set_theory.cardinal.ordinal | Mathlib porting status

(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

@@ -182,7 +182,7 @@ theorem aleph'_le_of_limit {o : ordinal} (l : o.is_limit) {c} :
   exact h _ h'
 end⟩
 
-theorem aleph'_limit {o : ordinal} (ho : is_limit o) : aleph' o = ⨆ a : Iio o, aleph' a :=
+theorem aleph'_limit {o : ordinal} (ho : o.is_limit) : aleph' o = ⨆ a : Iio o, aleph' a :=
 begin
   refine le_antisymm _ (csupr_le' (λ i, aleph'_le.2 (le_of_lt i.2))),
   rw aleph'_le_of_limit ho,
@@ -223,7 +223,7 @@ by rw [aleph, add_succ, aleph'_succ, aleph]
 @[simp] theorem aleph_zero : aleph 0 = ℵ₀ :=
 by rw [aleph, add_zero, aleph'_omega]
 
-theorem aleph_limit {o : ordinal} (ho : is_limit o) : aleph o = ⨆ a : Iio o, aleph a :=
+theorem aleph_limit {o : ordinal} (ho : o.is_limit) : aleph o = ⨆ a : Iio o, aleph a :=
 begin
   apply le_antisymm _ (csupr_le' _),
   { rw [aleph, aleph'_limit (ho.add _)],
@@ -261,7 +261,7 @@ begin
   exact λ h, (ord_injective h).not_gt (aleph_pos o)
 end
 
-theorem ord_aleph_is_limit (o : ordinal) : is_limit (aleph o).ord :=
+theorem ord_aleph_is_limit (o : ordinal) : (aleph o).ord.is_limit :=
 ord_is_limit $ aleph_0_le_aleph _
 
 instance (o : ordinal) : no_max_order (aleph o).ord.out.α :=
@@ -347,7 +347,7 @@ limit_rec_on_zero _ _ _
 @[simp] theorem beth_succ (o : ordinal) : beth (succ o) = 2 ^ beth o :=
 limit_rec_on_succ _ _ _ _
 
-theorem beth_limit {o : ordinal} : is_limit o → beth o = ⨆ a : Iio o, beth a :=
+theorem beth_limit {o : ordinal} : o.is_limit → beth o = ⨆ a : Iio o, beth a :=
 limit_rec_on_limit _ _ _ _
 
 theorem beth_strict_mono : strict_mono beth :=

chore(set_theory/ordinal/initial_seg): swap the names of init and init' (#18534)

The former init was stated with the non-preferred to_embedding spelling, and the primed init' used coe_fn. Swapping them around is consistent with how most other bundled morphisms are handled.

mathlib4 PR: https://github.com/leanprover-community/mathlib4/pull/2581

Diff

@@ -97,7 +97,7 @@ aleph_idx.initial_seg.to_rel_embedding.map_rel_iff
 by rw [← not_lt, ← not_lt, aleph_idx_lt]
 
 theorem aleph_idx.init {a b} : b < aleph_idx a → ∃ c, aleph_idx c = b :=
-aleph_idx.initial_seg.init _ _
+aleph_idx.initial_seg.init
 
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -64,7 +64,7 @@ open Ordinal
 theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
   by
   refine' ⟨fun h => aleph_0_ne_zero _, fun a => lt_imp_lt_of_le_imp_le fun h => _⟩
-  · rw [← Ordinal.le_zero, ord_le] at h 
+  · rw [← Ordinal.le_zero, ord_le] at h
     simpa only [card_zero, nonpos_iff_eq_zero] using co.trans h
   · rw [ord_le] at h ⊢
     rwa [← @add_one_of_aleph_0_le (card a), ← card_succ]
@@ -546,7 +546,7 @@ theorem beth_strictMono : StrictMono beth := by
   intro h
   rcases zero_or_succ_or_limit b with (rfl | ⟨c, rfl⟩ | hb)
   · exact (Ordinal.not_lt_zero a h).elim
-  · rw [lt_succ_iff] at h 
+  · rw [lt_succ_iff] at h
     rw [beth_succ]
     apply lt_of_le_of_lt _ (cantor _)
     rcases eq_or_lt_of_le h with (rfl | h); · rfl
@@ -657,7 +657,7 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c :=
       by
       intro q h
       simp only [s, embedding.coe_fn_mk, Order.Preimage, typein_lt_typein, Prod.lex_def,
-        typein_inj] at h 
+        typein_inj] at h
       exact max_le_iff.1 (le_iff_lt_or_eq.2 <| h.imp_right And.left)
     suffices H : (insert (g p) {x | r x (g p)} : Set α) ≃ Sum {x | r x (g p)} PUnit
     ·
@@ -845,12 +845,12 @@ theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧
     · have : a ≠ 0 := by rintro rfl; exact ha.not_lt aleph_0_pos
       left; use ha
       · rw [← not_lt]; exact fun hb => ne_of_gt (hb.trans_le (le_mul_left this)) h
-      · rintro rfl; apply this; rw [MulZeroClass.mul_zero] at h ; exact h.symm
+      · rintro rfl; apply this; rw [MulZeroClass.mul_zero] at h; exact h.symm
     right; by_cases h2a : a = 0; · exact Or.inr h2a
-    have hb : b ≠ 0 := by rintro rfl; apply h2a; rw [MulZeroClass.mul_zero] at h ; exact h.symm
-    left; rw [← h, mul_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha 
+    have hb : b ≠ 0 := by rintro rfl; apply h2a; rw [MulZeroClass.mul_zero] at h; exact h.symm
+    left; rw [← h, mul_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha
     rcases ha with (rfl | rfl | ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩); contradiction; contradiction
-    rw [← Ne] at h2a ; rw [← one_le_iff_ne_zero] at h2a hb ; norm_cast at h2a hb h ⊢
+    rw [← Ne] at h2a; rw [← one_le_iff_ne_zero] at h2a hb; norm_cast at h2a hb h ⊢
     apply le_antisymm _ hb; rw [← not_lt]
     apply fun h2b => ne_of_gt _ h; conv_lhs => rw [← mul_one n]
     rwa [mul_lt_mul_left]; apply Nat.lt_of_succ_le h2a
@@ -963,7 +963,7 @@ theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨
   · cases' le_or_lt ℵ₀ a with ha ha
     · left; use ha; rw [← not_lt]; apply fun hb => ne_of_gt _ h
       exact hb.trans_le (self_le_add_left b a)
-    right; rw [← h, add_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha 
+    right; rw [← h, add_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha
     rcases ha with ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩; norm_cast at h ⊢
     rw [← add_right_inj, h, add_zero]
   · rintro (⟨h1, h2⟩ | h3)
@@ -1002,7 +1002,7 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
     b = c := by
   cases' le_or_lt ℵ₀ b with hb hb
   · have : a < b := ha.trans_le hb
-    rw [add_eq_right hb this.le, eq_comm] at h 
+    rw [add_eq_right hb this.le, eq_comm] at h
     rw [eq_of_add_eq_of_aleph_0_le h this hb]
   · have hc : c < ℵ₀ := by
       rw [← not_le]; intro hc
@@ -1016,7 +1016,7 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
 
 #print Cardinal.eq_of_add_eq_add_right /-
 protected theorem eq_of_add_eq_add_right {a b c : Cardinal} (h : a + b = c + b) (hb : b < ℵ₀) :
-    a = c := by rw [add_comm a b, add_comm c b] at h ; exact Cardinal.eq_of_add_eq_add_left h hb
+    a = c := by rw [add_comm a b, add_comm c b] at h; exact Cardinal.eq_of_add_eq_add_left h hb
 #align cardinal.eq_of_add_eq_add_right Cardinal.eq_of_add_eq_add_right
 -/
 
@@ -1330,9 +1330,9 @@ theorem mk_bounded_set_le_of_infinite (α : Type u) [Infinite α] (c : Cardinal)
   use fun y => if h : ∃ x : s, g x = y then Sum.inl (Classical.choose h).val else Sum.inr ⟨⟩
   apply Subtype.eq; ext
   constructor
-  · rintro ⟨y, h⟩; dsimp only at h ; by_cases h' : ∃ z : s, g z = y
-    · rw [dif_pos h'] at h ; cases Sum.inl.inj h; exact (Classical.choose h').2
-    · rw [dif_neg h'] at h ; cases h
+  · rintro ⟨y, h⟩; dsimp only at h; by_cases h' : ∃ z : s, g z = y
+    · rw [dif_pos h'] at h; cases Sum.inl.inj h; exact (Classical.choose h').2
+    · rw [dif_neg h'] at h; cases h
   · intro h; have : ∃ z : s, g z = g ⟨x, h⟩ := ⟨⟨x, h⟩, rfl⟩
     use g ⟨x, h⟩; dsimp only; rw [dif_pos this]; congr
     suffices : Classical.choose this = ⟨x, h⟩; exact congr_arg Subtype.val this
@@ -1401,7 +1401,7 @@ theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α]
   classical
   lift s to Finset α using s.to_finite
   lift t to Finset β using t.to_finite
-  simp only [Finset.coe_sort_coe, mk_coe_finset, lift_nat_cast, Nat.cast_inj] at h2 
+  simp only [Finset.coe_sort_coe, mk_coe_finset, lift_nat_cast, Nat.cast_inj] at h2
   simp only [← Finset.coe_compl, Finset.coe_sort_coe, mk_coe_finset, Finset.card_compl,
     lift_nat_cast, Nat.cast_inj, h1, h2]
 #align cardinal.mk_compl_eq_mk_compl_finite_lift Cardinal.mk_compl_eq_mk_compl_finite_lift
@@ -1442,7 +1442,7 @@ theorem extend_function_finite {α β : Type _} [Finite α] {s : Set α} (f : s
   by
   apply extend_function f
   cases' id h with g
-  rw [← lift_mk_eq] at h 
+  rw [← lift_mk_eq] at h
   rw [← lift_mk_eq, mk_compl_eq_mk_compl_finite_lift h]
   rw [mk_range_eq_lift]; exact f.2
 #align cardinal.extend_function_finite Cardinal.extend_function_finite

bump to nightly-2024-02-14-08

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

b742255f

Diff

@@ -1070,18 +1070,18 @@ theorem add_le_add_iff_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < Cardinal
 #align cardinal.add_le_add_iff_of_lt_aleph_0 Cardinal.add_le_add_iff_of_lt_aleph0
 -/
 
-#print Cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0 /-
+#print Cardinal.add_nat_le_add_nat_iff /-
 @[simp]
-theorem add_nat_le_add_nat_iff_of_lt_aleph_0 {α β : Cardinal} (n : ℕ) : α + n ≤ β + n ↔ α ≤ β :=
+theorem add_nat_le_add_nat_iff {α β : Cardinal} (n : ℕ) : α + n ≤ β + n ↔ α ≤ β :=
   add_le_add_iff_of_lt_aleph0 (nat_lt_aleph0 n)
-#align cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0 Cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0
+#align cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0 Cardinal.add_nat_le_add_nat_iff
 -/
 
-#print Cardinal.add_one_le_add_one_iff_of_lt_aleph_0 /-
+#print Cardinal.add_one_le_add_one_iff /-
 @[simp]
-theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β + 1 ↔ α ≤ β :=
+theorem add_one_le_add_one_iff {α β : Cardinal} : α + 1 ≤ β + 1 ↔ α ≤ β :=
   add_le_add_iff_of_lt_aleph0 one_lt_aleph0
-#align cardinal.add_one_le_add_one_iff_of_lt_aleph_0 Cardinal.add_one_le_add_one_iff_of_lt_aleph_0
+#align cardinal.add_one_le_add_one_iff_of_lt_aleph_0 Cardinal.add_one_le_add_one_iff
 -/
 
 /-! ### Properties about power -/

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -1399,6 +1399,11 @@ theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α]
   rcases lift_mk_eq.1 h1 with ⟨e⟩; letI : Fintype β := Fintype.ofEquiv α e
   replace h1 : Fintype.card α = Fintype.card β := (Fintype.ofEquiv_card _).symm
   classical
+  lift s to Finset α using s.to_finite
+  lift t to Finset β using t.to_finite
+  simp only [Finset.coe_sort_coe, mk_coe_finset, lift_nat_cast, Nat.cast_inj] at h2 
+  simp only [← Finset.coe_compl, Finset.coe_sort_coe, mk_coe_finset, Finset.card_compl,
+    lift_nat_cast, Nat.cast_inj, h1, h2]
 #align cardinal.mk_compl_eq_mk_compl_finite_lift Cardinal.mk_compl_eq_mk_compl_finite_lift
 -/

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -1399,11 +1399,6 @@ theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α]
   rcases lift_mk_eq.1 h1 with ⟨e⟩; letI : Fintype β := Fintype.ofEquiv α e
   replace h1 : Fintype.card α = Fintype.card β := (Fintype.ofEquiv_card _).symm
   classical
-  lift s to Finset α using s.to_finite
-  lift t to Finset β using t.to_finite
-  simp only [Finset.coe_sort_coe, mk_coe_finset, lift_nat_cast, Nat.cast_inj] at h2 
-  simp only [← Finset.coe_compl, Finset.coe_sort_coe, mk_coe_finset, Finset.card_compl,
-    lift_nat_cast, Nat.cast_inj, h1, h2]
 #align cardinal.mk_compl_eq_mk_compl_finite_lift Cardinal.mk_compl_eq_mk_compl_finite_lift
 -/

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Floris van Doorn
 -/
-import Mathbin.Data.Finsupp.Multiset
-import Mathbin.Order.Bounded
-import Mathbin.SetTheory.Ordinal.Principal
+import Data.Finsupp.Multiset
+import Order.Bounded
+import SetTheory.Ordinal.Principal
 import Mathbin.Tactic.Linarith.Default
 
 #align_import set_theory.cardinal.ordinal from "leanprover-community/mathlib"@"7c2ce0c2da15516b4e65d0c9e254bb6dc93abd1f"

bump to nightly-2023-08-02-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

7aca3f15

Diff

@@ -349,7 +349,7 @@ theorem aleph_limit {o : Ordinal} (ho : o.IsLimit) : aleph o = ⨆ a : Iio o, al
     rintro ⟨i, hi⟩
     cases lt_or_le i ω
     · rcases lt_omega.1 h with ⟨n, rfl⟩
-      use ⟨0, ho.pos⟩
+      use⟨0, ho.pos⟩
       simpa using (nat_lt_aleph_0 n).le
     · exact ⟨⟨_, (sub_lt_of_le h).2 hi⟩, aleph'_le.2 (le_add_sub _ _)⟩
   · exact fun i => aleph_le.2 (le_of_lt i.2)

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Floris van Doorn
-
-! This file was ported from Lean 3 source module set_theory.cardinal.ordinal
-! 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.Data.Finsupp.Multiset
 import Mathbin.Order.Bounded
 import Mathbin.SetTheory.Ordinal.Principal
 import Mathbin.Tactic.Linarith.Default
 
+#align_import set_theory.cardinal.ordinal from "leanprover-community/mathlib"@"7c2ce0c2da15516b4e65d0c9e254bb6dc93abd1f"
+
 /-!
 # Cardinals and ordinals

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -105,10 +105,12 @@ def alephIdx : Cardinal → Ordinal :=
 #align cardinal.aleph_idx Cardinal.alephIdx
 -/
 
+#print Cardinal.alephIdx.initialSeg_coe /-
 @[simp]
 theorem alephIdx.initialSeg_coe : (alephIdx.initialSeg : Cardinal → Ordinal) = alephIdx :=
   rfl
 #align cardinal.aleph_idx.initial_seg_coe Cardinal.alephIdx.initialSeg_coe
+-/
 
 #print Cardinal.alephIdx_lt /-
 @[simp]
@@ -154,10 +156,12 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
 #align cardinal.aleph_idx.rel_iso Cardinal.alephIdx.relIso
 -/
 
+#print Cardinal.alephIdx.relIso_coe /-
 @[simp]
 theorem alephIdx.relIso_coe : (alephIdx.relIso : Cardinal → Ordinal) = alephIdx :=
   rfl
 #align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coe
+-/
 
 #print Cardinal.type_cardinal /-
 @[simp]
@@ -194,10 +198,12 @@ def aleph' : Ordinal → Cardinal :=
 #align cardinal.aleph' Cardinal.aleph'
 -/
 
+#print Cardinal.aleph'.relIso_coe /-
 @[simp]
 theorem aleph'.relIso_coe : (Aleph'.relIso : Ordinal → Cardinal) = aleph' :=
   rfl
 #align cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coe
+-/
 
 #print Cardinal.aleph'_lt /-
 @[simp]
@@ -234,6 +240,7 @@ theorem aleph'_zero : aleph' 0 = 0 := by rw [← nonpos_iff_eq_zero, ← aleph'_
 #align cardinal.aleph'_zero Cardinal.aleph'_zero
 -/
 
+#print Cardinal.aleph'_succ /-
 @[simp]
 theorem aleph'_succ {o : Ordinal} : aleph' (succ o) = succ (aleph' o) :=
   by
@@ -241,12 +248,15 @@ theorem aleph'_succ {o : Ordinal} : aleph' (succ o) = succ (aleph' o) :=
   rw [aleph_idx_aleph', succ_le_iff, ← aleph'_lt, aleph'_aleph_idx]
   apply lt_succ
 #align cardinal.aleph'_succ Cardinal.aleph'_succ
+-/
 
+#print Cardinal.aleph'_nat /-
 @[simp]
 theorem aleph'_nat : ∀ n : ℕ, aleph' n = n
   | 0 => aleph'_zero
   | n + 1 => show aleph' (succ n) = n.succ by rw [aleph'_succ, aleph'_nat, nat_succ]
 #align cardinal.aleph'_nat Cardinal.aleph'_nat
+-/
 
 #print Cardinal.aleph'_le_of_limit /-
 theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
@@ -260,12 +270,14 @@ theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
 #align cardinal.aleph'_le_of_limit Cardinal.aleph'_le_of_limit
 -/
 
+#print Cardinal.aleph'_limit /-
 theorem aleph'_limit {o : Ordinal} (ho : o.IsLimit) : aleph' o = ⨆ a : Iio o, aleph' a :=
   by
   refine' le_antisymm _ (ciSup_le' fun i => aleph'_le.2 (le_of_lt i.2))
   rw [aleph'_le_of_limit ho]
   exact fun a ha => le_ciSup (bdd_above_of_small _) (⟨a, ha⟩ : Iio o)
 #align cardinal.aleph'_limit Cardinal.aleph'_limit
+-/
 
 #print Cardinal.aleph'_omega /-
 @[simp]
@@ -308,6 +320,7 @@ theorem aleph_le {o₁ o₂ : Ordinal} : aleph o₁ ≤ aleph o₂ ↔ o₁ ≤
 #align cardinal.aleph_le Cardinal.aleph_le
 -/
 
+#print Cardinal.max_aleph_eq /-
 @[simp]
 theorem max_aleph_eq (o₁ o₂ : Ordinal) : max (aleph o₁) (aleph o₂) = aleph (max o₁ o₂) :=
   by
@@ -315,11 +328,14 @@ theorem max_aleph_eq (o₁ o₂ : Ordinal) : max (aleph o₁) (aleph o₂) = ale
   · rw [max_eq_right h, max_eq_right (aleph_le.1 h)]
   · rw [max_eq_left h, max_eq_left (aleph_le.1 h)]
 #align cardinal.max_aleph_eq Cardinal.max_aleph_eq
+-/
 
+#print Cardinal.aleph_succ /-
 @[simp]
 theorem aleph_succ {o : Ordinal} : aleph (succ o) = succ (aleph o) := by
   rw [aleph, add_succ, aleph'_succ, aleph]
 #align cardinal.aleph_succ Cardinal.aleph_succ
+-/
 
 #print Cardinal.aleph_zero /-
 @[simp]
@@ -327,6 +343,7 @@ theorem aleph_zero : aleph 0 = ℵ₀ := by rw [aleph, add_zero, aleph'_omega]
 #align cardinal.aleph_zero Cardinal.aleph_zero
 -/
 
+#print Cardinal.aleph_limit /-
 theorem aleph_limit {o : Ordinal} (ho : o.IsLimit) : aleph o = ⨆ a : Iio o, aleph a :=
   by
   apply le_antisymm _ (ciSup_le' _)
@@ -340,6 +357,7 @@ theorem aleph_limit {o : Ordinal} (ho : o.IsLimit) : aleph o = ⨆ a : Iio o, al
     · exact ⟨⟨_, (sub_lt_of_le h).2 hi⟩, aleph'_le.2 (le_add_sub _ _)⟩
   · exact fun i => aleph_le.2 (le_of_lt i.2)
 #align cardinal.aleph_limit Cardinal.aleph_limit
+-/
 
 #print Cardinal.aleph0_le_aleph' /-
 theorem aleph0_le_aleph' {o : Ordinal} : ℵ₀ ≤ aleph' o ↔ ω ≤ o := by rw [← aleph'_omega, aleph'_le]
@@ -370,10 +388,12 @@ theorem aleph_toNat (o : Ordinal) : (aleph o).toNat = 0 :=
 #align cardinal.aleph_to_nat Cardinal.aleph_toNat
 -/
 
+#print Cardinal.aleph_toPartENat /-
 @[simp]
 theorem aleph_toPartENat (o : Ordinal) : (aleph o).toPartENat = ⊤ :=
   toPartENat_apply_of_aleph0_le <| aleph0_le_aleph o
 #align cardinal.aleph_to_part_enat Cardinal.aleph_toPartENat
+-/
 
 #print Cardinal.nonempty_out_aleph /-
 instance nonempty_out_aleph (o : Ordinal) : Nonempty (aleph o).ord.out.α :=
@@ -415,15 +435,21 @@ theorem aleph_isNormal : IsNormal (ord ∘ aleph) :=
 #align cardinal.aleph_is_normal Cardinal.aleph_isNormal
 -/
 
+#print Cardinal.succ_aleph0 /-
 theorem succ_aleph0 : succ ℵ₀ = aleph 1 := by rw [← aleph_zero, ← aleph_succ, Ordinal.succ_zero]
 #align cardinal.succ_aleph_0 Cardinal.succ_aleph0
+-/
 
+#print Cardinal.aleph0_lt_aleph_one /-
 theorem aleph0_lt_aleph_one : ℵ₀ < aleph 1 := by rw [← succ_aleph_0]; apply lt_succ
 #align cardinal.aleph_0_lt_aleph_one Cardinal.aleph0_lt_aleph_one
+-/
 
+#print Cardinal.countable_iff_lt_aleph_one /-
 theorem countable_iff_lt_aleph_one {α : Type _} (s : Set α) : s.Countable ↔ (#s) < aleph 1 := by
   rw [← succ_aleph_0, lt_succ_iff, le_aleph_0_iff_set_countable]
 #align cardinal.countable_iff_lt_aleph_one Cardinal.countable_iff_lt_aleph_one
+-/
 
 #print Cardinal.ord_card_unbounded /-
 /-- Ordinals that are cardinals are unbounded. -/
@@ -503,14 +529,18 @@ theorem beth_zero : beth 0 = aleph0 :=
 #align cardinal.beth_zero Cardinal.beth_zero
 -/
 
+#print Cardinal.beth_succ /-
 @[simp]
 theorem beth_succ (o : Ordinal) : beth (succ o) = 2 ^ beth o :=
   limitRecOn_succ _ _ _ _
 #align cardinal.beth_succ Cardinal.beth_succ
+-/
 
+#print Cardinal.beth_limit /-
 theorem beth_limit {o : Ordinal} : o.IsLimit → beth o = ⨆ a : Iio o, beth a :=
   limitRecOn_limit _ _ _ _
 #align cardinal.beth_limit Cardinal.beth_limit
+-/
 
 #print Cardinal.beth_strictMono /-
 theorem beth_strictMono : StrictMono beth := by
@@ -594,6 +624,7 @@ theorem beth_normal : IsNormal.{u} fun o => (beth o).ord :=
 
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Cardinal.mul_eq_self /-
 /-- If `α` is an infinite type, then `α × α` and `α` have the same cardinality. -/
 theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c :=
   by
@@ -644,9 +675,11 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c :=
     rw [← lt_ord]; apply (ord_is_limit ol).2
     rw [mk_def, e]; apply typein_lt_type
 #align cardinal.mul_eq_self Cardinal.mul_eq_self
+-/
 
 end UsingOrdinals
 
+#print Cardinal.mul_eq_max /-
 /-- If `α` and `β` are infinite types, then the cardinality of `α × β` is the maximum
 of the cardinalities of `α` and `β`. -/
 theorem mul_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : ℵ₀ ≤ b) : a * b = max a b :=
@@ -656,60 +689,82 @@ theorem mul_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : ℵ₀ ≤ b) : a
     max_le (by simpa only [mul_one] using mul_le_mul_left' (one_le_aleph_0.trans hb) a)
       (by simpa only [one_mul] using mul_le_mul_right' (one_le_aleph_0.trans ha) b)
 #align cardinal.mul_eq_max Cardinal.mul_eq_max
+-/
 
+#print Cardinal.mul_mk_eq_max /-
 @[simp]
 theorem mul_mk_eq_max {α β : Type _} [Infinite α] [Infinite β] : (#α) * (#β) = max (#α) (#β) :=
   mul_eq_max (aleph0_le_mk α) (aleph0_le_mk β)
 #align cardinal.mul_mk_eq_max Cardinal.mul_mk_eq_max
+-/
 
+#print Cardinal.aleph_mul_aleph /-
 @[simp]
 theorem aleph_mul_aleph (o₁ o₂ : Ordinal) : aleph o₁ * aleph o₂ = aleph (max o₁ o₂) := by
   rw [Cardinal.mul_eq_max (aleph_0_le_aleph o₁) (aleph_0_le_aleph o₂), max_aleph_eq]
 #align cardinal.aleph_mul_aleph Cardinal.aleph_mul_aleph
+-/
 
+#print Cardinal.aleph0_mul_eq /-
 @[simp]
 theorem aleph0_mul_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : ℵ₀ * a = a :=
   (mul_eq_max le_rfl ha).trans (max_eq_right ha)
 #align cardinal.aleph_0_mul_eq Cardinal.aleph0_mul_eq
+-/
 
+#print Cardinal.mul_aleph0_eq /-
 @[simp]
 theorem mul_aleph0_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a * ℵ₀ = a :=
   (mul_eq_max ha le_rfl).trans (max_eq_left ha)
 #align cardinal.mul_aleph_0_eq Cardinal.mul_aleph0_eq
+-/
 
+#print Cardinal.aleph0_mul_mk_eq /-
 @[simp]
 theorem aleph0_mul_mk_eq {α : Type _} [Infinite α] : ℵ₀ * (#α) = (#α) :=
   aleph0_mul_eq (aleph0_le_mk α)
 #align cardinal.aleph_0_mul_mk_eq Cardinal.aleph0_mul_mk_eq
+-/
 
+#print Cardinal.mk_mul_aleph0_eq /-
 @[simp]
 theorem mk_mul_aleph0_eq {α : Type _} [Infinite α] : (#α) * ℵ₀ = (#α) :=
   mul_aleph0_eq (aleph0_le_mk α)
 #align cardinal.mk_mul_aleph_0_eq Cardinal.mk_mul_aleph0_eq
+-/
 
+#print Cardinal.aleph0_mul_aleph /-
 @[simp]
 theorem aleph0_mul_aleph (o : Ordinal) : ℵ₀ * aleph o = aleph o :=
   aleph0_mul_eq (aleph0_le_aleph o)
 #align cardinal.aleph_0_mul_aleph Cardinal.aleph0_mul_aleph
+-/
 
+#print Cardinal.aleph_mul_aleph0 /-
 @[simp]
 theorem aleph_mul_aleph0 (o : Ordinal) : aleph o * ℵ₀ = aleph o :=
   mul_aleph0_eq (aleph0_le_aleph o)
 #align cardinal.aleph_mul_aleph_0 Cardinal.aleph_mul_aleph0
+-/
 
+#print Cardinal.mul_lt_of_lt /-
 theorem mul_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b < c) : a * b < c :=
   (mul_le_mul' (le_max_left a b) (le_max_right a b)).trans_lt <|
     (lt_or_le (max a b) ℵ₀).elim (fun h => (mul_lt_aleph0 h h).trans_le hc) fun h => by
       rw [mul_eq_self h]; exact max_lt h1 h2
 #align cardinal.mul_lt_of_lt Cardinal.mul_lt_of_lt
+-/
 
+#print Cardinal.mul_le_max_of_aleph0_le_left /-
 theorem mul_le_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) : a * b ≤ max a b :=
   by
   convert mul_le_mul' (le_max_left a b) (le_max_right a b)
   rw [mul_eq_self]
   refine' h.trans (le_max_left a b)
 #align cardinal.mul_le_max_of_aleph_0_le_left Cardinal.mul_le_max_of_aleph0_le_left
+-/
 
+#print Cardinal.mul_eq_max_of_aleph0_le_left /-
 theorem mul_eq_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) (h' : b ≠ 0) : a * b = max a b :=
   by
   cases' le_or_lt ℵ₀ b with hb hb; · exact mul_eq_max h hb
@@ -718,24 +773,32 @@ theorem mul_eq_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) (h' : b
   rw [max_eq_left this]
   convert mul_le_mul_left' (one_le_iff_ne_zero.mpr h') _; rw [mul_one]
 #align cardinal.mul_eq_max_of_aleph_0_le_left Cardinal.mul_eq_max_of_aleph0_le_left
+-/
 
+#print Cardinal.mul_le_max_of_aleph0_le_right /-
 theorem mul_le_max_of_aleph0_le_right {a b : Cardinal} (h : ℵ₀ ≤ b) : a * b ≤ max a b := by
   simpa only [mul_comm, max_comm] using mul_le_max_of_aleph_0_le_left h
 #align cardinal.mul_le_max_of_aleph_0_le_right Cardinal.mul_le_max_of_aleph0_le_right
+-/
 
+#print Cardinal.mul_eq_max_of_aleph0_le_right /-
 theorem mul_eq_max_of_aleph0_le_right {a b : Cardinal} (h' : a ≠ 0) (h : ℵ₀ ≤ b) :
     a * b = max a b := by
   rw [mul_comm, max_comm]
   exact mul_eq_max_of_aleph_0_le_left h h'
 #align cardinal.mul_eq_max_of_aleph_0_le_right Cardinal.mul_eq_max_of_aleph0_le_right
+-/
 
+#print Cardinal.mul_eq_max' /-
 theorem mul_eq_max' {a b : Cardinal} (h : ℵ₀ ≤ a * b) : a * b = max a b :=
   by
   rcases aleph_0_le_mul_iff.mp h with ⟨ha, hb, ha' | hb'⟩
   · exact mul_eq_max_of_aleph_0_le_left ha' hb
   · exact mul_eq_max_of_aleph_0_le_right ha hb'
 #align cardinal.mul_eq_max' Cardinal.mul_eq_max'
+-/
 
+#print Cardinal.mul_le_max /-
 theorem mul_le_max (a b : Cardinal) : a * b ≤ max (max a b) ℵ₀ :=
   by
   rcases eq_or_ne a 0 with (rfl | ha0); · simp
@@ -748,25 +811,35 @@ theorem mul_le_max (a b : Cardinal) : a * b ≤ max (max a b) ℵ₀ :=
       exact le_max_left _ _
     · exact le_max_of_le_right (mul_lt_aleph_0 ha hb).le
 #align cardinal.mul_le_max Cardinal.mul_le_max
+-/
 
+#print Cardinal.mul_eq_left /-
 theorem mul_eq_left {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : b ≤ a) (hb' : b ≠ 0) : a * b = a := by
   rw [mul_eq_max_of_aleph_0_le_left ha hb', max_eq_left hb]
 #align cardinal.mul_eq_left Cardinal.mul_eq_left
+-/
 
+#print Cardinal.mul_eq_right /-
 theorem mul_eq_right {a b : Cardinal} (hb : ℵ₀ ≤ b) (ha : a ≤ b) (ha' : a ≠ 0) : a * b = b := by
   rw [mul_comm, mul_eq_left hb ha ha']
 #align cardinal.mul_eq_right Cardinal.mul_eq_right
+-/
 
+#print Cardinal.le_mul_left /-
 theorem le_mul_left {a b : Cardinal} (h : b ≠ 0) : a ≤ b * a :=
   by
   convert mul_le_mul_right' (one_le_iff_ne_zero.mpr h) _
   rw [one_mul]
 #align cardinal.le_mul_left Cardinal.le_mul_left
+-/
 
+#print Cardinal.le_mul_right /-
 theorem le_mul_right {a b : Cardinal} (h : b ≠ 0) : a ≤ a * b := by rw [mul_comm];
   exact le_mul_left h
 #align cardinal.le_mul_right Cardinal.le_mul_right
+-/
 
+#print Cardinal.mul_eq_left_iff /-
 theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧ b ≠ 0 ∨ b = 1 ∨ a = 0 :=
   by
   rw [max_le_iff]
@@ -788,10 +861,12 @@ theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧
     · rw [mul_eq_max_of_aleph_0_le_left ha hb, max_eq_left hab]
     all_goals simp
 #align cardinal.mul_eq_left_iff Cardinal.mul_eq_left_iff
+-/
 
 /-! ### Properties of `add` -/
 
 
+#print Cardinal.add_eq_self /-
 /-- If `α` is an infinite type, then `α ⊕ α` and `α` have the same cardinality. -/
 theorem add_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c + c = c :=
   le_antisymm
@@ -800,7 +875,9 @@ theorem add_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c + c = c :=
         mul_le_mul_right' ((nat_lt_aleph_0 2).le.trans h) c)
     (self_le_add_left c c)
 #align cardinal.add_eq_self Cardinal.add_eq_self
+-/
 
+#print Cardinal.add_eq_max /-
 /-- If `α` is an infinite type, then the cardinality of `α ⊕ β` is the maximum
 of the cardinalities of `α` and `β`. -/
 theorem add_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) : a + b = max a b :=
@@ -809,21 +886,29 @@ theorem add_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) : a + b = max a b :=
         add_le_add (le_max_left _ _) (le_max_right _ _)) <|
     max_le (self_le_add_right _ _) (self_le_add_left _ _)
 #align cardinal.add_eq_max Cardinal.add_eq_max
+-/
 
+#print Cardinal.add_eq_max' /-
 theorem add_eq_max' {a b : Cardinal} (ha : ℵ₀ ≤ b) : a + b = max a b := by
   rw [add_comm, max_comm, add_eq_max ha]
 #align cardinal.add_eq_max' Cardinal.add_eq_max'
+-/
 
+#print Cardinal.add_mk_eq_max /-
 @[simp]
 theorem add_mk_eq_max {α β : Type _} [Infinite α] : (#α) + (#β) = max (#α) (#β) :=
   add_eq_max (aleph0_le_mk α)
 #align cardinal.add_mk_eq_max Cardinal.add_mk_eq_max
+-/
 
+#print Cardinal.add_mk_eq_max' /-
 @[simp]
 theorem add_mk_eq_max' {α β : Type _} [Infinite β] : (#α) + (#β) = max (#α) (#β) :=
   add_eq_max' (aleph0_le_mk β)
 #align cardinal.add_mk_eq_max' Cardinal.add_mk_eq_max'
+-/
 
+#print Cardinal.add_le_max /-
 theorem add_le_max (a b : Cardinal) : a + b ≤ max (max a b) ℵ₀ :=
   by
   cases' le_or_lt ℵ₀ a with ha ha
@@ -834,17 +919,23 @@ theorem add_le_max (a b : Cardinal) : a + b ≤ max (max a b) ℵ₀ :=
       exact le_max_left _ _
     · exact le_max_of_le_right (add_lt_aleph_0 ha hb).le
 #align cardinal.add_le_max Cardinal.add_le_max
+-/
 
+#print Cardinal.add_le_of_le /-
 theorem add_le_of_le {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a ≤ c) (h2 : b ≤ c) : a + b ≤ c :=
   (add_le_add h1 h2).trans <| le_of_eq <| add_eq_self hc
 #align cardinal.add_le_of_le Cardinal.add_le_of_le
+-/
 
+#print Cardinal.add_lt_of_lt /-
 theorem add_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b < c) : a + b < c :=
   (add_le_add (le_max_left a b) (le_max_right a b)).trans_lt <|
     (lt_or_le (max a b) ℵ₀).elim (fun h => (add_lt_aleph0 h h).trans_le hc) fun h => by
       rw [add_eq_self h] <;> exact max_lt h1 h2
 #align cardinal.add_lt_of_lt Cardinal.add_lt_of_lt
+-/
 
+#print Cardinal.eq_of_add_eq_of_aleph0_le /-
 theorem eq_of_add_eq_of_aleph0_le {a b c : Cardinal} (h : a + b = c) (ha : a < c) (hc : ℵ₀ ≤ c) :
     b = c := by
   apply le_antisymm
@@ -853,15 +944,21 @@ theorem eq_of_add_eq_of_aleph0_le {a b c : Cardinal} (h : a + b = c) (ha : a < c
   have : a + b < c := add_lt_of_lt hc ha hb
   simpa [h, lt_irrefl] using this
 #align cardinal.eq_of_add_eq_of_aleph_0_le Cardinal.eq_of_add_eq_of_aleph0_le
+-/
 
+#print Cardinal.add_eq_left /-
 theorem add_eq_left {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : b ≤ a) : a + b = a := by
   rw [add_eq_max ha, max_eq_left hb]
 #align cardinal.add_eq_left Cardinal.add_eq_left
+-/
 
+#print Cardinal.add_eq_right /-
 theorem add_eq_right {a b : Cardinal} (hb : ℵ₀ ≤ b) (ha : a ≤ b) : a + b = b := by
   rw [add_comm, add_eq_left hb ha]
 #align cardinal.add_eq_right Cardinal.add_eq_right
+-/
 
+#print Cardinal.add_eq_left_iff /-
 theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨ b = 0 :=
   by
   rw [max_le_iff]
@@ -876,24 +973,34 @@ theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨
     · rw [add_eq_max h1, max_eq_left h2]
     · rw [h3, add_zero]
 #align cardinal.add_eq_left_iff Cardinal.add_eq_left_iff
+-/
 
+#print Cardinal.add_eq_right_iff /-
 theorem add_eq_right_iff {a b : Cardinal} : a + b = b ↔ max ℵ₀ a ≤ b ∨ a = 0 := by
   rw [add_comm, add_eq_left_iff]
 #align cardinal.add_eq_right_iff Cardinal.add_eq_right_iff
+-/
 
+#print Cardinal.add_nat_eq /-
 theorem add_nat_eq {a : Cardinal} (n : ℕ) (ha : ℵ₀ ≤ a) : a + n = a :=
   add_eq_left ha ((nat_lt_aleph0 _).le.trans ha)
 #align cardinal.add_nat_eq Cardinal.add_nat_eq
+-/
 
+#print Cardinal.add_one_eq /-
 theorem add_one_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a + 1 = a :=
   add_eq_left ha (one_le_aleph0.trans ha)
 #align cardinal.add_one_eq Cardinal.add_one_eq
+-/
 
+#print Cardinal.mk_add_one_eq /-
 @[simp]
 theorem mk_add_one_eq {α : Type _} [Infinite α] : (#α) + 1 = (#α) :=
   add_one_eq (aleph0_le_mk α)
 #align cardinal.mk_add_one_eq Cardinal.mk_add_one_eq
+-/
 
+#print Cardinal.eq_of_add_eq_add_left /-
 protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (ha : a < ℵ₀) :
     b = c := by
   cases' le_or_lt ℵ₀ b with hb hb
@@ -908,15 +1015,20 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
     rcases ha with ⟨n, rfl⟩; rcases hb with ⟨m, rfl⟩; rcases hc with ⟨k, rfl⟩
     norm_cast at h ⊢; apply add_left_cancel h
 #align cardinal.eq_of_add_eq_add_left Cardinal.eq_of_add_eq_add_left
+-/
 
+#print Cardinal.eq_of_add_eq_add_right /-
 protected theorem eq_of_add_eq_add_right {a b c : Cardinal} (h : a + b = c + b) (hb : b < ℵ₀) :
     a = c := by rw [add_comm a b, add_comm c b] at h ; exact Cardinal.eq_of_add_eq_add_left h hb
 #align cardinal.eq_of_add_eq_add_right Cardinal.eq_of_add_eq_add_right
+-/
 
+#print Cardinal.aleph_add_aleph /-
 @[simp]
 theorem aleph_add_aleph (o₁ o₂ : Ordinal) : aleph o₁ + aleph o₂ = aleph (max o₁ o₂) := by
   rw [Cardinal.add_eq_max (aleph_0_le_aleph o₁), max_aleph_eq]
 #align cardinal.aleph_add_aleph Cardinal.aleph_add_aleph
+-/
 
 #print Cardinal.principal_add_ord /-
 theorem principal_add_ord {c : Cardinal} (hc : ℵ₀ ≤ c) : Ordinal.Principal (· + ·) c.ord :=
@@ -930,20 +1042,27 @@ theorem principal_add_aleph (o : Ordinal) : Ordinal.Principal (· + ·) (aleph o
 #align cardinal.principal_add_aleph Cardinal.principal_add_aleph
 -/
 
+#print Cardinal.add_right_inj_of_lt_aleph0 /-
 theorem add_right_inj_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < aleph0) : α + γ = β + γ ↔ α = β :=
   ⟨fun h => Cardinal.eq_of_add_eq_add_right h γ₀, fun h => congr_fun (congr_arg (· + ·) h) γ⟩
 #align cardinal.add_right_inj_of_lt_aleph_0 Cardinal.add_right_inj_of_lt_aleph0
+-/
 
+#print Cardinal.add_nat_inj /-
 @[simp]
 theorem add_nat_inj {α β : Cardinal} (n : ℕ) : α + n = β + n ↔ α = β :=
   add_right_inj_of_lt_aleph0 (nat_lt_aleph0 _)
 #align cardinal.add_nat_inj Cardinal.add_nat_inj
+-/
 
+#print Cardinal.add_one_inj /-
 @[simp]
 theorem add_one_inj {α β : Cardinal} : α + 1 = β + 1 ↔ α = β :=
   add_right_inj_of_lt_aleph0 one_lt_aleph0
 #align cardinal.add_one_inj Cardinal.add_one_inj
+-/
 
+#print Cardinal.add_le_add_iff_of_lt_aleph0 /-
 theorem add_le_add_iff_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < Cardinal.aleph0) :
     α + γ ≤ β + γ ↔ α ≤ β :=
   by
@@ -952,16 +1071,21 @@ theorem add_le_add_iff_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < Cardinal
   rw [not_le, lt_iff_le_and_ne, Ne] at h ⊢
   exact ⟨add_le_add_right h.1 γ, mt (add_right_inj_of_lt_aleph_0 γ₀).1 h.2⟩
 #align cardinal.add_le_add_iff_of_lt_aleph_0 Cardinal.add_le_add_iff_of_lt_aleph0
+-/
 
+#print Cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0 /-
 @[simp]
 theorem add_nat_le_add_nat_iff_of_lt_aleph_0 {α β : Cardinal} (n : ℕ) : α + n ≤ β + n ↔ α ≤ β :=
   add_le_add_iff_of_lt_aleph0 (nat_lt_aleph0 n)
 #align cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0 Cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0
+-/
 
+#print Cardinal.add_one_le_add_one_iff_of_lt_aleph_0 /-
 @[simp]
 theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β + 1 ↔ α ≤ β :=
   add_le_add_iff_of_lt_aleph0 one_lt_aleph0
 #align cardinal.add_one_le_add_one_iff_of_lt_aleph_0 Cardinal.add_one_le_add_one_iff_of_lt_aleph_0
+-/
 
 /-! ### Properties about power -/
 
@@ -987,13 +1111,16 @@ theorem pow_eq {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : 1 ≤ μ) (H3 :
 #align cardinal.pow_eq Cardinal.pow_eq
 -/
 
