof r) ≤
     Cardinal.lift.{max u v} (Order.cof s) := by
-  rw [Order.cof, Order.cof, lift_infₛ, lift_infₛ,
-    le_cinfₛ_iff'' (nonempty_image_iff.2 (Order.cof_nonempty s))]
+  rw [Order.cof, Order.cof, lift_sInf, lift_sInf,
+    le_csInf_iff'' (nonempty_image_iff.2 (Order.cof_nonempty s))]
   rintro - ⟨-, ⟨u, H, rfl⟩, rfl⟩
-  apply cinfₛ_le'
+  apply csInf_le'
   refine'
     ⟨_, ⟨f.symm '' u, fun a => _, rfl⟩,
       lift_mk_eq.{u, v, max u v}.2 ⟨(f.symm.toEquiv.image u).symm⟩⟩
@@ -161,7 +161,7 @@ theorem cof_type (r : α → α → Prop) [IsWellOrder α r] : (type r).cof = St
 #align ordinal.cof_type Ordinal.cof_type
 
 theorem le_cof_type [IsWellOrder α r] {c} : c ≤ cof (type r) ↔ ∀ S, Unbounded r S → c ≤ (#S) :=
-  (le_cinfₛ_iff'' (StrictOrder.cof_nonempty r)).trans
+  (le_csInf_iff'' (StrictOrder.cof_nonempty r)).trans
     ⟨fun H S h => H _ ⟨S, h, rfl⟩, by
       rintro H d ⟨S, h, rfl⟩
       exact H _ h⟩
@@ -176,7 +176,7 @@ theorem lt_cof_type [IsWellOrder α r] {S : Set α} : (#S) < cof (type r) → Bo
 #align ordinal.lt_cof_type Ordinal.lt_cof_type
 
 theorem cof_eq (r : α → α → Prop) [IsWellOrder α r] : ∃ S, Unbounded r S ∧ (#S) = cof (type r) :=
-  cinfₛ_mem (StrictOrder.cof_nonempty r)
+  csInf_mem (StrictOrder.cof_nonempty r)
 #align ordinal.cof_eq Ordinal.cof_eq
 
 theorem ord_cof_eq (r : α → α → Prop) [IsWellOrder α r] :
@@ -227,9 +227,9 @@ theorem cof_lsub_def_nonempty (o) :
   ⟨_, card_mem_cof⟩
 #align ordinal.cof_lsub_def_nonempty Ordinal.cof_lsub_def_nonempty
 
-theorem cof_eq_infₛ_lsub (o : Ordinal.{u}) : cof o =
-    infₛ { a : Cardinal | ∃ (ι : Type u)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } := by
-  refine' le_antisymm (le_cinfₛ (cof_lsub_def_nonempty o) _) (cinfₛ_le' _)
+theorem cof_eq_sInf_lsub (o : Ordinal.{u}) : cof o =
+    sInf { a : Cardinal | ∃ (ι : Type u)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } := by
+  refine' le_antisymm (le_csInf (cof_lsub_def_nonempty o) _) (csInf_le' _)
   · rintro a ⟨ι, f, hf, rfl⟩
     rw [← type_lt o]
     refine'
@@ -259,7 +259,7 @@ theorem cof_eq_infₛ_lsub (o : Ordinal.{u}) : cof o =
     rcases hS (enum (· < ·) a ha) with ⟨b, hb, hb'⟩
     rw [← typein_le_typein, typein_enum] at hb'
     exact hb'.trans_lt (lt_lsub.{u, u} f ⟨b, hb⟩)
-#align ordinal.cof_eq_Inf_lsub Ordinal.cof_eq_infₛ_lsub
+#align ordinal.cof_eq_Inf_lsub Ordinal.cof_eq_sInf_lsub
 