+#print Cardinal.power_self_eq /-
 theorem power_self_eq {c : Cardinal} (h : ℵ₀ ≤ c) : c ^ c = 2 ^ c :=
   by
   apply ((power_le_power_right <| (cantor c).le).trans _).antisymm
   · convert power_le_power_right ((nat_lt_aleph_0 2).le.trans h); apply nat.cast_two.symm
   · rw [← power_mul, mul_eq_self h]
 #align cardinal.power_self_eq Cardinal.power_self_eq
+-/
 
+#print Cardinal.prod_eq_two_power /-
 theorem prod_eq_two_power {ι : Type u} [Infinite ι] {c : ι → Cardinal.{v}} (h₁ : ∀ i, 2 ≤ c i)
     (h₂ : ∀ i, lift.{u} (c i) ≤ lift.{v} (#ι)) : prod c = 2 ^ lift.{v} (#ι) :=
   by
@@ -1006,16 +1133,21 @@ theorem prod_eq_two_power {ι : Type u} [Infinite ι] {c : ι → Cardinal.{v}}
     rw [lift_two, ← lift_two.{u, v}, lift_le]
     exact h₁ i
 #align cardinal.prod_eq_two_power Cardinal.prod_eq_two_power
+-/
 
+#print Cardinal.power_eq_two_power /-
 theorem power_eq_two_power {c₁ c₂ : Cardinal} (h₁ : ℵ₀ ≤ c₁) (h₂ : 2 ≤ c₂) (h₂' : c₂ ≤ c₁) :
     c₂ ^ c₁ = 2 ^ c₁ :=
   le_antisymm (power_self_eq h₁ ▸ power_le_power_right h₂') (power_le_power_right h₂)
 #align cardinal.power_eq_two_power Cardinal.power_eq_two_power
+-/
 
+#print Cardinal.nat_power_eq /-
 theorem nat_power_eq {c : Cardinal.{u}} (h : ℵ₀ ≤ c) {n : ℕ} (hn : 2 ≤ n) :
     (n : Cardinal.{u}) ^ c = 2 ^ c :=
   power_eq_two_power h (by assumption_mod_cast) ((nat_lt_aleph0 n).le.trans h)
 #align cardinal.nat_power_eq Cardinal.nat_power_eq
+-/
 
 #print Cardinal.power_nat_le /-
 theorem power_nat_le {c : Cardinal.{u}} {n : ℕ} (h : ℵ₀ ≤ c) : c ^ n ≤ c :=
@@ -1029,12 +1161,14 @@ theorem power_nat_eq {c : Cardinal.{u}} {n : ℕ} (h1 : ℵ₀ ≤ c) (h2 : 1 
 #align cardinal.power_nat_eq Cardinal.power_nat_eq
 -/
 
+#print Cardinal.power_nat_le_max /-
 theorem power_nat_le_max {c : Cardinal.{u}} {n : ℕ} : c ^ (n : Cardinal.{u}) ≤ max c ℵ₀ :=
   by
   cases' le_or_lt ℵ₀ c with hc hc
   · exact le_max_of_le_left (power_nat_le hc)
   · exact le_max_of_le_right (power_lt_aleph_0 hc (nat_lt_aleph_0 _)).le
 #align cardinal.power_nat_le_max Cardinal.power_nat_le_max
+-/
 
 #print Cardinal.powerlt_aleph0 /-
 theorem powerlt_aleph0 {c : Cardinal} (h : ℵ₀ ≤ c) : c ^< ℵ₀ = c :=
@@ -1045,6 +1179,7 @@ theorem powerlt_aleph0 {c : Cardinal} (h : ℵ₀ ≤ c) : c ^< ℵ₀ = c :=
 #align cardinal.powerlt_aleph_0 Cardinal.powerlt_aleph0
 -/
 
+#print Cardinal.powerlt_aleph0_le /-
 theorem powerlt_aleph0_le (c : Cardinal) : c ^< ℵ₀ ≤ max c ℵ₀ :=
   by
   cases le_or_lt ℵ₀ c
@@ -1052,6 +1187,7 @@ theorem powerlt_aleph0_le (c : Cardinal) : c ^< ℵ₀ ≤ max c ℵ₀ :=
   rw [powerlt_le]
   exact fun c' hc' => (power_lt_aleph_0 h hc').le.trans (le_max_right _ _)
 #align cardinal.powerlt_aleph_0_le Cardinal.powerlt_aleph0_le
+-/
 
 /-! ### Computing cardinality of various types -/
 
@@ -1075,6 +1211,7 @@ theorem mk_list_eq_aleph0 (α : Type u) [Countable α] [Nonempty α] : (#List α
 #align cardinal.mk_list_eq_aleph_0 Cardinal.mk_list_eq_aleph0
 -/
 
+#print Cardinal.mk_list_eq_max_mk_aleph0 /-
 theorem mk_list_eq_max_mk_aleph0 (α : Type u) [Nonempty α] : (#List α) = max (#α) ℵ₀ :=
   by
   cases finite_or_infinite α
@@ -1083,7 +1220,9 @@ theorem mk_list_eq_max_mk_aleph0 (α : Type u) [Nonempty α] : (#List α) = max
   · rw [mk_list_eq_mk, eq_comm, max_eq_left]
     exact aleph_0_le_mk α
 #align cardinal.mk_list_eq_max_mk_aleph_0 Cardinal.mk_list_eq_max_mk_aleph0
+-/
 
+#print Cardinal.mk_list_le_max /-
 theorem mk_list_le_max (α : Type u) : (#List α) ≤ max ℵ₀ (#α) :=
   by
   cases finite_or_infinite α
@@ -1091,6 +1230,7 @@ theorem mk_list_le_max (α : Type u) : (#List α) ≤ max ℵ₀ (#α) :=
   · rw [mk_list_eq_mk]
     apply le_max_right
 #align cardinal.mk_list_le_max Cardinal.mk_list_le_max
+-/
 
 #print Cardinal.mk_finset_of_infinite /-
 @[simp]
@@ -1103,6 +1243,7 @@ theorem mk_finset_of_infinite (α : Type u) [Infinite α] : (#Finset α) = (#α)
 #align cardinal.mk_finset_of_infinite Cardinal.mk_finset_of_infinite
 -/
 
+#print Cardinal.mk_finsupp_lift_of_infinite /-
 @[simp]
 theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Zero β] [Nontrivial β] :
     (#α →₀ β) = max (lift.{v} (#α)) (lift.{u} (#β)) :=
@@ -1120,11 +1261,15 @@ theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Z
     · inhabit α
       exact lift_mk_le.{v, max u v, u}.2 ⟨⟨_, Finsupp.single_injective default⟩⟩
 #align cardinal.mk_finsupp_lift_of_infinite Cardinal.mk_finsupp_lift_of_infinite
+-/
 
+#print Cardinal.mk_finsupp_of_infinite /-
 theorem mk_finsupp_of_infinite (α β : Type u) [Infinite α] [Zero β] [Nontrivial β] :
     (#α →₀ β) = max (#α) (#β) := by simp
 #align cardinal.mk_finsupp_of_infinite Cardinal.mk_finsupp_of_infinite
+-/
 
+#print Cardinal.mk_finsupp_lift_of_infinite' /-
 @[simp]
 theorem mk_finsupp_lift_of_infinite' (α : Type u) (β : Type v) [Nonempty α] [Zero β] [Infinite β] :
     (#α →₀ β) = max (lift.{v} (#α)) (lift.{u} (#β)) :=
@@ -1136,18 +1281,25 @@ theorem mk_finsupp_lift_of_infinite' (α : Type u) (β : Type v) [Nonempty α] [
     exacts [Fintype.card_pos, lift_le_aleph_0.2 (lt_aleph_0_of_finite _).le]
   · apply mk_finsupp_lift_of_infinite
 #align cardinal.mk_finsupp_lift_of_infinite' Cardinal.mk_finsupp_lift_of_infinite'
+-/
 
+#print Cardinal.mk_finsupp_of_infinite' /-
 theorem mk_finsupp_of_infinite' (α β : Type u) [Nonempty α] [Zero β] [Infinite β] :
     (#α →₀ β) = max (#α) (#β) := by simp
 #align cardinal.mk_finsupp_of_infinite' Cardinal.mk_finsupp_of_infinite'
+-/
 
+#print Cardinal.mk_finsupp_nat /-
 theorem mk_finsupp_nat (α : Type u) [Nonempty α] : (#α →₀ ℕ) = max (#α) ℵ₀ := by simp
 #align cardinal.mk_finsupp_nat Cardinal.mk_finsupp_nat
+-/
 
+#print Cardinal.mk_multiset_of_nonempty /-
 @[simp]
 theorem mk_multiset_of_nonempty (α : Type u) [Nonempty α] : (#Multiset α) = max (#α) ℵ₀ :=
   Multiset.toFinsupp.toEquiv.cardinal_eq.trans (mk_finsupp_nat α)
 #align cardinal.mk_multiset_of_nonempty Cardinal.mk_multiset_of_nonempty
+-/
 
 #print Cardinal.mk_multiset_of_infinite /-
 theorem mk_multiset_of_infinite (α : Type u) [Infinite α] : (#Multiset α) = (#α) := by simp
@@ -1191,6 +1343,7 @@ theorem mk_bounded_set_le_of_infinite (α : Type u) [Infinite α] (c : Cardinal)
 #align cardinal.mk_bounded_set_le_of_infinite Cardinal.mk_bounded_set_le_of_infinite
 -/
 
+#print Cardinal.mk_bounded_set_le /-
 theorem mk_bounded_set_le (α : Type u) (c : Cardinal) :
     (#{ t : Set α // (#t) ≤ c }) ≤ max (#α) ℵ₀ ^ c :=
   by
@@ -1200,7 +1353,9 @@ theorem mk_bounded_set_le (α : Type u) (c : Cardinal) :
   apply (mk_bounded_set_le_of_infinite (Sum (ULift.{u} ℕ) α) c).trans
   rw [max_comm, ← add_eq_max] <;> rfl
 #align cardinal.mk_bounded_set_le Cardinal.mk_bounded_set_le
+-/
 
+#print Cardinal.mk_bounded_subset_le /-
 theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
     (#{ t : Set α // t ⊆ s ∧ (#t) ≤ c }) ≤ max (#s) ℵ₀ ^ c :=
   by
@@ -1211,25 +1366,33 @@ theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
     refine' (preimage_eq_preimage' _ _).1 h <;> rw [Subtype.range_coe] <;> assumption
   rintro ⟨t, h1t, h2t⟩; exact (mk_preimage_of_injective _ _ Subtype.val_injective).trans h2t
 #align cardinal.mk_bounded_subset_le Cardinal.mk_bounded_subset_le
+-/
 
 /-! ### Properties of `compl` -/
 
 
+#print Cardinal.mk_compl_of_infinite /-
 theorem mk_compl_of_infinite {α : Type _} [Infinite α] (s : Set α) (h2 : (#s) < (#α)) :
     (#(sᶜ : Set α)) = (#α) := by refine' eq_of_add_eq_of_aleph_0_le _ h2 (aleph_0_le_mk α);
   exact mk_sum_compl s
 #align cardinal.mk_compl_of_infinite Cardinal.mk_compl_of_infinite
+-/
 
+#print Cardinal.mk_compl_finset_of_infinite /-
 theorem mk_compl_finset_of_infinite {α : Type _} [Infinite α] (s : Finset α) :
     (#(↑sᶜ : Set α)) = (#α) := by apply mk_compl_of_infinite;
   exact (finset_card_lt_aleph_0 s).trans_le (aleph_0_le_mk α)
 #align cardinal.mk_compl_finset_of_infinite Cardinal.mk_compl_finset_of_infinite
+-/
 
+#print Cardinal.mk_compl_eq_mk_compl_infinite /-
 theorem mk_compl_eq_mk_compl_infinite {α : Type _} [Infinite α] {s t : Set α} (hs : (#s) < (#α))
     (ht : (#t) < (#α)) : (#(sᶜ : Set α)) = (#(tᶜ : Set α)) := by
   rw [mk_compl_of_infinite s hs, mk_compl_of_infinite t ht]
 #align cardinal.mk_compl_eq_mk_compl_infinite Cardinal.mk_compl_eq_mk_compl_infinite
+-/
 
+#print Cardinal.mk_compl_eq_mk_compl_finite_lift /-
 theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α] {s : Set α}
     {t : Set β} (h1 : lift.{max v w} (#α) = lift.{max u w} (#β))
     (h2 : lift.{max v w} (#s) = lift.{max u w} (#t)) :
@@ -1245,20 +1408,26 @@ theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α]
   simp only [← Finset.coe_compl, Finset.coe_sort_coe, mk_coe_finset, Finset.card_compl,
     lift_nat_cast, Nat.cast_inj, h1, h2]
 #align cardinal.mk_compl_eq_mk_compl_finite_lift Cardinal.mk_compl_eq_mk_compl_finite_lift
+-/
 
+#print Cardinal.mk_compl_eq_mk_compl_finite /-
 theorem mk_compl_eq_mk_compl_finite {α β : Type u} [Finite α] {s : Set α} {t : Set β}
     (h1 : (#α) = (#β)) (h : (#s) = (#t)) : (#(sᶜ : Set α)) = (#(tᶜ : Set β)) := by rw [← lift_inj];
   apply mk_compl_eq_mk_compl_finite_lift <;> rwa [lift_inj]
 #align cardinal.mk_compl_eq_mk_compl_finite Cardinal.mk_compl_eq_mk_compl_finite
+-/
 
+#print Cardinal.mk_compl_eq_mk_compl_finite_same /-
 theorem mk_compl_eq_mk_compl_finite_same {α : Type _} [Finite α] {s t : Set α} (h : (#s) = (#t)) :
     (#(sᶜ : Set α)) = (#(tᶜ : Set α)) :=
   mk_compl_eq_mk_compl_finite rfl h
 #align cardinal.mk_compl_eq_mk_compl_finite_same Cardinal.mk_compl_eq_mk_compl_finite_same
+-/
 
 /-! ### Extending an injection to an equiv -/
 
 
+#print Cardinal.extend_function /-
 theorem extend_function {α β : Type _} {s : Set α} (f : s ↪ β)
     (h : Nonempty ((sᶜ : Set α) ≃ (range fᶜ : Set β))) : ∃ g : α ≃ β, ∀ x : s, g x = f x :=
   by
@@ -1268,6 +1437,7 @@ theorem extend_function {α β : Type _} {s : Set α} (f : s ↪ β)
       ((sum_congr (Equiv.ofInjective f f.2) g).trans (set.sum_compl (range f)))
   refine' ⟨h, _⟩; rintro ⟨x, hx⟩; simp [set.sum_compl_symm_apply_of_mem, hx]
 #align cardinal.extend_function Cardinal.extend_function
+-/
 
 #print Cardinal.extend_function_finite /-
 theorem extend_function_finite {α β : Type _} [Finite α] {s : Set α} (f : s ↪ β)
@@ -1281,6 +1451,7 @@ theorem extend_function_finite {α β : Type _} [Finite α] {s : Set α} (f : s
 #align cardinal.extend_function_finite Cardinal.extend_function_finite
 -/
 
+#print Cardinal.extend_function_of_lt /-
 theorem extend_function_of_lt {α β : Type _} {s : Set α} (f : s ↪ β) (hs : (#s) < (#α))
     (h : Nonempty (α ≃ β)) : ∃ g : α ≃ β, ∀ x : s, g x = f x :=
   by
@@ -1291,6 +1462,7 @@ theorem extend_function_of_lt {α β : Type _} {s : Set α} (f : s ↪ β) (hs :
     rwa [mk_compl_of_infinite s hs, mk_compl_of_infinite]
     rwa [← lift_lt, mk_range_eq_of_injective f.injective, ← h, lift_lt]
 #align cardinal.extend_function_of_lt Cardinal.extend_function_of_lt
+-/
 
 section Bit

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -1066,7 +1066,6 @@ theorem mk_list_eq_mk (α : Type u) [Infinite α] : (#List α) = (#α) :=
         (#List α) = sum fun n : ℕ => (#α) ^ (n : Cardinal.{u}) := mk_list_eq_sum_pow α
         _ ≤ sum fun n : ℕ => #α := (sum_le_sum _ _ fun n => pow_le H1 <| nat_lt_aleph0 n)
         _ = (#α) := by simp [H1]
-        
 #align cardinal.mk_list_eq_mk Cardinal.mk_list_eq_mk
 -/
 
@@ -1101,7 +1100,6 @@ theorem mk_finset_of_infinite (α : Type u) [Infinite α] : (#Finset α) = (#α)
       calc
         (#Finset α) ≤ (#List α) := mk_le_of_surjective List.toFinset_surjective
         _ = (#α) := mk_list_eq_mk α
-        
 #align cardinal.mk_finset_of_infinite Cardinal.mk_finset_of_infinite
 -/
 
@@ -1116,7 +1114,6 @@ theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Z
       _ = (#α × β) := (mk_finset_of_infinite _)
       _ = max (lift.{v} (#α)) (lift.{u} (#β)) := by
         rw [mk_prod, mul_eq_max_of_aleph_0_le_left] <;> simp
-      
   · apply max_le <;> rw [← lift_id (#α →₀ β), ← lift_umax]
     · cases' exists_ne (0 : β) with b hb
       exact lift_mk_le.{u, max u v, v}.2 ⟨⟨_, Finsupp.single_left_injective hb⟩⟩

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -427,7 +427,7 @@ theorem countable_iff_lt_aleph_one {α : Type _} (s : Set α) : s.Countable ↔
 
 #print Cardinal.ord_card_unbounded /-
 /-- Ordinals that are cardinals are unbounded. -/
-theorem ord_card_unbounded : Unbounded (· < ·) { b : Ordinal | b.card.ord = b } :=
+theorem ord_card_unbounded : Unbounded (· < ·) {b : Ordinal | b.card.ord = b} :=
   unbounded_lt_iff.2 fun a => ⟨_, ⟨by dsimp; rw [card_ord], (lt_ord_succ_card a).le⟩⟩
 #align cardinal.ord_card_unbounded Cardinal.ord_card_unbounded
 -/
@@ -440,7 +440,7 @@ theorem eq_aleph'_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) : ∃ a, (a
 
 #print Cardinal.ord_aleph'_eq_enum_card /-
 /-- `ord ∘ aleph'` enumerates the ordinals that are cardinals. -/
-theorem ord_aleph'_eq_enum_card : ord ∘ aleph' = enumOrd { b : Ordinal | b.card.ord = b } :=
+theorem ord_aleph'_eq_enum_card : ord ∘ aleph' = enumOrd {b : Ordinal | b.card.ord = b} :=
   by
   rw [← eq_enum_ord _ ord_card_unbounded, range_eq_iff]
   exact
@@ -451,7 +451,7 @@ theorem ord_aleph'_eq_enum_card : ord ∘ aleph' = enumOrd { b : Ordinal | b.car
 
 #print Cardinal.ord_card_unbounded' /-
 /-- Infinite ordinals that are cardinals are unbounded. -/
-theorem ord_card_unbounded' : Unbounded (· < ·) { b : Ordinal | b.card.ord = b ∧ ω ≤ b } :=
+theorem ord_card_unbounded' : Unbounded (· < ·) {b : Ordinal | b.card.ord = b ∧ ω ≤ b} :=
   (unbounded_lt_inter_le ω).2 ord_card_unbounded
 #align cardinal.ord_card_unbounded' Cardinal.ord_card_unbounded'
 -/
@@ -470,7 +470,7 @@ theorem eq_aleph_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) (ho' : ω 
 
 #print Cardinal.ord_aleph_eq_enum_card /-
 /-- `ord ∘ aleph` enumerates the infinite ordinals that are cardinals. -/
-theorem ord_aleph_eq_enum_card : ord ∘ aleph = enumOrd { b : Ordinal | b.card.ord = b ∧ ω ≤ b } :=
+theorem ord_aleph_eq_enum_card : ord ∘ aleph = enumOrd {b : Ordinal | b.card.ord = b ∧ ω ≤ b} :=
   by
   rw [← eq_enum_ord _ ord_card_unbounded']
   use aleph_is_normal.strict_mono
@@ -625,13 +625,13 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c :=
   refine'
     lt_of_le_of_lt (_ : _ ≤ card (succ (typein (· < ·) (g p))) * card (succ (typein (· < ·) (g p))))
       _
-  · have : { q | s q p } ⊆ insert (g p) { x | x < g p } ×ˢ insert (g p) { x | x < g p } :=
+  · have : {q | s q p} ⊆ insert (g p) {x | x < g p} ×ˢ insert (g p) {x | x < g p} :=
       by
       intro q h
       simp only [s, embedding.coe_fn_mk, Order.Preimage, typein_lt_typein, Prod.lex_def,
         typein_inj] at h 
       exact max_le_iff.1 (le_iff_lt_or_eq.2 <| h.imp_right And.left)
-    suffices H : (insert (g p) { x | r x (g p) } : Set α) ≃ Sum { x | r x (g p) } PUnit
+    suffices H : (insert (g p) {x | r x (g p)} : Set α) ≃ Sum {x | r x (g p)} PUnit
     ·
       exact
         ⟨(Set.embeddingOfSubset _ _ this).trans
@@ -780,7 +780,7 @@ theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧
     have hb : b ≠ 0 := by rintro rfl; apply h2a; rw [MulZeroClass.mul_zero] at h ; exact h.symm
     left; rw [← h, mul_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha 
     rcases ha with (rfl | rfl | ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩); contradiction; contradiction
-    rw [← Ne] at h2a ; rw [← one_le_iff_ne_zero] at h2a hb ; norm_cast  at h2a hb h ⊢
+    rw [← Ne] at h2a ; rw [← one_le_iff_ne_zero] at h2a hb ; norm_cast at h2a hb h ⊢
     apply le_antisymm _ hb; rw [← not_lt]
     apply fun h2b => ne_of_gt _ h; conv_lhs => rw [← mul_one n]
     rwa [mul_lt_mul_left]; apply Nat.lt_of_succ_le h2a
@@ -870,7 +870,7 @@ theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨
     · left; use ha; rw [← not_lt]; apply fun hb => ne_of_gt _ h
       exact hb.trans_le (self_le_add_left b a)
     right; rw [← h, add_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha 
-    rcases ha with ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩; norm_cast  at h ⊢
+    rcases ha with ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩; norm_cast at h ⊢
     rw [← add_right_inj, h, add_zero]
   · rintro (⟨h1, h2⟩ | h3)
     · rw [add_eq_max h1, max_eq_left h2]
@@ -906,7 +906,7 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
       rw [← h]; apply add_lt_aleph_0 ha hb
     rw [lt_aleph_0] at *
     rcases ha with ⟨n, rfl⟩; rcases hb with ⟨m, rfl⟩; rcases hc with ⟨k, rfl⟩
-    norm_cast  at h ⊢; apply add_left_cancel h
+    norm_cast at h ⊢; apply add_left_cancel h
 #align cardinal.eq_of_add_eq_add_left Cardinal.eq_of_add_eq_add_left
 
 protected theorem eq_of_add_eq_add_right {a b c : Cardinal} (h : a + b = c + b) (hb : b < ℵ₀) :
@@ -1242,11 +1242,11 @@ theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α]
   rcases lift_mk_eq.1 h1 with ⟨e⟩; letI : Fintype β := Fintype.ofEquiv α e
   replace h1 : Fintype.card α = Fintype.card β := (Fintype.ofEquiv_card _).symm
   classical
-    lift s to Finset α using s.to_finite
-    lift t to Finset β using t.to_finite
-    simp only [Finset.coe_sort_coe, mk_coe_finset, lift_nat_cast, Nat.cast_inj] at h2 
-    simp only [← Finset.coe_compl, Finset.coe_sort_coe, mk_coe_finset, Finset.card_compl,
-      lift_nat_cast, Nat.cast_inj, h1, h2]
+  lift s to Finset α using s.to_finite
+  lift t to Finset β using t.to_finite
+  simp only [Finset.coe_sort_coe, mk_coe_finset, lift_nat_cast, Nat.cast_inj] at h2 
+  simp only [← Finset.coe_compl, Finset.coe_sort_coe, mk_coe_finset, Finset.card_compl,
+    lift_nat_cast, Nat.cast_inj, h1, h2]
 #align cardinal.mk_compl_eq_mk_compl_finite_lift Cardinal.mk_compl_eq_mk_compl_finite_lift
 
 theorem mk_compl_eq_mk_compl_finite {α β : Type u} [Finite α] {s : Set α} {t : Set β}

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -67,9 +67,9 @@ open Ordinal
 theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
   by
   refine' ⟨fun h => aleph_0_ne_zero _, fun a => lt_imp_lt_of_le_imp_le fun h => _⟩
-  · rw [← Ordinal.le_zero, ord_le] at h
+  · rw [← Ordinal.le_zero, ord_le] at h 
     simpa only [card_zero, nonpos_iff_eq_zero] using co.trans h
-  · rw [ord_le] at h⊢
+  · rw [ord_le] at h ⊢
     rwa [← @add_one_of_aleph_0_le (card a), ← card_succ]
     rw [← ord_le, ← le_succ_of_is_limit, ord_le]
     · exact co.trans h
@@ -519,7 +519,7 @@ theorem beth_strictMono : StrictMono beth := by
   intro h
   rcases zero_or_succ_or_limit b with (rfl | ⟨c, rfl⟩ | hb)
   · exact (Ordinal.not_lt_zero a h).elim
-  · rw [lt_succ_iff] at h
+  · rw [lt_succ_iff] at h 
     rw [beth_succ]
     apply lt_of_le_of_lt _ (cantor _)
     rcases eq_or_lt_of_le h with (rfl | h); · rfl
@@ -629,7 +629,7 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c :=
       by
       intro q h
       simp only [s, embedding.coe_fn_mk, Order.Preimage, typein_lt_typein, Prod.lex_def,
-        typein_inj] at h
+        typein_inj] at h 
       exact max_le_iff.1 (le_iff_lt_or_eq.2 <| h.imp_right And.left)
     suffices H : (insert (g p) { x | r x (g p) } : Set α) ≃ Sum { x | r x (g p) } PUnit
     ·
@@ -775,12 +775,12 @@ theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧
     · have : a ≠ 0 := by rintro rfl; exact ha.not_lt aleph_0_pos
       left; use ha
       · rw [← not_lt]; exact fun hb => ne_of_gt (hb.trans_le (le_mul_left this)) h
-      · rintro rfl; apply this; rw [MulZeroClass.mul_zero] at h; exact h.symm
+      · rintro rfl; apply this; rw [MulZeroClass.mul_zero] at h ; exact h.symm
     right; by_cases h2a : a = 0; · exact Or.inr h2a
-    have hb : b ≠ 0 := by rintro rfl; apply h2a; rw [MulZeroClass.mul_zero] at h; exact h.symm
-    left; rw [← h, mul_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha
+    have hb : b ≠ 0 := by rintro rfl; apply h2a; rw [MulZeroClass.mul_zero] at h ; exact h.symm
+    left; rw [← h, mul_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha 
     rcases ha with (rfl | rfl | ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩); contradiction; contradiction
-    rw [← Ne] at h2a; rw [← one_le_iff_ne_zero] at h2a hb; norm_cast  at h2a hb h⊢
+    rw [← Ne] at h2a ; rw [← one_le_iff_ne_zero] at h2a hb ; norm_cast  at h2a hb h ⊢
     apply le_antisymm _ hb; rw [← not_lt]
     apply fun h2b => ne_of_gt _ h; conv_lhs => rw [← mul_one n]
     rwa [mul_lt_mul_left]; apply Nat.lt_of_succ_le h2a
@@ -869,8 +869,8 @@ theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨
   · cases' le_or_lt ℵ₀ a with ha ha
     · left; use ha; rw [← not_lt]; apply fun hb => ne_of_gt _ h
       exact hb.trans_le (self_le_add_left b a)
-    right; rw [← h, add_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha
-    rcases ha with ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩; norm_cast  at h⊢
+    right; rw [← h, add_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha 
+    rcases ha with ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩; norm_cast  at h ⊢
     rw [← add_right_inj, h, add_zero]
   · rintro (⟨h1, h2⟩ | h3)
     · rw [add_eq_max h1, max_eq_left h2]
@@ -898,7 +898,7 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
     b = c := by
   cases' le_or_lt ℵ₀ b with hb hb
   · have : a < b := ha.trans_le hb
-    rw [add_eq_right hb this.le, eq_comm] at h
+    rw [add_eq_right hb this.le, eq_comm] at h 
     rw [eq_of_add_eq_of_aleph_0_le h this hb]
   · have hc : c < ℵ₀ := by
       rw [← not_le]; intro hc
@@ -906,11 +906,11 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
       rw [← h]; apply add_lt_aleph_0 ha hb
     rw [lt_aleph_0] at *
     rcases ha with ⟨n, rfl⟩; rcases hb with ⟨m, rfl⟩; rcases hc with ⟨k, rfl⟩
-    norm_cast  at h⊢; apply add_left_cancel h
+    norm_cast  at h ⊢; apply add_left_cancel h
 #align cardinal.eq_of_add_eq_add_left Cardinal.eq_of_add_eq_add_left
 
 protected theorem eq_of_add_eq_add_right {a b c : Cardinal} (h : a + b = c + b) (hb : b < ℵ₀) :
-    a = c := by rw [add_comm a b, add_comm c b] at h; exact Cardinal.eq_of_add_eq_add_left h hb
+    a = c := by rw [add_comm a b, add_comm c b] at h ; exact Cardinal.eq_of_add_eq_add_left h hb
 #align cardinal.eq_of_add_eq_add_right Cardinal.eq_of_add_eq_add_right
 
 @[simp]
@@ -949,7 +949,7 @@ theorem add_le_add_iff_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < Cardinal
   by
   refine' ⟨fun h => _, fun h => add_le_add_right h γ⟩
   contrapose h
-  rw [not_le, lt_iff_le_and_ne, Ne] at h⊢
+  rw [not_le, lt_iff_le_and_ne, Ne] at h ⊢
   exact ⟨add_le_add_right h.1 γ, mt (add_right_inj_of_lt_aleph_0 γ₀).1 h.2⟩
 #align cardinal.add_le_add_iff_of_lt_aleph_0 Cardinal.add_le_add_iff_of_lt_aleph0
 
@@ -1136,7 +1136,7 @@ theorem mk_finsupp_lift_of_infinite' (α : Type u) (β : Type v) [Nonempty α] [
   · rw [mk_finsupp_lift_of_fintype]
     have : ℵ₀ ≤ (#β).lift := aleph_0_le_lift.2 (aleph_0_le_mk β)
     rw [max_eq_right (le_trans _ this), power_nat_eq this]
-    exacts[Fintype.card_pos, lift_le_aleph_0.2 (lt_aleph_0_of_finite _).le]
+    exacts [Fintype.card_pos, lift_le_aleph_0.2 (lt_aleph_0_of_finite _).le]
   · apply mk_finsupp_lift_of_infinite
 #align cardinal.mk_finsupp_lift_of_infinite' Cardinal.mk_finsupp_lift_of_infinite'
 
@@ -1184,9 +1184,9 @@ theorem mk_bounded_set_le_of_infinite (α : Type u) [Infinite α] (c : Cardinal)
   use fun y => if h : ∃ x : s, g x = y then Sum.inl (Classical.choose h).val else Sum.inr ⟨⟩
   apply Subtype.eq; ext
   constructor
-  · rintro ⟨y, h⟩; dsimp only at h; by_cases h' : ∃ z : s, g z = y
-    · rw [dif_pos h'] at h; cases Sum.inl.inj h; exact (Classical.choose h').2
-    · rw [dif_neg h'] at h; cases h
+  · rintro ⟨y, h⟩; dsimp only at h ; by_cases h' : ∃ z : s, g z = y
+    · rw [dif_pos h'] at h ; cases Sum.inl.inj h; exact (Classical.choose h').2
+    · rw [dif_neg h'] at h ; cases h
   · intro h; have : ∃ z : s, g z = g ⟨x, h⟩ := ⟨⟨x, h⟩, rfl⟩
     use g ⟨x, h⟩; dsimp only; rw [dif_pos this]; congr
     suffices : Classical.choose this = ⟨x, h⟩; exact congr_arg Subtype.val this
@@ -1210,7 +1210,7 @@ theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
   refine' le_trans _ (mk_bounded_set_le s c)
   refine' ⟨Embedding.codRestrict _ _ _⟩
   use fun t => coe ⁻¹' t.1
-  · rintro ⟨t, ht1, ht2⟩ ⟨t', h1t', h2t'⟩ h; apply Subtype.eq; dsimp only at h⊢
+  · rintro ⟨t, ht1, ht2⟩ ⟨t', h1t', h2t'⟩ h; apply Subtype.eq; dsimp only at h ⊢
     refine' (preimage_eq_preimage' _ _).1 h <;> rw [Subtype.range_coe] <;> assumption
   rintro ⟨t, h1t, h2t⟩; exact (mk_preimage_of_injective _ _ Subtype.val_injective).trans h2t
 #align cardinal.mk_bounded_subset_le Cardinal.mk_bounded_subset_le
@@ -1244,7 +1244,7 @@ theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α]
   classical
     lift s to Finset α using s.to_finite
     lift t to Finset β using t.to_finite
-    simp only [Finset.coe_sort_coe, mk_coe_finset, lift_nat_cast, Nat.cast_inj] at h2
+    simp only [Finset.coe_sort_coe, mk_coe_finset, lift_nat_cast, Nat.cast_inj] at h2 
     simp only [← Finset.coe_compl, Finset.coe_sort_coe, mk_coe_finset, Finset.card_compl,
       lift_nat_cast, Nat.cast_inj, h1, h2]
 #align cardinal.mk_compl_eq_mk_compl_finite_lift Cardinal.mk_compl_eq_mk_compl_finite_lift
@@ -1265,7 +1265,7 @@ theorem mk_compl_eq_mk_compl_finite_same {α : Type _} [Finite α] {s t : Set α
 theorem extend_function {α β : Type _} {s : Set α} (f : s ↪ β)
     (h : Nonempty ((sᶜ : Set α) ≃ (range fᶜ : Set β))) : ∃ g : α ≃ β, ∀ x : s, g x = f x :=
   by
-  intros ; have := h; cases' this with g
+  intros; have := h; cases' this with g
   let h : α ≃ β :=
     (set.sum_compl (s : Set α)).symm.trans
       ((sum_congr (Equiv.ofInjective f f.2) g).trans (set.sum_compl (range f)))
@@ -1278,7 +1278,7 @@ theorem extend_function_finite {α β : Type _} [Finite α] {s : Set α} (f : s
   by
   apply extend_function f
   cases' id h with g
-  rw [← lift_mk_eq] at h
+  rw [← lift_mk_eq] at h 
   rw [← lift_mk_eq, mk_compl_eq_mk_compl_finite_lift h]
   rw [mk_range_eq_lift]; exact f.2
 #align cardinal.extend_function_finite Cardinal.extend_function_finite
@@ -1290,7 +1290,7 @@ theorem extend_function_of_lt {α β : Type _} {s : Set α} (f : s ↪ β) (hs :
   cases fintypeOrInfinite α
   · exact extend_function_finite f h
   · apply extend_function f; cases' id h with g; haveI := Infinite.of_injective _ g.injective
-    rw [← lift_mk_eq'] at h⊢
+    rw [← lift_mk_eq'] at h ⊢
     rwa [mk_compl_of_infinite s hs, mk_compl_of_infinite]
     rwa [← lift_lt, mk_range_eq_of_injective f.injective, ← h, lift_lt]
 #align cardinal.extend_function_of_lt Cardinal.extend_function_of_lt

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -53,7 +53,7 @@ noncomputable section
 
 open Function Cardinal Set Equiv Order
 
-open Classical Cardinal Ordinal
+open scoped Classical Cardinal Ordinal
 
 universe u v w
 
@@ -80,6 +80,7 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
 /-! ### Aleph cardinals -/
 
 
+#print Cardinal.alephIdx.initialSeg /-
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ω = ω`,
@@ -91,6 +92,7 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
 def alephIdx.initialSeg : @InitialSeg Cardinal Ordinal (· < ·) (· < ·) :=
   @RelEmbedding.collapse Cardinal Ordinal (· < ·) (· < ·) _ Cardinal.ord.orderEmbedding.ltEmbedding
 #align cardinal.aleph_idx.initial_seg Cardinal.alephIdx.initialSeg
+-/
 
 #print Cardinal.alephIdx /-
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
@@ -108,20 +110,27 @@ theorem alephIdx.initialSeg_coe : (alephIdx.initialSeg : Cardinal → Ordinal) =
   rfl
 #align cardinal.aleph_idx.initial_seg_coe Cardinal.alephIdx.initialSeg_coe
 
+#print Cardinal.alephIdx_lt /-
 @[simp]
 theorem alephIdx_lt {a b} : alephIdx a < alephIdx b ↔ a < b :=
   alephIdx.initialSeg.toRelEmbedding.map_rel_iff
 #align cardinal.aleph_idx_lt Cardinal.alephIdx_lt
+-/
 
+#print Cardinal.alephIdx_le /-
 @[simp]
 theorem alephIdx_le {a b} : alephIdx a ≤ alephIdx b ↔ a ≤ b := by
   rw [← not_lt, ← not_lt, aleph_idx_lt]
 #align cardinal.aleph_idx_le Cardinal.alephIdx_le
+-/
 
+#print Cardinal.alephIdx.init /-
 theorem alephIdx.init {a b} : b < alephIdx a → ∃ c, alephIdx c = b :=
   alephIdx.initialSeg.dropLast
 #align cardinal.aleph_idx.init Cardinal.alephIdx.init
+-/
 
+#print Cardinal.alephIdx.relIso /-
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ℵ₀ = ω`,
@@ -143,16 +152,19 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
           (Cardinal.bddAbove_range.{u, u} fun a : α => inv_fun aleph_idx (Ordinal.typein r a))
           (Ordinal.enum r _ (h (succ s)))
 #align cardinal.aleph_idx.rel_iso Cardinal.alephIdx.relIso
+-/
 
 @[simp]
 theorem alephIdx.relIso_coe : (alephIdx.relIso : Cardinal → Ordinal) = alephIdx :=
   rfl
 #align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coe
 
+#print Cardinal.type_cardinal /-
 @[simp]
 theorem type_cardinal : @type Cardinal (· < ·) _ = Ordinal.univ.{u, u + 1} := by
   rw [Ordinal.univ_id] <;> exact Quotient.sound ⟨aleph_idx.rel_iso⟩
 #align cardinal.type_cardinal Cardinal.type_cardinal
+-/
 
 #print Cardinal.mk_cardinal /-
 @[simp]
@@ -161,6 +173,7 @@ theorem mk_cardinal : (#Cardinal) = univ.{u, u + 1} := by
 #align cardinal.mk_cardinal Cardinal.mk_cardinal
 -/
 
+#print Cardinal.Aleph'.relIso /-
 /-- The `aleph'` function gives the cardinals listed by their ordinal
   index, and is the inverse of `aleph_idx`.
   `aleph' n = n`, `aleph' ω = ω`, `aleph' (ω + 1) = succ ℵ₀`, etc.
@@ -170,6 +183,7 @@ theorem mk_cardinal : (#Cardinal) = univ.{u, u + 1} := by
 def Aleph'.relIso :=
   Cardinal.alephIdx.relIso.symm
 #align cardinal.aleph'.rel_iso Cardinal.Aleph'.relIso
+-/
 
 #print Cardinal.aleph' /-
 /-- The `aleph'` function gives the cardinals listed by their ordinal
@@ -185,15 +199,19 @@ theorem aleph'.relIso_coe : (Aleph'.relIso : Ordinal → Cardinal) = aleph' :=
   rfl
 #align cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coe
 
+#print Cardinal.aleph'_lt /-
 @[simp]
 theorem aleph'_lt {o₁ o₂ : Ordinal} : aleph' o₁ < aleph' o₂ ↔ o₁ < o₂ :=
   Aleph'.relIso.map_rel_iff
 #align cardinal.aleph'_lt Cardinal.aleph'_lt
+-/
 
+#print Cardinal.aleph'_le /-
 @[simp]
 theorem aleph'_le {o₁ o₂ : Ordinal} : aleph' o₁ ≤ aleph' o₂ ↔ o₁ ≤ o₂ :=
   le_iff_le_iff_lt_iff_lt.2 aleph'_lt
 #align cardinal.aleph'_le Cardinal.aleph'_le
+-/
 
 #print Cardinal.aleph'_alephIdx /-
 @[simp]
@@ -230,6 +248,7 @@ theorem aleph'_nat : ∀ n : ℕ, aleph' n = n
   | n + 1 => show aleph' (succ n) = n.succ by rw [aleph'_succ, aleph'_nat, nat_succ]
 #align cardinal.aleph'_nat Cardinal.aleph'_nat
 
+#print Cardinal.aleph'_le_of_limit /-
 theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
     aleph' o ≤ c ↔ ∀ o' < o, aleph' o' ≤ c :=
   ⟨fun h o' h' => (aleph'_le.2 <| h'.le).trans h, fun h =>
@@ -239,6 +258,7 @@ theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
     rw [← aleph'_le, aleph'_aleph_idx]
     exact h _ h'⟩
 #align cardinal.aleph'_le_of_limit Cardinal.aleph'_le_of_limit
+-/
 
 theorem aleph'_limit {o : Ordinal} (ho : o.IsLimit) : aleph' o = ⨆ a : Iio o, aleph' a :=
   by
@@ -274,15 +294,19 @@ def aleph (o : Ordinal) : Cardinal :=
 #align cardinal.aleph Cardinal.aleph
 -/
 
+#print Cardinal.aleph_lt /-
 @[simp]
 theorem aleph_lt {o₁ o₂ : Ordinal} : aleph o₁ < aleph o₂ ↔ o₁ < o₂ :=
   aleph'_lt.trans (add_lt_add_iff_left _)
 #align cardinal.aleph_lt Cardinal.aleph_lt
+-/
 
+#print Cardinal.aleph_le /-
 @[simp]
 theorem aleph_le {o₁ o₂ : Ordinal} : aleph o₁ ≤ aleph o₂ ↔ o₁ ≤ o₂ :=
   le_iff_le_iff_lt_iff_lt.2 aleph_lt
 #align cardinal.aleph_le Cardinal.aleph_le
+-/
 
 @[simp]
 theorem max_aleph_eq (o₁ o₂ : Ordinal) : max (aleph o₁) (aleph o₂) = aleph (max o₁ o₂) :=
@@ -317,8 +341,10 @@ theorem aleph_limit {o : Ordinal} (ho : o.IsLimit) : aleph o = ⨆ a : Iio o, al
   · exact fun i => aleph_le.2 (le_of_lt i.2)
 #align cardinal.aleph_limit Cardinal.aleph_limit
 
+#print Cardinal.aleph0_le_aleph' /-
 theorem aleph0_le_aleph' {o : Ordinal} : ℵ₀ ≤ aleph' o ↔ ω ≤ o := by rw [← aleph'_omega, aleph'_le]
 #align cardinal.aleph_0_le_aleph' Cardinal.aleph0_le_aleph'
+-/
 
 #print Cardinal.aleph0_le_aleph /-
 theorem aleph0_le_aleph (o : Ordinal) : ℵ₀ ≤ aleph o := by rw [aleph, aleph_0_le_aleph'];
@@ -326,12 +352,16 @@ theorem aleph0_le_aleph (o : Ordinal) : ℵ₀ ≤ aleph o := by rw [aleph, alep
 #align cardinal.aleph_0_le_aleph Cardinal.aleph0_le_aleph
 -/
 
+#print Cardinal.aleph'_pos /-
 theorem aleph'_pos {o : Ordinal} (ho : 0 < o) : 0 < aleph' o := by rwa [← aleph'_zero, aleph'_lt]
 #align cardinal.aleph'_pos Cardinal.aleph'_pos
+-/
 
+#print Cardinal.aleph_pos /-
 theorem aleph_pos (o : Ordinal) : 0 < aleph o :=
   aleph0_pos.trans_le (aleph0_le_aleph o)
 #align cardinal.aleph_pos Cardinal.aleph_pos
+-/
 
 #print Cardinal.aleph_toNat /-
 @[simp]
@@ -395,10 +425,12 @@ theorem countable_iff_lt_aleph_one {α : Type _} (s : Set α) : s.Countable ↔
   rw [← succ_aleph_0, lt_succ_iff, le_aleph_0_iff_set_countable]
 #align cardinal.countable_iff_lt_aleph_one Cardinal.countable_iff_lt_aleph_one
 
+#print Cardinal.ord_card_unbounded /-
 /-- Ordinals that are cardinals are unbounded. -/
 theorem ord_card_unbounded : Unbounded (· < ·) { b : Ordinal | b.card.ord = b } :=
   unbounded_lt_iff.2 fun a => ⟨_, ⟨by dsimp; rw [card_ord], (lt_ord_succ_card a).le⟩⟩
 #align cardinal.ord_card_unbounded Cardinal.ord_card_unbounded
+-/
 
 #print Cardinal.eq_aleph'_of_eq_card_ord /-
 theorem eq_aleph'_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) : ∃ a, (aleph' a).ord = o :=
@@ -417,11 +449,14 @@ theorem ord_aleph'_eq_enum_card : ord ∘ aleph' = enumOrd { b : Ordinal | b.car
 #align cardinal.ord_aleph'_eq_enum_card Cardinal.ord_aleph'_eq_enum_card
 -/
 
+#print Cardinal.ord_card_unbounded' /-
 /-- Infinite ordinals that are cardinals are unbounded. -/
 theorem ord_card_unbounded' : Unbounded (· < ·) { b : Ordinal | b.card.ord = b ∧ ω ≤ b } :=
   (unbounded_lt_inter_le ω).2 ord_card_unbounded
 #align cardinal.ord_card_unbounded' Cardinal.ord_card_unbounded'
+-/
 
+#print Cardinal.eq_aleph_of_eq_card_ord /-
 theorem eq_aleph_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) (ho' : ω ≤ o) :
     ∃ a, (aleph a).ord = o :=
   by
@@ -431,7 +466,9 @@ theorem eq_aleph_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) (ho' : ω 
   rwa [Ordinal.add_sub_cancel_of_le]
   rwa [← aleph_0_le_aleph', ← ord_le_ord, ha, ord_aleph_0]
 #align cardinal.eq_aleph_of_eq_card_ord Cardinal.eq_aleph_of_eq_card_ord
+-/
 
+#print Cardinal.ord_aleph_eq_enum_card /-
 /-- `ord ∘ aleph` enumerates the infinite ordinals that are cardinals. -/
 theorem ord_aleph_eq_enum_card : ord ∘ aleph = enumOrd { b : Ordinal | b.card.ord = b ∧ ω ≤ b } :=
   by
@@ -443,6 +480,7 @@ theorem ord_aleph_eq_enum_card : ord ∘ aleph = enumOrd { b : Ordinal | b.card.
   · rw [← ord_aleph_0, ord_le_ord]
     exact aleph_0_le_aleph _
 #align cardinal.ord_aleph_eq_enum_card Cardinal.ord_aleph_eq_enum_card
+-/
 
 /-! ### Beth cardinals -/
 
@@ -498,15 +536,19 @@ theorem beth_mono : Monotone beth :=
 #align cardinal.beth_mono Cardinal.beth_mono
 -/
 
+#print Cardinal.beth_lt /-
 @[simp]
 theorem beth_lt {o₁ o₂ : Ordinal} : beth o₁ < beth o₂ ↔ o₁ < o₂ :=
   beth_strictMono.lt_iff_lt
 #align cardinal.beth_lt Cardinal.beth_lt
+-/
 
+#print Cardinal.beth_le /-
 @[simp]
 theorem beth_le {o₁ o₂ : Ordinal} : beth o₁ ≤ beth o₂ ↔ o₁ ≤ o₂ :=
   beth_strictMono.le_iff_le
 #align cardinal.beth_le Cardinal.beth_le
+-/
 
 #print Cardinal.aleph_le_beth /-
 theorem aleph_le_beth (o : Ordinal) : aleph o ≤ beth o :=
@@ -528,9 +570,11 @@ theorem aleph0_le_beth (o : Ordinal) : ℵ₀ ≤ beth o :=
 #align cardinal.aleph_0_le_beth Cardinal.aleph0_le_beth
 -/
 
+#print Cardinal.beth_pos /-
 theorem beth_pos (o : Ordinal) : 0 < beth o :=
   aleph0_pos.trans_le <| aleph0_le_beth o
 #align cardinal.beth_pos Cardinal.beth_pos
+-/
 
 #print Cardinal.beth_ne_zero /-
 theorem beth_ne_zero (o : Ordinal) : beth o ≠ 0 :=
@@ -922,6 +966,7 @@ theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β
 /-! ### Properties about power -/
 
 
+#print Cardinal.pow_le /-
 theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) : κ ^ μ ≤ κ :=
   let ⟨n, H3⟩ := lt_aleph0.1 H2
   H3.symm ▸
@@ -934,10 +979,13 @@ theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) :
             (mul_eq_self H1))
       H1
 #align cardinal.pow_le Cardinal.pow_le
+-/
 
+#print Cardinal.pow_eq /-
 theorem pow_eq {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : 1 ≤ μ) (H3 : μ < ℵ₀) : κ ^ μ = κ :=
   (pow_le H1 H3).antisymm <| self_le_power κ H2
 #align cardinal.pow_eq Cardinal.pow_eq
+-/
 
 theorem power_self_eq {c : Cardinal} (h : ℵ₀ ≤ c) : c ^ c = 2 ^ c :=
   by

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -80,12 +80,6 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
 /-! ### Aleph cardinals -/
 
 
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 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ω = ω`,
@@ -109,55 +103,25 @@ def alephIdx : Cardinal → Ordinal :=
 #align cardinal.aleph_idx Cardinal.alephIdx
 -/
 
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 @[simp]
 theorem alephIdx.initialSeg_coe : (alephIdx.initialSeg : Cardinal → Ordinal) = alephIdx :=
   rfl
 #align cardinal.aleph_idx.initial_seg_coe Cardinal.alephIdx.initialSeg_coe
 
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 @[simp]
 theorem alephIdx_lt {a b} : alephIdx a < alephIdx b ↔ a < b :=
   alephIdx.initialSeg.toRelEmbedding.map_rel_iff
 #align cardinal.aleph_idx_lt Cardinal.alephIdx_lt
 
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 @[simp]
 theorem alephIdx_le {a b} : alephIdx a ≤ alephIdx b ↔ a ≤ b := by
   rw [← not_lt, ← not_lt, aleph_idx_lt]
 #align cardinal.aleph_idx_le Cardinal.alephIdx_le
 
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 theorem alephIdx.init {a b} : b < alephIdx a → ∃ c, alephIdx c = b :=
   alephIdx.initialSeg.dropLast
 #align cardinal.aleph_idx.init Cardinal.alephIdx.init
 
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 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ℵ₀ = ω`,
@@ -180,23 +144,11 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
           (Ordinal.enum r _ (h (succ s)))
 #align cardinal.aleph_idx.rel_iso Cardinal.alephIdx.relIso
 
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 @[simp]
 theorem alephIdx.relIso_coe : (alephIdx.relIso : Cardinal → Ordinal) = alephIdx :=
   rfl
 #align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coe
 
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 @[simp]
 theorem type_cardinal : @type Cardinal (· < ·) _ = Ordinal.univ.{u, u + 1} := by
   rw [Ordinal.univ_id] <;> exact Quotient.sound ⟨aleph_idx.rel_iso⟩
@@ -209,12 +161,6 @@ theorem mk_cardinal : (#Cardinal) = univ.{u, u + 1} := by
 #align cardinal.mk_cardinal Cardinal.mk_cardinal
 -/
 
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 /-- The `aleph'` function gives the cardinals listed by their ordinal
   index, and is the inverse of `aleph_idx`.
   `aleph' n = n`, `aleph' ω = ω`, `aleph' (ω + 1) = succ ℵ₀`, etc.
@@ -234,34 +180,16 @@ def aleph' : Ordinal → Cardinal :=
 #align cardinal.aleph' Cardinal.aleph'
 -/
 
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 @[simp]
 theorem aleph'.relIso_coe : (Aleph'.relIso : Ordinal → Cardinal) = aleph' :=
   rfl
 #align cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coe
 
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 @[simp]
 theorem aleph'_lt {o₁ o₂ : Ordinal} : aleph' o₁ < aleph' o₂ ↔ o₁ < o₂ :=
   Aleph'.relIso.map_rel_iff
 #align cardinal.aleph'_lt Cardinal.aleph'_lt
 
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 @[simp]
 theorem aleph'_le {o₁ o₂ : Ordinal} : aleph' o₁ ≤ aleph' o₂ ↔ o₁ ≤ o₂ :=
   le_iff_le_iff_lt_iff_lt.2 aleph'_lt
@@ -288,12 +216,6 @@ theorem aleph'_zero : aleph' 0 = 0 := by rw [← nonpos_iff_eq_zero, ← aleph'_
 #align cardinal.aleph'_zero Cardinal.aleph'_zero
 -/
 
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 @[simp]
 theorem aleph'_succ {o : Ordinal} : aleph' (succ o) = succ (aleph' o) :=
   by
@@ -302,24 +224,12 @@ theorem aleph'_succ {o : Ordinal} : aleph' (succ o) = succ (aleph' o) :=
   apply lt_succ
 #align cardinal.aleph'_succ Cardinal.aleph'_succ
 
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 @[simp]
 theorem aleph'_nat : ∀ n : ℕ, aleph' n = n
   | 0 => aleph'_zero
   | n + 1 => show aleph' (succ n) = n.succ by rw [aleph'_succ, aleph'_nat, nat_succ]
 #align cardinal.aleph'_nat Cardinal.aleph'_nat
 
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 theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
     aleph' o ≤ c ↔ ∀ o' < o, aleph' o' ≤ c :=
   ⟨fun h o' h' => (aleph'_le.2 <| h'.le).trans h, fun h =>
@@ -330,12 +240,6 @@ theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
     exact h _ h'⟩
 #align cardinal.aleph'_le_of_limit Cardinal.aleph'_le_of_limit
 
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 theorem aleph'_limit {o : Ordinal} (ho : o.IsLimit) : aleph' o = ⨆ a : Iio o, aleph' a :=
   by
   refine' le_antisymm _ (ciSup_le' fun i => aleph'_le.2 (le_of_lt i.2))
@@ -370,34 +274,16 @@ def aleph (o : Ordinal) : Cardinal :=
 #align cardinal.aleph Cardinal.aleph
 -/
 
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 @[simp]
 theorem aleph_lt {o₁ o₂ : Ordinal} : aleph o₁ < aleph o₂ ↔ o₁ < o₂ :=
   aleph'_lt.trans (add_lt_add_iff_left _)
 #align cardinal.aleph_lt Cardinal.aleph_lt
 
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 @[simp]
 theorem aleph_le {o₁ o₂ : Ordinal} : aleph o₁ ≤ aleph o₂ ↔ o₁ ≤ o₂ :=
   le_iff_le_iff_lt_iff_lt.2 aleph_lt
 #align cardinal.aleph_le Cardinal.aleph_le
 
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 @[simp]
 theorem max_aleph_eq (o₁ o₂ : Ordinal) : max (aleph o₁) (aleph o₂) = aleph (max o₁ o₂) :=
   by
@@ -406,12 +292,6 @@ theorem max_aleph_eq (o₁ o₂ : Ordinal) : max (aleph o₁) (aleph o₂) = ale
   · rw [max_eq_left h, max_eq_left (aleph_le.1 h)]
 #align cardinal.max_aleph_eq Cardinal.max_aleph_eq
 
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 @[simp]
 theorem aleph_succ {o : Ordinal} : aleph (succ o) = succ (aleph o) := by
   rw [aleph, add_succ, aleph'_succ, aleph]
@@ -423,12 +303,6 @@ theorem aleph_zero : aleph 0 = ℵ₀ := by rw [aleph, add_zero, aleph'_omega]
 #align cardinal.aleph_zero Cardinal.aleph_zero
 -/
 
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 theorem aleph_limit {o : Ordinal} (ho : o.IsLimit) : aleph o = ⨆ a : Iio o, aleph a :=
   by
   apply le_antisymm _ (ciSup_le' _)
@@ -443,12 +317,6 @@ theorem aleph_limit {o : Ordinal} (ho : o.IsLimit) : aleph o = ⨆ a : Iio o, al
   · exact fun i => aleph_le.2 (le_of_lt i.2)
 #align cardinal.aleph_limit Cardinal.aleph_limit
 
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 theorem aleph0_le_aleph' {o : Ordinal} : ℵ₀ ≤ aleph' o ↔ ω ≤ o := by rw [← aleph'_omega, aleph'_le]
 #align cardinal.aleph_0_le_aleph' Cardinal.aleph0_le_aleph'
 
@@ -458,21 +326,9 @@ theorem aleph0_le_aleph (o : Ordinal) : ℵ₀ ≤ aleph o := by rw [aleph, alep
 #align cardinal.aleph_0_le_aleph Cardinal.aleph0_le_aleph
 -/
 
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 theorem aleph'_pos {o : Ordinal} (ho : 0 < o) : 0 < aleph' o := by rwa [← aleph'_zero, aleph'_lt]
 #align cardinal.aleph'_pos Cardinal.aleph'_pos
 
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 theorem aleph_pos (o : Ordinal) : 0 < aleph o :=
   aleph0_pos.trans_le (aleph0_le_aleph o)
 #align cardinal.aleph_pos Cardinal.aleph_pos
@@ -484,12 +340,6 @@ theorem aleph_toNat (o : Ordinal) : (aleph o).toNat = 0 :=
 #align cardinal.aleph_to_nat Cardinal.aleph_toNat
 -/
 
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 @[simp]
 theorem aleph_toPartENat (o : Ordinal) : (aleph o).toPartENat = ⊤ :=
   toPartENat_apply_of_aleph0_le <| aleph0_le_aleph o
@@ -535,40 +385,16 @@ theorem aleph_isNormal : IsNormal (ord ∘ aleph) :=
 #align cardinal.aleph_is_normal Cardinal.aleph_isNormal
 -/
 
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 theorem succ_aleph0 : succ ℵ₀ = aleph 1 := by rw [← aleph_zero, ← aleph_succ, Ordinal.succ_zero]
 #align cardinal.succ_aleph_0 Cardinal.succ_aleph0
 
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 theorem aleph0_lt_aleph_one : ℵ₀ < aleph 1 := by rw [← succ_aleph_0]; apply lt_succ
 #align cardinal.aleph_0_lt_aleph_one Cardinal.aleph0_lt_aleph_one
 
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 theorem countable_iff_lt_aleph_one {α : Type _} (s : Set α) : s.Countable ↔ (#s) < aleph 1 := by
   rw [← succ_aleph_0, lt_succ_iff, le_aleph_0_iff_set_countable]
 #align cardinal.countable_iff_lt_aleph_one Cardinal.countable_iff_lt_aleph_one
 
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 /-- Ordinals that are cardinals are unbounded. -/
 theorem ord_card_unbounded : Unbounded (· < ·) { b : Ordinal | b.card.ord = b } :=
   unbounded_lt_iff.2 fun a => ⟨_, ⟨by dsimp; rw [card_ord], (lt_ord_succ_card a).le⟩⟩
@@ -591,23 +417,11 @@ theorem ord_aleph'_eq_enum_card : ord ∘ aleph' = enumOrd { b : Ordinal | b.car
 #align cardinal.ord_aleph'_eq_enum_card Cardinal.ord_aleph'_eq_enum_card
 -/
 
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 /-- Infinite ordinals that are cardinals are unbounded. -/
 theorem ord_card_unbounded' : Unbounded (· < ·) { b : Ordinal | b.card.ord = b ∧ ω ≤ b } :=
   (unbounded_lt_inter_le ω).2 ord_card_unbounded
 #align cardinal.ord_card_unbounded' Cardinal.ord_card_unbounded'
 
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 theorem eq_aleph_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) (ho' : ω ≤ o) :
     ∃ a, (aleph a).ord = o :=
   by
@@ -618,12 +432,6 @@ theorem eq_aleph_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) (ho' : ω 
   rwa [← aleph_0_le_aleph', ← ord_le_ord, ha, ord_aleph_0]
 #align cardinal.eq_aleph_of_eq_card_ord Cardinal.eq_aleph_of_eq_card_ord
 
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 /-- `ord ∘ aleph` enumerates the infinite ordinals that are cardinals. -/
 theorem ord_aleph_eq_enum_card : ord ∘ aleph = enumOrd { b : Ordinal | b.card.ord = b ∧ ω ≤ b } :=
   by
@@ -657,23 +465,11 @@ theorem beth_zero : beth 0 = aleph0 :=
 #align cardinal.beth_zero Cardinal.beth_zero
 -/
 
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 @[simp]
 theorem beth_succ (o : Ordinal) : beth (succ o) = 2 ^ beth o :=
   limitRecOn_succ _ _ _ _
 #align cardinal.beth_succ Cardinal.beth_succ
 
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 theorem beth_limit {o : Ordinal} : o.IsLimit → beth o = ⨆ a : Iio o, beth a :=
   limitRecOn_limit _ _ _ _
 #align cardinal.beth_limit Cardinal.beth_limit
@@ -702,23 +498,11 @@ theorem beth_mono : Monotone beth :=
 #align cardinal.beth_mono Cardinal.beth_mono
 -/
 
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 @[simp]
 theorem beth_lt {o₁ o₂ : Ordinal} : beth o₁ < beth o₂ ↔ o₁ < o₂ :=
   beth_strictMono.lt_iff_lt
 #align cardinal.beth_lt Cardinal.beth_lt
 
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 @[simp]
 theorem beth_le {o₁ o₂ : Ordinal} : beth o₁ ≤ beth o₂ ↔ o₁ ≤ o₂ :=
   beth_strictMono.le_iff_le
@@ -744,12 +528,6 @@ theorem aleph0_le_beth (o : Ordinal) : ℵ₀ ≤ beth o :=
 #align cardinal.aleph_0_le_beth Cardinal.aleph0_le_beth
 -/
 
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 theorem beth_pos (o : Ordinal) : 0 < beth o :=
   aleph0_pos.trans_le <| aleph0_le_beth o
 #align cardinal.beth_pos Cardinal.beth_pos
@@ -771,12 +549,6 @@ theorem beth_normal : IsNormal.{u} fun o => (beth o).ord :=
 /-! ### Properties of `mul` -/
 
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- If `α` is an infinite type, then `α × α` and `α` have the same cardinality. -/
 theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c :=
@@ -831,12 +603,6 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c :=
 
 end UsingOrdinals
 
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 /-- If `α` and `β` are infinite types, then the cardinality of `α × β` is the maximum
 of the cardinalities of `α` and `β`. -/
 theorem mul_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : ℵ₀ ≤ b) : a * b = max a b :=
@@ -847,112 +613,52 @@ theorem mul_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : ℵ₀ ≤ b) : a
       (by simpa only [one_mul] using mul_le_mul_right' (one_le_aleph_0.trans ha) b)
 #align cardinal.mul_eq_max Cardinal.mul_eq_max
 
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 @[simp]
 theorem mul_mk_eq_max {α β : Type _} [Infinite α] [Infinite β] : (#α) * (#β) = max (#α) (#β) :=
   mul_eq_max (aleph0_le_mk α) (aleph0_le_mk β)
 #align cardinal.mul_mk_eq_max Cardinal.mul_mk_eq_max
 
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 @[simp]
 theorem aleph_mul_aleph (o₁ o₂ : Ordinal) : aleph o₁ * aleph o₂ = aleph (max o₁ o₂) := by
   rw [Cardinal.mul_eq_max (aleph_0_le_aleph o₁) (aleph_0_le_aleph o₂), max_aleph_eq]
 #align cardinal.aleph_mul_aleph Cardinal.aleph_mul_aleph
 
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 @[simp]
 theorem aleph0_mul_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : ℵ₀ * a = a :=
   (mul_eq_max le_rfl ha).trans (max_eq_right ha)
 #align cardinal.aleph_0_mul_eq Cardinal.aleph0_mul_eq
 
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 @[simp]
 theorem mul_aleph0_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a * ℵ₀ = a :=
   (mul_eq_max ha le_rfl).trans (max_eq_left ha)
 #align cardinal.mul_aleph_0_eq Cardinal.mul_aleph0_eq
 
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 @[simp]
 theorem aleph0_mul_mk_eq {α : Type _} [Infinite α] : ℵ₀ * (#α) = (#α) :=
   aleph0_mul_eq (aleph0_le_mk α)
 #align cardinal.aleph_0_mul_mk_eq Cardinal.aleph0_mul_mk_eq
 
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 @[simp]
 theorem mk_mul_aleph0_eq {α : Type _} [Infinite α] : (#α) * ℵ₀ = (#α) :=
   mul_aleph0_eq (aleph0_le_mk α)
 #align cardinal.mk_mul_aleph_0_eq Cardinal.mk_mul_aleph0_eq
 
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 @[simp]
 theorem aleph0_mul_aleph (o : Ordinal) : ℵ₀ * aleph o = aleph o :=
   aleph0_mul_eq (aleph0_le_aleph o)
 #align cardinal.aleph_0_mul_aleph Cardinal.aleph0_mul_aleph
 
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 @[simp]
 theorem aleph_mul_aleph0 (o : Ordinal) : aleph o * ℵ₀ = aleph o :=
   mul_aleph0_eq (aleph0_le_aleph o)
 #align cardinal.aleph_mul_aleph_0 Cardinal.aleph_mul_aleph0
 
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 theorem mul_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b < c) : a * b < c :=
   (mul_le_mul' (le_max_left a b) (le_max_right a b)).trans_lt <|
     (lt_or_le (max a b) ℵ₀).elim (fun h => (mul_lt_aleph0 h h).trans_le hc) fun h => by
       rw [mul_eq_self h]; exact max_lt h1 h2
 #align cardinal.mul_lt_of_lt Cardinal.mul_lt_of_lt
 
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 theorem mul_le_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) : a * b ≤ max a b :=
   by
   convert mul_le_mul' (le_max_left a b) (le_max_right a b)
@@ -960,12 +666,6 @@ theorem mul_le_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) : a * b
   refine' h.trans (le_max_left a b)
 #align cardinal.mul_le_max_of_aleph_0_le_left Cardinal.mul_le_max_of_aleph0_le_left
 
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 theorem mul_eq_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) (h' : b ≠ 0) : a * b = max a b :=
   by
   cases' le_or_lt ℵ₀ b with hb hb; · exact mul_eq_max h hb
@@ -975,34 +675,16 @@ theorem mul_eq_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) (h' : b
   convert mul_le_mul_left' (one_le_iff_ne_zero.mpr h') _; rw [mul_one]
 #align cardinal.mul_eq_max_of_aleph_0_le_left Cardinal.mul_eq_max_of_aleph0_le_left
 
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 theorem mul_le_max_of_aleph0_le_right {a b : Cardinal} (h : ℵ₀ ≤ b) : a * b ≤ max a b := by
   simpa only [mul_comm, max_comm] using mul_le_max_of_aleph_0_le_left h
 #align cardinal.mul_le_max_of_aleph_0_le_right Cardinal.mul_le_max_of_aleph0_le_right
 
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 theorem mul_eq_max_of_aleph0_le_right {a b : Cardinal} (h' : a ≠ 0) (h : ℵ₀ ≤ b) :
     a * b = max a b := by
   rw [mul_comm, max_comm]
   exact mul_eq_max_of_aleph_0_le_left h h'
 #align cardinal.mul_eq_max_of_aleph_0_le_right Cardinal.mul_eq_max_of_aleph0_le_right
 
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 theorem mul_eq_max' {a b : Cardinal} (h : ℵ₀ ≤ a * b) : a * b = max a b :=
   by
   rcases aleph_0_le_mul_iff.mp h with ⟨ha, hb, ha' | hb'⟩
@@ -1010,12 +692,6 @@ theorem mul_eq_max' {a b : Cardinal} (h : ℵ₀ ≤ a * b) : a * b = max a b :=
   · exact mul_eq_max_of_aleph_0_le_right ha hb'
 #align cardinal.mul_eq_max' Cardinal.mul_eq_max'
 
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 theorem mul_le_max (a b : Cardinal) : a * b ≤ max (max a b) ℵ₀ :=
   by
   rcases eq_or_ne a 0 with (rfl | ha0); · simp
@@ -1029,54 +705,24 @@ theorem mul_le_max (a b : Cardinal) : a * b ≤ max (max a b) ℵ₀ :=
     · exact le_max_of_le_right (mul_lt_aleph_0 ha hb).le
 #align cardinal.mul_le_max Cardinal.mul_le_max
 
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 theorem mul_eq_left {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : b ≤ a) (hb' : b ≠ 0) : a * b = a := by
   rw [mul_eq_max_of_aleph_0_le_left ha hb', max_eq_left hb]
 #align cardinal.mul_eq_left Cardinal.mul_eq_left
 
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 theorem mul_eq_right {a b : Cardinal} (hb : ℵ₀ ≤ b) (ha : a ≤ b) (ha' : a ≠ 0) : a * b = b := by
   rw [mul_comm, mul_eq_left hb ha ha']
 #align cardinal.mul_eq_right Cardinal.mul_eq_right
 
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 theorem le_mul_left {a b : Cardinal} (h : b ≠ 0) : a ≤ b * a :=
   by
   convert mul_le_mul_right' (one_le_iff_ne_zero.mpr h) _
   rw [one_mul]
 #align cardinal.le_mul_left Cardinal.le_mul_left
 
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 theorem le_mul_right {a b : Cardinal} (h : b ≠ 0) : a ≤ a * b := by rw [mul_comm];
   exact le_mul_left h
 #align cardinal.le_mul_right Cardinal.le_mul_right
 
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 theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧ b ≠ 0 ∨ b = 1 ∨ a = 0 :=
   by
   rw [max_le_iff]
@@ -1102,12 +748,6 @@ theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧
 /-! ### Properties of `add` -/
 
 
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 /-- If `α` is an infinite type, then `α ⊕ α` and `α` have the same cardinality. -/
 theorem add_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c + c = c :=
   le_antisymm
@@ -1117,12 +757,6 @@ theorem add_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c + c = c :=
     (self_le_add_left c c)
 #align cardinal.add_eq_self Cardinal.add_eq_self
 
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 /-- If `α` is an infinite type, then the cardinality of `α ⊕ β` is the maximum
 of the cardinalities of `α` and `β`. -/
 theorem add_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) : a + b = max a b :=
@@ -1132,44 +766,20 @@ theorem add_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) : a + b = max a b :=
     max_le (self_le_add_right _ _) (self_le_add_left _ _)
 #align cardinal.add_eq_max Cardinal.add_eq_max
 
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 theorem add_eq_max' {a b : Cardinal} (ha : ℵ₀ ≤ b) : a + b = max a b := by
   rw [add_comm, max_comm, add_eq_max ha]
 #align cardinal.add_eq_max' Cardinal.add_eq_max'
 
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 @[simp]
 theorem add_mk_eq_max {α β : Type _} [Infinite α] : (#α) + (#β) = max (#α) (#β) :=
   add_eq_max (aleph0_le_mk α)
 #align cardinal.add_mk_eq_max Cardinal.add_mk_eq_max
 
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 @[simp]
 theorem add_mk_eq_max' {α β : Type _} [Infinite β] : (#α) + (#β) = max (#α) (#β) :=
   add_eq_max' (aleph0_le_mk β)
 #align cardinal.add_mk_eq_max' Cardinal.add_mk_eq_max'
 
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 theorem add_le_max (a b : Cardinal) : a + b ≤ max (max a b) ℵ₀ :=
   by
   cases' le_or_lt ℵ₀ a with ha ha
@@ -1181,34 +791,16 @@ theorem add_le_max (a b : Cardinal) : a + b ≤ max (max a b) ℵ₀ :=
     · exact le_max_of_le_right (add_lt_aleph_0 ha hb).le
 #align cardinal.add_le_max Cardinal.add_le_max
 
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 theorem add_le_of_le {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a ≤ c) (h2 : b ≤ c) : a + b ≤ c :=
   (add_le_add h1 h2).trans <| le_of_eq <| add_eq_self hc
 #align cardinal.add_le_of_le Cardinal.add_le_of_le
 
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 theorem add_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b < c) : a + b < c :=
   (add_le_add (le_max_left a b) (le_max_right a b)).trans_lt <|
     (lt_or_le (max a b) ℵ₀).elim (fun h => (add_lt_aleph0 h h).trans_le hc) fun h => by
       rw [add_eq_self h] <;> exact max_lt h1 h2
 #align cardinal.add_lt_of_lt Cardinal.add_lt_of_lt
 
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 theorem eq_of_add_eq_of_aleph0_le {a b c : Cardinal} (h : a + b = c) (ha : a < c) (hc : ℵ₀ ≤ c) :
     b = c := by
   apply le_antisymm
@@ -1218,32 +810,14 @@ theorem eq_of_add_eq_of_aleph0_le {a b c : Cardinal} (h : a + b = c) (ha : a < c
   simpa [h, lt_irrefl] using this
 #align cardinal.eq_of_add_eq_of_aleph_0_le Cardinal.eq_of_add_eq_of_aleph0_le
 
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 theorem add_eq_left {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : b ≤ a) : a + b = a := by
   rw [add_eq_max ha, max_eq_left hb]
 #align cardinal.add_eq_left Cardinal.add_eq_left
 
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 theorem add_eq_right {a b : Cardinal} (hb : ℵ₀ ≤ b) (ha : a ≤ b) : a + b = b := by
   rw [add_comm, add_eq_left hb ha]
 #align cardinal.add_eq_right Cardinal.add_eq_right
 
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 theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨ b = 0 :=
   by
   rw [max_le_iff]
@@ -1259,53 +833,23 @@ theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨
     · rw [h3, add_zero]
 #align cardinal.add_eq_left_iff Cardinal.add_eq_left_iff
 
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 theorem add_eq_right_iff {a b : Cardinal} : a + b = b ↔ max ℵ₀ a ≤ b ∨ a = 0 := by
   rw [add_comm, add_eq_left_iff]
 #align cardinal.add_eq_right_iff Cardinal.add_eq_right_iff
 
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 theorem add_nat_eq {a : Cardinal} (n : ℕ) (ha : ℵ₀ ≤ a) : a + n = a :=
   add_eq_left ha ((nat_lt_aleph0 _).le.trans ha)
 #align cardinal.add_nat_eq Cardinal.add_nat_eq
 
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 theorem add_one_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a + 1 = a :=
   add_eq_left ha (one_le_aleph0.trans ha)
 #align cardinal.add_one_eq Cardinal.add_one_eq
 
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 @[simp]
 theorem mk_add_one_eq {α : Type _} [Infinite α] : (#α) + 1 = (#α) :=
   add_one_eq (aleph0_le_mk α)
 #align cardinal.mk_add_one_eq Cardinal.mk_add_one_eq
 
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 protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (ha : a < ℵ₀) :
     b = c := by
   cases' le_or_lt ℵ₀ b with hb hb
@@ -1321,22 +865,10 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
     norm_cast  at h⊢; apply add_left_cancel h
 #align cardinal.eq_of_add_eq_add_left Cardinal.eq_of_add_eq_add_left
 
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 protected theorem eq_of_add_eq_add_right {a b c : Cardinal} (h : a + b = c + b) (hb : b < ℵ₀) :
     a = c := by rw [add_comm a b, add_comm c b] at h; exact Cardinal.eq_of_add_eq_add_left h hb
 #align cardinal.eq_of_add_eq_add_right Cardinal.eq_of_add_eq_add_right
 
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 @[simp]
 theorem aleph_add_aleph (o₁ o₂ : Ordinal) : aleph o₁ + aleph o₂ = aleph (max o₁ o₂) := by
   rw [Cardinal.add_eq_max (aleph_0_le_aleph o₁), max_aleph_eq]
@@ -1354,44 +886,20 @@ theorem principal_add_aleph (o : Ordinal) : Ordinal.Principal (· + ·) (aleph o
 #align cardinal.principal_add_aleph Cardinal.principal_add_aleph
 -/
 
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 theorem add_right_inj_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < aleph0) : α + γ = β + γ ↔ α = β :=
   ⟨fun h => Cardinal.eq_of_add_eq_add_right h γ₀, fun h => congr_fun (congr_arg (· + ·) h) γ⟩
 #align cardinal.add_right_inj_of_lt_aleph_0 Cardinal.add_right_inj_of_lt_aleph0
 
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 @[simp]
 theorem add_nat_inj {α β : Cardinal} (n : ℕ) : α + n = β + n ↔ α = β :=
   add_right_inj_of_lt_aleph0 (nat_lt_aleph0 _)
 #align cardinal.add_nat_inj Cardinal.add_nat_inj
 
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 @[simp]
 theorem add_one_inj {α β : Cardinal} : α + 1 = β + 1 ↔ α = β :=
   add_right_inj_of_lt_aleph0 one_lt_aleph0
 #align cardinal.add_one_inj Cardinal.add_one_inj
 
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 theorem add_le_add_iff_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < Cardinal.aleph0) :
     α + γ ≤ β + γ ↔ α ≤ β :=
   by
@@ -1401,23 +909,11 @@ theorem add_le_add_iff_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < Cardinal
   exact ⟨add_le_add_right h.1 γ, mt (add_right_inj_of_lt_aleph_0 γ₀).1 h.2⟩
 #align cardinal.add_le_add_iff_of_lt_aleph_0 Cardinal.add_le_add_iff_of_lt_aleph0
 
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 @[simp]
 theorem add_nat_le_add_nat_iff_of_lt_aleph_0 {α β : Cardinal} (n : ℕ) : α + n ≤ β + n ↔ α ≤ β :=
   add_le_add_iff_of_lt_aleph0 (nat_lt_aleph0 n)
 #align cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0 Cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0
 
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 @[simp]
 theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β + 1 ↔ α ≤ β :=
   add_le_add_iff_of_lt_aleph0 one_lt_aleph0
@@ -1426,12 +922,6 @@ theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β
 /-! ### Properties about power -/
 
 
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 theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) : κ ^ μ ≤ κ :=
   let ⟨n, H3⟩ := lt_aleph0.1 H2
   H3.symm ▸
@@ -1445,22 +935,10 @@ theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) :
       H1
 #align cardinal.pow_le Cardinal.pow_le
 
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 theorem pow_eq {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : 1 ≤ μ) (H3 : μ < ℵ₀) : κ ^ μ = κ :=
   (pow_le H1 H3).antisymm <| self_le_power κ H2
 #align cardinal.pow_eq Cardinal.pow_eq
 
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 theorem power_self_eq {c : Cardinal} (h : ℵ₀ ≤ c) : c ^ c = 2 ^ c :=
   by
   apply ((power_le_power_right <| (cantor c).le).trans _).antisymm
@@ -1468,12 +946,6 @@ theorem power_self_eq {c : Cardinal} (h : ℵ₀ ≤ c) : c ^ c = 2 ^ c :=
   · rw [← power_mul, mul_eq_self h]
 #align cardinal.power_self_eq Cardinal.power_self_eq
 
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 theorem prod_eq_two_power {ι : Type u} [Infinite ι] {c : ι → Cardinal.{v}} (h₁ : ∀ i, 2 ≤ c i)
     (h₂ : ∀ i, lift.{u} (c i) ≤ lift.{v} (#ι)) : prod c = 2 ^ lift.{v} (#ι) :=
   by
@@ -1487,23 +959,11 @@ theorem prod_eq_two_power {ι : Type u} [Infinite ι] {c : ι → Cardinal.{v}}
     exact h₁ i
 #align cardinal.prod_eq_two_power Cardinal.prod_eq_two_power
 
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 theorem power_eq_two_power {c₁ c₂ : Cardinal} (h₁ : ℵ₀ ≤ c₁) (h₂ : 2 ≤ c₂) (h₂' : c₂ ≤ c₁) :
     c₂ ^ c₁ = 2 ^ c₁ :=
   le_antisymm (power_self_eq h₁ ▸ power_le_power_right h₂') (power_le_power_right h₂)
 #align cardinal.power_eq_two_power Cardinal.power_eq_two_power
 
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 theorem nat_power_eq {c : Cardinal.{u}} (h : ℵ₀ ≤ c) {n : ℕ} (hn : 2 ≤ n) :
     (n : Cardinal.{u}) ^ c = 2 ^ c :=
   power_eq_two_power h (by assumption_mod_cast) ((nat_lt_aleph0 n).le.trans h)
@@ -1521,12 +981,6 @@ theorem power_nat_eq {c : Cardinal.{u}} {n : ℕ} (h1 : ℵ₀ ≤ c) (h2 : 1 
 #align cardinal.power_nat_eq Cardinal.power_nat_eq
 -/
 
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 theorem power_nat_le_max {c : Cardinal.{u}} {n : ℕ} : c ^ (n : Cardinal.{u}) ≤ max c ℵ₀ :=
   by
   cases' le_or_lt ℵ₀ c with hc hc
@@ -1543,12 +997,6 @@ theorem powerlt_aleph0 {c : Cardinal} (h : ℵ₀ ≤ c) : c ^< ℵ₀ = c :=
 #align cardinal.powerlt_aleph_0 Cardinal.powerlt_aleph0
 -/
 
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 theorem powerlt_aleph0_le (c : Cardinal) : c ^< ℵ₀ ≤ max c ℵ₀ :=
   by
   cases le_or_lt ℵ₀ c
@@ -1580,12 +1028,6 @@ theorem mk_list_eq_aleph0 (α : Type u) [Countable α] [Nonempty α] : (#List α
 #align cardinal.mk_list_eq_aleph_0 Cardinal.mk_list_eq_aleph0
 -/
 
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 theorem mk_list_eq_max_mk_aleph0 (α : Type u) [Nonempty α] : (#List α) = max (#α) ℵ₀ :=
   by
   cases finite_or_infinite α
@@ -1595,12 +1037,6 @@ theorem mk_list_eq_max_mk_aleph0 (α : Type u) [Nonempty α] : (#List α) = max
     exact aleph_0_le_mk α
 #align cardinal.mk_list_eq_max_mk_aleph_0 Cardinal.mk_list_eq_max_mk_aleph0
 
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 theorem mk_list_le_max (α : Type u) : (#List α) ≤ max ℵ₀ (#α) :=
   by
   cases finite_or_infinite α
@@ -1621,12 +1057,6 @@ theorem mk_finset_of_infinite (α : Type u) [Infinite α] : (#Finset α) = (#α)
 #align cardinal.mk_finset_of_infinite Cardinal.mk_finset_of_infinite
 -/
 
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 @[simp]
 theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Zero β] [Nontrivial β] :
     (#α →₀ β) = max (lift.{v} (#α)) (lift.{u} (#β)) :=
@@ -1646,22 +1076,10 @@ theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Z
       exact lift_mk_le.{v, max u v, u}.2 ⟨⟨_, Finsupp.single_injective default⟩⟩
 #align cardinal.mk_finsupp_lift_of_infinite Cardinal.mk_finsupp_lift_of_infinite
 
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 theorem mk_finsupp_of_infinite (α β : Type u) [Infinite α] [Zero β] [Nontrivial β] :
     (#α →₀ β) = max (#α) (#β) := by simp
 #align cardinal.mk_finsupp_of_infinite Cardinal.mk_finsupp_of_infinite
 
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 @[simp]
 theorem mk_finsupp_lift_of_infinite' (α : Type u) (β : Type v) [Nonempty α] [Zero β] [Infinite β] :
     (#α →₀ β) = max (lift.{v} (#α)) (lift.{u} (#β)) :=
@@ -1674,31 +1092,13 @@ theorem mk_finsupp_lift_of_infinite' (α : Type u) (β : Type v) [Nonempty α] [
   · apply mk_finsupp_lift_of_infinite
 #align cardinal.mk_finsupp_lift_of_infinite' Cardinal.mk_finsupp_lift_of_infinite'
 
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 theorem mk_finsupp_of_infinite' (α β : Type u) [Nonempty α] [Zero β] [Infinite β] :
     (#α →₀ β) = max (#α) (#β) := by simp
 #align cardinal.mk_finsupp_of_infinite' Cardinal.mk_finsupp_of_infinite'
 
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 theorem mk_finsupp_nat (α : Type u) [Nonempty α] : (#α →₀ ℕ) = max (#α) ℵ₀ := by simp
 #align cardinal.mk_finsupp_nat Cardinal.mk_finsupp_nat
 
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 @[simp]
 theorem mk_multiset_of_nonempty (α : Type u) [Nonempty α] : (#Multiset α) = max (#α) ℵ₀ :=
   Multiset.toFinsupp.toEquiv.cardinal_eq.trans (mk_finsupp_nat α)
@@ -1746,12 +1146,6 @@ theorem mk_bounded_set_le_of_infinite (α : Type u) [Infinite α] (c : Cardinal)
 #align cardinal.mk_bounded_set_le_of_infinite Cardinal.mk_bounded_set_le_of_infinite
 -/
 
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 theorem mk_bounded_set_le (α : Type u) (c : Cardinal) :
     (#{ t : Set α // (#t) ≤ c }) ≤ max (#α) ℵ₀ ^ c :=
   by
@@ -1762,12 +1156,6 @@ theorem mk_bounded_set_le (α : Type u) (c : Cardinal) :
   rw [max_comm, ← add_eq_max] <;> rfl
 #align cardinal.mk_bounded_set_le Cardinal.mk_bounded_set_le
 
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 theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
     (#{ t : Set α // t ⊆ s ∧ (#t) ≤ c }) ≤ max (#s) ℵ₀ ^ c :=
   by
@@ -1782,45 +1170,21 @@ theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
 /-! ### Properties of `compl` -/
 
 
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 theorem mk_compl_of_infinite {α : Type _} [Infinite α] (s : Set α) (h2 : (#s) < (#α)) :
     (#(sᶜ : Set α)) = (#α) := by refine' eq_of_add_eq_of_aleph_0_le _ h2 (aleph_0_le_mk α);
   exact mk_sum_compl s
 #align cardinal.mk_compl_of_infinite Cardinal.mk_compl_of_infinite
 
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 theorem mk_compl_finset_of_infinite {α : Type _} [Infinite α] (s : Finset α) :
     (#(↑sᶜ : Set α)) = (#α) := by apply mk_compl_of_infinite;
   exact (finset_card_lt_aleph_0 s).trans_le (aleph_0_le_mk α)
 #align cardinal.mk_compl_finset_of_infinite Cardinal.mk_compl_finset_of_infinite
 
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 theorem mk_compl_eq_mk_compl_infinite {α : Type _} [Infinite α] {s t : Set α} (hs : (#s) < (#α))
     (ht : (#t) < (#α)) : (#(sᶜ : Set α)) = (#(tᶜ : Set α)) := by
   rw [mk_compl_of_infinite s hs, mk_compl_of_infinite t ht]
 #align cardinal.mk_compl_eq_mk_compl_infinite Cardinal.mk_compl_eq_mk_compl_infinite
 
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 theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α] {s : Set α}
     {t : Set β} (h1 : lift.{max v w} (#α) = lift.{max u w} (#β))
     (h2 : lift.{max v w} (#s) = lift.{max u w} (#t)) :
@@ -1837,23 +1201,11 @@ theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α]
       lift_nat_cast, Nat.cast_inj, h1, h2]
 #align cardinal.mk_compl_eq_mk_compl_finite_lift Cardinal.mk_compl_eq_mk_compl_finite_lift
 