 @[simp]
 theorem lift_cof (o) : Cardinal.lift.{u, v} (cof o) = cof (Ordinal.lift.{u, v} o) := by
@@ -286,8 +286,8 @@ theorem lift_cof (o) : Cardinal.lift.{u, v} (cof o) = cof (Ordinal.lift.{u, v} o
 #align ordinal.lift_cof Ordinal.lift_cof
 
 theorem cof_le_card (o) : cof o ≤ card o := by
-  rw [cof_eq_infₛ_lsub]
-  exact cinfₛ_le' card_mem_cof
+  rw [cof_eq_sInf_lsub]
+  exact csInf_le' card_mem_cof
 #align ordinal.cof_le_card Ordinal.cof_le_card
 
 theorem cof_ord_le (c : Cardinal) : c.ord.cof ≤ c := by simpa using cof_le_card c.ord
@@ -299,13 +299,13 @@ theorem ord_cof_le (o : Ordinal.{u}) : o.cof.ord ≤ o :=
 
 theorem exists_lsub_cof (o : Ordinal) :
     ∃ (ι : _)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = cof o := by
-  rw [cof_eq_infₛ_lsub]
-  exact cinfₛ_mem (cof_lsub_def_nonempty o)
+  rw [cof_eq_sInf_lsub]
+  exact csInf_mem (cof_lsub_def_nonempty o)
 #align ordinal.exists_lsub_cof Ordinal.exists_lsub_cof
 
 theorem cof_lsub_le {ι} (f : ι → Ordinal) : cof (lsub.{u, u} f) ≤ (#ι) := by
-  rw [cof_eq_infₛ_lsub]
-  exact cinfₛ_le' ⟨ι, f, rfl, rfl⟩
+  rw [cof_eq_sInf_lsub]
+  exact csInf_le' ⟨ι, f, rfl, rfl⟩
 #align ordinal.cof_lsub_le Ordinal.cof_lsub_le
 
 theorem cof_lsub_le_lift {ι} (f : ι → Ordinal) :
@@ -319,9 +319,9 @@ theorem cof_lsub_le_lift {ι} (f : ι → Ordinal) :
 
 theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
     a ≤ cof o ↔ ∀ {ι} (f : ι → Ordinal), lsub.{u, u} f = o → a ≤ (#ι) := by
-  rw [cof_eq_infₛ_lsub]
+  rw [cof_eq_sInf_lsub]
   exact
-    (le_cinfₛ_iff'' (cof_lsub_def_nonempty o)).trans
+    (le_csInf_iff'' (cof_lsub_def_nonempty o)).trans
       ⟨fun H ι f hf => H _ ⟨ι, f, hf, rfl⟩, fun H b ⟨ι, f, hf, hb⟩ => by
         rw [← hb]
         exact H _ hf⟩
@@ -363,19 +363,19 @@ theorem sup_lt_ord {ι} {f : ι → Ordinal} {c : Ordinal} (hι : (#ι) < c.cof)
   sup_lt_ord_lift (by rwa [(#ι).lift_id])
 #align ordinal.sup_lt_ord Ordinal.sup_lt_ord
 
-theorem supᵢ_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal}
+theorem iSup_lt_lift {ι} {f : ι → Cardinal} {c : Cardinal}
     (hι : Cardinal.lift.{v, u} (#ι) < c.ord.cof)
-    (hf : ∀ i, f i < c) : supᵢ.{max u v + 1, u + 1} f < c := by
-  rw [← ord_lt_ord, supᵢ_ord (Cardinal.bddAbove_range.{u, v} _)]
+    (hf : ∀ i, f i < c) : iSup.{max u v + 1, u + 1} f < c := by
+  rw [← ord_lt_ord, iSup_ord (Cardinal.bddAbove_range.{u, v} _)]
   refine' sup_lt_ord_lift hι fun i => _
   rw [ord_lt_ord]
   apply hf
-#align ordinal.supr_lt_lift Ordinal.supᵢ_lt_lift
+#align ordinal.supr_lt_lift Ordinal.iSup_lt_lift
 
-theorem supᵢ_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : (#ι) < c.ord.cof) :
-    (∀ i, f i < c) → supᵢ f < c :=
-  supᵢ_lt_lift (by rwa [(#ι).lift_id])
-#align ordinal.supr_lt Ordinal.supᵢ_lt
+theorem iSup_lt {ι} {f : ι → Cardinal} {c : Cardinal} (hι : (#ι) < c.ord.cof) :
+    (∀ i, f i < c) → iSup f < c :=
+  iSup_lt_lift (by rwa [(#ι).lift_id])
+#align ordinal.supr_lt Ordinal.iSup_lt
 
 theorem nfpFamily_lt_ord_lift {ι} {f : ι → Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c)
     (hc' : Cardinal.lift.{v, u} (#ι) < cof c) (hf : ∀ (i), ∀ b < c, f i b < c) {a} (ha : a < c) :
@@ -443,7 +443,7 @@ theorem cof_blsub_le {o} (f : ∀ a < o, Ordinal) : cof (blsub.{u, u} o f) ≤ o
 theorem blsub_lt_ord_lift {o : Ordinal.{u}} {f : ∀ a < o, Ordinal} {c : Ordinal}
     (ho : Cardinal.lift.{v, u} o.card < c.cof) (hf : ∀ i hi, f i hi < c) : blsub.{u, v} o f < c :=
   lt_of_le_of_ne (blsub_le hf) fun h =>
-    ho.not_le (by simpa [← supᵢ_ord, hf, h] using cof_blsub_le_lift.{u, v} f)
+    ho.not_le (by simpa [← iSup_ord, hf, h] using cof_blsub_le_lift.{u, v} f)
 #align ordinal.blsub_lt_ord_lift Ordinal.blsub_lt_ord_lift
 
 theorem blsub_lt_ord {o : Ordinal} {f : ∀ a < o, Ordinal} {c : Ordinal} (ho : o.card < c.cof)
@@ -659,7 +659,7 @@ protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u
   refine' ⟨_, @fun i j _ _ h => hf.strictMono (hg.2.1 _ _ h), _⟩
   · rcases exists_lsub_cof (f a) with ⟨ι, f', hf', hι⟩
     rw [← hg.cof_eq, ord_le_ord, ← hι]
-    suffices (lsub.{u, u} fun i => infₛ { b : Ordinal | f' i ≤ f b }) = a by
+    suffices (lsub.{u, u} fun i => sInf { b : Ordinal | f' i ≤ f b }) = a by
       rw [← this]
       apply cof_lsub_le
     have H : ∀ i, ∃ b < a, f' i ≤ f b := fun i => by
@@ -668,13 +668,13 @@ protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u
       simpa using this
     refine' (lsub_le fun i => _).antisymm (le_of_forall_lt fun b hb => _)
     · rcases H i with ⟨b, hb, hb'⟩
-      exact lt_of_le_of_lt (cinfₛ_le' hb') hb
+      exact lt_of_le_of_lt (csInf_le' hb') hb
     · have := hf.strictMono hb
       rw [← hf', lt_lsub_iff] at this
       cases' this with i hi
       rcases H i with ⟨b, _, hb⟩
       exact
-        ((le_cinfₛ_iff'' ⟨b, by exact hb⟩).2 fun c hc =>
+        ((le_csInf_iff'' ⟨b, by exact hb⟩).2 fun c hc =>
           hf.strictMono.le_iff_le.1 (hi.trans hc)).trans_lt (lt_lsub _ i)
   · rw [@blsub_comp.{u, u, u} a _ (fun b _ => f b) (@fun i j _ _ h => hf.strictMono.monotone h) g
         hg.2.2]
@@ -780,25 +780,25 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ.{u, v} :=
 
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
-theorem unbounded_of_unbounded_unionₛ (r : α → α → Prop) [wo : IsWellOrder α r] {s : Set (Set α)}
+theorem unbounded_of_unbounded_sUnion (r : α → α → Prop) [wo : IsWellOrder α r] {s : Set (Set α)}
     (h₁ : Unbounded r <| ⋃₀ s) (h₂ : (#s) < StrictOrder.cof r) : ∃ x ∈ s, Unbounded r x := by
   by_contra' h
   simp_rw [not_unbounded_iff] at h
   let f : s → α := fun x : s => wo.wf.sup x (h x.1 x.2)
-  refine' h₂.not_le (le_trans (cinfₛ_le' ⟨range f, fun x => _, rfl⟩) mk_range_le)
+  refine' h₂.not_le (le_trans (csInf_le' ⟨range f, fun x => _, rfl⟩) mk_range_le)
   rcases h₁ x with ⟨y, ⟨c, hc, hy⟩, hxy⟩
   exact ⟨f ⟨c, hc⟩, mem_range_self _, fun hxz => hxy (Trans.trans (wo.wf.lt_sup _ hy) hxz)⟩
-#align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_unionₛ
+#align ordinal.unbounded_of_unbounded_sUnion Ordinal.unbounded_of_unbounded_sUnion
 