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 theorem mk_compl_eq_mk_compl_finite {α β : Type u} [Finite α] {s : Set α} {t : Set β}
     (h1 : (#α) = (#β)) (h : (#s) = (#t)) : (#(sᶜ : Set α)) = (#(tᶜ : Set β)) := by rw [← lift_inj];
   apply mk_compl_eq_mk_compl_finite_lift <;> rwa [lift_inj]
 #align cardinal.mk_compl_eq_mk_compl_finite Cardinal.mk_compl_eq_mk_compl_finite
 
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 theorem mk_compl_eq_mk_compl_finite_same {α : Type _} [Finite α] {s t : Set α} (h : (#s) = (#t)) :
     (#(sᶜ : Set α)) = (#(tᶜ : Set α)) :=
   mk_compl_eq_mk_compl_finite rfl h
@@ -1862,12 +1214,6 @@ theorem mk_compl_eq_mk_compl_finite_same {α : Type _} [Finite α] {s t : Set α
 /-! ### Extending an injection to an equiv -/
 
 
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 theorem extend_function {α β : Type _} {s : Set α} (f : s ↪ β)
     (h : Nonempty ((sᶜ : Set α) ≃ (range fᶜ : Set β))) : ∃ g : α ≃ β, ∀ x : s, g x = f x :=
   by
@@ -1890,12 +1236,6 @@ theorem extend_function_finite {α β : Type _} [Finite α] {s : Set α} (f : s
 #align cardinal.extend_function_finite Cardinal.extend_function_finite
 -/
 
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 theorem extend_function_of_lt {α β : Type _} {s : Set α} (f : s ↪ β) (hs : (#s) < (#α))
     (h : Nonempty (α ≃ β)) : ∃ g : α ≃ β, ∀ x : s, g x = f x :=
   by

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -73,8 +73,7 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
     rwa [← @add_one_of_aleph_0_le (card a), ← card_succ]
     rw [← ord_le, ← le_succ_of_is_limit, ord_le]
     · exact co.trans h
-    · rw [ord_aleph_0]
-      exact omega_is_limit
+    · rw [ord_aleph_0]; exact omega_is_limit
 #align cardinal.ord_is_limit Cardinal.ord_isLimit
 -/
 
@@ -284,9 +283,7 @@ theorem alephIdx_aleph' (o : Ordinal) : (aleph' o).alephIdx = o :=
 
 #print Cardinal.aleph'_zero /-
 @[simp]
-theorem aleph'_zero : aleph' 0 = 0 :=
-  by
-  rw [← nonpos_iff_eq_zero, ← aleph'_aleph_idx 0, aleph'_le]
+theorem aleph'_zero : aleph' 0 = 0 := by rw [← nonpos_iff_eq_zero, ← aleph'_aleph_idx 0, aleph'_le];
   apply Ordinal.zero_le
 #align cardinal.aleph'_zero Cardinal.aleph'_zero
 -/
@@ -456,9 +453,7 @@ theorem aleph0_le_aleph' {o : Ordinal} : ℵ₀ ≤ aleph' o ↔ ω ≤ o := by
 #align cardinal.aleph_0_le_aleph' Cardinal.aleph0_le_aleph'
 
 #print Cardinal.aleph0_le_aleph /-
-theorem aleph0_le_aleph (o : Ordinal) : ℵ₀ ≤ aleph o :=
-  by
-  rw [aleph, aleph_0_le_aleph']
+theorem aleph0_le_aleph (o : Ordinal) : ℵ₀ ≤ aleph o := by rw [aleph, aleph_0_le_aleph'];
   apply Ordinal.le_add_right
 #align cardinal.aleph_0_le_aleph Cardinal.aleph0_le_aleph
 -/
@@ -555,10 +550,7 @@ lean 3 declaration is
 but is expected to have type
   LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{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.aleph_0_lt_aleph_one Cardinal.aleph0_lt_aleph_oneₓ'. -/
-theorem aleph0_lt_aleph_one : ℵ₀ < aleph 1 :=
-  by
-  rw [← succ_aleph_0]
-  apply lt_succ
+theorem aleph0_lt_aleph_one : ℵ₀ < aleph 1 := by rw [← succ_aleph_0]; apply lt_succ
 #align cardinal.aleph_0_lt_aleph_one Cardinal.aleph0_lt_aleph_one
 
 /- warning: cardinal.countable_iff_lt_aleph_one -> Cardinal.countable_iff_lt_aleph_one is a dubious translation:
@@ -579,11 +571,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align cardinal.ord_card_unbounded Cardinal.ord_card_unboundedₓ'. -/
 /-- Ordinals that are cardinals are unbounded. -/
 theorem ord_card_unbounded : Unbounded (· < ·) { b : Ordinal | b.card.ord = b } :=
-  unbounded_lt_iff.2 fun a =>
-    ⟨_,
-      ⟨by
-        dsimp
-        rw [card_ord], (lt_ord_succ_card a).le⟩⟩
+  unbounded_lt_iff.2 fun a => ⟨_, ⟨by dsimp; rw [card_ord], (lt_ord_succ_card a).le⟩⟩
 #align cardinal.ord_card_unbounded Cardinal.ord_card_unbounded
 
 #print Cardinal.eq_aleph'_of_eq_card_ord /-
@@ -599,9 +587,7 @@ theorem ord_aleph'_eq_enum_card : ord ∘ aleph' = enumOrd { b : Ordinal | b.car
   rw [← eq_enum_ord _ ord_card_unbounded, range_eq_iff]
   exact
     ⟨aleph'_is_normal.strict_mono,
-      ⟨fun a => by
-        dsimp
-        rw [card_ord], fun b hb => eq_aleph'_of_eq_card_ord hb⟩⟩
+      ⟨fun a => by dsimp; rw [card_ord], fun b hb => eq_aleph'_of_eq_card_ord hb⟩⟩
 #align cardinal.ord_aleph'_eq_enum_card Cardinal.ord_aleph'_eq_enum_card
 -/
 
@@ -702,8 +688,7 @@ theorem beth_strictMono : StrictMono beth := by
   · rw [lt_succ_iff] at h
     rw [beth_succ]
     apply lt_of_le_of_lt _ (cantor _)
-    rcases eq_or_lt_of_le h with (rfl | h)
-    · rfl
+    rcases eq_or_lt_of_le h with (rfl | h); · rfl
     exact (IH c (lt_succ c) h).le
   · apply (cantor _).trans_le
     rw [beth_limit hb, ← beth_succ]
@@ -778,9 +763,7 @@ theorem beth_ne_zero (o : Ordinal) : beth o ≠ 0 :=
 #print Cardinal.beth_normal /-
 theorem beth_normal : IsNormal.{u} fun o => (beth o).ord :=
   (isNormal_iff_strictMono_limit _).2
-    ⟨ord_strictMono.comp beth_strictMono, fun o ho a ha =>
-      by
-      rw [beth_limit ho, ord_le]
+    ⟨ord_strictMono.comp beth_strictMono, fun o ho a ha => by rw [beth_limit ho, ord_le];
       exact ciSup_le' fun b => ord_le.1 (ha _ b.2)⟩
 #align cardinal.beth_normal Cardinal.beth_normal
 -/
@@ -802,7 +785,7 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c :=
   -- the only nontrivial part is `c * c ≤ c`. We prove it inductively.
   refine' Acc.recOn (cardinal.lt_wf.apply c) (fun c _ => Quotient.inductionOn c fun α IH ol => _) h
   -- consider the minimal well-order `r` on `α` (a type with cardinality `c`).
-  rcases ord_eq α with ⟨r, wo, e⟩
+  rcases ord_eq α with ⟨r, wo, e⟩;
   skip
   letI := linearOrderOfSTO r
   haveI : IsWellOrder α (· < ·) := wo
@@ -841,12 +824,9 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c :=
     apply @irrefl _ r
   cases' lt_or_le (card (succ (typein (· < ·) (g p)))) ℵ₀ with qo qo
   · exact (mul_lt_aleph_0 qo qo).trans_le ol
-  · suffices
-    · exact (IH _ this qo).trans_lt this
-    rw [← lt_ord]
-    apply (ord_is_limit ol).2
-    rw [mk_def, e]
-    apply typein_lt_type
+  · suffices; · exact (IH _ this qo).trans_lt this
+    rw [← lt_ord]; apply (ord_is_limit ol).2
+    rw [mk_def, e]; apply typein_lt_type
 #align cardinal.mul_eq_self Cardinal.mul_eq_self
 
 end UsingOrdinals
@@ -963,10 +943,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_lt_of_lt Cardinal.mul_lt_of_ltₓ'. -/
 theorem mul_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b < c) : a * b < c :=
   (mul_le_mul' (le_max_left a b) (le_max_right a b)).trans_lt <|
-    (lt_or_le (max a b) ℵ₀).elim (fun h => (mul_lt_aleph0 h h).trans_le hc) fun h =>
-      by
-      rw [mul_eq_self h]
-      exact max_lt h1 h2
+    (lt_or_le (max a b) ℵ₀).elim (fun h => (mul_lt_aleph0 h h).trans_le hc) fun h => by
+      rw [mul_eq_self h]; exact max_lt h1 h2
 #align cardinal.mul_lt_of_lt Cardinal.mul_lt_of_lt
 
 /- warning: cardinal.mul_le_max_of_aleph_0_le_left -> Cardinal.mul_le_max_of_aleph0_le_left is a dubious translation:
@@ -990,13 +968,11 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_eq_max_of_aleph_0_le_left Cardinal.mul_eq_max_of_aleph0_le_leftₓ'. -/
 theorem mul_eq_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) (h' : b ≠ 0) : a * b = max a b :=
   by
-  cases' le_or_lt ℵ₀ b with hb hb
-  · exact mul_eq_max h hb
+  cases' le_or_lt ℵ₀ b with hb hb; · exact mul_eq_max h hb
   refine' (mul_le_max_of_aleph_0_le_left h).antisymm _
   have : b ≤ a := hb.le.trans h
   rw [max_eq_left this]
-  convert mul_le_mul_left' (one_le_iff_ne_zero.mpr h') _
-  rw [mul_one]
+  convert mul_le_mul_left' (one_le_iff_ne_zero.mpr h') _; rw [mul_one]
 #align cardinal.mul_eq_max_of_aleph_0_le_left Cardinal.mul_eq_max_of_aleph0_le_left
 
 /- warning: cardinal.mul_le_max_of_aleph_0_le_right -> Cardinal.mul_le_max_of_aleph0_le_right is a dubious translation:
@@ -1091,9 +1067,7 @@ lean 3 declaration is
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (Ne.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1}))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} a (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b))
 Case conversion may be inaccurate. Consider using '#align cardinal.le_mul_right Cardinal.le_mul_rightₓ'. -/
-theorem le_mul_right {a b : Cardinal} (h : b ≠ 0) : a ≤ a * b :=
-  by
-  rw [mul_comm]
+theorem le_mul_right {a b : Cardinal} (h : b ≠ 0) : a ≤ a * b := by rw [mul_comm];
   exact le_mul_left h
 #align cardinal.le_mul_right Cardinal.le_mul_right
 
@@ -1108,39 +1082,18 @@ theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧
   rw [max_le_iff]
   refine' ⟨fun h => _, _⟩
   · cases' le_or_lt ℵ₀ a with ha ha
-    · have : a ≠ 0 := by
-        rintro rfl
-        exact ha.not_lt aleph_0_pos
-      left
-      use ha
-      · rw [← not_lt]
-        exact fun hb => ne_of_gt (hb.trans_le (le_mul_left this)) h
-      · rintro rfl
-        apply this
-        rw [MulZeroClass.mul_zero] at h
-        exact h.symm
-    right
-    by_cases h2a : a = 0
-    · exact Or.inr h2a
-    have hb : b ≠ 0 := by
-      rintro rfl
-      apply h2a
-      rw [MulZeroClass.mul_zero] at h
-      exact h.symm
-    left
-    rw [← h, mul_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha
-    rcases ha with (rfl | rfl | ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩)
-    contradiction
-    contradiction
-    rw [← Ne] at h2a
-    rw [← one_le_iff_ne_zero] at h2a hb
-    norm_cast  at h2a hb h⊢
-    apply le_antisymm _ hb
-    rw [← not_lt]
-    apply fun h2b => ne_of_gt _ h
-    conv_lhs => rw [← mul_one n]
-    rwa [mul_lt_mul_left]
-    apply Nat.lt_of_succ_le h2a
+    · have : a ≠ 0 := by rintro rfl; exact ha.not_lt aleph_0_pos
+      left; use ha
+      · rw [← not_lt]; exact fun hb => ne_of_gt (hb.trans_le (le_mul_left this)) h
+      · rintro rfl; apply this; rw [MulZeroClass.mul_zero] at h; exact h.symm
+    right; by_cases h2a : a = 0; · exact Or.inr h2a
+    have hb : b ≠ 0 := by rintro rfl; apply h2a; rw [MulZeroClass.mul_zero] at h; exact h.symm
+    left; rw [← h, mul_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha
+    rcases ha with (rfl | rfl | ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩); contradiction; contradiction
+    rw [← Ne] at h2a; rw [← one_le_iff_ne_zero] at h2a hb; norm_cast  at h2a hb h⊢
+    apply le_antisymm _ hb; rw [← not_lt]
+    apply fun h2b => ne_of_gt _ h; conv_lhs => rw [← mul_one n]
+    rwa [mul_lt_mul_left]; apply Nat.lt_of_succ_le h2a
   · rintro (⟨⟨ha, hab⟩, hb⟩ | rfl | rfl)
     · rw [mul_eq_max_of_aleph_0_le_left ha hb, max_eq_left hab]
     all_goals simp
@@ -1259,8 +1212,7 @@ Case conversion may be inaccurate. Consider using '#align cardinal.eq_of_add_eq_
 theorem eq_of_add_eq_of_aleph0_le {a b c : Cardinal} (h : a + b = c) (ha : a < c) (hc : ℵ₀ ≤ c) :
     b = c := by
   apply le_antisymm
-  · rw [← h]
-    apply self_le_add_left
+  · rw [← h]; apply self_le_add_left
   rw [← not_lt]; intro hb
   have : a + b < c := add_lt_of_lt hc ha hb
   simpa [h, lt_irrefl] using this
@@ -1297,15 +1249,10 @@ theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨
   rw [max_le_iff]
   refine' ⟨fun h => _, _⟩
   · cases' le_or_lt ℵ₀ a with ha ha
-    · left
-      use ha
-      rw [← not_lt]
-      apply fun hb => ne_of_gt _ h
+    · left; use ha; rw [← not_lt]; apply fun hb => ne_of_gt _ h
       exact hb.trans_le (self_le_add_left b a)
-    right
-    rw [← h, add_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha
-    rcases ha with ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩
-    norm_cast  at h⊢
+    right; rw [← h, add_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha
+    rcases ha with ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩; norm_cast  at h⊢
     rw [← add_right_inj, h, add_zero]
   · rintro (⟨h1, h2⟩ | h3)
     · rw [add_eq_max h1, max_eq_left h2]
@@ -1366,18 +1313,12 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
     rw [add_eq_right hb this.le, eq_comm] at h
     rw [eq_of_add_eq_of_aleph_0_le h this hb]
   · have hc : c < ℵ₀ := by
-      rw [← not_le]
-      intro hc
-      apply lt_irrefl ℵ₀
-      apply (hc.trans (self_le_add_left _ a)).trans_lt
-      rw [← h]
-      apply add_lt_aleph_0 ha hb
+      rw [← not_le]; intro hc
+      apply lt_irrefl ℵ₀; apply (hc.trans (self_le_add_left _ a)).trans_lt
+      rw [← h]; apply add_lt_aleph_0 ha hb
     rw [lt_aleph_0] at *
-    rcases ha with ⟨n, rfl⟩
-    rcases hb with ⟨m, rfl⟩
-    rcases hc with ⟨k, rfl⟩
-    norm_cast  at h⊢
-    apply add_left_cancel h
+    rcases ha with ⟨n, rfl⟩; rcases hb with ⟨m, rfl⟩; rcases hc with ⟨k, rfl⟩
+    norm_cast  at h⊢; apply add_left_cancel h
 #align cardinal.eq_of_add_eq_add_left Cardinal.eq_of_add_eq_add_left
 
 /- warning: cardinal.eq_of_add_eq_add_right -> Cardinal.eq_of_add_eq_add_right is a dubious translation:
@@ -1387,9 +1328,7 @@ but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) c b)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{u1} a c)
 Case conversion may be inaccurate. Consider using '#align cardinal.eq_of_add_eq_add_right Cardinal.eq_of_add_eq_add_rightₓ'. -/
 protected theorem eq_of_add_eq_add_right {a b c : Cardinal} (h : a + b = c + b) (hb : b < ℵ₀) :
-    a = c := by
-  rw [add_comm a b, add_comm c b] at h
-  exact Cardinal.eq_of_add_eq_add_left h hb
+    a = c := by rw [add_comm a b, add_comm c b] at h; exact Cardinal.eq_of_add_eq_add_left h hb
 #align cardinal.eq_of_add_eq_add_right Cardinal.eq_of_add_eq_add_right
 
 /- warning: cardinal.aleph_add_aleph -> Cardinal.aleph_add_aleph is a dubious translation:
@@ -1405,9 +1344,7 @@ theorem aleph_add_aleph (o₁ o₂ : Ordinal) : aleph o₁ + aleph o₂ = aleph
 
 #print Cardinal.principal_add_ord /-
 theorem principal_add_ord {c : Cardinal} (hc : ℵ₀ ≤ c) : Ordinal.Principal (· + ·) c.ord :=
-  fun a b ha hb => by
-  rw [lt_ord, Ordinal.card_add] at *
-  exact add_lt_of_lt hc ha hb
+  fun a b ha hb => by rw [lt_ord, Ordinal.card_add] at *; exact add_lt_of_lt hc ha hb
 #align cardinal.principal_add_ord Cardinal.principal_add_ord
 -/
 
@@ -1500,17 +1437,10 @@ theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) :
   H3.symm ▸
     Quotient.inductionOn κ
       (fun α H1 =>
-        Nat.recOn n
-          (lt_of_lt_of_le
-              (by
-                rw [Nat.cast_zero, power_zero]
-                exact one_lt_aleph_0)
-              H1).le
+        Nat.recOn n (lt_of_lt_of_le (by rw [Nat.cast_zero, power_zero]; exact one_lt_aleph_0) H1).le
           fun n ih =>
           trans_rel_left _
-            (by
-              rw [Nat.cast_succ, power_add, power_one]
-              exact mul_le_mul_right' ih _)
+            (by rw [Nat.cast_succ, power_add, power_one]; exact mul_le_mul_right' ih _)
             (mul_eq_self H1))
       H1
 #align cardinal.pow_le Cardinal.pow_le
@@ -1534,8 +1464,7 @@ Case conversion may be inaccurate. Consider using '#align cardinal.power_self_eq
 theorem power_self_eq {c : Cardinal} (h : ℵ₀ ≤ c) : c ^ c = 2 ^ c :=
   by
   apply ((power_le_power_right <| (cantor c).le).trans _).antisymm
-  · convert power_le_power_right ((nat_lt_aleph_0 2).le.trans h)
-    apply nat.cast_two.symm
+  · convert power_le_power_right ((nat_lt_aleph_0 2).le.trans h); apply nat.cast_two.symm
   · rw [← power_mul, mul_eq_self h]
 #align cardinal.power_self_eq Cardinal.power_self_eq
 
@@ -1609,11 +1538,7 @@ theorem power_nat_le_max {c : Cardinal.{u}} {n : ℕ} : c ^ (n : Cardinal.{u}) 
 theorem powerlt_aleph0 {c : Cardinal} (h : ℵ₀ ≤ c) : c ^< ℵ₀ = c :=
   by
   apply le_antisymm
-  · rw [powerlt_le]
-    intro c'
-    rw [lt_aleph_0]
-    rintro ⟨n, rfl⟩
-    apply power_nat_le h
+  · rw [powerlt_le]; intro c'; rw [lt_aleph_0]; rintro ⟨n, rfl⟩; apply power_nat_le h
   convert le_powerlt c one_lt_aleph_0; rw [power_one]
 #align cardinal.powerlt_aleph_0 Cardinal.powerlt_aleph0
 -/
@@ -1627,8 +1552,7 @@ Case conversion may be inaccurate. Consider using '#align cardinal.powerlt_aleph
 theorem powerlt_aleph0_le (c : Cardinal) : c ^< ℵ₀ ≤ max c ℵ₀ :=
   by
   cases le_or_lt ℵ₀ c
-  · rw [powerlt_aleph_0 h]
-    apply le_max_left
+  · rw [powerlt_aleph_0 h]; apply le_max_left
   rw [powerlt_le]
   exact fun c' hc' => (power_lt_aleph_0 h hc').le.trans (le_max_right _ _)
 #align cardinal.powerlt_aleph_0_le Cardinal.powerlt_aleph0_le
@@ -1805,32 +1729,20 @@ theorem mk_bounded_set_le_of_infinite (α : Type u) [Infinite α] (c : Cardinal)
   refine' le_trans _ (by rw [← add_one_eq (aleph_0_le_mk α)])
   induction' c using Cardinal.inductionOn with β
   fapply mk_le_of_surjective
-  · intro f
-    use Sum.inl ⁻¹' range f
+  · intro f; use Sum.inl ⁻¹' range f
     refine' le_trans (mk_preimage_of_injective _ _ fun x y => Sum.inl.inj) _
     apply mk_range_le
   rintro ⟨s, ⟨g⟩⟩
   use fun y => if h : ∃ x : s, g x = y then Sum.inl (Classical.choose h).val else Sum.inr ⟨⟩
   apply Subtype.eq; ext
   constructor
-  · rintro ⟨y, h⟩
-    dsimp only at h
-    by_cases h' : ∃ z : s, g z = y
-    · rw [dif_pos h'] at h
-      cases Sum.inl.inj h
-      exact (Classical.choose h').2
-    · rw [dif_neg h'] at h
-      cases h
-  · intro h
-    have : ∃ z : s, g z = g ⟨x, h⟩ := ⟨⟨x, h⟩, rfl⟩
-    use g ⟨x, h⟩
-    dsimp only
-    rw [dif_pos this]
-    congr
-    suffices : Classical.choose this = ⟨x, h⟩
-    exact congr_arg Subtype.val this
-    apply g.2
-    exact Classical.choose_spec this
+  · rintro ⟨y, h⟩; dsimp only at h; by_cases h' : ∃ z : s, g z = y
+    · rw [dif_pos h'] at h; cases Sum.inl.inj h; exact (Classical.choose h').2
+    · rw [dif_neg h'] at h; cases h
+  · intro h; have : ∃ z : s, g z = g ⟨x, h⟩ := ⟨⟨x, h⟩, rfl⟩
+    use g ⟨x, h⟩; dsimp only; rw [dif_pos this]; congr
+    suffices : Classical.choose this = ⟨x, h⟩; exact congr_arg Subtype.val this
+    apply g.2; exact Classical.choose_spec this
 #align cardinal.mk_bounded_set_le_of_infinite Cardinal.mk_bounded_set_le_of_infinite
 -/
 
@@ -1844,12 +1756,8 @@ theorem mk_bounded_set_le (α : Type u) (c : Cardinal) :
     (#{ t : Set α // (#t) ≤ c }) ≤ max (#α) ℵ₀ ^ c :=
   by
   trans #{ t : Set (Sum (ULift.{u} ℕ) α) // (#t) ≤ c }
-  · refine' ⟨embedding.subtype_map _ _⟩
-    apply embedding.image
-    use Sum.inr
-    apply Sum.inr.inj
-    intro s hs
-    exact mk_image_le.trans hs
+  · refine' ⟨embedding.subtype_map _ _⟩; apply embedding.image
+    use Sum.inr; apply Sum.inr.inj; intro s hs; exact mk_image_le.trans hs
   apply (mk_bounded_set_le_of_infinite (Sum (ULift.{u} ℕ) α) c).trans
   rw [max_comm, ← add_eq_max] <;> rfl
 #align cardinal.mk_bounded_set_le Cardinal.mk_bounded_set_le
@@ -1866,9 +1774,7 @@ theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
   refine' le_trans _ (mk_bounded_set_le s c)
   refine' ⟨Embedding.codRestrict _ _ _⟩
   use fun t => coe ⁻¹' t.1
-  · rintro ⟨t, ht1, ht2⟩ ⟨t', h1t', h2t'⟩ h
-    apply Subtype.eq
-    dsimp only at h⊢
+  · rintro ⟨t, ht1, ht2⟩ ⟨t', h1t', h2t'⟩ h; apply Subtype.eq; dsimp only at h⊢
     refine' (preimage_eq_preimage' _ _).1 h <;> rw [Subtype.range_coe] <;> assumption
   rintro ⟨t, h1t, h2t⟩; exact (mk_preimage_of_injective _ _ Subtype.val_injective).trans h2t
 #align cardinal.mk_bounded_subset_le Cardinal.mk_bounded_subset_le
@@ -1883,9 +1789,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] (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)) (Cardinal.mk.{u1} α)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Set.Elem.{u1} α (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) s))) (Cardinal.mk.{u1} α))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_of_infinite Cardinal.mk_compl_of_infiniteₓ'. -/
 theorem mk_compl_of_infinite {α : Type _} [Infinite α] (s : Set α) (h2 : (#s) < (#α)) :
-    (#(sᶜ : Set α)) = (#α) :=
-  by
-  refine' eq_of_add_eq_of_aleph_0_le _ h2 (aleph_0_le_mk α)
+    (#(sᶜ : Set α)) = (#α) := by refine' eq_of_add_eq_of_aleph_0_le _ h2 (aleph_0_le_mk α);
   exact mk_sum_compl s
 #align cardinal.mk_compl_of_infinite Cardinal.mk_compl_of_infinite
 
@@ -1896,8 +1800,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] (s : Finset.{u1} α), Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Set.Elem.{u1} α (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) (Finset.toSet.{u1} α s)))) (Cardinal.mk.{u1} α)
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_finset_of_infinite Cardinal.mk_compl_finset_of_infiniteₓ'. -/
 theorem mk_compl_finset_of_infinite {α : Type _} [Infinite α] (s : Finset α) :
-    (#(↑sᶜ : Set α)) = (#α) := by
-  apply mk_compl_of_infinite
+    (#(↑sᶜ : Set α)) = (#α) := by apply mk_compl_of_infinite;
   exact (finset_card_lt_aleph_0 s).trans_le (aleph_0_le_mk α)
 #align cardinal.mk_compl_finset_of_infinite Cardinal.mk_compl_finset_of_infinite
 
@@ -1941,9 +1844,7 @@ but is expected to have type
   forall {α : Type.{u}} {β : Type.{u}} [_inst_1 : Finite.{succ u} α] {s : Set.{u} α} {t : Set.{u} β}, (Eq.{succ (succ u)} Cardinal.{u} (Cardinal.mk.{u} α) (Cardinal.mk.{u} β)) -> (Eq.{succ (succ u)} Cardinal.{u} (Cardinal.mk.{u} (Set.Elem.{u} α s)) (Cardinal.mk.{u} (Set.Elem.{u} β t))) -> (Eq.{succ (succ u)} Cardinal.{u} (Cardinal.mk.{u} (Set.Elem.{u} α (HasCompl.compl.{u} (Set.{u} α) (BooleanAlgebra.toHasCompl.{u} (Set.{u} α) (Set.instBooleanAlgebraSet.{u} α)) s))) (Cardinal.mk.{u} (Set.Elem.{u} β (HasCompl.compl.{u} (Set.{u} β) (BooleanAlgebra.toHasCompl.{u} (Set.{u} β) (Set.instBooleanAlgebraSet.{u} β)) t))))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_eq_mk_compl_finite Cardinal.mk_compl_eq_mk_compl_finiteₓ'. -/
 theorem mk_compl_eq_mk_compl_finite {α β : Type u} [Finite α] {s : Set α} {t : Set β}
-    (h1 : (#α) = (#β)) (h : (#s) = (#t)) : (#(sᶜ : Set α)) = (#(tᶜ : Set β)) :=
-  by
-  rw [← lift_inj]
+    (h1 : (#α) = (#β)) (h : (#s) = (#t)) : (#(sᶜ : Set α)) = (#(tᶜ : Set β)) := by rw [← lift_inj];
   apply mk_compl_eq_mk_compl_finite_lift <;> rwa [lift_inj]
 #align cardinal.mk_compl_eq_mk_compl_finite Cardinal.mk_compl_eq_mk_compl_finite
 
@@ -2000,9 +1901,7 @@ theorem extend_function_of_lt {α β : Type _} {s : Set α} (f : s ↪ β) (hs :
   by
   cases fintypeOrInfinite α
   · exact extend_function_finite f h
-  · apply extend_function f
-    cases' id h with g
-    haveI := Infinite.of_injective _ g.injective
+  · apply extend_function f; cases' id h with g; haveI := Infinite.of_injective _ g.injective
     rw [← lift_mk_eq'] at h⊢
     rwa [mk_compl_of_infinite s hs, mk_compl_of_infinite]
     rwa [← lift_lt, mk_range_eq_of_injective f.injective, ← h, lift_lt]
@@ -2034,10 +1933,7 @@ theorem bit1_ne_zero (a : Cardinal) : ¬bit1 a = 0 := by simp [bit1]
 #align cardinal.bit1_ne_zero Cardinal.bit1_ne_zero
 
 @[simp]
-theorem zero_lt_bit0 (a : Cardinal) : 0 < bit0 a ↔ 0 < a :=
-  by
-  rw [← not_iff_not]
-  simp [bit0]
+theorem zero_lt_bit0 (a : Cardinal) : 0 < bit0 a ↔ 0 < a := by rw [← not_iff_not]; simp [bit0]
 #align cardinal.zero_lt_bit0 Cardinal.zero_lt_bit0
 
 @[simp]
@@ -2065,10 +1961,7 @@ theorem bit0_lt_aleph0 {c : Cardinal} : bit0 c < ℵ₀ ↔ c < ℵ₀ := by sim
 #align cardinal.bit0_lt_aleph_0 Cardinal.bit0_lt_aleph0
 
 @[simp]
-theorem aleph0_le_bit0 {c : Cardinal} : ℵ₀ ≤ bit0 c ↔ ℵ₀ ≤ c :=
-  by
-  rw [← not_iff_not]
-  simp
+theorem aleph0_le_bit0 {c : Cardinal} : ℵ₀ ≤ bit0 c ↔ ℵ₀ ≤ c := by rw [← not_iff_not]; simp
 #align cardinal.aleph_0_le_bit0 Cardinal.aleph0_le_bit0
 
 @[simp]
@@ -2089,10 +1982,7 @@ theorem bit1_lt_aleph0 {c : Cardinal} : bit1 c < ℵ₀ ↔ c < ℵ₀ := by
 #align cardinal.bit1_lt_aleph_0 Cardinal.bit1_lt_aleph0
 
 @[simp]
-theorem aleph0_le_bit1 {c : Cardinal} : ℵ₀ ≤ bit1 c ↔ ℵ₀ ≤ c :=
-  by
-  rw [← not_iff_not]
-  simp
+theorem aleph0_le_bit1 {c : Cardinal} : ℵ₀ ≤ bit1 c ↔ ℵ₀ ≤ c := by rw [← not_iff_not]; simp
 #align cardinal.aleph_0_le_bit1 Cardinal.aleph0_le_bit1
 
 @[simp]
@@ -2227,9 +2117,8 @@ theorem bit0_lt_bit1 {a b : Cardinal} : bit0 a < bit1 b ↔ a < b ∨ a ≤ b 
 #align cardinal.bit0_lt_bit1 Cardinal.bit0_lt_bit1
 
 theorem one_lt_two : (1 : Cardinal) < 2 :=
-  by
-  -- This strategy works generally to prove inequalities between numerals in `cardinality`.
-  norm_cast
+  by-- This strategy works generally to prove inequalities between numerals in `cardinality`.
+  norm_cast;
   norm_num
 #align cardinal.one_lt_two Cardinal.one_lt_two

bump to nightly-2023-05-19-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

a31df521

Diff

@@ -1965,7 +1965,7 @@ theorem mk_compl_eq_mk_compl_finite_same {α : Type _} [Finite α] {s t : Set α
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} (f : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β), (Nonempty.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s)) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (HasCompl.compl.{u2} (Set.{u2} β) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} β) (Set.booleanAlgebra.{u2} β)) (Set.range.{u2, succ u1} β (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) (fun (_x : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) f)))))) -> (Exists.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{succ u1, succ u2} α β) (fun (g : Equiv.{succ u1, succ u2} α β) => forall (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s), Eq.{succ u2} β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) (fun (_x : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) f x)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} (f : Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β), (Nonempty.{max (succ u1) (succ u2)} (Equiv.{succ u2, succ u1} (Set.Elem.{u2} α (HasCompl.compl.{u2} (Set.{u2} α) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} α) (Set.instBooleanAlgebraSet.{u2} α)) s)) (Set.Elem.{u1} β (HasCompl.compl.{u1} (Set.{u1} β) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} β) (Set.instBooleanAlgebraSet.{u1} β)) (Set.range.{u1, succ u2} β (Set.Elem.{u2} α s) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f)))))) -> (Exists.{max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} α β) (fun (g : Equiv.{succ u2, succ u1} α β) => forall (x : Set.Elem.{u2} α s), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) g (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f x)))
+  forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} (f : Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β), (Nonempty.{max (succ u1) (succ u2)} (Equiv.{succ u2, succ u1} (Set.Elem.{u2} α (HasCompl.compl.{u2} (Set.{u2} α) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} α) (Set.instBooleanAlgebraSet.{u2} α)) s)) (Set.Elem.{u1} β (HasCompl.compl.{u1} (Set.{u1} β) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} β) (Set.instBooleanAlgebraSet.{u1} β)) (Set.range.{u1, succ u2} β (Set.Elem.{u2} α s) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f)))))) -> (Exists.{max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} α β) (fun (g : Equiv.{succ u2, succ u1} α β) => forall (x : Set.Elem.{u2} α s), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => β) (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) g (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f x)))
 Case conversion may be inaccurate. Consider using '#align cardinal.extend_function Cardinal.extend_functionₓ'. -/
 theorem extend_function {α β : Type _} {s : Set α} (f : s ↪ β)
     (h : Nonempty ((sᶜ : Set α) ≃ (range fᶜ : Set β))) : ∃ g : α ≃ β, ∀ x : s, g x = f x :=
@@ -1993,7 +1993,7 @@ theorem extend_function_finite {α β : Type _} [Finite α] {s : Set α} (f : s
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} (f : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) 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} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Cardinal.mk.{u1} α)) -> (Nonempty.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{succ u1, succ u2} α β)) -> (Exists.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{succ u1, succ u2} α β) (fun (g : Equiv.{succ u1, succ u2} α β) => forall (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s), Eq.{succ u2} β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) (fun (_x : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) f x)))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} (f : Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β), (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Cardinal.mk.{u2} (Set.Elem.{u2} α s)) (Cardinal.mk.{u2} α)) -> (Nonempty.{max (succ u1) (succ u2)} (Equiv.{succ u2, succ u1} α β)) -> (Exists.{max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} α β) (fun (g : Equiv.{succ u2, succ u1} α β) => forall (x : Set.Elem.{u2} α s), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) g (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f x)))
+  forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} (f : Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β), (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Cardinal.mk.{u2} (Set.Elem.{u2} α s)) (Cardinal.mk.{u2} α)) -> (Nonempty.{max (succ u1) (succ u2)} (Equiv.{succ u2, succ u1} α β)) -> (Exists.{max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} α β) (fun (g : Equiv.{succ u2, succ u1} α β) => forall (x : Set.Elem.{u2} α s), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => β) (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) g (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f x)))
 Case conversion may be inaccurate. Consider using '#align cardinal.extend_function_of_lt Cardinal.extend_function_of_ltₓ'. -/
 theorem extend_function_of_lt {α β : Type _} {s : Set α} (f : s ↪ β) (hs : (#s) < (#α))
     (h : Nonempty (α ≃ β)) : ∃ g : α ≃ β, ∀ x : s, g x = f x :=

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -81,7 +81,12 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
 /-! ### Aleph cardinals -/
 
 
-#print Cardinal.alephIdx.initialSeg /-
+/- warning: cardinal.aleph_idx.initial_seg -> Cardinal.alephIdx.initialSeg is a dubious translation:
+lean 3 declaration is
+  InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))
+but is expected to have type
+  InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.initial_seg Cardinal.alephIdx.initialSegₓ'. -/
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ω = ω`,
@@ -93,7 +98,6 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
 def alephIdx.initialSeg : @InitialSeg Cardinal Ordinal (· < ·) (· < ·) :=
   @RelEmbedding.collapse Cardinal Ordinal (· < ·) (· < ·) _ Cardinal.ord.orderEmbedding.ltEmbedding
 #align cardinal.aleph_idx.initial_seg Cardinal.alephIdx.initialSeg
--/
 
 #print Cardinal.alephIdx /-
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
@@ -108,7 +112,7 @@ def alephIdx : Cardinal → Ordinal :=
 
 /- warning: cardinal.aleph_idx.initial_seg_coe -> Cardinal.alephIdx.initialSeg_coe is a dubious translation:
 lean 3 declaration is
-  Eq.{succ (succ u1)} ((fun (_x : InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.initialSeg.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (FunLike.hasCoeToFun.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => Ordinal.{u1}) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.{u1} Ordinal.{u1} (InitialSeg.embeddingLike.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))))) Cardinal.alephIdx.initialSeg.{u1}) Cardinal.alephIdx.{u1}
+  Eq.{succ (succ u1)} ((fun (_x : InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.initialSeg.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (FunLike.hasCoeToFun.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => Ordinal.{u1}) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.{u1} Ordinal.{u1} (InitialSeg.embeddingLike.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))))) Cardinal.alephIdx.initialSeg.{u1}) Cardinal.alephIdx.{u1}
 but is expected to have type
   Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249)) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249)) Cardinal.{u1} Ordinal.{u1} (InitialSeg.instEmbeddingLikeInitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249))) Cardinal.alephIdx.initialSeg.{u1}) Cardinal.alephIdx.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.initial_seg_coe Cardinal.alephIdx.initialSeg_coeₓ'. -/
@@ -117,27 +121,44 @@ theorem alephIdx.initialSeg_coe : (alephIdx.initialSeg : Cardinal → Ordinal) =
   rfl
 #align cardinal.aleph_idx.initial_seg_coe Cardinal.alephIdx.initialSeg_coe
 
-#print Cardinal.alephIdx_lt /-
+/- warning: cardinal.aleph_idx_lt -> Cardinal.alephIdx_lt is a dubious translation:
+lean 3 declaration is
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.alephIdx.{u1} a) (Cardinal.alephIdx.{u1} b)) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a b)
+but is expected to have type
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.alephIdx.{u1} a) (Cardinal.alephIdx.{u1} b)) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a b)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx_lt Cardinal.alephIdx_ltₓ'. -/
 @[simp]
 theorem alephIdx_lt {a b} : alephIdx a < alephIdx b ↔ a < b :=
   alephIdx.initialSeg.toRelEmbedding.map_rel_iff
 #align cardinal.aleph_idx_lt Cardinal.alephIdx_lt
--/
 
-#print Cardinal.alephIdx_le /-
+/- warning: cardinal.aleph_idx_le -> Cardinal.alephIdx_le is a dubious translation:
+lean 3 declaration is
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.alephIdx.{u1} a) (Cardinal.alephIdx.{u1} b)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} a b)
+but is expected to have type
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.alephIdx.{u1} a) (Cardinal.alephIdx.{u1} b)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} a b)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx_le Cardinal.alephIdx_leₓ'. -/
 @[simp]
 theorem alephIdx_le {a b} : alephIdx a ≤ alephIdx b ↔ a ≤ b := by
   rw [← not_lt, ← not_lt, aleph_idx_lt]
 #align cardinal.aleph_idx_le Cardinal.alephIdx_le
--/
 
-#print Cardinal.alephIdx.init /-
+/- warning: cardinal.aleph_idx.init -> Cardinal.alephIdx.init is a dubious translation:
+lean 3 declaration is
+  forall {a : Cardinal.{u1}} {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 (Cardinal.alephIdx.{u1} a)) -> (Exists.{succ (succ u1)} Cardinal.{u1} (fun (c : Cardinal.{u1}) => Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.alephIdx.{u1} c) b))
+but is expected to have type
+  forall {a : Cardinal.{u1}} {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 (Cardinal.alephIdx.{u1} a)) -> (Exists.{succ (succ u1)} Cardinal.{u1} (fun (c : Cardinal.{u1}) => Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.alephIdx.{u1} c) b))
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.init Cardinal.alephIdx.initₓ'. -/
 theorem alephIdx.init {a b} : b < alephIdx a → ∃ c, alephIdx c = b :=
   alephIdx.initialSeg.dropLast
 #align cardinal.aleph_idx.init Cardinal.alephIdx.init
--/
 
-#print Cardinal.alephIdx.relIso /-
+/- warning: cardinal.aleph_idx.rel_iso -> Cardinal.alephIdx.relIso is a dubious translation:
+lean 3 declaration is
+  RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))
+but is expected to have type
+  RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.rel_iso Cardinal.alephIdx.relIsoₓ'. -/
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ℵ₀ = ω`,
@@ -159,11 +180,10 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
           (Cardinal.bddAbove_range.{u, u} fun a : α => inv_fun aleph_idx (Ordinal.typein r a))
           (Ordinal.enum r _ (h (succ s)))
 #align cardinal.aleph_idx.rel_iso Cardinal.alephIdx.relIso
--/
 
 /- warning: cardinal.aleph_idx.rel_iso_coe -> Cardinal.alephIdx.relIso_coe is a dubious translation:
 lean 3 declaration is
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+  Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.alephIdx.relIso.{u1}) Cardinal.alephIdx.{u1}
 but is expected to have type
   Eq.{succ (succ u1)} (Cardinal.{u1} -> Ordinal.{u1}) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465)) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => Ordinal.{u1}) (RelHomClass.toFunLike.{succ u1, succ u1, succ u1} (RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465)) Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (RelIso.instRelHomClassRelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465))) Cardinal.alephIdx.relIso.{u1}) Cardinal.alephIdx.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coeₓ'. -/
@@ -172,12 +192,16 @@ theorem alephIdx.relIso_coe : (alephIdx.relIso : Cardinal → Ordinal) = alephId
   rfl
 #align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coe
 
-#print Cardinal.type_cardinal /-
+/- warning: cardinal.type_cardinal -> Cardinal.type_cardinal is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ (succ u1))} Ordinal.{succ u1} (Ordinal.type.{succ u1} Cardinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) Cardinal.wo.{u1}) Ordinal.univ.{u1, succ u1}
+but is expected to have type
+  Eq.{succ (succ (succ u1))} Ordinal.{succ u1} (Ordinal.type.{succ u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.737 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.739 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.737 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.739) Cardinal.wo.{u1}) Ordinal.univ.{u1, succ u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.type_cardinal Cardinal.type_cardinalₓ'. -/
 @[simp]
 theorem type_cardinal : @type Cardinal (· < ·) _ = Ordinal.univ.{u, u + 1} := by
   rw [Ordinal.univ_id] <;> exact Quotient.sound ⟨aleph_idx.rel_iso⟩
 #align cardinal.type_cardinal Cardinal.type_cardinal
--/
 
 #print Cardinal.mk_cardinal /-
 @[simp]
@@ -186,7 +210,12 @@ theorem mk_cardinal : (#Cardinal) = univ.{u, u + 1} := by
 #align cardinal.mk_cardinal Cardinal.mk_cardinal
 -/
 
-#print Cardinal.Aleph'.relIso /-
+/- warning: cardinal.aleph'.rel_iso -> Cardinal.Aleph'.relIso is a dubious translation:
+lean 3 declaration is
+  RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))
+but is expected to have type
+  RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph'.rel_iso Cardinal.Aleph'.relIsoₓ'. -/
 /-- The `aleph'` function gives the cardinals listed by their ordinal
   index, and is the inverse of `aleph_idx`.
   `aleph' n = n`, `aleph' ω = ω`, `aleph' (ω + 1) = succ ℵ₀`, etc.
@@ -196,7 +225,6 @@ theorem mk_cardinal : (#Cardinal) = univ.{u, u + 1} := by
 def Aleph'.relIso :=
   Cardinal.alephIdx.relIso.symm
 #align cardinal.aleph'.rel_iso Cardinal.Aleph'.relIso
--/
 