 /-- If the union of s is unbounded and s is smaller than the cofinality,
   then s has an unbounded member -/
-theorem unbounded_of_unbounded_unionᵢ {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
+theorem unbounded_of_unbounded_iUnion {α β : Type u} (r : α → α → Prop) [wo : IsWellOrder α r]
     (s : β → Set α) (h₁ : Unbounded r <| ⋃ x, s x) (h₂ : (#β) < StrictOrder.cof r) :
     ∃ x : β, Unbounded r (s x) := by
-  rw [← unionₛ_range] at h₁
-  rcases unbounded_of_unbounded_unionₛ r h₁ (mk_range_le.trans_lt h₂) with ⟨_, ⟨x, rfl⟩, u⟩
+  rw [← sUnion_range] at h₁
+  rcases unbounded_of_unbounded_sUnion r h₁ (mk_range_le.trans_lt h₂) with ⟨_, ⟨x, rfl⟩, u⟩
   exact ⟨x, u⟩
-#align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_unionᵢ
+#align ordinal.unbounded_of_unbounded_Union Ordinal.unbounded_of_unbounded_iUnion
 
 /-- The infinite pigeonhole principle -/
 theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤ (#β)) (h₂ : (#α) < (#β).ord.cof) :
@@ -806,10 +806,10 @@ theorem infinite_pigeonhole {β α : Type u} (f : β → α) (h₁ : ℵ₀ ≤
   have : ∃ a, (#β) ≤ (#f ⁻¹' {a}) := by
     by_contra' h
     apply mk_univ.not_lt
-    rw [← preimage_univ, ← unionᵢ_of_singleton, preimage_unionᵢ]
+    rw [← preimage_univ, ← iUnion_of_singleton, preimage_iUnion]
     exact
-      mk_unionᵢ_le_sum_mk.trans_lt
-        ((sum_le_supᵢ _).trans_lt <| mul_lt_of_lt h₁ (h₂.trans_le <| cof_ord_le _) (supᵢ_lt h₂ h))
+      mk_iUnion_le_sum_mk.trans_lt
+        ((sum_le_iSup _).trans_lt <| mul_lt_of_lt h₁ (h₂.trans_le <| cof_ord_le _) (iSup_lt h₂ h))
   cases' this with x h
   refine' ⟨x, h.antisymm' _⟩
   rw [le_mk_iff_exists_set]
@@ -888,7 +888,7 @@ theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (be
     exact isStrongLimit_aleph0
   · refine' ⟨beth_ne_zero o, fun a ha => _⟩
     rw [beth_limit ⟨h, isSuccLimit_iff_succ_lt.1 H⟩] at ha
-    rcases exists_lt_of_lt_csupᵢ' ha with ⟨⟨i, hi⟩, ha⟩
+    rcases exists_lt_of_lt_ciSup' ha with ⟨⟨i, hi⟩, ha⟩
     have := power_le_power_left two_ne_zero ha.le
     rw [← beth_succ] at this
     exact this.trans_lt (beth_lt.2 (H.succ_lt hi))
@@ -908,10 +908,10 @@ theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α
   apply le_antisymm
   · have : { s : Set α | Bounded r s } = ⋃ i, 𝒫{ j | r j i } := setOf_exists _
     rw [← coe_setOf, this]
-    refine mk_unionᵢ_le_sum_mk.trans ((sum_le_supᵢ (fun i => #(𝒫{ j | r j i }))).trans
+    refine mk_iUnion_le_sum_mk.trans ((sum_le_iSup (fun i => #(𝒫{ j | r j i }))).trans
       ((mul_le_max_of_aleph0_le_left ha).trans ?_))
     rw [max_eq_left]
-    apply csupᵢ_le' _
+    apply ciSup_le' _
     intro i
     rw [mk_powerset]
     apply (h'.two_power_lt _).le
@@ -1100,19 +1100,19 @@ theorem bsup_lt_ord_of_isRegular {o : Ordinal} {f : ∀ a < o, Ordinal} {c} (hc
   bsup_lt_ord (by rwa [hc.cof_eq])
 #align cardinal.bsup_lt_ord_of_is_regular Cardinal.bsup_lt_ord_of_isRegular
 
-theorem supᵢ_lt_lift_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c)
-    (hι : Cardinal.lift.{v, u} (#ι) < c) : (∀ i, f i < c) → supᵢ.{max u v + 1, u + 1} f < c :=
-  supᵢ_lt_lift.{u, v} (by rwa [hc.cof_eq])
-#align cardinal.supr_lt_lift_of_is_regular Cardinal.supᵢ_lt_lift_of_isRegular
+theorem iSup_lt_lift_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c)
+    (hι : Cardinal.lift.{v, u} (#ι) < c) : (∀ i, f i < c) → iSup.{max u v + 1, u + 1} f < c :=
+  iSup_lt_lift.{u, v} (by rwa [hc.cof_eq])
+#align cardinal.supr_lt_lift_of_is_regular Cardinal.iSup_lt_lift_of_isRegular
 
-theorem supᵢ_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
-    (∀ i, f i < c) → supᵢ f < c :=
-  supᵢ_lt (by rwa [hc.cof_eq])
-#align cardinal.supr_lt_of_is_regular Cardinal.supᵢ_lt_of_isRegular
+theorem iSup_lt_of_isRegular {ι} {f : ι → Cardinal} {c} (hc : IsRegular c) (hι : (#ι) < c) :
+    (∀ i, f i < c) → iSup f < c :=
+  iSup_lt (by rwa [hc.cof_eq])
+#align cardinal.supr_lt_of_is_regular Cardinal.iSup_lt_of_isRegular
 
 theorem sum_lt_lift_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)
     (hι : Cardinal.lift.{v, u} (#ι) < c) (hf : ∀ i, f i < c) : sum f < c :=
-  (sum_le_supᵢ_lift _).trans_lt <| mul_lt_of_lt hc.1 hι (supᵢ_lt_lift_of_isRegular hc hι hf)
+  (sum_le_iSup_lift _).trans_lt <| mul_lt_of_lt hc.1 hι (iSup_lt_lift_of_isRegular hc hι hf)
 #align cardinal.sum_lt_lift_of_is_regular Cardinal.sum_lt_lift_of_isRegular
 
 theorem sum_lt_of_isRegular {ι : Type u} {f : ι → Cardinal} {c : Cardinal} (hc : IsRegular c)

7c2ce0c2

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

@@ -90,8 +90,8 @@ theorem le_cof {r : α → α → Prop} [IsRefl α r] (c : Cardinal) :
 end Order
 
 theorem RelIso.cof_le_lift {α : Type u} {β : Type v} {r : α → α → Prop} {s} [IsRefl β s]
-    (f : r ≃r s) : Cardinal.lift.{max u v} (Order.cof r) ≤ Cardinal.lift.{max u v} (Order.cof s) :=
-  by
+    (f : r ≃r s) : Cardinal.lift.{max u v} (Order.cof r) ≤
+    Cardinal.lift.{max u v} (Order.cof s) := by
   rw [Order.cof, Order.cof, lift_infₛ, lift_infₛ,
     le_cinfₛ_iff'' (nonempty_image_iff.2 (Order.cof_nonempty s))]
   rintro - ⟨-, ⟨u, H, rfl⟩, rfl⟩
@@ -227,9 +227,8 @@ theorem cof_lsub_def_nonempty (o) :
   ⟨_, card_mem_cof⟩
 #align ordinal.cof_lsub_def_nonempty Ordinal.cof_lsub_def_nonempty
 