 #print Cardinal.aleph' /-
 /-- The `aleph'` function gives the cardinals listed by their ordinal
@@ -209,7 +237,7 @@ def aleph' : Ordinal → Cardinal :=
 
 /- warning: cardinal.aleph'.rel_iso_coe -> Cardinal.aleph'.relIso_coe is a dubious translation:
 lean 3 declaration is
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+  Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) => Ordinal.{u1} -> Cardinal.{u1}) Cardinal.Aleph'.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) => Ordinal.{u1} -> Cardinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) Cardinal.Aleph'.relIso.{u1}) Cardinal.aleph'.{u1}
 but is expected to have type
   Eq.{succ (succ u1)} (Ordinal.{u1} -> Cardinal.{u1}) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => Cardinal.{u1}) (RelHomClass.toFunLike.{succ u1, succ u1, succ u1} (RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450)) Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (RelIso.instRelHomClassRelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450))) Cardinal.Aleph'.relIso.{u1}) Cardinal.aleph'.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coeₓ'. -/
@@ -218,19 +246,27 @@ theorem aleph'.relIso_coe : (Aleph'.relIso : Ordinal → Cardinal) = aleph' :=
   rfl
 #align cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coe
 
-#print Cardinal.aleph'_lt /-
+/- warning: cardinal.aleph'_lt -> Cardinal.aleph'_lt is a dubious translation:
+lean 3 declaration is
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.aleph'.{u1} o₁) (Cardinal.aleph'.{u1} o₂)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+but is expected to have type
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.aleph'.{u1} o₁) (Cardinal.aleph'.{u1} o₂)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph'_lt Cardinal.aleph'_ltₓ'. -/
 @[simp]
 theorem aleph'_lt {o₁ o₂ : Ordinal} : aleph' o₁ < aleph' o₂ ↔ o₁ < o₂ :=
   Aleph'.relIso.map_rel_iff
 #align cardinal.aleph'_lt Cardinal.aleph'_lt
--/
 
-#print Cardinal.aleph'_le /-
+/- warning: cardinal.aleph'_le -> Cardinal.aleph'_le is a dubious translation:
+lean 3 declaration is
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.aleph'.{u1} o₁) (Cardinal.aleph'.{u1} o₂)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+but is expected to have type
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.aleph'.{u1} o₁) (Cardinal.aleph'.{u1} o₂)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph'_le Cardinal.aleph'_leₓ'. -/
 @[simp]
 theorem aleph'_le {o₁ o₂ : Ordinal} : aleph' o₁ ≤ aleph' o₂ ↔ o₁ ≤ o₂ :=
   le_iff_le_iff_lt_iff_lt.2 aleph'_lt
 #align cardinal.aleph'_le Cardinal.aleph'_le
--/
 
 #print Cardinal.aleph'_alephIdx /-
 @[simp]
@@ -281,7 +317,12 @@ theorem aleph'_nat : ∀ n : ℕ, aleph' n = n
   | n + 1 => show aleph' (succ n) = n.succ by rw [aleph'_succ, aleph'_nat, nat_succ]
 #align cardinal.aleph'_nat Cardinal.aleph'_nat
 
-#print Cardinal.aleph'_le_of_limit /-
+/- warning: cardinal.aleph'_le_of_limit -> Cardinal.aleph'_le_of_limit is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, (Ordinal.IsLimit.{u1} o) -> (forall {c : Cardinal.{u1}}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.aleph'.{u1} o) c) (forall (o' : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o' o) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.aleph'.{u1} o') c)))
+but is expected to have type
+  forall {o : Ordinal.{u1}}, (Ordinal.IsLimit.{u1} o) -> (forall {c : Cardinal.{u1}}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.aleph'.{u1} o) c) (forall (o' : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o' o) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.aleph'.{u1} o') c)))
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph'_le_of_limit Cardinal.aleph'_le_of_limitₓ'. -/
 theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
     aleph' o ≤ c ↔ ∀ o' < o, aleph' o' ≤ c :=
   ⟨fun h o' h' => (aleph'_le.2 <| h'.le).trans h, fun h =>
@@ -291,7 +332,6 @@ theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
     rw [← aleph'_le, aleph'_aleph_idx]
     exact h _ h'⟩
 #align cardinal.aleph'_le_of_limit Cardinal.aleph'_le_of_limit
--/
 
 /- warning: cardinal.aleph'_limit -> Cardinal.aleph'_limit is a dubious translation:
 lean 3 declaration is
@@ -333,19 +373,27 @@ def aleph (o : Ordinal) : Cardinal :=
 #align cardinal.aleph Cardinal.aleph
 -/
 
-#print Cardinal.aleph_lt /-
+/- warning: cardinal.aleph_lt -> Cardinal.aleph_lt is a dubious translation:
+lean 3 declaration is
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.aleph.{u1} o₁) (Cardinal.aleph.{u1} o₂)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+but is expected to have type
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.aleph.{u1} o₁) (Cardinal.aleph.{u1} o₂)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_lt Cardinal.aleph_ltₓ'. -/
 @[simp]
 theorem aleph_lt {o₁ o₂ : Ordinal} : aleph o₁ < aleph o₂ ↔ o₁ < o₂ :=
   aleph'_lt.trans (add_lt_add_iff_left _)
 #align cardinal.aleph_lt Cardinal.aleph_lt
--/
 
-#print Cardinal.aleph_le /-
+/- warning: cardinal.aleph_le -> Cardinal.aleph_le is a dubious translation:
+lean 3 declaration is
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.aleph.{u1} o₁) (Cardinal.aleph.{u1} o₂)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+but is expected to have type
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.aleph.{u1} o₁) (Cardinal.aleph.{u1} o₂)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_le Cardinal.aleph_leₓ'. -/
 @[simp]
 theorem aleph_le {o₁ o₂ : Ordinal} : aleph o₁ ≤ aleph o₂ ↔ o₁ ≤ o₂ :=
   le_iff_le_iff_lt_iff_lt.2 aleph_lt
 #align cardinal.aleph_le Cardinal.aleph_le
--/
 
 /- warning: cardinal.max_aleph_eq -> Cardinal.max_aleph_eq is a dubious translation:
 lean 3 declaration is
@@ -398,10 +446,14 @@ theorem aleph_limit {o : Ordinal} (ho : o.IsLimit) : aleph o = ⨆ a : Iio o, al
   · exact fun i => aleph_le.2 (le_of_lt i.2)
 #align cardinal.aleph_limit Cardinal.aleph_limit
 
-#print Cardinal.aleph0_le_aleph' /-
+/- warning: cardinal.aleph_0_le_aleph' -> Cardinal.aleph0_le_aleph' is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} (Cardinal.aleph'.{u1} o)) (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)
+but is expected to have type
+  forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} (Cardinal.aleph'.{u1} o)) (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)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_0_le_aleph' Cardinal.aleph0_le_aleph'ₓ'. -/
 theorem aleph0_le_aleph' {o : Ordinal} : ℵ₀ ≤ aleph' o ↔ ω ≤ o := by rw [← aleph'_omega, aleph'_le]
 #align cardinal.aleph_0_le_aleph' Cardinal.aleph0_le_aleph'
--/
 
 #print Cardinal.aleph0_le_aleph /-
 theorem aleph0_le_aleph (o : Ordinal) : ℵ₀ ≤ aleph o :=
@@ -411,16 +463,24 @@ theorem aleph0_le_aleph (o : Ordinal) : ℵ₀ ≤ aleph o :=
 #align cardinal.aleph_0_le_aleph Cardinal.aleph0_le_aleph
 -/
 
-#print Cardinal.aleph'_pos /-
+/- warning: cardinal.aleph'_pos -> Cardinal.aleph'_pos is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, (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}))) o) -> (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}))) (Cardinal.aleph'.{u1} o))
+but is expected to have type
+  forall {o : Ordinal.{u1}}, (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})) o) -> (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})) (Cardinal.aleph'.{u1} o))
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph'_pos Cardinal.aleph'_posₓ'. -/
 theorem aleph'_pos {o : Ordinal} (ho : 0 < o) : 0 < aleph' o := by rwa [← aleph'_zero, aleph'_lt]
 #align cardinal.aleph'_pos Cardinal.aleph'_pos
--/
 
-#print Cardinal.aleph_pos /-
+/- warning: cardinal.aleph_pos -> Cardinal.aleph_pos is a dubious translation:
+lean 3 declaration is
+  forall (o : Ordinal.{u1}), 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}))) (Cardinal.aleph.{u1} o)
+but is expected to have type
+  forall (o : Ordinal.{u1}), 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})) (Cardinal.aleph.{u1} o)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_pos Cardinal.aleph_posₓ'. -/
 theorem aleph_pos (o : Ordinal) : 0 < aleph o :=
   aleph0_pos.trans_le (aleph0_le_aleph o)
 #align cardinal.aleph_pos Cardinal.aleph_pos
--/
 
 #print Cardinal.aleph_toNat /-
 @[simp]
@@ -491,7 +551,7 @@ theorem succ_aleph0 : succ ℵ₀ = aleph 1 := by rw [← aleph_zero, ← aleph_
 
 /- warning: cardinal.aleph_0_lt_aleph_one -> Cardinal.aleph0_lt_aleph_one is a dubious translation:
 lean 3 declaration is
-  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{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}))))
+  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{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
   LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{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.aleph_0_lt_aleph_one Cardinal.aleph0_lt_aleph_oneₓ'. -/
@@ -503,7 +563,7 @@ theorem aleph0_lt_aleph_one : ℵ₀ < aleph 1 :=
 
 /- warning: cardinal.countable_iff_lt_aleph_one -> Cardinal.countable_iff_lt_aleph_one is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (s : Set.{u1} α), Iff (Set.Countable.{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} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (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})))))
+  forall {α : Type.{u1}} (s : Set.{u1} α), Iff (Set.Countable.{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} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (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
   forall {α : Type.{u1}} (s : Set.{u1} α), Iff (Set.Countable.{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} α s)) (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.countable_iff_lt_aleph_one Cardinal.countable_iff_lt_aleph_oneₓ'. -/
@@ -511,7 +571,12 @@ theorem countable_iff_lt_aleph_one {α : Type _} (s : Set α) : s.Countable ↔
   rw [← succ_aleph_0, lt_succ_iff, le_aleph_0_iff_set_countable]
 #align cardinal.countable_iff_lt_aleph_one Cardinal.countable_iff_lt_aleph_one
 
-#print Cardinal.ord_card_unbounded /-
+/- warning: cardinal.ord_card_unbounded -> Cardinal.ord_card_unbounded is a dubious translation:
+lean 3 declaration is
+  Set.Unbounded.{succ u1} Ordinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (setOf.{succ u1} Ordinal.{u1} (fun (b : Ordinal.{u1}) => Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.card.{u1} b)) b))
+but is expected to have type
+  Set.Unbounded.{succ u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.2408 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.2410 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.2408 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.2410) (setOf.{succ u1} Ordinal.{u1} (fun (b : Ordinal.{u1}) => Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.card.{u1} b)) b))
+Case conversion may be inaccurate. Consider using '#align cardinal.ord_card_unbounded Cardinal.ord_card_unboundedₓ'. -/
 /-- Ordinals that are cardinals are unbounded. -/
 theorem ord_card_unbounded : Unbounded (· < ·) { b : Ordinal | b.card.ord = b } :=
   unbounded_lt_iff.2 fun a =>
@@ -520,7 +585,6 @@ theorem ord_card_unbounded : Unbounded (· < ·) { b : Ordinal | b.card.ord = b
         dsimp
         rw [card_ord], (lt_ord_succ_card a).le⟩⟩
 #align cardinal.ord_card_unbounded Cardinal.ord_card_unbounded
--/
 
 #print Cardinal.eq_aleph'_of_eq_card_ord /-
 theorem eq_aleph'_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) : ∃ a, (aleph' a).ord = o :=
@@ -541,14 +605,23 @@ theorem ord_aleph'_eq_enum_card : ord ∘ aleph' = enumOrd { b : Ordinal | b.car
 #align cardinal.ord_aleph'_eq_enum_card Cardinal.ord_aleph'_eq_enum_card
 -/
 
-#print Cardinal.ord_card_unbounded' /-
+/- warning: cardinal.ord_card_unbounded' -> Cardinal.ord_card_unbounded' is a dubious translation:
+lean 3 declaration is
+  Set.Unbounded.{succ u1} Ordinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (setOf.{succ u1} Ordinal.{u1} (fun (b : Ordinal.{u1}) => And (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.card.{u1} b)) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.omega.{u1} b)))
+but is expected to have type
+  Set.Unbounded.{succ u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.2621 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.2623 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.2621 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.2623) (setOf.{succ u1} Ordinal.{u1} (fun (b : Ordinal.{u1}) => And (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.card.{u1} b)) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.omega.{u1} b)))
+Case conversion may be inaccurate. Consider using '#align cardinal.ord_card_unbounded' Cardinal.ord_card_unbounded'ₓ'. -/
 /-- Infinite ordinals that are cardinals are unbounded. -/
 theorem ord_card_unbounded' : Unbounded (· < ·) { b : Ordinal | b.card.ord = b ∧ ω ≤ b } :=
   (unbounded_lt_inter_le ω).2 ord_card_unbounded
 #align cardinal.ord_card_unbounded' Cardinal.ord_card_unbounded'
--/
 
-#print Cardinal.eq_aleph_of_eq_card_ord /-
+/- warning: cardinal.eq_aleph_of_eq_card_ord -> Cardinal.eq_aleph_of_eq_card_ord is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.card.{u1} o)) o) -> (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) -> (Exists.{succ (succ u1)} Ordinal.{u1} (fun (a : Ordinal.{u1}) => Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.aleph.{u1} a)) o))
+but is expected to have type
+  forall {o : Ordinal.{u1}}, (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.card.{u1} o)) o) -> (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) -> (Exists.{succ (succ u1)} Ordinal.{u1} (fun (a : Ordinal.{u1}) => Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.aleph.{u1} a)) o))
+Case conversion may be inaccurate. Consider using '#align cardinal.eq_aleph_of_eq_card_ord Cardinal.eq_aleph_of_eq_card_ordₓ'. -/
 theorem eq_aleph_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) (ho' : ω ≤ o) :
     ∃ a, (aleph a).ord = o :=
   by
@@ -558,9 +631,13 @@ theorem eq_aleph_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) (ho' : ω 
   rwa [Ordinal.add_sub_cancel_of_le]
   rwa [← aleph_0_le_aleph', ← ord_le_ord, ha, ord_aleph_0]
 #align cardinal.eq_aleph_of_eq_card_ord Cardinal.eq_aleph_of_eq_card_ord
--/
 
-#print Cardinal.ord_aleph_eq_enum_card /-
+/- warning: cardinal.ord_aleph_eq_enum_card -> Cardinal.ord_aleph_eq_enum_card is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} (Ordinal.{u1} -> Ordinal.{u1}) (Function.comp.{succ (succ u1), succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1} Ordinal.{u1} Cardinal.ord.{u1} Cardinal.aleph.{u1}) (Ordinal.enumOrd.{u1} (setOf.{succ u1} Ordinal.{u1} (fun (b : Ordinal.{u1}) => And (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.card.{u1} b)) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.omega.{u1} b))))
+but is expected to have type
+  Eq.{succ (succ u1)} (Ordinal.{u1} -> Ordinal.{u1}) (Function.comp.{succ (succ u1), succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1} Ordinal.{u1} Cardinal.ord.{u1} Cardinal.aleph.{u1}) (Ordinal.enumOrd.{u1} (setOf.{succ u1} Ordinal.{u1} (fun (b : Ordinal.{u1}) => And (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Ordinal.card.{u1} b)) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.omega.{u1} b))))
+Case conversion may be inaccurate. Consider using '#align cardinal.ord_aleph_eq_enum_card Cardinal.ord_aleph_eq_enum_cardₓ'. -/
 /-- `ord ∘ aleph` enumerates the infinite ordinals that are cardinals. -/
 theorem ord_aleph_eq_enum_card : ord ∘ aleph = enumOrd { b : Ordinal | b.card.ord = b ∧ ω ≤ b } :=
   by
@@ -572,7 +649,6 @@ theorem ord_aleph_eq_enum_card : ord ∘ aleph = enumOrd { b : Ordinal | b.card.
   · rw [← ord_aleph_0, ord_le_ord]
     exact aleph_0_le_aleph _
 #align cardinal.ord_aleph_eq_enum_card Cardinal.ord_aleph_eq_enum_card
--/
 
 /-! ### Beth cardinals -/
 
@@ -641,19 +717,27 @@ theorem beth_mono : Monotone beth :=
 #align cardinal.beth_mono Cardinal.beth_mono
 -/
 
-#print Cardinal.beth_lt /-
+/- warning: cardinal.beth_lt -> Cardinal.beth_lt is a dubious translation:
+lean 3 declaration is
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.beth.{u1} o₁) (Cardinal.beth.{u1} o₂)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+but is expected to have type
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.beth.{u1} o₁) (Cardinal.beth.{u1} o₂)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+Case conversion may be inaccurate. Consider using '#align cardinal.beth_lt Cardinal.beth_ltₓ'. -/
 @[simp]
 theorem beth_lt {o₁ o₂ : Ordinal} : beth o₁ < beth o₂ ↔ o₁ < o₂ :=
   beth_strictMono.lt_iff_lt
 #align cardinal.beth_lt Cardinal.beth_lt
--/
 
-#print Cardinal.beth_le /-
+/- warning: cardinal.beth_le -> Cardinal.beth_le is a dubious translation:
+lean 3 declaration is
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.beth.{u1} o₁) (Cardinal.beth.{u1} o₂)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+but is expected to have type
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.beth.{u1} o₁) (Cardinal.beth.{u1} o₂)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+Case conversion may be inaccurate. Consider using '#align cardinal.beth_le Cardinal.beth_leₓ'. -/
 @[simp]
 theorem beth_le {o₁ o₂ : Ordinal} : beth o₁ ≤ beth o₂ ↔ o₁ ≤ o₂ :=
   beth_strictMono.le_iff_le
 #align cardinal.beth_le Cardinal.beth_le
--/
 
 #print Cardinal.aleph_le_beth /-
 theorem aleph_le_beth (o : Ordinal) : aleph o ≤ beth o :=
@@ -675,11 +759,15 @@ theorem aleph0_le_beth (o : Ordinal) : ℵ₀ ≤ beth o :=
 #align cardinal.aleph_0_le_beth Cardinal.aleph0_le_beth
 -/
 
-#print Cardinal.beth_pos /-
+/- warning: cardinal.beth_pos -> Cardinal.beth_pos is a dubious translation:
+lean 3 declaration is
+  forall (o : Ordinal.{u1}), 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}))) (Cardinal.beth.{u1} o)
+but is expected to have type
+  forall (o : Ordinal.{u1}), 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})) (Cardinal.beth.{u1} o)
+Case conversion may be inaccurate. Consider using '#align cardinal.beth_pos Cardinal.beth_posₓ'. -/
 theorem beth_pos (o : Ordinal) : 0 < beth o :=
   aleph0_pos.trans_le <| aleph0_le_beth o
 #align cardinal.beth_pos Cardinal.beth_pos
--/
 
 #print Cardinal.beth_ne_zero /-
 theorem beth_ne_zero (o : Ordinal) : beth o ≠ 0 :=
@@ -869,7 +957,7 @@ theorem aleph_mul_aleph0 (o : Ordinal) : aleph o * ℵ₀ = aleph o :=
 
 /- warning: cardinal.mul_lt_of_lt -> Cardinal.mul_lt_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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} Cardinal.partialOrder.{u1})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) c)
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) c)
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_lt_of_lt Cardinal.mul_lt_of_ltₓ'. -/
@@ -1152,7 +1240,7 @@ theorem add_le_of_le {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a ≤ c) (h2 :
 
 /- warning: cardinal.add_lt_of_lt -> Cardinal.add_lt_of_lt is a dubious translation:
 lean 3 declaration is
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+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) c)
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.add_lt_of_lt Cardinal.add_lt_of_ltₓ'. -/
@@ -1164,7 +1252,7 @@ theorem add_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b
 
 /- warning: cardinal.eq_of_add_eq_of_aleph_0_le -> Cardinal.eq_of_add_eq_of_aleph0_le is a dubious translation:
 lean 3 declaration is
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+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align cardinal.eq_of_add_eq_of_aleph_0_le Cardinal.eq_of_add_eq_of_aleph0_leₓ'. -/
@@ -1267,7 +1355,7 @@ theorem mk_add_one_eq {α : Type _} [Infinite α] : (#α) + 1 = (#α) :=
 
 /- warning: cardinal.eq_of_add_eq_add_left -> Cardinal.eq_of_add_eq_add_left 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 cardinal.eq_of_add_eq_add_left Cardinal.eq_of_add_eq_add_leftₓ'. -/
@@ -1294,7 +1382,7 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
 
 /- warning: cardinal.eq_of_add_eq_add_right -> Cardinal.eq_of_add_eq_add_right is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) c b)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{u1} a c)
 Case conversion may be inaccurate. Consider using '#align cardinal.eq_of_add_eq_add_right Cardinal.eq_of_add_eq_add_rightₓ'. -/
@@ -1331,7 +1419,7 @@ theorem principal_add_aleph (o : Ordinal) : Ordinal.Principal (· + ·) (aleph o
 
 /- warning: cardinal.add_right_inj_of_lt_aleph_0 -> Cardinal.add_right_inj_of_lt_aleph0 is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) γ Cardinal.aleph0.{u1}) -> (Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) β γ)) (Eq.{succ (succ u1)} Cardinal.{u1} α β))
 Case conversion may be inaccurate. Consider using '#align cardinal.add_right_inj_of_lt_aleph_0 Cardinal.add_right_inj_of_lt_aleph0ₓ'. -/
@@ -1363,7 +1451,7 @@ theorem add_one_inj {α β : Cardinal} : α + 1 = β + 1 ↔ α = β :=
 
 /- warning: cardinal.add_le_add_iff_of_lt_aleph_0 -> Cardinal.add_le_add_iff_of_lt_aleph0 is a dubious translation:
 lean 3 declaration is
-  forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) γ Cardinal.aleph0.{u1}) -> (Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) β γ)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} α β))
+  forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) γ Cardinal.aleph0.{u1}) -> (Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) β γ)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} α β))
 but is expected to have type
   forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) γ Cardinal.aleph0.{u1}) -> (Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) β γ)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} α β))
 Case conversion may be inaccurate. Consider using '#align cardinal.add_le_add_iff_of_lt_aleph_0 Cardinal.add_le_add_iff_of_lt_aleph0ₓ'. -/
@@ -1401,7 +1489,12 @@ theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β
 /-! ### Properties about power -/
 
 
-#print Cardinal.pow_le /-
+/- warning: cardinal.pow_le -> Cardinal.pow_le is a dubious translation:
+lean 3 declaration is
+  forall {κ : Cardinal.{u1}} {μ : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} κ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) μ Cardinal.aleph0.{u1}) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{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}) κ μ) κ)
+but is expected to have type
+  forall {κ : Cardinal.{u1}} {μ : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} κ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) μ Cardinal.aleph0.{u1}) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{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}) κ μ) κ)
+Case conversion may be inaccurate. Consider using '#align cardinal.pow_le Cardinal.pow_leₓ'. -/
 theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) : κ ^ μ ≤ κ :=
   let ⟨n, H3⟩ := lt_aleph0.1 H2
   H3.symm ▸
@@ -1421,13 +1514,16 @@ theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) :
             (mul_eq_self H1))
       H1
 #align cardinal.pow_le Cardinal.pow_le
--/
 
-#print Cardinal.pow_eq /-
+/- warning: cardinal.pow_eq -> Cardinal.pow_eq is a dubious translation:
+lean 3 declaration is
+  forall {κ : Cardinal.{u1}} {μ : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} κ) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (OfNat.mk.{succ u1} Cardinal.{u1} 1 (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1}))) μ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) μ Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{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}) κ μ) κ)
+but is expected to have type
+  forall {κ : Cardinal.{u1}} {μ : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} κ) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (One.toOfNat1.{succ u1} Cardinal.{u1} Cardinal.instOneCardinal.{u1})) μ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) μ Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{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}) κ μ) κ)
+Case conversion may be inaccurate. Consider using '#align cardinal.pow_eq Cardinal.pow_eqₓ'. -/
 theorem pow_eq {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : 1 ≤ μ) (H3 : μ < ℵ₀) : κ ^ μ = κ :=
   (pow_le H1 H3).antisymm <| self_le_power κ H2
 #align cardinal.pow_eq Cardinal.pow_eq
--/
 
 /- warning: cardinal.power_self_eq -> Cardinal.power_self_eq is a dubious translation:
 lean 3 declaration is
@@ -1782,7 +1878,7 @@ theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
 
 /- warning: cardinal.mk_compl_of_infinite -> Cardinal.mk_compl_of_infinite is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] (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)) (Cardinal.mk.{u1} α)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s))) (Cardinal.mk.{u1} α))
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_of_infinite Cardinal.mk_compl_of_infiniteₓ'. -/
@@ -1807,7 +1903,7 @@ theorem mk_compl_finset_of_infinite {α : Type _} [Infinite α] (s : Finset α)
 
 /- warning: cardinal.mk_compl_eq_mk_compl_infinite -> Cardinal.mk_compl_eq_mk_compl_infinite is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_eq_mk_compl_infinite Cardinal.mk_compl_eq_mk_compl_infiniteₓ'. -/
@@ -1895,7 +1991,7 @@ theorem extend_function_finite {α β : Type _} [Finite α] {s : Set α} (f : s
 
 /- warning: cardinal.extend_function_of_lt -> Cardinal.extend_function_of_lt is a dubious translation:
 lean 3 declaration is
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   forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} (f : Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β), (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Cardinal.mk.{u2} (Set.Elem.{u2} α s)) (Cardinal.mk.{u2} α)) -> (Nonempty.{max (succ u1) (succ u2)} (Equiv.{succ u2, succ u1} α β)) -> (Exists.{max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} α β) (fun (g : Equiv.{succ u2, succ u1} α β) => forall (x : Set.Elem.{u2} α s), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) g (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f x)))
 Case conversion may be inaccurate. Consider using '#align cardinal.extend_function_of_lt Cardinal.extend_function_of_ltₓ'. -/

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -155,7 +155,7 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
       apply (lt_succ s).not_le
       have I : injective aleph_idx := aleph_idx.initial_seg.to_embedding.injective
       simpa only [typein_enum, left_inverse_inv_fun I (succ s)] using
-        le_csupᵢ
+        le_ciSup
           (Cardinal.bddAbove_range.{u, u} fun a : α => inv_fun aleph_idx (Ordinal.typein r a))
           (Ordinal.enum r _ (h (succ s)))
 #align cardinal.aleph_idx.rel_iso Cardinal.alephIdx.relIso
@@ -295,15 +295,15 @@ theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
 
 /- warning: cardinal.aleph'_limit -> Cardinal.aleph'_limit is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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+  forall {o : Ordinal.{u1}}, (Ordinal.IsLimit.{u1} o) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph'.{u1} o) (iSup.{succ u1, succ (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}))) (Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) (fun (a : Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) => Cardinal.aleph'.{u1} (Subtype.val.{succ (succ u1)} Ordinal.{u1} (fun (x : Ordinal.{u1}) => Membership.mem.{succ u1, succ u1} Ordinal.{u1} (Set.{succ u1} Ordinal.{u1}) (Set.instMembershipSet.{succ u1} Ordinal.{u1}) x (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) a))))
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph'_limit Cardinal.aleph'_limitₓ'. -/
 theorem aleph'_limit {o : Ordinal} (ho : o.IsLimit) : aleph' o = ⨆ a : Iio o, aleph' a :=
   by
-  refine' le_antisymm _ (csupᵢ_le' fun i => aleph'_le.2 (le_of_lt i.2))
+  refine' le_antisymm _ (ciSup_le' fun i => aleph'_le.2 (le_of_lt i.2))
   rw [aleph'_le_of_limit ho]
-  exact fun a ha => le_csupᵢ (bdd_above_of_small _) (⟨a, ha⟩ : Iio o)
+  exact fun a ha => le_ciSup (bdd_above_of_small _) (⟨a, ha⟩ : Iio o)
 #align cardinal.aleph'_limit Cardinal.aleph'_limit
 
 #print Cardinal.aleph'_omega /-
@@ -380,15 +380,15 @@ theorem aleph_zero : aleph 0 = ℵ₀ := by rw [aleph, add_zero, aleph'_omega]
 
 /- warning: cardinal.aleph_limit -> Cardinal.aleph_limit is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
-  forall {o : Ordinal.{u1}}, (Ordinal.IsLimit.{u1} o) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph.{u1} o) (supᵢ.{succ u1, succ (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}))) (Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) (fun (a : Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) => Cardinal.aleph.{u1} (Subtype.val.{succ (succ u1)} Ordinal.{u1} (fun (x : Ordinal.{u1}) => Membership.mem.{succ u1, succ u1} Ordinal.{u1} (Set.{succ u1} Ordinal.{u1}) (Set.instMembershipSet.{succ u1} Ordinal.{u1}) x (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) a))))
+  forall {o : Ordinal.{u1}}, (Ordinal.IsLimit.{u1} o) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph.{u1} o) (iSup.{succ u1, succ (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}))) (Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) (fun (a : Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) => Cardinal.aleph.{u1} (Subtype.val.{succ (succ u1)} Ordinal.{u1} (fun (x : Ordinal.{u1}) => Membership.mem.{succ u1, succ u1} Ordinal.{u1} (Set.{succ u1} Ordinal.{u1}) (Set.instMembershipSet.{succ u1} Ordinal.{u1}) x (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) a))))
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_limit Cardinal.aleph_limitₓ'. -/
 theorem aleph_limit {o : Ordinal} (ho : o.IsLimit) : aleph o = ⨆ a : Iio o, aleph a :=
   by
-  apply le_antisymm _ (csupᵢ_le' _)
+  apply le_antisymm _ (ciSup_le' _)
   · rw [aleph, aleph'_limit (ho.add _)]
-    refine' csupᵢ_mono' (bdd_above_of_small _) _
+    refine' ciSup_mono' (bdd_above_of_small _) _
     rintro ⟨i, hi⟩
     cases lt_or_le i ω
     · rcases lt_omega.1 h with ⟨n, rfl⟩
@@ -608,9 +608,9 @@ theorem beth_succ (o : Ordinal) : beth (succ o) = 2 ^ beth o :=
 
 /- warning: cardinal.beth_limit -> Cardinal.beth_limit is a dubious translation:
 lean 3 declaration is
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+  forall {o : Ordinal.{u1}}, (Ordinal.IsLimit.{u1} o) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.beth.{u1} o) (iSup.{succ u1, succ (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}))) (coeSort.{succ (succ u1), succ (succ (succ u1))} (Set.{succ u1} Ordinal.{u1}) Type.{succ u1} (Set.hasCoeToSort.{succ u1} Ordinal.{u1}) (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) (fun (a : coeSort.{succ (succ u1), succ (succ (succ u1))} (Set.{succ u1} Ordinal.{u1}) Type.{succ u1} (Set.hasCoeToSort.{succ u1} Ordinal.{u1}) (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) => Cardinal.beth.{u1} ((fun (a : Type.{succ u1}) (b : Type.{succ u1}) [self : HasLiftT.{succ (succ u1), succ (succ u1)} a b] => self.0) (coeSort.{succ (succ u1), succ (succ (succ u1))} (Set.{succ u1} Ordinal.{u1}) Type.{succ u1} (Set.hasCoeToSort.{succ u1} Ordinal.{u1}) (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) Ordinal.{u1} (HasLiftT.mk.{succ (succ u1), succ (succ u1)} (coeSort.{succ (succ u1), succ (succ (succ u1))} (Set.{succ u1} Ordinal.{u1}) Type.{succ u1} (Set.hasCoeToSort.{succ u1} Ordinal.{u1}) (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) Ordinal.{u1} (CoeTCₓ.coe.{succ (succ u1), succ (succ u1)} (coeSort.{succ (succ u1), succ (succ (succ u1))} (Set.{succ u1} Ordinal.{u1}) Type.{succ u1} (Set.hasCoeToSort.{succ u1} Ordinal.{u1}) (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) Ordinal.{u1} (coeBase.{succ (succ u1), succ (succ u1)} (coeSort.{succ (succ u1), succ (succ (succ u1))} (Set.{succ u1} Ordinal.{u1}) Type.{succ u1} (Set.hasCoeToSort.{succ u1} Ordinal.{u1}) (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) Ordinal.{u1} (coeSubtype.{succ (succ u1)} Ordinal.{u1} (fun (x : Ordinal.{u1}) => Membership.Mem.{succ u1, succ u1} Ordinal.{u1} (Set.{succ u1} Ordinal.{u1}) (Set.hasMem.{succ u1} Ordinal.{u1}) x (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)))))) a))))
 but is expected to have type
-  forall {o : Ordinal.{u1}}, (Ordinal.IsLimit.{u1} o) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.beth.{u1} o) (supᵢ.{succ u1, succ (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}))) (Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) (fun (a : Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) => Cardinal.beth.{u1} (Subtype.val.{succ (succ u1)} Ordinal.{u1} (fun (x : Ordinal.{u1}) => Membership.mem.{succ u1, succ u1} Ordinal.{u1} (Set.{succ u1} Ordinal.{u1}) (Set.instMembershipSet.{succ u1} Ordinal.{u1}) x (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) a))))
+  forall {o : Ordinal.{u1}}, (Ordinal.IsLimit.{u1} o) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.beth.{u1} o) (iSup.{succ u1, succ (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}))) (Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) (fun (a : Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) => Cardinal.beth.{u1} (Subtype.val.{succ (succ u1)} Ordinal.{u1} (fun (x : Ordinal.{u1}) => Membership.mem.{succ u1, succ u1} Ordinal.{u1} (Set.{succ u1} Ordinal.{u1}) (Set.instMembershipSet.{succ u1} Ordinal.{u1}) x (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) a))))
 Case conversion may be inaccurate. Consider using '#align cardinal.beth_limit Cardinal.beth_limitₓ'. -/
 theorem beth_limit {o : Ordinal} : o.IsLimit → beth o = ⨆ a : Iio o, beth a :=
   limitRecOn_limit _ _ _ _
@@ -631,7 +631,7 @@ theorem beth_strictMono : StrictMono beth := by
     exact (IH c (lt_succ c) h).le
   · apply (cantor _).trans_le
     rw [beth_limit hb, ← beth_succ]
-    exact le_csupᵢ (bdd_above_of_small _) (⟨_, hb.succ_lt h⟩ : Iio b)
+    exact le_ciSup (bdd_above_of_small _) (⟨_, hb.succ_lt h⟩ : Iio b)
 #align cardinal.beth_strict_mono Cardinal.beth_strictMono
 -/
 
@@ -665,7 +665,7 @@ theorem aleph_le_beth (o : Ordinal) : aleph o ≤ beth o :=
     exact (cantor _).trans_le (power_le_power_left two_ne_zero h)
   · intro o ho IH
     rw [aleph_limit ho, beth_limit ho]
-    exact csupᵢ_mono (bdd_above_of_small _) fun x => IH x.1 x.2
+    exact ciSup_mono (bdd_above_of_small _) fun x => IH x.1 x.2
 #align cardinal.aleph_le_beth Cardinal.aleph_le_beth
 -/
 
@@ -693,7 +693,7 @@ theorem beth_normal : IsNormal.{u} fun o => (beth o).ord :=
     ⟨ord_strictMono.comp beth_strictMono, fun o ho a ha =>
       by
       rw [beth_limit ho, ord_le]
-      exact csupᵢ_le' fun b => ord_le.1 (ha _ b.2)⟩
+      exact ciSup_le' fun b => ord_le.1 (ha _ b.2)⟩
 #align cardinal.beth_normal Cardinal.beth_normal
 -/

bump to nightly-2023-04-20-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

fbfe5c3e

Diff

@@ -165,7 +165,7 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
 lean 3 declaration is
   Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.alephIdx.relIso.{u1}) Cardinal.alephIdx.{u1}
 but is expected to have type
-  Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (RelIso.toRelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) Cardinal.alephIdx.relIso.{u1}))) Cardinal.alephIdx.{u1}
+  Eq.{succ (succ u1)} (Cardinal.{u1} -> Ordinal.{u1}) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465)) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => Ordinal.{u1}) (RelHomClass.toFunLike.{succ u1, succ u1, succ u1} (RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465)) Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (RelIso.instRelHomClassRelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465))) Cardinal.alephIdx.relIso.{u1}) Cardinal.alephIdx.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coeₓ'. -/
 @[simp]
 theorem alephIdx.relIso_coe : (alephIdx.relIso : Cardinal → Ordinal) = alephIdx :=
@@ -211,7 +211,7 @@ def aleph' : Ordinal → Cardinal :=
 lean 3 declaration is
   Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) => Ordinal.{u1} -> Cardinal.{u1}) Cardinal.Aleph'.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) => Ordinal.{u1} -> Cardinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) Cardinal.Aleph'.relIso.{u1}) Cardinal.aleph'.{u1}
 but is expected to have type
-  Eq.{succ (succ u1)} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Cardinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Cardinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1}) Ordinal.{u1} Cardinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (RelIso.toRelEmbedding.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) Cardinal.Aleph'.relIso.{u1}))) Cardinal.aleph'.{u1}
+  Eq.{succ (succ u1)} (Ordinal.{u1} -> Cardinal.{u1}) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => Cardinal.{u1}) (RelHomClass.toFunLike.{succ u1, succ u1, succ u1} (RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450)) Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (RelIso.instRelHomClassRelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450))) Cardinal.Aleph'.relIso.{u1}) Cardinal.aleph'.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coeₓ'. -/
 @[simp]
 theorem aleph'.relIso_coe : (Aleph'.relIso : Ordinal → Cardinal) = aleph' :=

bump to nightly-2023-04-13-02

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

bd75793a

Diff

@@ -108,7 +108,7 @@ def alephIdx : Cardinal → Ordinal :=
 
 /- warning: cardinal.aleph_idx.initial_seg_coe -> Cardinal.alephIdx.initialSeg_coe is a dubious translation:
 lean 3 declaration is
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+  Eq.{succ (succ u1)} ((fun (_x : InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.initialSeg.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (FunLike.hasCoeToFun.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => Ordinal.{u1}) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.{u1} Ordinal.{u1} (InitialSeg.embeddingLike.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))))) Cardinal.alephIdx.initialSeg.{u1}) Cardinal.alephIdx.{u1}
 but is expected to have type
   Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249)) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249)) Cardinal.{u1} Ordinal.{u1} (InitialSeg.instEmbeddingLikeInitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249))) Cardinal.alephIdx.initialSeg.{u1}) Cardinal.alephIdx.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.initial_seg_coe Cardinal.alephIdx.initialSeg_coeₓ'. -/
@@ -163,7 +163,7 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
 
 /- warning: cardinal.aleph_idx.rel_iso_coe -> Cardinal.alephIdx.relIso_coe is a dubious translation:
 lean 3 declaration is
-  Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.alephIdx.relIso.{u1}) Cardinal.alephIdx.{u1}
+  Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.alephIdx.relIso.{u1}) Cardinal.alephIdx.{u1}
 but is expected to have type
   Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (RelIso.toRelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) Cardinal.alephIdx.relIso.{u1}))) Cardinal.alephIdx.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coeₓ'. -/
@@ -209,7 +209,7 @@ def aleph' : Ordinal → Cardinal :=
 
 /- warning: cardinal.aleph'.rel_iso_coe -> Cardinal.aleph'.relIso_coe is a dubious translation:
 lean 3 declaration is
-  Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{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.{u1} -> Cardinal.{u1}) Cardinal.Aleph'.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{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})))))))) (fun (_x : RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{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.{u1} -> Cardinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{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.Aleph'.relIso.{u1}) Cardinal.aleph'.{u1}
+  Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) => Ordinal.{u1} -> Cardinal.{u1}) Cardinal.Aleph'.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) => Ordinal.{u1} -> Cardinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) Cardinal.Aleph'.relIso.{u1}) Cardinal.aleph'.{u1}
 but is expected to have type
   Eq.{succ (succ u1)} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Cardinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Cardinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1}) Ordinal.{u1} Cardinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (RelIso.toRelEmbedding.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) Cardinal.Aleph'.relIso.{u1}))) Cardinal.aleph'.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coeₓ'. -/
@@ -257,7 +257,7 @@ theorem aleph'_zero : aleph' 0 = 0 :=
 
 /- warning: cardinal.aleph'_succ -> Cardinal.aleph'_succ is a dubious translation:
 lean 3 declaration is
-  forall {o : Ordinal.{u1}}, Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph'.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)) (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} (Cardinal.aleph'.{u1} o))
+  forall {o : Ordinal.{u1}}, Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph'.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)) (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.succOrder.{u1} (Cardinal.aleph'.{u1} o))
 but is expected to have type
   forall {o : Ordinal.{u1}}, Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph'.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)) (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} (Cardinal.aleph'.{u1} o))
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph'_succ Cardinal.aleph'_succₓ'. -/
@@ -363,7 +363,7 @@ theorem max_aleph_eq (o₁ o₂ : Ordinal) : max (aleph o₁) (aleph o₂) = ale
 
 /- warning: cardinal.aleph_succ -> Cardinal.aleph_succ is a dubious translation:
 lean 3 declaration is
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+  forall {o : Ordinal.{u1}}, Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)) (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.succOrder.{u1} (Cardinal.aleph.{u1} o))
 but is expected to have type
   forall {o : Ordinal.{u1}}, Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)) (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} (Cardinal.aleph.{u1} o))
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_succ Cardinal.aleph_succₓ'. -/
@@ -482,7 +482,7 @@ theorem aleph_isNormal : IsNormal (ord ∘ aleph) :=
 
 /- warning: cardinal.succ_aleph_0 -> Cardinal.succ_aleph0 is a dubious translation:
 lean 3 declaration is
-  Eq.{succ (succ u1)} Cardinal.{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} Cardinal.aleph0.{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}))))
+  Eq.{succ (succ u1)} Cardinal.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.succOrder.{u1} Cardinal.aleph0.{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
   Eq.{succ (succ u1)} Cardinal.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} Cardinal.aleph0.{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.succ_aleph_0 Cardinal.succ_aleph0ₓ'. -/
@@ -491,7 +491,7 @@ theorem succ_aleph0 : succ ℵ₀ = aleph 1 := by rw [← aleph_zero, ← aleph_
 
 /- warning: cardinal.aleph_0_lt_aleph_one -> Cardinal.aleph0_lt_aleph_one is a dubious translation:
 lean 3 declaration is
-  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} (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}))))
+  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{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
   LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{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.aleph_0_lt_aleph_one Cardinal.aleph0_lt_aleph_oneₓ'. -/
@@ -503,7 +503,7 @@ theorem aleph0_lt_aleph_one : ℵ₀ < aleph 1 :=
 
 /- warning: cardinal.countable_iff_lt_aleph_one -> Cardinal.countable_iff_lt_aleph_one is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (s : Set.{u1} α), Iff (Set.Countable.{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} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (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})))))
+  forall {α : Type.{u1}} (s : Set.{u1} α), Iff (Set.Countable.{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} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (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
   forall {α : Type.{u1}} (s : Set.{u1} α), Iff (Set.Countable.{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} α s)) (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.countable_iff_lt_aleph_one Cardinal.countable_iff_lt_aleph_oneₓ'. -/
@@ -869,7 +869,7 @@ theorem aleph_mul_aleph0 (o : Ordinal) : aleph o * ℵ₀ = aleph o :=
 