-theorem cof_eq_infₛ_lsub (o : Ordinal.{u}) :
-    cof o = infₛ { a : Cardinal | ∃ (ι : Type u)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } :=
-  by
+theorem cof_eq_infₛ_lsub (o : Ordinal.{u}) : cof o =
+    infₛ { a : Cardinal | ∃ (ι : Type u)(f : ι → Ordinal), lsub.{u, u} f = o ∧ (#ι) = a } := by
   refine' le_antisymm (le_cinfₛ (cof_lsub_def_nonempty o) _) (cinfₛ_le' _)
   · rintro a ⟨ι, f, hf, rfl⟩
     rw [← type_lt o]
@@ -323,8 +322,7 @@ theorem le_cof_iff_lsub {o : Ordinal} {a : Cardinal} :
   rw [cof_eq_infₛ_lsub]
   exact
     (le_cinfₛ_iff'' (cof_lsub_def_nonempty o)).trans
-      ⟨fun H ι f hf => H _ ⟨ι, f, hf, rfl⟩, fun H b ⟨ι, f, hf, hb⟩ =>
-        by
+      ⟨fun H ι f hf => H _ ⟨ι, f, hf, rfl⟩, fun H b ⟨ι, f, hf, hb⟩ => by
         rw [← hb]
         exact H _ hf⟩
 #align ordinal.le_cof_iff_lsub Ordinal.le_cof_iff_lsub
@@ -413,8 +411,8 @@ theorem nfp_lt_ord {f : Ordinal → Ordinal} {c} (hc : ℵ₀ < cof c) (hf : ∀
   nfpFamily_lt_ord_lift hc (by simpa using Cardinal.one_lt_aleph0.trans hc) fun _ => hf
 #align ordinal.nfp_lt_ord Ordinal.nfp_lt_ord
 
-theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, blsub.{u, u} _ f = o :=
-  by
+theorem exists_blsub_cof (o : Ordinal) :
+    ∃ f : ∀ a < (cof o).ord, Ordinal, blsub.{u, u} _ f = o := by
   rcases exists_lsub_cof o with ⟨ι, f, hf, hι⟩
   rcases Cardinal.ord_eq ι with ⟨r, hr, hι'⟩
   rw [← @blsub_eq_lsub' ι r hr] at hf
@@ -425,8 +423,7 @@ theorem exists_blsub_cof (o : Ordinal) : ∃ f : ∀ a < (cof o).ord, Ordinal, b
 theorem le_cof_iff_blsub {b : Ordinal} {a : Cardinal} :
     a ≤ cof b ↔ ∀ {o} (f : ∀ a < o, Ordinal), blsub.{u, u} o f = b → a ≤ o.card :=
   le_cof_iff_lsub.trans
-    ⟨fun H o f hf => by simpa using H _ hf, fun H ι f hf =>
-      by
+    ⟨fun H o f hf => by simpa using H _ hf, fun H ι f hf => by
       rcases Cardinal.ord_eq ι with ⟨r, hr, hι'⟩
       rw [← @blsub_eq_lsub' ι r hr] at hf
       simpa using H _ hf⟩
@@ -616,8 +613,8 @@ theorem trans {a o o' : Ordinal.{u}} {f : ∀ b < o, Ordinal.{u}} (hf : IsFundam
 end IsFundamentalSequence
 
 /-- Every ordinal has a fundamental sequence. -/
-theorem exists_fundamental_sequence (a : Ordinal.{u}) : ∃ f, IsFundamentalSequence a a.cof.ord f :=
-  by
+theorem exists_fundamental_sequence (a : Ordinal.{u}) :
+    ∃ f, IsFundamentalSequence a a.cof.ord f := by
   suffices h : ∃ o f, IsFundamentalSequence a o f
   · rcases h with ⟨o, f, hf⟩
     exact ⟨_, hf.ord_cof⟩
@@ -662,8 +659,7 @@ protected theorem IsNormal.isFundamentalSequence {f : Ordinal.{u} → Ordinal.{u
   refine' ⟨_, @fun i j _ _ h => hf.strictMono (hg.2.1 _ _ h), _⟩
   · rcases exists_lsub_cof (f a) with ⟨ι, f', hf', hι⟩
     rw [← hg.cof_eq, ord_le_ord, ← hι]
-    suffices (lsub.{u, u} fun i => infₛ { b : Ordinal | f' i ≤ f b }) = a
-      by
+    suffices (lsub.{u, u} fun i => infₛ { b : Ordinal | f' i ≤ f b }) = a by
       rw [← this]
       apply cof_lsub_le
     have H : ∀ i, ∃ b < a, f' i ≤ f b := fun i => by
@@ -737,8 +733,7 @@ theorem aleph_cof {o : Ordinal} (ho : o.IsLimit) : (aleph o).ord.cof = o.cof :=
 