 /- warning: cardinal.mul_lt_of_lt -> Cardinal.mul_lt_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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})))))) a 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})))))) b 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})))))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) c)
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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} Cardinal.partialOrder.{u1})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) c)
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_lt_of_lt Cardinal.mul_lt_of_ltₓ'. -/
@@ -1152,7 +1152,7 @@ theorem add_le_of_le {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a ≤ c) (h2 :
 
 /- warning: cardinal.add_lt_of_lt -> Cardinal.add_lt_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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})))))) a 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})))))) b 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})))))) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) c)
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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} Cardinal.partialOrder.{u1})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) c)
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.add_lt_of_lt Cardinal.add_lt_of_ltₓ'. -/
@@ -1164,7 +1164,7 @@ theorem add_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b
 
 /- warning: cardinal.eq_of_add_eq_of_aleph_0_le -> Cardinal.eq_of_add_eq_of_aleph0_le is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) 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})))))) a c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} c) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
 Case conversion may be inaccurate. Consider using '#align cardinal.eq_of_add_eq_of_aleph_0_le Cardinal.eq_of_add_eq_of_aleph0_leₓ'. -/
@@ -1267,7 +1267,7 @@ theorem mk_add_one_eq {α : Type _} [Infinite α] : (#α) + 1 = (#α) :=
 
 /- warning: cardinal.eq_of_add_eq_add_left -> Cardinal.eq_of_add_eq_add_left is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a 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})))))) a Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a c)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a c)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
 Case conversion may be inaccurate. Consider using '#align cardinal.eq_of_add_eq_add_left Cardinal.eq_of_add_eq_add_leftₓ'. -/
@@ -1294,7 +1294,7 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
 
 /- warning: cardinal.eq_of_add_eq_add_right -> Cardinal.eq_of_add_eq_add_right is a dubious translation:
 lean 3 declaration is
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+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) c b)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{u1} a c)
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) c b)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{u1} a c)
 Case conversion may be inaccurate. Consider using '#align cardinal.eq_of_add_eq_add_right Cardinal.eq_of_add_eq_add_rightₓ'. -/
@@ -1331,7 +1331,7 @@ theorem principal_add_aleph (o : Ordinal) : Ordinal.Principal (· + ·) (aleph o
 
 /- warning: cardinal.add_right_inj_of_lt_aleph_0 -> Cardinal.add_right_inj_of_lt_aleph0 is a dubious translation:
 lean 3 declaration is
-  forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : 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})))))) γ Cardinal.aleph0.{u1}) -> (Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) β γ)) (Eq.{succ (succ u1)} Cardinal.{u1} α β))
+  forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) γ Cardinal.aleph0.{u1}) -> (Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) β γ)) (Eq.{succ (succ u1)} Cardinal.{u1} α β))
 but is expected to have type
   forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) γ Cardinal.aleph0.{u1}) -> (Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) β γ)) (Eq.{succ (succ u1)} Cardinal.{u1} α β))
 Case conversion may be inaccurate. Consider using '#align cardinal.add_right_inj_of_lt_aleph_0 Cardinal.add_right_inj_of_lt_aleph0ₓ'. -/
@@ -1363,7 +1363,7 @@ theorem add_one_inj {α β : Cardinal} : α + 1 = β + 1 ↔ α = β :=
 
 /- warning: cardinal.add_le_add_iff_of_lt_aleph_0 -> Cardinal.add_le_add_iff_of_lt_aleph0 is a dubious translation:
 lean 3 declaration is
-  forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : 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})))))) γ Cardinal.aleph0.{u1}) -> (Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) β γ)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} α β))
+  forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) γ Cardinal.aleph0.{u1}) -> (Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) β γ)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} α β))
 but is expected to have type
   forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) γ Cardinal.aleph0.{u1}) -> (Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) β γ)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} α β))
 Case conversion may be inaccurate. Consider using '#align cardinal.add_le_add_iff_of_lt_aleph_0 Cardinal.add_le_add_iff_of_lt_aleph0ₓ'. -/
@@ -1782,7 +1782,7 @@ theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
 
 /- warning: cardinal.mk_compl_of_infinite -> Cardinal.mk_compl_of_infinite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] (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)) (Cardinal.mk.{u1} α)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s))) (Cardinal.mk.{u1} α))
+  forall {α : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] (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)) (Cardinal.mk.{u1} α)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s))) (Cardinal.mk.{u1} α))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] (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)) (Cardinal.mk.{u1} α)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Set.Elem.{u1} α (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) s))) (Cardinal.mk.{u1} α))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_of_infinite Cardinal.mk_compl_of_infiniteₓ'. -/
@@ -1807,7 +1807,7 @@ theorem mk_compl_finset_of_infinite {α : Type _} [Infinite α] (s : Finset α)
 
 /- warning: cardinal.mk_compl_eq_mk_compl_infinite -> Cardinal.mk_compl_eq_mk_compl_infinite 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 cardinal.mk_compl_eq_mk_compl_infinite Cardinal.mk_compl_eq_mk_compl_infiniteₓ'. -/
@@ -1895,7 +1895,7 @@ theorem extend_function_finite {α β : Type _} [Finite α] {s : Set α} (f : s
 
 /- warning: cardinal.extend_function_of_lt -> Cardinal.extend_function_of_lt is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align cardinal.extend_function_of_lt Cardinal.extend_function_of_ltₓ'. -/

bump to nightly-2023-04-10-00

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

542f5cb1

Diff

@@ -81,12 +81,7 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
 /-! ### Aleph cardinals -/
 
 
-/- warning: cardinal.aleph_idx.initial_seg -> Cardinal.alephIdx.initialSeg is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.initial_seg Cardinal.alephIdx.initialSegₓ'. -/
+#print Cardinal.alephIdx.initialSeg /-
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ω = ω`,
@@ -98,6 +93,7 @@ Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.ini
 def alephIdx.initialSeg : @InitialSeg Cardinal Ordinal (· < ·) (· < ·) :=
   @RelEmbedding.collapse Cardinal Ordinal (· < ·) (· < ·) _ Cardinal.ord.orderEmbedding.ltEmbedding
 #align cardinal.aleph_idx.initial_seg Cardinal.alephIdx.initialSeg
+-/
 
 #print Cardinal.alephIdx /-
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
@@ -121,16 +117,12 @@ theorem alephIdx.initialSeg_coe : (alephIdx.initialSeg : Cardinal → Ordinal) =
   rfl
 #align cardinal.aleph_idx.initial_seg_coe Cardinal.alephIdx.initialSeg_coe
 
-/- warning: cardinal.aleph_idx_lt -> Cardinal.alephIdx_lt is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx_lt Cardinal.alephIdx_ltₓ'. -/
+#print Cardinal.alephIdx_lt /-
 @[simp]
 theorem alephIdx_lt {a b} : alephIdx a < alephIdx b ↔ a < b :=
   alephIdx.initialSeg.toRelEmbedding.map_rel_iff
 #align cardinal.aleph_idx_lt Cardinal.alephIdx_lt
+-/
 
 #print Cardinal.alephIdx_le /-
 @[simp]
@@ -145,12 +137,7 @@ theorem alephIdx.init {a b} : b < alephIdx a → ∃ c, alephIdx c = b :=
 #align cardinal.aleph_idx.init Cardinal.alephIdx.init
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.rel_iso Cardinal.alephIdx.relIsoₓ'. -/
+#print Cardinal.alephIdx.relIso /-
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ℵ₀ = ω`,
@@ -172,6 +159,7 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
           (Cardinal.bddAbove_range.{u, u} fun a : α => inv_fun aleph_idx (Ordinal.typein r a))
           (Ordinal.enum r _ (h (succ s)))
 #align cardinal.aleph_idx.rel_iso Cardinal.alephIdx.relIso
+-/
 
 /- warning: cardinal.aleph_idx.rel_iso_coe -> Cardinal.alephIdx.relIso_coe is a dubious translation:
 lean 3 declaration is
@@ -184,16 +172,12 @@ theorem alephIdx.relIso_coe : (alephIdx.relIso : Cardinal → Ordinal) = alephId
   rfl
 #align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coe
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.type_cardinal Cardinal.type_cardinalₓ'. -/
+#print Cardinal.type_cardinal /-
 @[simp]
 theorem type_cardinal : @type Cardinal (· < ·) _ = Ordinal.univ.{u, u + 1} := by
   rw [Ordinal.univ_id] <;> exact Quotient.sound ⟨aleph_idx.rel_iso⟩
 #align cardinal.type_cardinal Cardinal.type_cardinal
+-/
 
 #print Cardinal.mk_cardinal /-
 @[simp]
@@ -202,12 +186,7 @@ theorem mk_cardinal : (#Cardinal) = univ.{u, u + 1} := by
 #align cardinal.mk_cardinal Cardinal.mk_cardinal
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.aleph'.rel_iso Cardinal.Aleph'.relIsoₓ'. -/
+#print Cardinal.Aleph'.relIso /-
 /-- The `aleph'` function gives the cardinals listed by their ordinal
   index, and is the inverse of `aleph_idx`.
   `aleph' n = n`, `aleph' ω = ω`, `aleph' (ω + 1) = succ ℵ₀`, etc.
@@ -217,6 +196,7 @@ Case conversion may be inaccurate. Consider using '#align cardinal.aleph'.rel_is
 def Aleph'.relIso :=
   Cardinal.alephIdx.relIso.symm
 #align cardinal.aleph'.rel_iso Cardinal.Aleph'.relIso
+-/
 
 #print Cardinal.aleph' /-
 /-- The `aleph'` function gives the cardinals listed by their ordinal
@@ -238,16 +218,12 @@ theorem aleph'.relIso_coe : (Aleph'.relIso : Ordinal → Cardinal) = aleph' :=
   rfl
 #align cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coe
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.aleph'_lt Cardinal.aleph'_ltₓ'. -/
+#print Cardinal.aleph'_lt /-
 @[simp]
 theorem aleph'_lt {o₁ o₂ : Ordinal} : aleph' o₁ < aleph' o₂ ↔ o₁ < o₂ :=
   Aleph'.relIso.map_rel_iff
 #align cardinal.aleph'_lt Cardinal.aleph'_lt
+-/
 
 #print Cardinal.aleph'_le /-
 @[simp]
@@ -357,16 +333,12 @@ def aleph (o : Ordinal) : Cardinal :=
 #align cardinal.aleph Cardinal.aleph
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.aleph_lt Cardinal.aleph_ltₓ'. -/
+#print Cardinal.aleph_lt /-
 @[simp]
 theorem aleph_lt {o₁ o₂ : Ordinal} : aleph o₁ < aleph o₂ ↔ o₁ < o₂ :=
   aleph'_lt.trans (add_lt_add_iff_left _)
 #align cardinal.aleph_lt Cardinal.aleph_lt
+-/
 
 #print Cardinal.aleph_le /-
 @[simp]
@@ -439,24 +411,16 @@ theorem aleph0_le_aleph (o : Ordinal) : ℵ₀ ≤ aleph o :=
 #align cardinal.aleph_0_le_aleph Cardinal.aleph0_le_aleph
 -/
 
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+#print Cardinal.aleph'_pos /-
 theorem aleph'_pos {o : Ordinal} (ho : 0 < o) : 0 < aleph' o := by rwa [← aleph'_zero, aleph'_lt]
 #align cardinal.aleph'_pos Cardinal.aleph'_pos
+-/
 
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+#print Cardinal.aleph_pos /-
 theorem aleph_pos (o : Ordinal) : 0 < aleph o :=
   aleph0_pos.trans_le (aleph0_le_aleph o)
 #align cardinal.aleph_pos Cardinal.aleph_pos
+-/
 
 #print Cardinal.aleph_toNat /-
 @[simp]
@@ -469,7 +433,7 @@ theorem aleph_toNat (o : Ordinal) : (aleph o).toNat = 0 :=
 lean 3 declaration is
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(AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))))) Cardinal.toPartENat.{u1} (Cardinal.aleph.{u1} o)) (Top.top.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) (Cardinal.aleph.{u1} o)) PartENat.instTopPartENat)
+  forall (o : Ordinal.{u1}), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) (Cardinal.aleph.{u1} o)) (FunLike.coe.{succ (succ u1), succ (succ u1), 1} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) _x) (AddHomClass.toFunLike.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddZeroClass.toAdd.{succ u1} Cardinal.{u1} (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1}))))))))) (AddZeroClass.toAdd.{0} PartENat (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) (AddMonoidHomClass.toAddHomClass.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} 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(AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))))) Cardinal.toPartENat.{u1} (Cardinal.aleph.{u1} o)) (Top.top.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) (Cardinal.aleph.{u1} o)) PartENat.instTopPartENat)
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_to_part_enat Cardinal.aleph_toPartENatₓ'. -/
 @[simp]
 theorem aleph_toPartENat (o : Ordinal) : (aleph o).toPartENat = ⊤ :=
@@ -652,12 +616,7 @@ theorem beth_limit {o : Ordinal} : o.IsLimit → beth o = ⨆ a : Iio o, beth a
   limitRecOn_limit _ _ _ _
 #align cardinal.beth_limit Cardinal.beth_limit
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.beth_strict_mono Cardinal.beth_strictMonoₓ'. -/
+#print Cardinal.beth_strictMono /-
 theorem beth_strictMono : StrictMono beth := by
   intro a b
   induction' b using Ordinal.induction with b IH generalizing a
@@ -674,27 +633,20 @@ theorem beth_strictMono : StrictMono beth := by
     rw [beth_limit hb, ← beth_succ]
     exact le_csupᵢ (bdd_above_of_small _) (⟨_, hb.succ_lt h⟩ : Iio b)
 #align cardinal.beth_strict_mono Cardinal.beth_strictMono
+-/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.beth_mono Cardinal.beth_monoₓ'. -/
+#print Cardinal.beth_mono /-
 theorem beth_mono : Monotone beth :=
   beth_strictMono.Monotone
 #align cardinal.beth_mono Cardinal.beth_mono
+-/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.beth_lt Cardinal.beth_ltₓ'. -/
+#print Cardinal.beth_lt /-
 @[simp]
 theorem beth_lt {o₁ o₂ : Ordinal} : beth o₁ < beth o₂ ↔ o₁ < o₂ :=
   beth_strictMono.lt_iff_lt
 #align cardinal.beth_lt Cardinal.beth_lt
+-/
 
 #print Cardinal.beth_le /-
 @[simp]
@@ -723,15 +675,11 @@ theorem aleph0_le_beth (o : Ordinal) : ℵ₀ ≤ beth o :=
 #align cardinal.aleph_0_le_beth Cardinal.aleph0_le_beth
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.beth_pos Cardinal.beth_posₓ'. -/
+#print Cardinal.beth_pos /-
 theorem beth_pos (o : Ordinal) : 0 < beth o :=
   aleph0_pos.trans_le <| aleph0_le_beth o
 #align cardinal.beth_pos Cardinal.beth_pos
+-/
 
 #print Cardinal.beth_ne_zero /-
 theorem beth_ne_zero (o : Ordinal) : beth o ≠ 0 :=
@@ -1453,12 +1401,7 @@ theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β
 /-! ### Properties about power -/
 
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.pow_le Cardinal.pow_leₓ'. -/
+#print Cardinal.pow_le /-
 theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) : κ ^ μ ≤ κ :=
   let ⟨n, H3⟩ := lt_aleph0.1 H2
   H3.symm ▸
@@ -1478,16 +1421,13 @@ theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) :
             (mul_eq_self H1))
       H1
 #align cardinal.pow_le Cardinal.pow_le
+-/
 
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-Case conversion may be inaccurate. Consider using '#align cardinal.pow_eq Cardinal.pow_eqₓ'. -/
+#print Cardinal.pow_eq /-
 theorem pow_eq {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : 1 ≤ μ) (H3 : μ < ℵ₀) : κ ^ μ = κ :=
   (pow_le H1 H3).antisymm <| self_le_power κ H2
 #align cardinal.pow_eq Cardinal.pow_eq
+-/
 
 /- warning: cardinal.power_self_eq -> Cardinal.power_self_eq is a dubious translation:
 lean 3 declaration is
@@ -1544,25 +1484,17 @@ theorem nat_power_eq {c : Cardinal.{u}} (h : ℵ₀ ≤ c) {n : ℕ} (hn : 2 ≤
   power_eq_two_power h (by assumption_mod_cast) ((nat_lt_aleph0 n).le.trans h)
 #align cardinal.nat_power_eq Cardinal.nat_power_eq
 
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-  forall {c : Cardinal.{u1}} {n : Nat}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (HPow.hPow.{succ u1, 0, succ u1} Cardinal.{u1} Nat Cardinal.{u1} (instHPow.{succ u1, 0} Cardinal.{u1} Nat (Monoid.Pow.{succ u1} Cardinal.{u1} (MonoidWithZero.toMonoid.{succ u1} Cardinal.{u1} (Semiring.toMonoidWithZero.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1}))))))) c n) c)
-Case conversion may be inaccurate. Consider using '#align cardinal.power_nat_le Cardinal.power_nat_leₓ'. -/
+#print Cardinal.power_nat_le /-
 theorem power_nat_le {c : Cardinal.{u}} {n : ℕ} (h : ℵ₀ ≤ c) : c ^ n ≤ c :=
   pow_le h (nat_lt_aleph0 n)
 #align cardinal.power_nat_le Cardinal.power_nat_le
+-/
 
-/- warning: cardinal.power_nat_eq -> Cardinal.power_nat_eq is a dubious translation:
-lean 3 declaration is
-  forall {c : Cardinal.{u1}} {n : Nat}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (LE.le.{0} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) n) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HPow.hPow.{succ u1, 0, succ u1} Cardinal.{u1} Nat Cardinal.{u1} (instHPow.{succ u1, 0} Cardinal.{u1} Nat (Monoid.Pow.{succ u1} Cardinal.{u1} (MonoidWithZero.toMonoid.{succ u1} Cardinal.{u1} (Semiring.toMonoidWithZero.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1}))))))) c n) c)
-but is expected to have type
-  forall {c : Cardinal.{u1}} {n : Nat}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} c) -> (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) n) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HPow.hPow.{succ u1, 0, succ u1} Cardinal.{u1} Nat Cardinal.{u1} (instHPow.{succ u1, 0} Cardinal.{u1} Nat (Monoid.Pow.{succ u1} Cardinal.{u1} (MonoidWithZero.toMonoid.{succ u1} Cardinal.{u1} (Semiring.toMonoidWithZero.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1}))))))) c n) c)
-Case conversion may be inaccurate. Consider using '#align cardinal.power_nat_eq Cardinal.power_nat_eqₓ'. -/
+#print Cardinal.power_nat_eq /-
 theorem power_nat_eq {c : Cardinal.{u}} {n : ℕ} (h1 : ℵ₀ ≤ c) (h2 : 1 ≤ n) : c ^ n = c :=
   pow_eq h1 (by exact_mod_cast h2) (nat_lt_aleph0 n)
 #align cardinal.power_nat_eq Cardinal.power_nat_eq
+-/
 
 /- warning: cardinal.power_nat_le_max -> Cardinal.power_nat_le_max is a dubious translation:
 lean 3 declaration is

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: Johannes Hölzl, Mario Carneiro, Floris van Doorn
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.ordinal
-! leanprover-community/mathlib commit 8da9e30545433fdd8fe55a0d3da208e5d9263f03
+! leanprover-community/mathlib commit 7c2ce0c2da15516b4e65d0c9e254bb6dc93abd1f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -323,7 +323,7 @@ lean 3 declaration is
 but is expected to have type
   forall {o : Ordinal.{u1}}, (Ordinal.IsLimit.{u1} o) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph'.{u1} o) (supᵢ.{succ u1, succ (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}))) (Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) (fun (a : Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) => Cardinal.aleph'.{u1} (Subtype.val.{succ (succ u1)} Ordinal.{u1} (fun (x : Ordinal.{u1}) => Membership.mem.{succ u1, succ u1} Ordinal.{u1} (Set.{succ u1} Ordinal.{u1}) (Set.instMembershipSet.{succ u1} Ordinal.{u1}) x (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) a))))
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph'_limit Cardinal.aleph'_limitₓ'. -/
-theorem aleph'_limit {o : Ordinal} (ho : IsLimit o) : aleph' o = ⨆ a : Iio o, aleph' a :=
+theorem aleph'_limit {o : Ordinal} (ho : o.IsLimit) : aleph' o = ⨆ a : Iio o, aleph' a :=
   by
   refine' le_antisymm _ (csupᵢ_le' fun i => aleph'_le.2 (le_of_lt i.2))
   rw [aleph'_le_of_limit ho]
@@ -412,7 +412,7 @@ lean 3 declaration is
 but is expected to have type
   forall {o : Ordinal.{u1}}, (Ordinal.IsLimit.{u1} o) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph.{u1} o) (supᵢ.{succ u1, succ (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}))) (Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) (fun (a : Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) => Cardinal.aleph.{u1} (Subtype.val.{succ (succ u1)} Ordinal.{u1} (fun (x : Ordinal.{u1}) => Membership.mem.{succ u1, succ u1} Ordinal.{u1} (Set.{succ u1} Ordinal.{u1}) (Set.instMembershipSet.{succ u1} Ordinal.{u1}) x (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) a))))
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_limit Cardinal.aleph_limitₓ'. -/
-theorem aleph_limit {o : Ordinal} (ho : IsLimit o) : aleph o = ⨆ a : Iio o, aleph a :=
+theorem aleph_limit {o : Ordinal} (ho : o.IsLimit) : aleph o = ⨆ a : Iio o, aleph a :=
   by
   apply le_antisymm _ (csupᵢ_le' _)
   · rw [aleph, aleph'_limit (ho.add _)]
@@ -485,7 +485,7 @@ instance nonempty_out_aleph (o : Ordinal) : Nonempty (aleph o).ord.out.α :=
 -/
 
 #print Cardinal.ord_aleph_isLimit /-
-theorem ord_aleph_isLimit (o : Ordinal) : IsLimit (aleph o).ord :=
+theorem ord_aleph_isLimit (o : Ordinal) : (aleph o).ord.IsLimit :=
   ord_isLimit <| aleph0_le_aleph _
 #align cardinal.ord_aleph_is_limit Cardinal.ord_aleph_isLimit
 -/
@@ -648,7 +648,7 @@ lean 3 declaration is
 but is expected to have type
   forall {o : Ordinal.{u1}}, (Ordinal.IsLimit.{u1} o) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.beth.{u1} o) (supᵢ.{succ u1, succ (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}))) (Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) (fun (a : Set.Elem.{succ u1} Ordinal.{u1} (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) => Cardinal.beth.{u1} (Subtype.val.{succ (succ u1)} Ordinal.{u1} (fun (x : Ordinal.{u1}) => Membership.mem.{succ u1, succ u1} Ordinal.{u1} (Set.{succ u1} Ordinal.{u1}) (Set.instMembershipSet.{succ u1} Ordinal.{u1}) x (Set.Iio.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) o)) a))))
 Case conversion may be inaccurate. Consider using '#align cardinal.beth_limit Cardinal.beth_limitₓ'. -/
-theorem beth_limit {o : Ordinal} : IsLimit o → beth o = ⨆ a : Iio o, beth a :=
+theorem beth_limit {o : Ordinal} : o.IsLimit → beth o = ⨆ a : Iio o, beth a :=
   limitRecOn_limit _ _ _ _
 #align cardinal.beth_limit Cardinal.beth_limit

bump to nightly-2023-04-03-02

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

8477bcac

Diff

@@ -81,7 +81,12 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
 /-! ### Aleph cardinals -/
 
 
-#print Cardinal.alephIdx.initialSeg /-
+/- warning: cardinal.aleph_idx.initial_seg -> Cardinal.alephIdx.initialSeg is a dubious translation:
+lean 3 declaration is
+  InitialSeg.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))
+but is expected to have type
+  InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.initial_seg Cardinal.alephIdx.initialSegₓ'. -/
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ω = ω`,
@@ -93,7 +98,6 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
 def alephIdx.initialSeg : @InitialSeg Cardinal Ordinal (· < ·) (· < ·) :=
   @RelEmbedding.collapse Cardinal Ordinal (· < ·) (· < ·) _ Cardinal.ord.orderEmbedding.ltEmbedding
 #align cardinal.aleph_idx.initial_seg Cardinal.alephIdx.initialSeg
--/
 
 #print Cardinal.alephIdx /-
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
@@ -108,7 +112,7 @@ def alephIdx : Cardinal → Ordinal :=
 
 /- warning: cardinal.aleph_idx.initial_seg_coe -> Cardinal.alephIdx.initialSeg_coe is a dubious translation:
 lean 3 declaration is
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+  Eq.{succ (succ u1)} ((fun (_x : InitialSeg.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.initialSeg.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : InitialSeg.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (FunLike.hasCoeToFun.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => Ordinal.{u1}) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.{u1} Ordinal.{u1} (InitialSeg.embeddingLike.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))))) Cardinal.alephIdx.initialSeg.{u1}) Cardinal.alephIdx.{u1}
 but is expected to have type
   Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249)) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249)) Cardinal.{u1} Ordinal.{u1} (InitialSeg.instEmbeddingLikeInitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249))) Cardinal.alephIdx.initialSeg.{u1}) Cardinal.alephIdx.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.initial_seg_coe Cardinal.alephIdx.initialSeg_coeₓ'. -/
@@ -117,12 +121,16 @@ theorem alephIdx.initialSeg_coe : (alephIdx.initialSeg : Cardinal → Ordinal) =
   rfl
 #align cardinal.aleph_idx.initial_seg_coe Cardinal.alephIdx.initialSeg_coe
 
-#print Cardinal.alephIdx_lt /-
+/- warning: cardinal.aleph_idx_lt -> Cardinal.alephIdx_lt is a dubious translation:
+lean 3 declaration is
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.alephIdx.{u1} a) (Cardinal.alephIdx.{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 b)
+but is expected to have type
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.alephIdx.{u1} a) (Cardinal.alephIdx.{u1} b)) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a b)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx_lt Cardinal.alephIdx_ltₓ'. -/
 @[simp]
 theorem alephIdx_lt {a b} : alephIdx a < alephIdx b ↔ a < b :=
   alephIdx.initialSeg.toRelEmbedding.map_rel_iff
 #align cardinal.aleph_idx_lt Cardinal.alephIdx_lt
--/
 
 #print Cardinal.alephIdx_le /-
 @[simp]
@@ -137,7 +145,12 @@ theorem alephIdx.init {a b} : b < alephIdx a → ∃ c, alephIdx c = b :=
 #align cardinal.aleph_idx.init Cardinal.alephIdx.init
 -/
 
-#print Cardinal.alephIdx.relIso /-
+/- warning: cardinal.aleph_idx.rel_iso -> Cardinal.alephIdx.relIso is a dubious translation:
+lean 3 declaration is
+  RelIso.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))
+but is expected to have type
+  RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.rel_iso Cardinal.alephIdx.relIsoₓ'. -/
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ℵ₀ = ω`,
@@ -159,11 +172,10 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
           (Cardinal.bddAbove_range.{u, u} fun a : α => inv_fun aleph_idx (Ordinal.typein r a))
           (Ordinal.enum r _ (h (succ s)))
 #align cardinal.aleph_idx.rel_iso Cardinal.alephIdx.relIso
--/
 
 /- warning: cardinal.aleph_idx.rel_iso_coe -> Cardinal.alephIdx.relIso_coe is a dubious translation:
 lean 3 declaration is
-  Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.alephIdx.relIso.{u1}) Cardinal.alephIdx.{u1}
+  Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Cardinal.{u1} 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}))))))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.alephIdx.relIso.{u1}) Cardinal.alephIdx.{u1}
 but is expected to have type
   Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (RelIso.toRelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) Cardinal.alephIdx.relIso.{u1}))) Cardinal.alephIdx.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coeₓ'. -/
@@ -172,12 +184,16 @@ theorem alephIdx.relIso_coe : (alephIdx.relIso : Cardinal → Ordinal) = alephId
   rfl
 #align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coe
 
-#print Cardinal.type_cardinal /-
+/- warning: cardinal.type_cardinal -> Cardinal.type_cardinal is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ (succ u1))} Ordinal.{succ u1} (Ordinal.type.{succ u1} 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.wo.{u1}) Ordinal.univ.{u1, succ u1}
+but is expected to have type
+  Eq.{succ (succ (succ u1))} Ordinal.{succ u1} (Ordinal.type.{succ u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.737 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.739 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.737 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.739) Cardinal.wo.{u1}) Ordinal.univ.{u1, succ u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.type_cardinal Cardinal.type_cardinalₓ'. -/
 @[simp]
 theorem type_cardinal : @type Cardinal (· < ·) _ = Ordinal.univ.{u, u + 1} := by
   rw [Ordinal.univ_id] <;> exact Quotient.sound ⟨aleph_idx.rel_iso⟩
 #align cardinal.type_cardinal Cardinal.type_cardinal
--/
 
 #print Cardinal.mk_cardinal /-
 @[simp]
@@ -186,7 +202,12 @@ theorem mk_cardinal : (#Cardinal) = univ.{u, u + 1} := by
 #align cardinal.mk_cardinal Cardinal.mk_cardinal
 -/
 
-#print Cardinal.Aleph'.relIso /-
+/- warning: cardinal.aleph'.rel_iso -> Cardinal.Aleph'.relIso is a dubious translation:
+lean 3 declaration is
+  RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{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})))))))
+but is expected to have type
+  RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph'.rel_iso Cardinal.Aleph'.relIsoₓ'. -/
 /-- The `aleph'` function gives the cardinals listed by their ordinal
   index, and is the inverse of `aleph_idx`.
   `aleph' n = n`, `aleph' ω = ω`, `aleph' (ω + 1) = succ ℵ₀`, etc.
@@ -196,7 +217,6 @@ theorem mk_cardinal : (#Cardinal) = univ.{u, u + 1} := by
 def Aleph'.relIso :=
   Cardinal.alephIdx.relIso.symm
 #align cardinal.aleph'.rel_iso Cardinal.Aleph'.relIso
--/
 
 #print Cardinal.aleph' /-
 /-- The `aleph'` function gives the cardinals listed by their ordinal
@@ -209,7 +229,7 @@ def aleph' : Ordinal → Cardinal :=
 
 /- warning: cardinal.aleph'.rel_iso_coe -> Cardinal.aleph'.relIso_coe 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 cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coeₓ'. -/
@@ -218,12 +238,16 @@ theorem aleph'.relIso_coe : (Aleph'.relIso : Ordinal → Cardinal) = aleph' :=
   rfl
 #align cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coe
 
-#print Cardinal.aleph'_lt /-
+/- warning: cardinal.aleph'_lt -> Cardinal.aleph'_lt is a dubious translation:
+lean 3 declaration is
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (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.aleph'.{u1} o₁) (Cardinal.aleph'.{u1} o₂)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+but is expected to have type
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.aleph'.{u1} o₁) (Cardinal.aleph'.{u1} o₂)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph'_lt Cardinal.aleph'_ltₓ'. -/
 @[simp]
 theorem aleph'_lt {o₁ o₂ : Ordinal} : aleph' o₁ < aleph' o₂ ↔ o₁ < o₂ :=
   Aleph'.relIso.map_rel_iff
 #align cardinal.aleph'_lt Cardinal.aleph'_lt
--/
 
 #print Cardinal.aleph'_le /-
 @[simp]
@@ -257,7 +281,7 @@ theorem aleph'_zero : aleph' 0 = 0 :=
 
 /- warning: cardinal.aleph'_succ -> Cardinal.aleph'_succ is a dubious translation:
 lean 3 declaration is
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+  forall {o : Ordinal.{u1}}, Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph'.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)) (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} (Cardinal.aleph'.{u1} o))
 but is expected to have type
   forall {o : Ordinal.{u1}}, Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph'.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)) (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} (Cardinal.aleph'.{u1} o))
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph'_succ Cardinal.aleph'_succₓ'. -/
@@ -333,12 +357,16 @@ def aleph (o : Ordinal) : Cardinal :=
 #align cardinal.aleph Cardinal.aleph
 -/
 
-#print Cardinal.aleph_lt /-
+/- warning: cardinal.aleph_lt -> Cardinal.aleph_lt is a dubious translation:
+lean 3 declaration is
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (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.aleph.{u1} o₁) (Cardinal.aleph.{u1} o₂)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+but is expected to have type
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.aleph.{u1} o₁) (Cardinal.aleph.{u1} o₂)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_lt Cardinal.aleph_ltₓ'. -/
 @[simp]
 theorem aleph_lt {o₁ o₂ : Ordinal} : aleph o₁ < aleph o₂ ↔ o₁ < o₂ :=
   aleph'_lt.trans (add_lt_add_iff_left _)
 #align cardinal.aleph_lt Cardinal.aleph_lt
--/
 
 #print Cardinal.aleph_le /-
 @[simp]
@@ -349,7 +377,7 @@ theorem aleph_le {o₁ o₂ : Ordinal} : aleph o₁ ≤ aleph o₂ ↔ o₁ ≤
 
 /- warning: cardinal.max_aleph_eq -> Cardinal.max_aleph_eq is a dubious translation:
 lean 3 declaration is
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+  forall (o₁ : Ordinal.{u1}) (o₂ : Ordinal.{u1}), Eq.{succ (succ u1)} Cardinal.{u1} (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.aleph.{u1} o₁) (Cardinal.aleph.{u1} o₂)) (Cardinal.aleph.{u1} (LinearOrder.max.{succ u1} Ordinal.{u1} Ordinal.linearOrder.{u1} o₁ o₂))
 but is expected to have type
   forall (o₁ : Ordinal.{u1}) (o₂ : Ordinal.{u1}), Eq.{succ (succ u1)} Cardinal.{u1} (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.aleph.{u1} o₁) (Cardinal.aleph.{u1} o₂)) (Cardinal.aleph.{u1} (Max.max.{succ u1} Ordinal.{u1} (LinearOrder.toMax.{succ u1} Ordinal.{u1} Ordinal.linearOrder.{u1}) o₁ o₂))
 Case conversion may be inaccurate. Consider using '#align cardinal.max_aleph_eq Cardinal.max_aleph_eqₓ'. -/
@@ -363,7 +391,7 @@ theorem max_aleph_eq (o₁ o₂ : Ordinal) : max (aleph o₁) (aleph o₂) = ale
 
 /- warning: cardinal.aleph_succ -> Cardinal.aleph_succ is a dubious translation:
 lean 3 declaration is
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+  forall {o : Ordinal.{u1}}, Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)) (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} (Cardinal.aleph.{u1} o))
 but is expected to have type
   forall {o : Ordinal.{u1}}, Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.aleph.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)) (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} (Cardinal.aleph.{u1} o))
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_succ Cardinal.aleph_succₓ'. -/
@@ -411,16 +439,24 @@ theorem aleph0_le_aleph (o : Ordinal) : ℵ₀ ≤ aleph o :=
 #align cardinal.aleph_0_le_aleph Cardinal.aleph0_le_aleph
 -/
 
-#print Cardinal.aleph'_pos /-
+/- warning: cardinal.aleph'_pos -> Cardinal.aleph'_pos is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, (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 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) o) -> (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}))) (Cardinal.aleph'.{u1} o))
+but is expected to have type
+  forall {o : Ordinal.{u1}}, (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})) o) -> (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})) (Cardinal.aleph'.{u1} o))
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph'_pos Cardinal.aleph'_posₓ'. -/
 theorem aleph'_pos {o : Ordinal} (ho : 0 < o) : 0 < aleph' o := by rwa [← aleph'_zero, aleph'_lt]
 #align cardinal.aleph'_pos Cardinal.aleph'_pos
--/
 
-#print Cardinal.aleph_pos /-
+/- warning: cardinal.aleph_pos -> Cardinal.aleph_pos is a dubious translation:
+lean 3 declaration is
+  forall (o : 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})))))) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1}))) (Cardinal.aleph.{u1} o)
+but is expected to have type
+  forall (o : Ordinal.{u1}), 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})) (Cardinal.aleph.{u1} o)
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_pos Cardinal.aleph_posₓ'. -/
 theorem aleph_pos (o : Ordinal) : 0 < aleph o :=
   aleph0_pos.trans_le (aleph0_le_aleph o)
 #align cardinal.aleph_pos Cardinal.aleph_pos
--/
 
 #print Cardinal.aleph_toNat /-
 @[simp]
@@ -482,7 +518,7 @@ theorem aleph_isNormal : IsNormal (ord ∘ aleph) :=
 
 /- warning: cardinal.succ_aleph_0 -> Cardinal.succ_aleph0 is a dubious translation:
 lean 3 declaration is
-  Eq.{succ (succ u1)} Cardinal.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.succOrder.{u1} Cardinal.aleph0.{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}))))
+  Eq.{succ (succ u1)} Cardinal.{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} Cardinal.aleph0.{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
   Eq.{succ (succ u1)} Cardinal.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} Cardinal.aleph0.{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.succ_aleph_0 Cardinal.succ_aleph0ₓ'. -/
@@ -491,7 +527,7 @@ theorem succ_aleph0 : succ ℵ₀ = aleph 1 := by rw [← aleph_zero, ← aleph_
 
 /- warning: cardinal.aleph_0_lt_aleph_one -> Cardinal.aleph0_lt_aleph_one is a dubious translation:
 lean 3 declaration is
-  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{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}))))
+  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} (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
   LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{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.aleph_0_lt_aleph_one Cardinal.aleph0_lt_aleph_oneₓ'. -/
@@ -503,7 +539,7 @@ theorem aleph0_lt_aleph_one : ℵ₀ < aleph 1 :=
 
 /- warning: cardinal.countable_iff_lt_aleph_one -> Cardinal.countable_iff_lt_aleph_one is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (s : Set.{u1} α), Iff (Set.Countable.{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} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (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})))))
+  forall {α : Type.{u1}} (s : Set.{u1} α), Iff (Set.Countable.{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} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (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
   forall {α : Type.{u1}} (s : Set.{u1} α), Iff (Set.Countable.{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} α s)) (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.countable_iff_lt_aleph_one Cardinal.countable_iff_lt_aleph_oneₓ'. -/
@@ -616,7 +652,12 @@ theorem beth_limit {o : Ordinal} : IsLimit o → beth o = ⨆ a : Iio o, beth a
   limitRecOn_limit _ _ _ _
 #align cardinal.beth_limit Cardinal.beth_limit
 
-#print Cardinal.beth_strictMono /-
+/- warning: cardinal.beth_strict_mono -> Cardinal.beth_strictMono is a dubious translation:
+lean 3 declaration is
+  StrictMono.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{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.beth.{u1}
+but is expected to have type
+  StrictMono.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.beth.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.beth_strict_mono Cardinal.beth_strictMonoₓ'. -/
 theorem beth_strictMono : StrictMono beth := by
   intro a b
   induction' b using Ordinal.induction with b IH generalizing a
@@ -633,20 +674,27 @@ theorem beth_strictMono : StrictMono beth := by
     rw [beth_limit hb, ← beth_succ]
     exact le_csupᵢ (bdd_above_of_small _) (⟨_, hb.succ_lt h⟩ : Iio b)
 #align cardinal.beth_strict_mono Cardinal.beth_strictMono
--/
 
-#print Cardinal.beth_mono /-
+/- warning: cardinal.beth_mono -> Cardinal.beth_mono is a dubious translation:
+lean 3 declaration is
+  Monotone.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{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.beth.{u1}
+but is expected to have type
+  Monotone.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.beth.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.beth_mono Cardinal.beth_monoₓ'. -/
 theorem beth_mono : Monotone beth :=
   beth_strictMono.Monotone
 #align cardinal.beth_mono Cardinal.beth_mono
--/
 
-#print Cardinal.beth_lt /-
+/- warning: cardinal.beth_lt -> Cardinal.beth_lt is a dubious translation:
+lean 3 declaration is
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (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.beth.{u1} o₁) (Cardinal.beth.{u1} o₂)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+but is expected to have type
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Cardinal.beth.{u1} o₁) (Cardinal.beth.{u1} o₂)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂)
+Case conversion may be inaccurate. Consider using '#align cardinal.beth_lt Cardinal.beth_ltₓ'. -/
 @[simp]
 theorem beth_lt {o₁ o₂ : Ordinal} : beth o₁ < beth o₂ ↔ o₁ < o₂ :=
   beth_strictMono.lt_iff_lt
 #align cardinal.beth_lt Cardinal.beth_lt
--/
 
 #print Cardinal.beth_le /-
 @[simp]
@@ -675,11 +723,15 @@ theorem aleph0_le_beth (o : Ordinal) : ℵ₀ ≤ beth o :=
 #align cardinal.aleph_0_le_beth Cardinal.aleph0_le_beth
 -/
 
-#print Cardinal.beth_pos /-
+/- warning: cardinal.beth_pos -> Cardinal.beth_pos is a dubious translation:
+lean 3 declaration is
+  forall (o : 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})))))) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1}))) (Cardinal.beth.{u1} o)
+but is expected to have type
+  forall (o : Ordinal.{u1}), 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})) (Cardinal.beth.{u1} o)
+Case conversion may be inaccurate. Consider using '#align cardinal.beth_pos Cardinal.beth_posₓ'. -/
 theorem beth_pos (o : Ordinal) : 0 < beth o :=
   aleph0_pos.trans_le <| aleph0_le_beth o
 #align cardinal.beth_pos Cardinal.beth_pos
--/
 
 #print Cardinal.beth_ne_zero /-
 theorem beth_ne_zero (o : Ordinal) : beth o ≠ 0 :=
@@ -765,7 +817,7 @@ end UsingOrdinals
 
 /- warning: cardinal.mul_eq_max -> Cardinal.mul_eq_max 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) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} b) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) a b))
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} b) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} a b))
 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) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} b) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) a b))
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_eq_max Cardinal.mul_eq_maxₓ'. -/
@@ -781,7 +833,7 @@ theorem mul_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : ℵ₀ ≤ b) : a
 
 /- warning: cardinal.mul_mk_eq_max -> Cardinal.mul_mk_eq_max is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] [_inst_2 : Infinite.{succ u1} β], Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] [_inst_2 : Infinite.{succ u1} β], Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_mk_eq_max Cardinal.mul_mk_eq_maxₓ'. -/
@@ -869,7 +921,7 @@ theorem aleph_mul_aleph0 (o : Ordinal) : aleph o * ℵ₀ = aleph o :=
 
 /- warning: cardinal.mul_lt_of_lt -> Cardinal.mul_lt_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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} Cardinal.partialOrder.{u1})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) c)
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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})))))) a 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})))))) b 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})))))) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) c)
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_lt_of_lt Cardinal.mul_lt_of_ltₓ'. -/
@@ -883,7 +935,7 @@ theorem mul_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b
 
 /- warning: cardinal.mul_le_max_of_aleph_0_le_left -> Cardinal.mul_le_max_of_aleph0_le_left 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) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) a b))
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} a b))
 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) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) a b))
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_le_max_of_aleph_0_le_left Cardinal.mul_le_max_of_aleph0_le_leftₓ'. -/
@@ -896,7 +948,7 @@ theorem mul_le_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) : a * b
 
 /- warning: cardinal.mul_eq_max_of_aleph_0_le_left -> Cardinal.mul_eq_max_of_aleph0_le_left 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) -> (Ne.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1})))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) a b))
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (Ne.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1})))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} a b))
 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) -> (Ne.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1}))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) a b))
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_eq_max_of_aleph_0_le_left Cardinal.mul_eq_max_of_aleph0_le_leftₓ'. -/
@@ -913,7 +965,7 @@ theorem mul_eq_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) (h' : b
 
 /- warning: cardinal.mul_le_max_of_aleph_0_le_right -> Cardinal.mul_le_max_of_aleph0_le_right 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} b) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) a b))
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} b) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} a b))
 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} b) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) a b))
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_le_max_of_aleph_0_le_right Cardinal.mul_le_max_of_aleph0_le_rightₓ'. -/
@@ -923,7 +975,7 @@ theorem mul_le_max_of_aleph0_le_right {a b : Cardinal} (h : ℵ₀ ≤ b) : a *
 
 /- warning: cardinal.mul_eq_max_of_aleph_0_le_right -> Cardinal.mul_eq_max_of_aleph0_le_right is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (Ne.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1})))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} b) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) a b))
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (Ne.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1})))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} b) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} a b))
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (Ne.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1}))) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} b) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) a b))
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_eq_max_of_aleph_0_le_right Cardinal.mul_eq_max_of_aleph0_le_rightₓ'. -/
@@ -935,7 +987,7 @@ theorem mul_eq_max_of_aleph0_le_right {a b : Cardinal} (h' : a ≠ 0) (h : ℵ
 
 /- warning: cardinal.mul_eq_max' -> Cardinal.mul_eq_max' is a dubious translation:
 lean 3 declaration is
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+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} a b))
 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} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) a b))
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_eq_max' Cardinal.mul_eq_max'ₓ'. -/
@@ -948,7 +1000,7 @@ theorem mul_eq_max' {a b : Cardinal} (h : ℵ₀ ≤ a * b) : a * b = max a b :=
 
 /- warning: cardinal.mul_le_max -> Cardinal.mul_le_max is a dubious translation:
 lean 3 declaration is
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+  forall (a : Cardinal.{u1}) (b : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} a b) Cardinal.aleph0.{u1})
 but is expected to have type
   forall (a : Cardinal.{u1}) (b : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) a b) Cardinal.aleph0.{u1})
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_le_max Cardinal.mul_le_maxₓ'. -/
@@ -1011,7 +1063,7 @@ theorem le_mul_right {a b : Cardinal} (h : b ≠ 0) : a ≤ a * b :=
 
 /- warning: cardinal.mul_eq_left_iff -> Cardinal.mul_eq_left_iff is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) a) (Or (And (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) Cardinal.aleph0.{u1} b) a) (Ne.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1}))))) (Or (Eq.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (OfNat.mk.{succ u1} Cardinal.{u1} 1 (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) (Eq.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1}))))))
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) a b) a) (Or (And (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} Cardinal.aleph0.{u1} b) a) (Ne.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1}))))) (Or (Eq.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (OfNat.mk.{succ u1} Cardinal.{u1} 1 (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) (Eq.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1}))))))
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) a b) a) (Or (And (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) Cardinal.aleph0.{u1} b) a) (Ne.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1})))) (Or (Eq.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (One.toOfNat1.{succ u1} Cardinal.{u1} Cardinal.instOneCardinal.{u1}))) (Eq.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1})))))
 Case conversion may be inaccurate. Consider using '#align cardinal.mul_eq_left_iff Cardinal.mul_eq_left_iffₓ'. -/
@@ -1078,7 +1130,7 @@ theorem add_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c + c = c :=
 
 /- warning: cardinal.add_eq_max -> Cardinal.add_eq_max 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) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) a b))
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} a b))
 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) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) a b))
 Case conversion may be inaccurate. Consider using '#align cardinal.add_eq_max Cardinal.add_eq_maxₓ'. -/
@@ -1093,7 +1145,7 @@ theorem add_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) : a + b = max a b :=
 
 /- warning: cardinal.add_eq_max' -> Cardinal.add_eq_max' 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} b) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) a b))
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} b) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} a b))
 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} b) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) a b))
 Case conversion may be inaccurate. Consider using '#align cardinal.add_eq_max' Cardinal.add_eq_max'ₓ'. -/
@@ -1103,7 +1155,7 @@ theorem add_eq_max' {a b : Cardinal} (ha : ℵ₀ ≤ b) : a + b = max a b := by
 
 /- warning: cardinal.add_mk_eq_max -> Cardinal.add_mk_eq_max is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u1}} [_inst_1 : Infinite.{succ u1} α], Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
+  forall {α : Type.{u1}} {β : Type.{u1}} [_inst_1 : Infinite.{succ u1} α], Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u1}} [_inst_1 : Infinite.{succ u1} α], Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
 Case conversion may be inaccurate. Consider using '#align cardinal.add_mk_eq_max Cardinal.add_mk_eq_maxₓ'. -/
@@ -1114,7 +1166,7 @@ theorem add_mk_eq_max {α β : Type _} [Infinite α] : (#α) + (#β) = max (#α)
 
 /- warning: cardinal.add_mk_eq_max' -> Cardinal.add_mk_eq_max' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u1}} [_inst_1 : Infinite.{succ u1} β], Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
+  forall {α : Type.{u1}} {β : Type.{u1}} [_inst_1 : Infinite.{succ u1} β], Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u1}} [_inst_1 : Infinite.{succ u1} β], Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β)) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
 Case conversion may be inaccurate. Consider using '#align cardinal.add_mk_eq_max' Cardinal.add_mk_eq_max'ₓ'. -/
@@ -1125,7 +1177,7 @@ theorem add_mk_eq_max' {α β : Type _} [Infinite β] : (#α) + (#β) = max (#α
 
 /- warning: cardinal.add_le_max -> Cardinal.add_le_max is a dubious translation:
 lean 3 declaration is
-  forall (a : Cardinal.{u1}) (b : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) a b) Cardinal.aleph0.{u1})
+  forall (a : Cardinal.{u1}) (b : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} a b) Cardinal.aleph0.{u1})
 but is expected to have type
   forall (a : Cardinal.{u1}) (b : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) a b) Cardinal.aleph0.{u1})
 Case conversion may be inaccurate. Consider using '#align cardinal.add_le_max Cardinal.add_le_maxₓ'. -/
@@ -1152,7 +1204,7 @@ theorem add_le_of_le {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a ≤ c) (h2 :
 
 /- warning: cardinal.add_lt_of_lt -> Cardinal.add_lt_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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} Cardinal.partialOrder.{u1})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) c)
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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})))))) a 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})))))) b 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})))))) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) c)
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {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})) a c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.add_lt_of_lt Cardinal.add_lt_of_ltₓ'. -/
@@ -1164,7 +1216,7 @@ theorem add_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b
 
 /- warning: cardinal.eq_of_add_eq_of_aleph_0_le -> Cardinal.eq_of_add_eq_of_aleph0_le is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) 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})))))) a c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} c) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) c) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a c) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} c) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
 Case conversion may be inaccurate. Consider using '#align cardinal.eq_of_add_eq_of_aleph_0_le Cardinal.eq_of_add_eq_of_aleph0_leₓ'. -/
@@ -1200,7 +1252,7 @@ theorem add_eq_right {a b : Cardinal} (hb : ℵ₀ ≤ b) (ha : a ≤ b) : a + b
 
 /- warning: cardinal.add_eq_left_iff -> Cardinal.add_eq_left_iff is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) Cardinal.aleph0.{u1} b) a) (Eq.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1})))))
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} Cardinal.aleph0.{u1} b) a) (Eq.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1})))))
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) Cardinal.aleph0.{u1} b) a) (Eq.{succ (succ u1)} Cardinal.{u1} b (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1}))))
 Case conversion may be inaccurate. Consider using '#align cardinal.add_eq_left_iff Cardinal.add_eq_left_iffₓ'. -/
@@ -1226,7 +1278,7 @@ theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨
 
 /- warning: cardinal.add_eq_right_iff -> Cardinal.add_eq_right_iff is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) b) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) Cardinal.aleph0.{u1} a) b) (Eq.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1})))))
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) b) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} Cardinal.aleph0.{u1} a) b) (Eq.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1})))))
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}}, Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) b) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) Cardinal.aleph0.{u1} a) b) (Eq.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1}))))
 Case conversion may be inaccurate. Consider using '#align cardinal.add_eq_right_iff Cardinal.add_eq_right_iffₓ'. -/
@@ -1267,7 +1319,7 @@ theorem mk_add_one_eq {α : Type _} [Infinite α] : (#α) + 1 = (#α) :=
 
 /- warning: cardinal.eq_of_add_eq_add_left -> Cardinal.eq_of_add_eq_add_left is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a c)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a 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})))))) a Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a c)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) a Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{u1} b c)
 Case conversion may be inaccurate. Consider using '#align cardinal.eq_of_add_eq_add_left Cardinal.eq_of_add_eq_add_leftₓ'. -/
@@ -1294,7 +1346,7 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
 
 /- warning: cardinal.eq_of_add_eq_add_right -> Cardinal.eq_of_add_eq_add_right is a dubious translation:
 lean 3 declaration is
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+  forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) a b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) c 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})))))) b Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{u1} a c)
 but is expected to have type
   forall {a : Cardinal.{u1}} {b : Cardinal.{u1}} {c : Cardinal.{u1}}, (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) a b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) c b)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) b Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{u1} a c)
 Case conversion may be inaccurate. Consider using '#align cardinal.eq_of_add_eq_add_right Cardinal.eq_of_add_eq_add_rightₓ'. -/
@@ -1331,7 +1383,7 @@ theorem principal_add_aleph (o : Ordinal) : Ordinal.Principal (· + ·) (aleph o
 
 /- warning: cardinal.add_right_inj_of_lt_aleph_0 -> Cardinal.add_right_inj_of_lt_aleph0 is a dubious translation:
 lean 3 declaration is
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+  forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : 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})))))) γ Cardinal.aleph0.{u1}) -> (Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) β γ)) (Eq.{succ (succ u1)} Cardinal.{u1} α β))
 but is expected to have type
   forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) γ Cardinal.aleph0.{u1}) -> (Iff (Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) β γ)) (Eq.{succ (succ u1)} Cardinal.{u1} α β))
 Case conversion may be inaccurate. Consider using '#align cardinal.add_right_inj_of_lt_aleph_0 Cardinal.add_right_inj_of_lt_aleph0ₓ'. -/
@@ -1363,7 +1415,7 @@ theorem add_one_inj {α β : Cardinal} : α + 1 = β + 1 ↔ α = β :=
 
 /- warning: cardinal.add_le_add_iff_of_lt_aleph_0 -> Cardinal.add_le_add_iff_of_lt_aleph0 is a dubious translation:
 lean 3 declaration is
-  forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) γ Cardinal.aleph0.{u1}) -> (Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) β γ)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} α β))
+  forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : 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})))))) γ Cardinal.aleph0.{u1}) -> (Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) β γ)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} α β))
 but is expected to have type
   forall {α : Cardinal.{u1}} {β : Cardinal.{u1}} {γ : Cardinal.{u1}}, (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) γ Cardinal.aleph0.{u1}) -> (Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) α γ) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) β γ)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} α β))
 Case conversion may be inaccurate. Consider using '#align cardinal.add_le_add_iff_of_lt_aleph_0 Cardinal.add_le_add_iff_of_lt_aleph0ₓ'. -/
@@ -1401,7 +1453,12 @@ theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β
 /-! ### Properties about power -/
 
 
-#print Cardinal.pow_le /-
+/- warning: cardinal.pow_le -> Cardinal.pow_le is a dubious translation:
+lean 3 declaration is
+  forall {κ : Cardinal.{u1}} {μ : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} κ) -> (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})))))) μ Cardinal.aleph0.{u1}) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{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}) κ μ) κ)
+but is expected to have type
+  forall {κ : Cardinal.{u1}} {μ : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} κ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) μ Cardinal.aleph0.{u1}) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{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}) κ μ) κ)
+Case conversion may be inaccurate. Consider using '#align cardinal.pow_le Cardinal.pow_leₓ'. -/
 theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) : κ ^ μ ≤ κ :=
   let ⟨n, H3⟩ := lt_aleph0.1 H2
   H3.symm ▸
@@ -1421,13 +1478,16 @@ theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) :
             (mul_eq_self H1))
       H1
 #align cardinal.pow_le Cardinal.pow_le
--/
 
-#print Cardinal.pow_eq /-
+/- warning: cardinal.pow_eq -> Cardinal.pow_eq is a dubious translation:
+lean 3 declaration is
+  forall {κ : Cardinal.{u1}} {μ : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} κ) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (OfNat.mk.{succ u1} Cardinal.{u1} 1 (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1}))) μ) -> (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})))))) μ Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{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}) κ μ) κ)
+but is expected to have type
+  forall {κ : Cardinal.{u1}} {μ : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} κ) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (One.toOfNat1.{succ u1} Cardinal.{u1} Cardinal.instOneCardinal.{u1})) μ) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) μ Cardinal.aleph0.{u1}) -> (Eq.{succ (succ u1)} Cardinal.{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}) κ μ) κ)
+Case conversion may be inaccurate. Consider using '#align cardinal.pow_eq Cardinal.pow_eqₓ'. -/
 theorem pow_eq {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : 1 ≤ μ) (H3 : μ < ℵ₀) : κ ^ μ = κ :=
   (pow_le H1 H3).antisymm <| self_le_power κ H2
 #align cardinal.pow_eq Cardinal.pow_eq
--/
 
 /- warning: cardinal.power_self_eq -> Cardinal.power_self_eq is a dubious translation:
 lean 3 declaration is
@@ -1506,7 +1566,7 @@ theorem power_nat_eq {c : Cardinal.{u}} {n : ℕ} (h1 : ℵ₀ ≤ c) (h2 : 1 
 
 /- warning: cardinal.power_nat_le_max -> Cardinal.power_nat_le_max is a dubious translation:
 lean 3 declaration is
-  forall {c : Cardinal.{u1}} {n : Nat}, LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{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}) c ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) c Cardinal.aleph0.{u1})
+  forall {c : Cardinal.{u1}} {n : Nat}, LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{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}) c ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} c Cardinal.aleph0.{u1})
 but is expected to have type
   forall {c : Cardinal.{u1}} {n : Nat}, LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{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}) c (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) c Cardinal.aleph0.{u1})
 Case conversion may be inaccurate. Consider using '#align cardinal.power_nat_le_max Cardinal.power_nat_le_maxₓ'. -/
@@ -1532,7 +1592,7 @@ theorem powerlt_aleph0 {c : Cardinal} (h : ℵ₀ ≤ c) : c ^< ℵ₀ = c :=
 
 /- warning: cardinal.powerlt_aleph_0_le -> Cardinal.powerlt_aleph0_le is a dubious translation:
 lean 3 declaration is
-  forall (c : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.powerlt.{u1} c Cardinal.aleph0.{u1}) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) c Cardinal.aleph0.{u1})
+  forall (c : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.powerlt.{u1} c Cardinal.aleph0.{u1}) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} c Cardinal.aleph0.{u1})
 but is expected to have type
   forall (c : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.powerlt.{u1} c Cardinal.aleph0.{u1}) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) c Cardinal.aleph0.{u1})
 Case conversion may be inaccurate. Consider using '#align cardinal.powerlt_aleph_0_le Cardinal.powerlt_aleph0_leₓ'. -/
@@ -1570,7 +1630,7 @@ theorem mk_list_eq_aleph0 (α : Type u) [Countable α] [Nonempty α] : (#List α
 
 /- warning: cardinal.mk_list_eq_max_mk_aleph_0 -> Cardinal.mk_list_eq_max_mk_aleph0 is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}) [_inst_1 : Nonempty.{succ u1} α], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (List.{u1} α)) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
+  forall (α : Type.{u1}) [_inst_1 : Nonempty.{succ u1} α], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (List.{u1} α)) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
 but is expected to have type
   forall (α : Type.{u1}) [_inst_1 : Nonempty.{succ u1} α], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (List.{u1} α)) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_list_eq_max_mk_aleph_0 Cardinal.mk_list_eq_max_mk_aleph0ₓ'. -/
@@ -1585,7 +1645,7 @@ theorem mk_list_eq_max_mk_aleph0 (α : Type u) [Nonempty α] : (#List α) = max
 
 /- warning: cardinal.mk_list_le_max -> Cardinal.mk_list_le_max is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (List.{u1} α)) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) Cardinal.aleph0.{u1} (Cardinal.mk.{u1} α))
+  forall (α : Type.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (List.{u1} α)) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} Cardinal.aleph0.{u1} (Cardinal.mk.{u1} α))
 but is expected to have type
   forall (α : Type.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (List.{u1} α)) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) Cardinal.aleph0.{u1} (Cardinal.mk.{u1} α))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_list_le_max Cardinal.mk_list_le_maxₓ'. -/
@@ -1611,7 +1671,7 @@ theorem mk_finset_of_infinite (α : Type u) [Infinite α] : (#Finset α) = (#α)
 
 /- warning: cardinal.mk_finsupp_lift_of_infinite -> Cardinal.mk_finsupp_lift_of_infinite is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : Infinite.{succ u1} α] [_inst_2 : Zero.{u2} β] [_inst_3 : Nontrivial.{u2} β], Eq.{succ (succ (max u1 u2))} Cardinal.{max u1 u2} (Cardinal.mk.{max u1 u2} (Finsupp.{u1, u2} α β _inst_2)) (LinearOrder.max.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyLinearOrderedAddMonoid.{max u1 u2}) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} α)) (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} β)))
+  forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : Infinite.{succ u1} α] [_inst_2 : Zero.{u2} β] [_inst_3 : Nontrivial.{u2} β], Eq.{succ (succ (max u1 u2))} Cardinal.{max u1 u2} (Cardinal.mk.{max u1 u2} (Finsupp.{u1, u2} α β _inst_2)) (LinearOrder.max.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.linearOrder.{max u1 u2} (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} α)) (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} β)))
 but is expected to have type
   forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : Infinite.{succ u1} α] [_inst_2 : Zero.{u2} β] [_inst_3 : Nontrivial.{u2} β], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u2 u1} (Cardinal.mk.{max u2 u1} (Finsupp.{u1, u2} α β _inst_2)) (Max.max.{max (succ u2) (succ u1)} Cardinal.{max u1 u2} (CanonicallyLinearOrderedAddMonoid.toMax.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{max u1 u2}) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} α)) (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} β)))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_finsupp_lift_of_infinite Cardinal.mk_finsupp_lift_of_infiniteₓ'. -/
@@ -1636,7 +1696,7 @@ theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Z
 
 /- warning: cardinal.mk_finsupp_of_infinite -> Cardinal.mk_finsupp_of_infinite is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}) (β : Type.{u1}) [_inst_1 : Infinite.{succ u1} α] [_inst_2 : Zero.{u1} β] [_inst_3 : Nontrivial.{u1} β], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Finsupp.{u1, u1} α β _inst_2)) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
+  forall (α : Type.{u1}) (β : Type.{u1}) [_inst_1 : Infinite.{succ u1} α] [_inst_2 : Zero.{u1} β] [_inst_3 : Nontrivial.{u1} β], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Finsupp.{u1, u1} α β _inst_2)) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
 but is expected to have type
   forall (α : Type.{u1}) (β : Type.{u1}) [_inst_1 : Infinite.{succ u1} α] [_inst_2 : Zero.{u1} β] [_inst_3 : Nontrivial.{u1} β], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Finsupp.{u1, u1} α β _inst_2)) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_finsupp_of_infinite Cardinal.mk_finsupp_of_infiniteₓ'. -/
@@ -1646,7 +1706,7 @@ theorem mk_finsupp_of_infinite (α β : Type u) [Infinite α] [Zero β] [Nontriv
 
 /- warning: cardinal.mk_finsupp_lift_of_infinite' -> Cardinal.mk_finsupp_lift_of_infinite' is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : Nonempty.{succ u1} α] [_inst_2 : Zero.{u2} β] [_inst_3 : Infinite.{succ u2} β], Eq.{succ (succ (max u1 u2))} Cardinal.{max u1 u2} (Cardinal.mk.{max u1 u2} (Finsupp.{u1, u2} α β _inst_2)) (LinearOrder.max.{succ (max u1 u2)} Cardinal.{max u1 u2} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.canonicallyLinearOrderedAddMonoid.{max u1 u2}) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} α)) (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} β)))
+  forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : Nonempty.{succ u1} α] [_inst_2 : Zero.{u2} β] [_inst_3 : Infinite.{succ u2} β], Eq.{succ (succ (max u1 u2))} Cardinal.{max u1 u2} (Cardinal.mk.{max u1 u2} (Finsupp.{u1, u2} α β _inst_2)) (LinearOrder.max.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.linearOrder.{max u1 u2} (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} α)) (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} β)))
 but is expected to have type
   forall (α : Type.{u1}) (β : Type.{u2}) [_inst_1 : Nonempty.{succ u1} α] [_inst_2 : Zero.{u2} β] [_inst_3 : Infinite.{succ u2} β], Eq.{max (succ (succ u1)) (succ (succ u2))} Cardinal.{max u2 u1} (Cardinal.mk.{max u2 u1} (Finsupp.{u1, u2} α β _inst_2)) (Max.max.{max (succ u2) (succ u1)} Cardinal.{max u1 u2} (CanonicallyLinearOrderedAddMonoid.toMax.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{max u1 u2}) (Cardinal.lift.{u2, u1} (Cardinal.mk.{u1} α)) (Cardinal.lift.{u1, u2} (Cardinal.mk.{u2} β)))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_finsupp_lift_of_infinite' Cardinal.mk_finsupp_lift_of_infinite'ₓ'. -/
@@ -1664,7 +1724,7 @@ theorem mk_finsupp_lift_of_infinite' (α : Type u) (β : Type v) [Nonempty α] [
 
 /- warning: cardinal.mk_finsupp_of_infinite' -> Cardinal.mk_finsupp_of_infinite' is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}) (β : Type.{u1}) [_inst_1 : Nonempty.{succ u1} α] [_inst_2 : Zero.{u1} β] [_inst_3 : Infinite.{succ u1} β], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Finsupp.{u1, u1} α β _inst_2)) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
+  forall (α : Type.{u1}) (β : Type.{u1}) [_inst_1 : Nonempty.{succ u1} α] [_inst_2 : Zero.{u1} β] [_inst_3 : Infinite.{succ u1} β], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Finsupp.{u1, u1} α β _inst_2)) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
 but is expected to have type
   forall (α : Type.{u1}) (β : Type.{u1}) [_inst_1 : Nonempty.{succ u1} α] [_inst_2 : Zero.{u1} β] [_inst_3 : Infinite.{succ u1} β], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Finsupp.{u1, u1} α β _inst_2)) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} α) (Cardinal.mk.{u1} β))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_finsupp_of_infinite' Cardinal.mk_finsupp_of_infinite'ₓ'. -/
@@ -1674,7 +1734,7 @@ theorem mk_finsupp_of_infinite' (α β : Type u) [Nonempty α] [Zero β] [Infini
 
 /- warning: cardinal.mk_finsupp_nat -> Cardinal.mk_finsupp_nat is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}) [_inst_1 : Nonempty.{succ u1} α], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Finsupp.{u1, 0} α Nat Nat.hasZero)) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
+  forall (α : Type.{u1}) [_inst_1 : Nonempty.{succ u1} α], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Finsupp.{u1, 0} α Nat Nat.hasZero)) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
 but is expected to have type
   forall (α : Type.{u1}) [_inst_1 : Nonempty.{succ u1} α], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Finsupp.{u1, 0} α Nat (LinearOrderedCommMonoidWithZero.toZero.{0} Nat Nat.linearOrderedCommMonoidWithZero))) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_finsupp_nat Cardinal.mk_finsupp_natₓ'. -/
@@ -1683,7 +1743,7 @@ theorem mk_finsupp_nat (α : Type u) [Nonempty α] : (#α →₀ ℕ) = max (#α
 
 /- warning: cardinal.mk_multiset_of_nonempty -> Cardinal.mk_multiset_of_nonempty is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}) [_inst_1 : Nonempty.{succ u1} α], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Multiset.{u1} α)) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
+  forall (α : Type.{u1}) [_inst_1 : Nonempty.{succ u1} α], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Multiset.{u1} α)) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
 but is expected to have type
   forall (α : Type.{u1}) [_inst_1 : Nonempty.{succ u1} α], Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Multiset.{u1} α)) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1})
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_multiset_of_nonempty Cardinal.mk_multiset_of_nonemptyₓ'. -/
@@ -1748,7 +1808,7 @@ theorem mk_bounded_set_le_of_infinite (α : Type u) [Infinite α] (c : Cardinal)
 
 /- warning: cardinal.mk_bounded_set_le -> Cardinal.mk_bounded_set_le is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}) (c : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) t)) 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}) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1}) c)
+  forall (α : Type.{u1}) (c : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) t)) 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}) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1}) c)
 but is expected to have type
   forall (α : Type.{u1}) (c : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (Set.Elem.{u1} α t)) 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}) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} α) Cardinal.aleph0.{u1}) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_bounded_set_le Cardinal.mk_bounded_set_leₓ'. -/
@@ -1768,7 +1828,7 @@ theorem mk_bounded_set_le (α : Type u) (c : Cardinal) :
 
 /- warning: cardinal.mk_bounded_subset_le -> Cardinal.mk_bounded_subset_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (s : Set.{u1} α) (c : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) t)) 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}) (LinearOrder.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toLinearOrder.{succ u1} Cardinal.{u1} Cardinal.canonicallyLinearOrderedAddMonoid.{u1}) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) Cardinal.aleph0.{u1}) c)
+  forall {α : Type.{u1}} (s : Set.{u1} α) (c : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) t)) 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}) (LinearOrder.max.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) Cardinal.aleph0.{u1}) c)
 but is expected to have type
   forall {α : Type.{u1}} (s : Set.{u1} α) (c : Cardinal.{u1}), LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (Subtype.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.mk.{u1} (Set.Elem.{u1} α t)) 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}) (Max.max.{succ u1} Cardinal.{u1} (CanonicallyLinearOrderedAddMonoid.toMax.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyLinearOrderedAddMonoidCardinal.{u1}) (Cardinal.mk.{u1} (Set.Elem.{u1} α s)) Cardinal.aleph0.{u1}) c)
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_bounded_subset_le Cardinal.mk_bounded_subset_leₓ'. -/
@@ -1790,7 +1850,7 @@ theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
 
 /- warning: cardinal.mk_compl_of_infinite -> Cardinal.mk_compl_of_infinite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] (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)) (Cardinal.mk.{u1} α)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s))) (Cardinal.mk.{u1} α))
+  forall {α : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] (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)) (Cardinal.mk.{u1} α)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s))) (Cardinal.mk.{u1} α))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] (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)) (Cardinal.mk.{u1} α)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Set.Elem.{u1} α (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) s))) (Cardinal.mk.{u1} α))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_of_infinite Cardinal.mk_compl_of_infiniteₓ'. -/
@@ -1815,7 +1875,7 @@ theorem mk_compl_finset_of_infinite {α : Type _} [Infinite α] (s : Finset α)
 
 /- warning: cardinal.mk_compl_eq_mk_compl_infinite -> Cardinal.mk_compl_eq_mk_compl_infinite is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] {s : Set.{u1} α} {t : 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)) (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})) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) t)) (Cardinal.mk.{u1} α)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s))) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) t))))
+  forall {α : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] {s : Set.{u1} α} {t : 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)) (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})))))) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) t)) (Cardinal.mk.{u1} α)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s))) (Cardinal.mk.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) t))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : Infinite.{succ u1} α] {s : Set.{u1} α} {t : 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)) (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})) (Cardinal.mk.{u1} (Set.Elem.{u1} α t)) (Cardinal.mk.{u1} α)) -> (Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.mk.{u1} (Set.Elem.{u1} α (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) s))) (Cardinal.mk.{u1} (Set.Elem.{u1} α (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) t))))
 Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_eq_mk_compl_infinite Cardinal.mk_compl_eq_mk_compl_infiniteₓ'. -/
@@ -1903,7 +1963,7 @@ theorem extend_function_finite {α β : Type _} [Finite α] {s : Set α} (f : s
 
 /- warning: cardinal.extend_function_of_lt -> Cardinal.extend_function_of_lt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} (f : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) 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} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Cardinal.mk.{u1} α)) -> (Nonempty.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{succ u1, succ u2} α β)) -> (Exists.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{succ u1, succ u2} α β) (fun (g : Equiv.{succ u1, succ u2} α β) => forall (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s), Eq.{succ u2} β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) (fun (_x : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) f x)))
+  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} (f : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) 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} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Cardinal.mk.{u1} α)) -> (Nonempty.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{succ u1, succ u2} α β)) -> (Exists.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{succ u1, succ u2} α β) (fun (g : Equiv.{succ u1, succ u2} α β) => forall (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s), Eq.{succ u2} β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) (fun (_x : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) f x)))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} (f : Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β), (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Cardinal.mk.{u2} (Set.Elem.{u2} α s)) (Cardinal.mk.{u2} α)) -> (Nonempty.{max (succ u1) (succ u2)} (Equiv.{succ u2, succ u1} α β)) -> (Exists.{max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} α β) (fun (g : Equiv.{succ u2, succ u1} α β) => forall (x : Set.Elem.{u2} α s), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) g (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f x)))
 Case conversion may be inaccurate. Consider using '#align cardinal.extend_function_of_lt Cardinal.extend_function_of_ltₓ'. -/

bump to nightly-2023-03-11-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

a8ee822f

Diff

@@ -165,7 +165,7 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
 lean 3 declaration is
   Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.alephIdx.relIso.{u1}) Cardinal.alephIdx.{u1}
 but is expected to have type
-  Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463) (RelIso.toRelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463) Cardinal.alephIdx.relIso.{u1}))) Cardinal.alephIdx.{u1}
+  Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (RelIso.toRelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) Cardinal.alephIdx.relIso.{u1}))) Cardinal.alephIdx.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coeₓ'. -/
 @[simp]
 theorem alephIdx.relIso_coe : (alephIdx.relIso : Cardinal → Ordinal) = alephIdx :=
@@ -211,7 +211,7 @@ def aleph' : Ordinal → Cardinal :=
 lean 3 declaration is
   Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) => Ordinal.{u1} -> Cardinal.{u1}) Cardinal.Aleph'.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) => Ordinal.{u1} -> Cardinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) Cardinal.Aleph'.relIso.{u1}) Cardinal.aleph'.{u1}
 but is expected to have type
-  Eq.{succ (succ u1)} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Cardinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Cardinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1}) Ordinal.{u1} Cardinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448) (RelIso.toRelEmbedding.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448) Cardinal.Aleph'.relIso.{u1}))) Cardinal.aleph'.{u1}
+  Eq.{succ (succ u1)} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Cardinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Cardinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1}) Ordinal.{u1} Cardinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (RelIso.toRelEmbedding.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) Cardinal.Aleph'.relIso.{u1}))) Cardinal.aleph'.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coeₓ'. -/
 @[simp]
 theorem aleph'.relIso_coe : (Aleph'.relIso : Ordinal → Cardinal) = aleph' :=
@@ -433,7 +433,7 @@ theorem aleph_toNat (o : Ordinal) : (aleph o).toNat = 0 :=
 lean 3 declaration is
   forall (o : Ordinal.{u1}), Eq.{1} PartENat (coeFn.{succ (succ u1), succ (succ u1)} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) (fun (_x : AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) => Cardinal.{u1} -> PartENat) (AddMonoidHom.hasCoeToFun.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) Cardinal.toPartENat.{u1} (Cardinal.aleph.{u1} o)) (Top.top.{0} PartENat PartENat.hasTop)
 but is expected to have type
-  forall (o : Ordinal.{u1}), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Cardinal.{u1}) => PartENat) (Cardinal.aleph.{u1} o)) (FunLike.coe.{succ (succ u1), succ (succ u1), 1} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Cardinal.{u1}) => PartENat) _x) (AddHomClass.toFunLike.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddZeroClass.toAdd.{succ u1} Cardinal.{u1} (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1}))))))))) (AddZeroClass.toAdd.{0} PartENat (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) (AddMonoidHomClass.toAddHomClass.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat))) (AddMonoidHom.addMonoidHomClass.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))))) Cardinal.toPartENat.{u1} (Cardinal.aleph.{u1} o)) (Top.top.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Cardinal.{u1}) => PartENat) (Cardinal.aleph.{u1} o)) PartENat.instTopPartENat)
+  forall (o : Ordinal.{u1}), Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) (Cardinal.aleph.{u1} o)) (FunLike.coe.{succ (succ u1), succ (succ u1), 1} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) _x) (AddHomClass.toFunLike.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddZeroClass.toAdd.{succ u1} Cardinal.{u1} (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1}))))))))) (AddZeroClass.toAdd.{0} PartENat (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) (AddMonoidHomClass.toAddHomClass.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat))) (AddMonoidHom.addMonoidHomClass.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))))) Cardinal.toPartENat.{u1} (Cardinal.aleph.{u1} o)) (Top.top.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) (Cardinal.aleph.{u1} o)) PartENat.instTopPartENat)
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_to_part_enat Cardinal.aleph_toPartENatₓ'. -/
 @[simp]
 theorem aleph_toPartENat (o : Ordinal) : (aleph o).toPartENat = ⊤ :=
@@ -1877,7 +1877,7 @@ theorem mk_compl_eq_mk_compl_finite_same {α : Type _} [Finite α] {s t : Set α
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} (f : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β), (Nonempty.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s)) (coeSort.{succ u2, succ (succ u2)} (Set.{u2} β) Type.{u2} (Set.hasCoeToSort.{u2} β) (HasCompl.compl.{u2} (Set.{u2} β) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} β) (Set.booleanAlgebra.{u2} β)) (Set.range.{u2, succ u1} β (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) (fun (_x : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) f)))))) -> (Exists.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{succ u1, succ u2} α β) (fun (g : Equiv.{succ u1, succ u2} α β) => forall (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s), Eq.{succ u2} β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) (fun (_x : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) f x)))
 but is expected to have type
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+  forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} (f : Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β), (Nonempty.{max (succ u1) (succ u2)} (Equiv.{succ u2, succ u1} (Set.Elem.{u2} α (HasCompl.compl.{u2} (Set.{u2} α) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} α) (Set.instBooleanAlgebraSet.{u2} α)) s)) (Set.Elem.{u1} β (HasCompl.compl.{u1} (Set.{u1} β) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} β) (Set.instBooleanAlgebraSet.{u1} β)) (Set.range.{u1, succ u2} β (Set.Elem.{u2} α s) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f)))))) -> (Exists.{max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} α β) (fun (g : Equiv.{succ u2, succ u1} α β) => forall (x : Set.Elem.{u2} α s), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) g (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f x)))
 Case conversion may be inaccurate. Consider using '#align cardinal.extend_function Cardinal.extend_functionₓ'. -/
 theorem extend_function {α β : Type _} {s : Set α} (f : s ↪ β)
     (h : Nonempty ((sᶜ : Set α) ≃ (range fᶜ : Set β))) : ∃ g : α ≃ β, ∀ x : s, g x = f x :=
@@ -1905,7 +1905,7 @@ theorem extend_function_finite {α β : Type _} [Finite α] {s : Set α} (f : s
 lean 3 declaration is
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 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} (f : Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β), (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Cardinal.mk.{u2} (Set.Elem.{u2} α s)) (Cardinal.mk.{u2} α)) -> (Nonempty.{max (succ u1) (succ u2)} (Equiv.{succ u2, succ u1} α β)) -> (Exists.{max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} α β) (fun (g : Equiv.{succ u2, succ u1} α β) => forall (x : Set.Elem.{u2} α s), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => β) (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) g (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f x)))
+  forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} (f : Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β), (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Cardinal.mk.{u2} (Set.Elem.{u2} α s)) (Cardinal.mk.{u2} α)) -> (Nonempty.{max (succ u1) (succ u2)} (Equiv.{succ u2, succ u1} α β)) -> (Exists.{max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} α β) (fun (g : Equiv.{succ u2, succ u1} α β) => forall (x : Set.Elem.{u2} α s), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) g (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f x)))
 Case conversion may be inaccurate. Consider using '#align cardinal.extend_function_of_lt Cardinal.extend_function_of_ltₓ'. -/
 theorem extend_function_of_lt {α β : Type _} {s : Set α} (f : s ↪ β) (hs : (#s) < (#α))
     (h : Nonempty (α ≃ β)) : ∃ g : α ≃ β, ∀ x : s, g x = f x :=

bump to nightly-2023-03-11-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

cd44fb92

Diff

@@ -1029,7 +1029,7 @@ theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧
         exact fun hb => ne_of_gt (hb.trans_le (le_mul_left this)) h
       · rintro rfl
         apply this
-        rw [mul_zero] at h
+        rw [MulZeroClass.mul_zero] at h
         exact h.symm
     right
     by_cases h2a : a = 0
@@ -1037,7 +1037,7 @@ theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧
     have hb : b ≠ 0 := by
       rintro rfl
       apply h2a
-      rw [mul_zero] at h
+      rw [MulZeroClass.mul_zero] at h
       exact h.symm
     left
     rw [← h, mul_lt_aleph_0_iff, lt_aleph_0, lt_aleph_0] at ha

bump to nightly-2023-03-03-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

7fe4dd24

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Floris van Doorn
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.ordinal
-! leanprover-community/mathlib commit ef7acf407d265ad4081c8998687e994fa80ba70c
+! leanprover-community/mathlib commit 8da9e30545433fdd8fe55a0d3da208e5d9263f03
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -133,7 +133,7 @@ theorem alephIdx_le {a b} : alephIdx a ≤ alephIdx b ↔ a ≤ b := by
 
 #print Cardinal.alephIdx.init /-
 theorem alephIdx.init {a b} : b < alephIdx a → ∃ c, alephIdx c = b :=
-  alephIdx.initialSeg.dropLast _ _
+  alephIdx.initialSeg.dropLast
 #align cardinal.aleph_idx.init Cardinal.alephIdx.init
 -/

ef7acf40

bump to nightly-2023-03-02-23

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

ec1a9cbb

Diff

@@ -165,7 +165,7 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
 lean 3 declaration is
   Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.alephIdx.relIso.{u1}) Cardinal.alephIdx.{u1}
 but is expected to have type
-  Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (RelIso.toRelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) Cardinal.alephIdx.relIso.{u1}))) Cardinal.alephIdx.{u1}
+  Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1}) Cardinal.{u1} Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Cardinal.{u1} Ordinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463) (RelIso.toRelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463) Cardinal.alephIdx.relIso.{u1}))) Cardinal.alephIdx.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coeₓ'. -/
 @[simp]
 theorem alephIdx.relIso_coe : (alephIdx.relIso : Cardinal → Ordinal) = alephIdx :=
@@ -211,7 +211,7 @@ def aleph' : Ordinal → Cardinal :=
 lean 3 declaration is
   Eq.{succ (succ u1)} ((fun (_x : RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) => Ordinal.{u1} -> Cardinal.{u1}) Cardinal.Aleph'.relIso.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) (fun (_x : RelIso.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) => Ordinal.{u1} -> Cardinal.{u1}) (RelIso.hasCoeToFun.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})))) Cardinal.Aleph'.relIso.{u1}) Cardinal.aleph'.{u1}
 but is expected to have type
-  Eq.{succ (succ u1)} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Cardinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Cardinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1}) Ordinal.{u1} Cardinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) (RelIso.toRelEmbedding.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.465) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.450) Cardinal.Aleph'.relIso.{u1}))) Cardinal.aleph'.{u1}
+  Eq.{succ (succ u1)} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Cardinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Cardinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (Function.Embedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1}) Ordinal.{u1} Cardinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (succ u1)} Ordinal.{u1} Cardinal.{u1})) (RelEmbedding.toEmbedding.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448) (RelIso.toRelEmbedding.{succ u1, succ u1} Ordinal.{u1} Cardinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.461 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.463) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.446 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.448) Cardinal.Aleph'.relIso.{u1}))) Cardinal.aleph'.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coeₓ'. -/
 @[simp]
 theorem aleph'.relIso_coe : (Aleph'.relIso : Ordinal → Cardinal) = aleph' :=

ef7acf40

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -1556,7 +1556,7 @@ theorem mk_list_eq_mk (α : Type u) [Infinite α] : (#List α) = (#α) :=
     le_antisymm ⟨⟨fun x => [x], fun x y H => (List.cons.inj H).1⟩⟩ <|
       calc
         (#List α) = sum fun n : ℕ => (#α) ^ (n : Cardinal.{u}) := mk_list_eq_sum_pow α
-        _ ≤ sum fun n : ℕ => #α := sum_le_sum _ _ fun n => pow_le H1 <| nat_lt_aleph0 n
+        _ ≤ sum fun n : ℕ => #α := (sum_le_sum _ _ fun n => pow_le H1 <| nat_lt_aleph0 n)
         _ = (#α) := by simp [H1]
         
 #align cardinal.mk_list_eq_mk Cardinal.mk_list_eq_mk
@@ -1623,7 +1623,7 @@ theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Z
   ·
     calc
       (#α →₀ β) ≤ (#Finset (α × β)) := mk_le_of_injective (Finsupp.graph_injective α β)
-      _ = (#α × β) := mk_finset_of_infinite _
+      _ = (#α × β) := (mk_finset_of_infinite _)
       _ = max (lift.{v} (#α)) (lift.{u} (#β)) := by
         rw [mk_prod, mul_eq_max_of_aleph_0_le_left] <;> simp

ef7acf40

bump to nightly-2023-02-25-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

39ef98db

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Floris van Doorn
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.ordinal
-! leanprover-community/mathlib commit 40494fe75ecbd6d2ec61711baa630cf0a7b7d064
+! leanprover-community/mathlib commit ef7acf407d265ad4081c8998687e994fa80ba70c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Tactic.Linarith.Default
 /-!
 # Cardinals and ordinals
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Relationships between cardinals and ordinals, properties of cardinals that are proved
 using ordinals.

bump to nightly-2023-02-23-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

6ff36814

Diff

@@ -60,6 +60,7 @@ section UsingOrdinals
 
 open Ordinal
 
+#print Cardinal.ord_isLimit /-
 theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
   by
   refine' ⟨fun h => aleph_0_ne_zero _, fun a => lt_imp_lt_of_le_imp_le fun h => _⟩
@@ -72,10 +73,12 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
     · rw [ord_aleph_0]
       exact omega_is_limit
 #align cardinal.ord_is_limit Cardinal.ord_isLimit
+-/
 
 /-! ### Aleph cardinals -/
 
 
+#print Cardinal.alephIdx.initialSeg /-
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ω = ω`,
@@ -84,38 +87,54 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit :=
   i.e., it is order preserving and its range is an initial segment of the ordinals.
   For the basic function version, see `aleph_idx`.
   For an upgraded version stating that the range is everything, see `aleph_idx.rel_iso`. -/
-def AlephIdx.initialSeg : @InitialSeg Cardinal Ordinal (· < ·) (· < ·) :=
+def alephIdx.initialSeg : @InitialSeg Cardinal Ordinal (· < ·) (· < ·) :=
   @RelEmbedding.collapse Cardinal Ordinal (· < ·) (· < ·) _ Cardinal.ord.orderEmbedding.ltEmbedding
-#align cardinal.aleph_idx.initial_seg Cardinal.AlephIdx.initialSeg
+#align cardinal.aleph_idx.initial_seg Cardinal.alephIdx.initialSeg
+-/
 
+#print Cardinal.alephIdx /-
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ω = ω`,
   `aleph_idx ℵ₁ = ω + 1` and so on.)
   For an upgraded version stating that the range is everything, see `aleph_idx.rel_iso`. -/
 def alephIdx : Cardinal → Ordinal :=
-  AlephIdx.initialSeg
+  alephIdx.initialSeg
 #align cardinal.aleph_idx Cardinal.alephIdx
+-/
 
+/- warning: cardinal.aleph_idx.initial_seg_coe -> Cardinal.alephIdx.initialSeg_coe is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} ((fun (_x : InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.alephIdx.initialSeg.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (FunLike.hasCoeToFun.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => Ordinal.{u1}) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.{u1} Ordinal.{u1} (InitialSeg.embeddingLike.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}))) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))))) Cardinal.alephIdx.initialSeg.{u1}) Cardinal.alephIdx.{u1}
+but is expected to have type
+  Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249)) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Cardinal.{u1}) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ (succ u1), succ (succ u1)} (InitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249)) Cardinal.{u1} Ordinal.{u1} (InitialSeg.instEmbeddingLikeInitialSeg.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 : Cardinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234 : Cardinal.{u1}) => LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.232 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.234) (fun (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249 : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.247 x._@.Mathlib.SetTheory.Cardinal.Ordinal._hyg.249))) Cardinal.alephIdx.initialSeg.{u1}) Cardinal.alephIdx.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_idx.initial_seg_coe Cardinal.alephIdx.initialSeg_coeₓ'. -/
 @[simp]
-theorem alephIdx.initialSeg_coe : (AlephIdx.initialSeg : Cardinal → Ordinal) = alephIdx :=
+theorem alephIdx.initialSeg_coe : (alephIdx.initialSeg : Cardinal → Ordinal) = alephIdx :=
   rfl
 #align cardinal.aleph_idx.initial_seg_coe Cardinal.alephIdx.initialSeg_coe
 