 @[simp]
 theorem cof_omega : cof ω = ℵ₀ :=
-  (aleph0_le_cof.2 omega_isLimit).antisymm' <|
-    by
+  (aleph0_le_cof.2 omega_isLimit).antisymm' <| by
     rw [← card_omega]
     apply cof_le_card
 #align ordinal.cof_omega Ordinal.cof_omega
@@ -1054,8 +1049,7 @@ theorem le_range_of_union_finset_eq_top {α β : Type _} [Infinite β] (f : α 
   simp only [not_le] at h
   let u : ∀ b, ∃ a, b ∈ f a := fun b => by simpa using (w.ge : _) (Set.mem_univ b)
   let u' : β → range f := fun b => ⟨f (u b).choose, by simp⟩
-  have v' : ∀ a, u' ⁻¹' {⟨f a, by simp⟩} ≤ f a :=
-    by
+  have v' : ∀ a, u' ⁻¹' {⟨f a, by simp⟩} ≤ f a := by
     rintro a p m
     simp at m
     rw [← m]
@@ -1222,8 +1216,7 @@ theorem IsInaccessible.mk {c} (h₁ : ℵ₀ < c) (h₂ : c ≤ c.ord.cof) (h₃
 
 -- Lean's foundations prove the existence of ℵ₀ many inaccessible cardinals
 theorem univ_inaccessible : IsInaccessible univ.{u, v} :=
-  IsInaccessible.mk (by simpa using lift_lt_univ' ℵ₀) (by simp) fun c h =>
-    by
+  IsInaccessible.mk (by simpa using lift_lt_univ' ℵ₀) (by simp) fun c h => by
     rcases lt_univ'.1 h with ⟨c, rfl⟩
     rw [← lift_two_power.{u, max (u + 1) v}]
     apply lift_lt_univ'

7c2ce0c2

feat: port LinearAlgebra.FreeModule.Rank (#3377)

This PR also fixes the order of universes in Cardinal.lift_lift.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>

2870d41a

Diff

@@ -766,7 +766,7 @@ theorem cof_univ : cof univ.{u, v} = Cardinal.univ.{u, v} :=
       refine' le_of_forall_lt fun c h => _
       rcases lt_univ'.1 h with ⟨c, rfl⟩
       rcases @cof_eq Ordinal.{u} (· < ·) _ with ⟨S, H, Se⟩
-      rw [univ, ← lift_cof, ← Cardinal.lift_lift.{u, u + 1, v}, Cardinal.lift_lt, ← Se]
+      rw [univ, ← lift_cof, ← Cardinal.lift_lift.{u+1, v, u}, Cardinal.lift_lt, ← Se]
       refine' lt_of_not_ge fun h => _
       cases' Cardinal.lift_down h with a e
       refine' Quotient.inductionOn a (fun α e => _) e

7c2ce0c2

feat: port changes to Cardinal files (#3343)

My bad for letting these pile up.

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

f13648cc

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Floris van Doorn, Violeta Hernández Palacios
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.cofinality
-! leanprover-community/mathlib commit bb168510ef455e9280a152e7f31673cabd3d7496
+! leanprover-community/mathlib commit 7c2ce0c2da15516b4e65d0c9e254bb6dc93abd1f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -21,7 +21,6 @@ This file contains the definition of cofinality of an ordinal number and regular
 * `Ordinal.cof o` is the cofinality of the ordinal `o`.
   If `o` is the order type of the relation `<` on `α`, then `o.cof` is the smallest cardinality of a
   subset `s` of α that is *cofinal* in `α`, i.e. `∀ x : α, ∃ y ∈ s, ¬ y < x`.
-* `Cardinal.IsLimit c` means that `c` is a (weak) limit cardinal: `c ≠ 0 ∧ ∀ x < c, succ x < c`.
 * `Cardinal.IsStrongLimit c` means that `c` is a strong limit cardinal:
   `c ≠ 0 ∧ ∀ x < c, 2 ^ x < c`.
 * `Cardinal.IsRegular c` means that `c` is a regular cardinal: `ℵ₀ ≤ c ∧ c.ord.cof = c`.
@@ -860,27 +859,6 @@ open Ordinal
 -- mathport name: cardinal.pow
 --local infixr:0 "^" => @HPow.hPow Cardinal Cardinal Cardinal instHPow
 
-/-- A cardinal is a limit if it is not zero or a successor
-  cardinal. Note that `ℵ₀` is a limit cardinal by this definition. -/
-def IsLimit (c : Cardinal) : Prop :=
-  c ≠ 0 ∧ ∀ x < c, succ x < c
-#align cardinal.is_limit Cardinal.IsLimit
-
-theorem IsLimit.ne_zero {c} (h : IsLimit c) : c ≠ 0 :=
-  h.1
-#align cardinal.is_limit.ne_zero Cardinal.IsLimit.ne_zero
-
-theorem IsLimit.succ_lt {x c} (h : IsLimit c) : x < c → succ x < c :=
-  h.2 x
-#align cardinal.is_limit.succ_lt Cardinal.IsLimit.succ_lt
-
-theorem IsLimit.aleph0_le {c} (h : IsLimit c) : ℵ₀ ≤ c := by
-  by_contra' h'
-  rcases lt_aleph0.1 h' with ⟨_ | n, rfl⟩
-  · exact h.1.irrefl
-  · simpa using h.2 n
-#align cardinal.is_limit.aleph_0_le Cardinal.IsLimit.aleph0_le
-
 /-- A cardinal is a strong limit if it is not zero and it is
   closed under powersets. Note that `ℵ₀` is a strong limit by this definition. -/
 def IsStrongLimit (c : Cardinal) : Prop :=
@@ -901,24 +879,24 @@ theorem isStrongLimit_aleph0 : IsStrongLimit ℵ₀ :=
     exact_mod_cast nat_lt_aleph0 (2 ^ n)⟩
 #align cardinal.is_strong_limit_aleph_0 Cardinal.isStrongLimit_aleph0
 
+protected theorem IsStrongLimit.isSuccLimit {c} (H : IsStrongLimit c) : IsSuccLimit c :=
+  isSuccLimit_of_succ_lt fun x h => (succ_le_of_lt <| cantor x).trans_lt (H.two_power_lt h)
+#align cardinal.is_strong_limit.is_succ_limit Cardinal.IsStrongLimit.isSuccLimit
+
 theorem IsStrongLimit.isLimit {c} (H : IsStrongLimit c) : IsLimit c :=
-  ⟨H.1, fun x h => (succ_le_of_lt <| cantor x).trans_lt (H.2 _ h)⟩
+  ⟨H.ne_zero, H.isSuccLimit⟩
 #align cardinal.is_strong_limit.is_limit Cardinal.IsStrongLimit.isLimit
 
-theorem isLimit_aleph0 : IsLimit ℵ₀ :=
-  isStrongLimit_aleph0.isLimit
-#align cardinal.is_limit_aleph_0 Cardinal.isLimit_aleph0
-
-theorem isStrongLimit_beth {o : Ordinal} (H : ∀ a < o, succ a < o) : IsStrongLimit (beth o) := by
+theorem isStrongLimit_beth {o : Ordinal} (H : IsSuccLimit o) : IsStrongLimit (beth o) := by
   rcases eq_or_ne o 0 with (rfl | h)
   · rw [beth_zero]
     exact isStrongLimit_aleph0
   · refine' ⟨beth_ne_zero o, fun a ha => _⟩
-    rw [beth_limit ⟨h, H⟩] at ha
+    rw [beth_limit ⟨h, isSuccLimit_iff_succ_lt.1 H⟩] at ha
     rcases exists_lt_of_lt_csupᵢ' ha with ⟨⟨i, hi⟩, ha⟩
     have := power_le_power_left two_ne_zero ha.le
     rw [← beth_succ] at this
-    exact this.trans_lt (beth_lt.2 (H i hi))
+    exact this.trans_lt (beth_lt.2 (H.succ_lt hi))
 #align cardinal.is_strong_limit_beth Cardinal.isStrongLimit_beth
 
 theorem mk_bounded_subset {α : Type _} (h : ∀ x < #α, (2^x) < (#α)) {r : α → α → Prop}

bb168510

feat port: SetTheory.Cardinal.Cofinality (#2479)

6c36fbf6

`set_theory.cardinal.cofinality` ⟷ `Mathlib.SetTheory.Cardinal.Cofinality`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 348

set_theory.cardinal.cofinality ⟷ Mathlib.SetTheory.Cardinal.Cofinality

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 348

`set_theory.cardinal.cofinality` ⟷ `Mathlib.SetTheory.Cardinal.Cofinality`