+#print Cardinal.alephIdx_lt /-
 @[simp]
 theorem alephIdx_lt {a b} : alephIdx a < alephIdx b ↔ a < b :=
-  AlephIdx.initialSeg.toRelEmbedding.map_rel_iff
+  alephIdx.initialSeg.toRelEmbedding.map_rel_iff
 #align cardinal.aleph_idx_lt Cardinal.alephIdx_lt
+-/
 
+#print Cardinal.alephIdx_le /-
 @[simp]
 theorem alephIdx_le {a b} : alephIdx a ≤ alephIdx b ↔ a ≤ b := by
   rw [← not_lt, ← not_lt, aleph_idx_lt]
 #align cardinal.aleph_idx_le Cardinal.alephIdx_le
+-/
 
+#print Cardinal.alephIdx.init /-
 theorem alephIdx.init {a b} : b < alephIdx a → ∃ c, alephIdx c = b :=
-  AlephIdx.initialSeg.dropLast _ _
+  alephIdx.initialSeg.dropLast _ _
 #align cardinal.aleph_idx.init Cardinal.alephIdx.init
+-/
 
+#print Cardinal.alephIdx.relIso /-
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
   finite stages. So `aleph_idx n = n`, `aleph_idx ℵ₀ = ω`,
@@ -124,8 +143,8 @@ theorem alephIdx.init {a b} : b < alephIdx a → ∃ c, alephIdx c = b :=
   between cardinals and ordinals.
   For the basic function version, see `aleph_idx`. -/
 def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
-  @RelIso.ofSurjective Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) AlephIdx.initialSeg.{u} <|
-    (InitialSeg.eq_or_principal AlephIdx.initialSeg.{u}).resolve_right fun ⟨o, e⟩ =>
+  @RelIso.ofSurjective Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) alephIdx.initialSeg.{u} <|
+    (InitialSeg.eq_or_principal alephIdx.initialSeg.{u}).resolve_right fun ⟨o, e⟩ =>
       by
       have : ∀ c, aleph_idx c < o := fun c => (e _).2 ⟨_, rfl⟩
       refine' Ordinal.inductionOn o _ this; intro α r _ h
@@ -137,22 +156,34 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
           (Cardinal.bddAbove_range.{u, u} fun a : α => inv_fun aleph_idx (Ordinal.typein r a))
           (Ordinal.enum r _ (h (succ s)))
 #align cardinal.aleph_idx.rel_iso Cardinal.alephIdx.relIso
+-/
 
+/- warning: cardinal.aleph_idx.rel_iso_coe -> Cardinal.alephIdx.relIso_coe is a dubious translation:
+lean 3 declaration is
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 @[simp]
 theorem alephIdx.relIso_coe : (alephIdx.relIso : Cardinal → Ordinal) = alephIdx :=
   rfl
 #align cardinal.aleph_idx.rel_iso_coe Cardinal.alephIdx.relIso_coe
 
+#print Cardinal.type_cardinal /-
 @[simp]
 theorem type_cardinal : @type Cardinal (· < ·) _ = Ordinal.univ.{u, u + 1} := by
   rw [Ordinal.univ_id] <;> exact Quotient.sound ⟨aleph_idx.rel_iso⟩
 #align cardinal.type_cardinal Cardinal.type_cardinal
+-/
 
+#print Cardinal.mk_cardinal /-
 @[simp]
 theorem mk_cardinal : (#Cardinal) = univ.{u, u + 1} := by
   simpa only [card_type, card_univ] using congr_arg card type_cardinal
 #align cardinal.mk_cardinal Cardinal.mk_cardinal
+-/
 
+#print Cardinal.Aleph'.relIso /-
 /-- The `aleph'` function gives the cardinals listed by their ordinal
   index, and is the inverse of `aleph_idx`.
   `aleph' n = n`, `aleph' ω = ω`, `aleph' (ω + 1) = succ ℵ₀`, etc.
@@ -162,46 +193,71 @@ theorem mk_cardinal : (#Cardinal) = univ.{u, u + 1} := by
 def Aleph'.relIso :=
   Cardinal.alephIdx.relIso.symm
 #align cardinal.aleph'.rel_iso Cardinal.Aleph'.relIso
+-/
 
+#print Cardinal.aleph' /-
 /-- The `aleph'` function gives the cardinals listed by their ordinal
   index, and is the inverse of `aleph_idx`.
   `aleph' n = n`, `aleph' ω = ω`, `aleph' (ω + 1) = succ ℵ₀`, etc. -/
 def aleph' : Ordinal → Cardinal :=
   Aleph'.relIso
 #align cardinal.aleph' Cardinal.aleph'
+-/
 
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 @[simp]
 theorem aleph'.relIso_coe : (Aleph'.relIso : Ordinal → Cardinal) = aleph' :=
   rfl
 #align cardinal.aleph'.rel_iso_coe Cardinal.aleph'.relIso_coe
 
+#print Cardinal.aleph'_lt /-
 @[simp]
 theorem aleph'_lt {o₁ o₂ : Ordinal} : aleph' o₁ < aleph' o₂ ↔ o₁ < o₂ :=
   Aleph'.relIso.map_rel_iff
 #align cardinal.aleph'_lt Cardinal.aleph'_lt
+-/
 
+#print Cardinal.aleph'_le /-
 @[simp]
 theorem aleph'_le {o₁ o₂ : Ordinal} : aleph' o₁ ≤ aleph' o₂ ↔ o₁ ≤ o₂ :=
   le_iff_le_iff_lt_iff_lt.2 aleph'_lt
 #align cardinal.aleph'_le Cardinal.aleph'_le
+-/
 
+#print Cardinal.aleph'_alephIdx /-
 @[simp]
 theorem aleph'_alephIdx (c : Cardinal) : aleph' c.alephIdx = c :=
   Cardinal.alephIdx.relIso.toEquiv.symm_apply_apply c
 #align cardinal.aleph'_aleph_idx Cardinal.aleph'_alephIdx
+-/
 
+#print Cardinal.alephIdx_aleph' /-
 @[simp]
 theorem alephIdx_aleph' (o : Ordinal) : (aleph' o).alephIdx = o :=
   Cardinal.alephIdx.relIso.toEquiv.apply_symm_apply o
 #align cardinal.aleph_idx_aleph' Cardinal.alephIdx_aleph'
+-/
 
+#print Cardinal.aleph'_zero /-
 @[simp]
 theorem aleph'_zero : aleph' 0 = 0 :=
   by
   rw [← nonpos_iff_eq_zero, ← aleph'_aleph_idx 0, aleph'_le]
   apply Ordinal.zero_le
 #align cardinal.aleph'_zero Cardinal.aleph'_zero
+-/
 
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 @[simp]
 theorem aleph'_succ {o : Ordinal} : aleph' (succ o) = succ (aleph' o) :=
   by
@@ -210,12 +266,19 @@ theorem aleph'_succ {o : Ordinal} : aleph' (succ o) = succ (aleph' o) :=
   apply lt_succ
 #align cardinal.aleph'_succ Cardinal.aleph'_succ
 
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 @[simp]
 theorem aleph'_nat : ∀ n : ℕ, aleph' n = n
   | 0 => aleph'_zero
   | n + 1 => show aleph' (succ n) = n.succ by rw [aleph'_succ, aleph'_nat, nat_succ]
 #align cardinal.aleph'_nat Cardinal.aleph'_nat
 
+#print Cardinal.aleph'_le_of_limit /-
 theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
     aleph' o ≤ c ↔ ∀ o' < o, aleph' o' ≤ c :=
   ⟨fun h o' h' => (aleph'_le.2 <| h'.le).trans h, fun h =>
@@ -225,7 +288,14 @@ theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
     rw [← aleph'_le, aleph'_aleph_idx]
     exact h _ h'⟩
 #align cardinal.aleph'_le_of_limit Cardinal.aleph'_le_of_limit
+-/
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.aleph'_limit Cardinal.aleph'_limitₓ'. -/
 theorem aleph'_limit {o : Ordinal} (ho : IsLimit o) : aleph' o = ⨆ a : Iio o, aleph' a :=
   by
   refine' le_antisymm _ (csupᵢ_le' fun i => aleph'_le.2 (le_of_lt i.2))
@@ -233,6 +303,7 @@ theorem aleph'_limit {o : Ordinal} (ho : IsLimit o) : aleph' o = ⨆ a : Iio o,
   exact fun a ha => le_csupᵢ (bdd_above_of_small _) (⟨a, ha⟩ : Iio o)
 #align cardinal.aleph'_limit Cardinal.aleph'_limit
 
+#print Cardinal.aleph'_omega /-
 @[simp]
 theorem aleph'_omega : aleph' ω = ℵ₀ :=
   eq_of_forall_ge_iff fun c =>
@@ -240,30 +311,45 @@ theorem aleph'_omega : aleph' ω = ℵ₀ :=
     simp only [aleph'_le_of_limit omega_is_limit, lt_omega, exists_imp, aleph_0_le]
     exact forall_swap.trans (forall_congr' fun n => by simp only [forall_eq, aleph'_nat])
 #align cardinal.aleph'_omega Cardinal.aleph'_omega
+-/
 
+#print Cardinal.aleph'Equiv /-
 /-- `aleph'` and `aleph_idx` form an equivalence between `ordinal` and `cardinal` -/
 @[simp]
 def aleph'Equiv : Ordinal ≃ Cardinal :=
   ⟨aleph', alephIdx, alephIdx_aleph', aleph'_alephIdx⟩
 #align cardinal.aleph'_equiv Cardinal.aleph'Equiv
+-/
 
+#print Cardinal.aleph /-
 /-- The `aleph` function gives the infinite cardinals listed by their
   ordinal index. `aleph 0 = ℵ₀`, `aleph 1 = succ ℵ₀` is the first
   uncountable cardinal, and so on. -/
 def aleph (o : Ordinal) : Cardinal :=
   aleph' (ω + o)
 #align cardinal.aleph Cardinal.aleph
+-/
 
+#print Cardinal.aleph_lt /-
 @[simp]
 theorem aleph_lt {o₁ o₂ : Ordinal} : aleph o₁ < aleph o₂ ↔ o₁ < o₂ :=
   aleph'_lt.trans (add_lt_add_iff_left _)
 #align cardinal.aleph_lt Cardinal.aleph_lt
+-/
 
+#print Cardinal.aleph_le /-
 @[simp]
 theorem aleph_le {o₁ o₂ : Ordinal} : aleph o₁ ≤ aleph o₂ ↔ o₁ ≤ o₂ :=
   le_iff_le_iff_lt_iff_lt.2 aleph_lt
 #align cardinal.aleph_le Cardinal.aleph_le
+-/
 
+/- warning: cardinal.max_aleph_eq -> Cardinal.max_aleph_eq is a dubious translation:
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 @[simp]
 theorem max_aleph_eq (o₁ o₂ : Ordinal) : max (aleph o₁) (aleph o₂) = aleph (max o₁ o₂) :=
   by
@@ -272,15 +358,29 @@ theorem max_aleph_eq (o₁ o₂ : Ordinal) : max (aleph o₁) (aleph o₂) = ale
   · rw [max_eq_left h, max_eq_left (aleph_le.1 h)]
 #align cardinal.max_aleph_eq Cardinal.max_aleph_eq
 
+/- warning: cardinal.aleph_succ -> Cardinal.aleph_succ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_succ Cardinal.aleph_succₓ'. -/
 @[simp]
 theorem aleph_succ {o : Ordinal} : aleph (succ o) = succ (aleph o) := by
   rw [aleph, add_succ, aleph'_succ, aleph]
 #align cardinal.aleph_succ Cardinal.aleph_succ
 
+#print Cardinal.aleph_zero /-
 @[simp]
 theorem aleph_zero : aleph 0 = ℵ₀ := by rw [aleph, add_zero, aleph'_omega]
 #align cardinal.aleph_zero Cardinal.aleph_zero
+-/
 
+/- warning: cardinal.aleph_limit -> Cardinal.aleph_limit is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_limit Cardinal.aleph_limitₓ'. -/
 theorem aleph_limit {o : Ordinal} (ho : IsLimit o) : aleph o = ⨆ a : Iio o, aleph a :=
   by
   apply le_antisymm _ (csupᵢ_le' _)
@@ -295,45 +395,66 @@ theorem aleph_limit {o : Ordinal} (ho : IsLimit o) : aleph o = ⨆ a : Iio o, al
   · exact fun i => aleph_le.2 (le_of_lt i.2)
 #align cardinal.aleph_limit Cardinal.aleph_limit
 
+#print Cardinal.aleph0_le_aleph' /-
 theorem aleph0_le_aleph' {o : Ordinal} : ℵ₀ ≤ aleph' o ↔ ω ≤ o := by rw [← aleph'_omega, aleph'_le]
 #align cardinal.aleph_0_le_aleph' Cardinal.aleph0_le_aleph'
+-/
 
+#print Cardinal.aleph0_le_aleph /-
 theorem aleph0_le_aleph (o : Ordinal) : ℵ₀ ≤ aleph o :=
   by
   rw [aleph, aleph_0_le_aleph']
   apply Ordinal.le_add_right
 #align cardinal.aleph_0_le_aleph Cardinal.aleph0_le_aleph
+-/
 
+#print Cardinal.aleph'_pos /-
 theorem aleph'_pos {o : Ordinal} (ho : 0 < o) : 0 < aleph' o := by rwa [← aleph'_zero, aleph'_lt]
 #align cardinal.aleph'_pos Cardinal.aleph'_pos
+-/
 
+#print Cardinal.aleph_pos /-
 theorem aleph_pos (o : Ordinal) : 0 < aleph o :=
   aleph0_pos.trans_le (aleph0_le_aleph o)
 #align cardinal.aleph_pos Cardinal.aleph_pos
+-/
 
+#print Cardinal.aleph_toNat /-
 @[simp]
 theorem aleph_toNat (o : Ordinal) : (aleph o).toNat = 0 :=
   toNat_apply_of_aleph0_le <| aleph0_le_aleph o
 #align cardinal.aleph_to_nat Cardinal.aleph_toNat
+-/
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_to_part_enat Cardinal.aleph_toPartENatₓ'. -/
 @[simp]
 theorem aleph_toPartENat (o : Ordinal) : (aleph o).toPartENat = ⊤ :=
   toPartENat_apply_of_aleph0_le <| aleph0_le_aleph o
 #align cardinal.aleph_to_part_enat Cardinal.aleph_toPartENat
 
+#print Cardinal.nonempty_out_aleph /-
 instance nonempty_out_aleph (o : Ordinal) : Nonempty (aleph o).ord.out.α :=
   by
   rw [out_nonempty_iff_ne_zero, ← ord_zero]
   exact fun h => (ord_injective h).not_gt (aleph_pos o)
 #align cardinal.nonempty_out_aleph Cardinal.nonempty_out_aleph
+-/
 
+#print Cardinal.ord_aleph_isLimit /-
 theorem ord_aleph_isLimit (o : Ordinal) : IsLimit (aleph o).ord :=
   ord_isLimit <| aleph0_le_aleph _
 #align cardinal.ord_aleph_is_limit Cardinal.ord_aleph_isLimit
+-/
 
 instance (o : Ordinal) : NoMaxOrder (aleph o).ord.out.α :=
   out_no_max_of_succ_lt (ord_aleph_isLimit o).2
 
+#print Cardinal.exists_aleph /-
 theorem exists_aleph {c : Cardinal} : ℵ₀ ≤ c ↔ ∃ o, c = aleph o :=
   ⟨fun h =>
     ⟨alephIdx c - ω, by
@@ -341,29 +462,53 @@ theorem exists_aleph {c : Cardinal} : ℵ₀ ≤ c ↔ ∃ o, c = aleph o :=
       rwa [← aleph_0_le_aleph', aleph'_aleph_idx]⟩,
     fun ⟨o, e⟩ => e.symm ▸ aleph0_le_aleph _⟩
 #align cardinal.exists_aleph Cardinal.exists_aleph
+-/
 
+#print Cardinal.aleph'_isNormal /-
 theorem aleph'_isNormal : IsNormal (ord ∘ aleph') :=
   ⟨fun o => ord_lt_ord.2 <| aleph'_lt.2 <| lt_succ o, fun o l a => by
     simp only [ord_le, aleph'_le_of_limit l]⟩
 #align cardinal.aleph'_is_normal Cardinal.aleph'_isNormal
+-/
 
+#print Cardinal.aleph_isNormal /-
 theorem aleph_isNormal : IsNormal (ord ∘ aleph) :=
   aleph'_isNormal.trans <| add_isNormal ω
 #align cardinal.aleph_is_normal Cardinal.aleph_isNormal
+-/
 
+/- warning: cardinal.succ_aleph_0 -> Cardinal.succ_aleph0 is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.succ_aleph_0 Cardinal.succ_aleph0ₓ'. -/
 theorem succ_aleph0 : succ ℵ₀ = aleph 1 := by rw [← aleph_zero, ← aleph_succ, Ordinal.succ_zero]
 #align cardinal.succ_aleph_0 Cardinal.succ_aleph0
 
+/- warning: cardinal.aleph_0_lt_aleph_one -> Cardinal.aleph0_lt_aleph_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_0_lt_aleph_one Cardinal.aleph0_lt_aleph_oneₓ'. -/
 theorem aleph0_lt_aleph_one : ℵ₀ < aleph 1 :=
   by
   rw [← succ_aleph_0]
   apply lt_succ
 #align cardinal.aleph_0_lt_aleph_one Cardinal.aleph0_lt_aleph_one
 
+/- warning: cardinal.countable_iff_lt_aleph_one -> Cardinal.countable_iff_lt_aleph_one is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.countable_iff_lt_aleph_one Cardinal.countable_iff_lt_aleph_oneₓ'. -/
 theorem countable_iff_lt_aleph_one {α : Type _} (s : Set α) : s.Countable ↔ (#s) < aleph 1 := by
   rw [← succ_aleph_0, lt_succ_iff, le_aleph_0_iff_set_countable]
 #align cardinal.countable_iff_lt_aleph_one Cardinal.countable_iff_lt_aleph_one
 
+#print Cardinal.ord_card_unbounded /-
 /-- Ordinals that are cardinals are unbounded. -/
 theorem ord_card_unbounded : Unbounded (· < ·) { b : Ordinal | b.card.ord = b } :=
   unbounded_lt_iff.2 fun a =>
@@ -372,11 +517,15 @@ theorem ord_card_unbounded : Unbounded (· < ·) { b : Ordinal | b.card.ord = b
         dsimp
         rw [card_ord], (lt_ord_succ_card a).le⟩⟩
 #align cardinal.ord_card_unbounded Cardinal.ord_card_unbounded
+-/
 
+#print Cardinal.eq_aleph'_of_eq_card_ord /-
 theorem eq_aleph'_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) : ∃ a, (aleph' a).ord = o :=
   ⟨Cardinal.alephIdx.relIso o.card, by simpa using ho⟩
 #align cardinal.eq_aleph'_of_eq_card_ord Cardinal.eq_aleph'_of_eq_card_ord
+-/
 
+#print Cardinal.ord_aleph'_eq_enum_card /-
 /-- `ord ∘ aleph'` enumerates the ordinals that are cardinals. -/
 theorem ord_aleph'_eq_enum_card : ord ∘ aleph' = enumOrd { b : Ordinal | b.card.ord = b } :=
   by
@@ -387,12 +536,16 @@ theorem ord_aleph'_eq_enum_card : ord ∘ aleph' = enumOrd { b : Ordinal | b.car
         dsimp
         rw [card_ord], fun b hb => eq_aleph'_of_eq_card_ord hb⟩⟩
 #align cardinal.ord_aleph'_eq_enum_card Cardinal.ord_aleph'_eq_enum_card
+-/
 
+#print Cardinal.ord_card_unbounded' /-
 /-- Infinite ordinals that are cardinals are unbounded. -/
 theorem ord_card_unbounded' : Unbounded (· < ·) { b : Ordinal | b.card.ord = b ∧ ω ≤ b } :=
   (unbounded_lt_inter_le ω).2 ord_card_unbounded
 #align cardinal.ord_card_unbounded' Cardinal.ord_card_unbounded'
+-/
 
+#print Cardinal.eq_aleph_of_eq_card_ord /-
 theorem eq_aleph_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) (ho' : ω ≤ o) :
     ∃ a, (aleph a).ord = o :=
   by
@@ -402,7 +555,9 @@ theorem eq_aleph_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) (ho' : ω 
   rwa [Ordinal.add_sub_cancel_of_le]
   rwa [← aleph_0_le_aleph', ← ord_le_ord, ha, ord_aleph_0]
 #align cardinal.eq_aleph_of_eq_card_ord Cardinal.eq_aleph_of_eq_card_ord
+-/
 
+#print Cardinal.ord_aleph_eq_enum_card /-
 /-- `ord ∘ aleph` enumerates the infinite ordinals that are cardinals. -/
 theorem ord_aleph_eq_enum_card : ord ∘ aleph = enumOrd { b : Ordinal | b.card.ord = b ∧ ω ≤ b } :=
   by
@@ -414,10 +569,12 @@ theorem ord_aleph_eq_enum_card : ord ∘ aleph = enumOrd { b : Ordinal | b.card.
   · rw [← ord_aleph_0, ord_le_ord]
     exact aleph_0_le_aleph _
 #align cardinal.ord_aleph_eq_enum_card Cardinal.ord_aleph_eq_enum_card
+-/
 
 /-! ### Beth cardinals -/
 
 
+#print Cardinal.beth /-
 /-- Beth numbers are defined so that `beth 0 = ℵ₀`, `beth (succ o) = 2 ^ (beth o)`, and when `o` is
 a limit ordinal, `beth o` is the supremum of `beth o'` for `o' < o`.
 
@@ -426,21 +583,37 @@ every `o`. -/
 def beth (o : Ordinal.{u}) : Cardinal.{u} :=
   limitRecOn o aleph0 (fun _ x => 2 ^ x) fun a ha IH => ⨆ b : Iio a, IH b.1 b.2
 #align cardinal.beth Cardinal.beth
+-/
 
+#print Cardinal.beth_zero /-
 @[simp]
 theorem beth_zero : beth 0 = aleph0 :=
   limitRecOn_zero _ _ _
 #align cardinal.beth_zero Cardinal.beth_zero
+-/
 
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 @[simp]
 theorem beth_succ (o : Ordinal) : beth (succ o) = 2 ^ beth o :=
   limitRecOn_succ _ _ _ _
 #align cardinal.beth_succ Cardinal.beth_succ
 
+/- warning: cardinal.beth_limit -> Cardinal.beth_limit is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.beth_limit Cardinal.beth_limitₓ'. -/
 theorem beth_limit {o : Ordinal} : IsLimit o → beth o = ⨆ a : Iio o, beth a :=
   limitRecOn_limit _ _ _ _
 #align cardinal.beth_limit Cardinal.beth_limit
 
+#print Cardinal.beth_strictMono /-
 theorem beth_strictMono : StrictMono beth := by
   intro a b
   induction' b using Ordinal.induction with b IH generalizing a
@@ -457,21 +630,29 @@ theorem beth_strictMono : StrictMono beth := by
     rw [beth_limit hb, ← beth_succ]
     exact le_csupᵢ (bdd_above_of_small _) (⟨_, hb.succ_lt h⟩ : Iio b)
 #align cardinal.beth_strict_mono Cardinal.beth_strictMono
+-/
 
+#print Cardinal.beth_mono /-
 theorem beth_mono : Monotone beth :=
   beth_strictMono.Monotone
 #align cardinal.beth_mono Cardinal.beth_mono
+-/
 
+#print Cardinal.beth_lt /-
 @[simp]
 theorem beth_lt {o₁ o₂ : Ordinal} : beth o₁ < beth o₂ ↔ o₁ < o₂ :=
   beth_strictMono.lt_iff_lt
 #align cardinal.beth_lt Cardinal.beth_lt
+-/
 
+#print Cardinal.beth_le /-
 @[simp]
 theorem beth_le {o₁ o₂ : Ordinal} : beth o₁ ≤ beth o₂ ↔ o₁ ≤ o₂ :=
   beth_strictMono.le_iff_le
 #align cardinal.beth_le Cardinal.beth_le
+-/
 
+#print Cardinal.aleph_le_beth /-
 theorem aleph_le_beth (o : Ordinal) : aleph o ≤ beth o :=
   by
   apply limit_rec_on o
@@ -483,19 +664,27 @@ theorem aleph_le_beth (o : Ordinal) : aleph o ≤ beth o :=
     rw [aleph_limit ho, beth_limit ho]
     exact csupᵢ_mono (bdd_above_of_small _) fun x => IH x.1 x.2
 #align cardinal.aleph_le_beth Cardinal.aleph_le_beth
+-/
 
+#print Cardinal.aleph0_le_beth /-
 theorem aleph0_le_beth (o : Ordinal) : ℵ₀ ≤ beth o :=
   (aleph0_le_aleph o).trans <| aleph_le_beth o
 #align cardinal.aleph_0_le_beth Cardinal.aleph0_le_beth
+-/
 
+#print Cardinal.beth_pos /-
 theorem beth_pos (o : Ordinal) : 0 < beth o :=
   aleph0_pos.trans_le <| aleph0_le_beth o
 #align cardinal.beth_pos Cardinal.beth_pos
+-/
 
+#print Cardinal.beth_ne_zero /-
 theorem beth_ne_zero (o : Ordinal) : beth o ≠ 0 :=
   (beth_pos o).ne'
 #align cardinal.beth_ne_zero Cardinal.beth_ne_zero
+-/
 
+#print Cardinal.beth_normal /-
 theorem beth_normal : IsNormal.{u} fun o => (beth o).ord :=
   (isNormal_iff_strictMono_limit _).2
     ⟨ord_strictMono.comp beth_strictMono, fun o ho a ha =>
@@ -503,10 +692,17 @@ theorem beth_normal : IsNormal.{u} fun o => (beth o).ord :=
       rw [beth_limit ho, ord_le]
       exact csupᵢ_le' fun b => ord_le.1 (ha _ b.2)⟩
 #align cardinal.beth_normal Cardinal.beth_normal
+-/
 
 /-! ### Properties of `mul` -/
 
 
+/- warning: cardinal.mul_eq_self -> Cardinal.mul_eq_self is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.mul_eq_self Cardinal.mul_eq_selfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- If `α` is an infinite type, then `α × α` and `α` have the same cardinality. -/
 theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c :=
@@ -564,6 +760,12 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c :=
 
 end UsingOrdinals
 
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 /-- If `α` and `β` are infinite types, then the cardinality of `α × β` is the maximum
 of the cardinalities of `α` and `β`. -/
 theorem mul_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : ℵ₀ ≤ b) : a * b = max a b :=
@@ -574,46 +776,100 @@ theorem mul_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : ℵ₀ ≤ b) : a
       (by simpa only [one_mul] using mul_le_mul_right' (one_le_aleph_0.trans ha) b)
 #align cardinal.mul_eq_max Cardinal.mul_eq_max
 
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 @[simp]
 theorem mul_mk_eq_max {α β : Type _} [Infinite α] [Infinite β] : (#α) * (#β) = max (#α) (#β) :=
   mul_eq_max (aleph0_le_mk α) (aleph0_le_mk β)
 #align cardinal.mul_mk_eq_max Cardinal.mul_mk_eq_max
 
+/- warning: cardinal.aleph_mul_aleph -> Cardinal.aleph_mul_aleph is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_mul_aleph Cardinal.aleph_mul_alephₓ'. -/
 @[simp]
 theorem aleph_mul_aleph (o₁ o₂ : Ordinal) : aleph o₁ * aleph o₂ = aleph (max o₁ o₂) := by
   rw [Cardinal.mul_eq_max (aleph_0_le_aleph o₁) (aleph_0_le_aleph o₂), max_aleph_eq]
 #align cardinal.aleph_mul_aleph Cardinal.aleph_mul_aleph
 
+/- warning: cardinal.aleph_0_mul_eq -> Cardinal.aleph0_mul_eq is a dubious translation:
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 @[simp]
 theorem aleph0_mul_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : ℵ₀ * a = a :=
   (mul_eq_max le_rfl ha).trans (max_eq_right ha)
 #align cardinal.aleph_0_mul_eq Cardinal.aleph0_mul_eq
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.mul_aleph_0_eq Cardinal.mul_aleph0_eqₓ'. -/
 @[simp]
 theorem mul_aleph0_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a * ℵ₀ = a :=
   (mul_eq_max ha le_rfl).trans (max_eq_left ha)
 #align cardinal.mul_aleph_0_eq Cardinal.mul_aleph0_eq
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_0_mul_mk_eq Cardinal.aleph0_mul_mk_eqₓ'. -/
 @[simp]
 theorem aleph0_mul_mk_eq {α : Type _} [Infinite α] : ℵ₀ * (#α) = (#α) :=
   aleph0_mul_eq (aleph0_le_mk α)
 #align cardinal.aleph_0_mul_mk_eq Cardinal.aleph0_mul_mk_eq
 
+/- warning: cardinal.mk_mul_aleph_0_eq -> Cardinal.mk_mul_aleph0_eq is a dubious translation:
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 @[simp]
 theorem mk_mul_aleph0_eq {α : Type _} [Infinite α] : (#α) * ℵ₀ = (#α) :=
   mul_aleph0_eq (aleph0_le_mk α)
 #align cardinal.mk_mul_aleph_0_eq Cardinal.mk_mul_aleph0_eq
 
+/- warning: cardinal.aleph_0_mul_aleph -> Cardinal.aleph0_mul_aleph is a dubious translation:
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 @[simp]
 theorem aleph0_mul_aleph (o : Ordinal) : ℵ₀ * aleph o = aleph o :=
   aleph0_mul_eq (aleph0_le_aleph o)
 #align cardinal.aleph_0_mul_aleph Cardinal.aleph0_mul_aleph
 
+/- warning: cardinal.aleph_mul_aleph_0 -> Cardinal.aleph_mul_aleph0 is a dubious translation:
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 @[simp]
 theorem aleph_mul_aleph0 (o : Ordinal) : aleph o * ℵ₀ = aleph o :=
   mul_aleph0_eq (aleph0_le_aleph o)
 #align cardinal.aleph_mul_aleph_0 Cardinal.aleph_mul_aleph0
 
+/- warning: cardinal.mul_lt_of_lt -> Cardinal.mul_lt_of_lt is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.mul_lt_of_lt Cardinal.mul_lt_of_ltₓ'. -/
 theorem mul_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b < c) : a * b < c :=
   (mul_le_mul' (le_max_left a b) (le_max_right a b)).trans_lt <|
     (lt_or_le (max a b) ℵ₀).elim (fun h => (mul_lt_aleph0 h h).trans_le hc) fun h =>
@@ -622,6 +878,12 @@ theorem mul_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b
       exact max_lt h1 h2
 #align cardinal.mul_lt_of_lt Cardinal.mul_lt_of_lt
 
+/- warning: cardinal.mul_le_max_of_aleph_0_le_left -> Cardinal.mul_le_max_of_aleph0_le_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.mul_le_max_of_aleph_0_le_left Cardinal.mul_le_max_of_aleph0_le_leftₓ'. -/
 theorem mul_le_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) : a * b ≤ max a b :=
   by
   convert mul_le_mul' (le_max_left a b) (le_max_right a b)
@@ -629,6 +891,12 @@ theorem mul_le_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) : a * b
   refine' h.trans (le_max_left a b)
 #align cardinal.mul_le_max_of_aleph_0_le_left Cardinal.mul_le_max_of_aleph0_le_left
 
+/- warning: cardinal.mul_eq_max_of_aleph_0_le_left -> Cardinal.mul_eq_max_of_aleph0_le_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.mul_eq_max_of_aleph_0_le_left Cardinal.mul_eq_max_of_aleph0_le_leftₓ'. -/
 theorem mul_eq_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) (h' : b ≠ 0) : a * b = max a b :=
   by
   cases' le_or_lt ℵ₀ b with hb hb
@@ -640,16 +908,34 @@ theorem mul_eq_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) (h' : b
   rw [mul_one]
 #align cardinal.mul_eq_max_of_aleph_0_le_left Cardinal.mul_eq_max_of_aleph0_le_left
 
+/- warning: cardinal.mul_le_max_of_aleph_0_le_right -> Cardinal.mul_le_max_of_aleph0_le_right is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.mul_le_max_of_aleph_0_le_right Cardinal.mul_le_max_of_aleph0_le_rightₓ'. -/
 theorem mul_le_max_of_aleph0_le_right {a b : Cardinal} (h : ℵ₀ ≤ b) : a * b ≤ max a b := by
   simpa only [mul_comm, max_comm] using mul_le_max_of_aleph_0_le_left h
 #align cardinal.mul_le_max_of_aleph_0_le_right Cardinal.mul_le_max_of_aleph0_le_right
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.mul_eq_max_of_aleph_0_le_right Cardinal.mul_eq_max_of_aleph0_le_rightₓ'. -/
 theorem mul_eq_max_of_aleph0_le_right {a b : Cardinal} (h' : a ≠ 0) (h : ℵ₀ ≤ b) :
     a * b = max a b := by
   rw [mul_comm, max_comm]
   exact mul_eq_max_of_aleph_0_le_left h h'
 #align cardinal.mul_eq_max_of_aleph_0_le_right Cardinal.mul_eq_max_of_aleph0_le_right
 
+/- warning: cardinal.mul_eq_max' -> Cardinal.mul_eq_max' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.mul_eq_max' Cardinal.mul_eq_max'ₓ'. -/
 theorem mul_eq_max' {a b : Cardinal} (h : ℵ₀ ≤ a * b) : a * b = max a b :=
   by
   rcases aleph_0_le_mul_iff.mp h with ⟨ha, hb, ha' | hb'⟩
@@ -657,6 +943,12 @@ theorem mul_eq_max' {a b : Cardinal} (h : ℵ₀ ≤ a * b) : a * b = max a b :=
   · exact mul_eq_max_of_aleph_0_le_right ha hb'
 #align cardinal.mul_eq_max' Cardinal.mul_eq_max'
 
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 theorem mul_le_max (a b : Cardinal) : a * b ≤ max (max a b) ℵ₀ :=
   by
   rcases eq_or_ne a 0 with (rfl | ha0); · simp
@@ -670,26 +962,56 @@ theorem mul_le_max (a b : Cardinal) : a * b ≤ max (max a b) ℵ₀ :=
     · exact le_max_of_le_right (mul_lt_aleph_0 ha hb).le
 #align cardinal.mul_le_max Cardinal.mul_le_max
 
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 theorem mul_eq_left {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : b ≤ a) (hb' : b ≠ 0) : a * b = a := by
   rw [mul_eq_max_of_aleph_0_le_left ha hb', max_eq_left hb]
 #align cardinal.mul_eq_left Cardinal.mul_eq_left
 
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 theorem mul_eq_right {a b : Cardinal} (hb : ℵ₀ ≤ b) (ha : a ≤ b) (ha' : a ≠ 0) : a * b = b := by
   rw [mul_comm, mul_eq_left hb ha ha']
 #align cardinal.mul_eq_right Cardinal.mul_eq_right
 
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 theorem le_mul_left {a b : Cardinal} (h : b ≠ 0) : a ≤ b * a :=
   by
   convert mul_le_mul_right' (one_le_iff_ne_zero.mpr h) _
   rw [one_mul]
 #align cardinal.le_mul_left Cardinal.le_mul_left
 
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 theorem le_mul_right {a b : Cardinal} (h : b ≠ 0) : a ≤ a * b :=
   by
   rw [mul_comm]
   exact le_mul_left h
 #align cardinal.le_mul_right Cardinal.le_mul_right
 
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 theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧ b ≠ 0 ∨ b = 1 ∨ a = 0 :=
   by
   rw [max_le_iff]
@@ -736,6 +1058,12 @@ theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧
 /-! ### Properties of `add` -/
 
 
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 /-- If `α` is an infinite type, then `α ⊕ α` and `α` have the same cardinality. -/
 theorem add_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c + c = c :=
   le_antisymm
@@ -745,6 +1073,12 @@ theorem add_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c + c = c :=
     (self_le_add_left c c)
 #align cardinal.add_eq_self Cardinal.add_eq_self
 
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 /-- If `α` is an infinite type, then the cardinality of `α ⊕ β` is the maximum
 of the cardinalities of `α` and `β`. -/
 theorem add_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) : a + b = max a b :=
@@ -754,20 +1088,44 @@ theorem add_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) : a + b = max a b :=
     max_le (self_le_add_right _ _) (self_le_add_left _ _)
 #align cardinal.add_eq_max Cardinal.add_eq_max
 
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 theorem add_eq_max' {a b : Cardinal} (ha : ℵ₀ ≤ b) : a + b = max a b := by
   rw [add_comm, max_comm, add_eq_max ha]
 #align cardinal.add_eq_max' Cardinal.add_eq_max'
 
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 @[simp]
 theorem add_mk_eq_max {α β : Type _} [Infinite α] : (#α) + (#β) = max (#α) (#β) :=
   add_eq_max (aleph0_le_mk α)
 #align cardinal.add_mk_eq_max Cardinal.add_mk_eq_max
 
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 @[simp]
 theorem add_mk_eq_max' {α β : Type _} [Infinite β] : (#α) + (#β) = max (#α) (#β) :=
   add_eq_max' (aleph0_le_mk β)
 #align cardinal.add_mk_eq_max' Cardinal.add_mk_eq_max'
 
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 theorem add_le_max (a b : Cardinal) : a + b ≤ max (max a b) ℵ₀ :=
   by
   cases' le_or_lt ℵ₀ a with ha ha
@@ -779,16 +1137,34 @@ theorem add_le_max (a b : Cardinal) : a + b ≤ max (max a b) ℵ₀ :=
     · exact le_max_of_le_right (add_lt_aleph_0 ha hb).le
 #align cardinal.add_le_max Cardinal.add_le_max
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.add_le_of_le Cardinal.add_le_of_leₓ'. -/
 theorem add_le_of_le {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a ≤ c) (h2 : b ≤ c) : a + b ≤ c :=
   (add_le_add h1 h2).trans <| le_of_eq <| add_eq_self hc
 #align cardinal.add_le_of_le Cardinal.add_le_of_le
 
+/- warning: cardinal.add_lt_of_lt -> Cardinal.add_lt_of_lt is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.add_lt_of_lt Cardinal.add_lt_of_ltₓ'. -/
 theorem add_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b < c) : a + b < c :=
   (add_le_add (le_max_left a b) (le_max_right a b)).trans_lt <|
     (lt_or_le (max a b) ℵ₀).elim (fun h => (add_lt_aleph0 h h).trans_le hc) fun h => by
       rw [add_eq_self h] <;> exact max_lt h1 h2
 #align cardinal.add_lt_of_lt Cardinal.add_lt_of_lt
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.eq_of_add_eq_of_aleph_0_le Cardinal.eq_of_add_eq_of_aleph0_leₓ'. -/
 theorem eq_of_add_eq_of_aleph0_le {a b c : Cardinal} (h : a + b = c) (ha : a < c) (hc : ℵ₀ ≤ c) :
     b = c := by
   apply le_antisymm
@@ -799,14 +1175,32 @@ theorem eq_of_add_eq_of_aleph0_le {a b c : Cardinal} (h : a + b = c) (ha : a < c
   simpa [h, lt_irrefl] using this
 #align cardinal.eq_of_add_eq_of_aleph_0_le Cardinal.eq_of_add_eq_of_aleph0_le
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.add_eq_left Cardinal.add_eq_leftₓ'. -/
 theorem add_eq_left {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : b ≤ a) : a + b = a := by
   rw [add_eq_max ha, max_eq_left hb]
 #align cardinal.add_eq_left Cardinal.add_eq_left
 
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 theorem add_eq_right {a b : Cardinal} (hb : ℵ₀ ≤ b) (ha : a ≤ b) : a + b = b := by
   rw [add_comm, add_eq_left hb ha]
 #align cardinal.add_eq_right Cardinal.add_eq_right
 
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 theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨ b = 0 :=
   by
   rw [max_le_iff]
@@ -827,23 +1221,53 @@ theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨
     · rw [h3, add_zero]
 #align cardinal.add_eq_left_iff Cardinal.add_eq_left_iff
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.add_eq_right_iff Cardinal.add_eq_right_iffₓ'. -/
 theorem add_eq_right_iff {a b : Cardinal} : a + b = b ↔ max ℵ₀ a ≤ b ∨ a = 0 := by
   rw [add_comm, add_eq_left_iff]
 #align cardinal.add_eq_right_iff Cardinal.add_eq_right_iff
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.add_nat_eq Cardinal.add_nat_eqₓ'. -/
 theorem add_nat_eq {a : Cardinal} (n : ℕ) (ha : ℵ₀ ≤ a) : a + n = a :=
   add_eq_left ha ((nat_lt_aleph0 _).le.trans ha)
 #align cardinal.add_nat_eq Cardinal.add_nat_eq
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.add_one_eq Cardinal.add_one_eqₓ'. -/
 theorem add_one_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a + 1 = a :=
   add_eq_left ha (one_le_aleph0.trans ha)
 #align cardinal.add_one_eq Cardinal.add_one_eq
 
+/- warning: cardinal.mk_add_one_eq -> Cardinal.mk_add_one_eq is a dubious translation:
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 @[simp]
 theorem mk_add_one_eq {α : Type _} [Infinite α] : (#α) + 1 = (#α) :=
   add_one_eq (aleph0_le_mk α)
 #align cardinal.mk_add_one_eq Cardinal.mk_add_one_eq
 
+/- warning: cardinal.eq_of_add_eq_add_left -> Cardinal.eq_of_add_eq_add_left is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.eq_of_add_eq_add_left Cardinal.eq_of_add_eq_add_leftₓ'. -/
 protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (ha : a < ℵ₀) :
     b = c := by
   cases' le_or_lt ℵ₀ b with hb hb
@@ -865,41 +1289,81 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
     apply add_left_cancel h
 #align cardinal.eq_of_add_eq_add_left Cardinal.eq_of_add_eq_add_left
 
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 protected theorem eq_of_add_eq_add_right {a b c : Cardinal} (h : a + b = c + b) (hb : b < ℵ₀) :
     a = c := by
   rw [add_comm a b, add_comm c b] at h
   exact Cardinal.eq_of_add_eq_add_left h hb
 #align cardinal.eq_of_add_eq_add_right Cardinal.eq_of_add_eq_add_right
 
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 @[simp]
 theorem aleph_add_aleph (o₁ o₂ : Ordinal) : aleph o₁ + aleph o₂ = aleph (max o₁ o₂) := by
   rw [Cardinal.add_eq_max (aleph_0_le_aleph o₁), max_aleph_eq]
 #align cardinal.aleph_add_aleph Cardinal.aleph_add_aleph
 
+#print Cardinal.principal_add_ord /-
 theorem principal_add_ord {c : Cardinal} (hc : ℵ₀ ≤ c) : Ordinal.Principal (· + ·) c.ord :=
   fun a b ha hb => by
   rw [lt_ord, Ordinal.card_add] at *
   exact add_lt_of_lt hc ha hb
 #align cardinal.principal_add_ord Cardinal.principal_add_ord
+-/
 
+#print Cardinal.principal_add_aleph /-
 theorem principal_add_aleph (o : Ordinal) : Ordinal.Principal (· + ·) (aleph o).ord :=
   principal_add_ord <| aleph0_le_aleph o
 #align cardinal.principal_add_aleph Cardinal.principal_add_aleph
+-/
 
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 theorem add_right_inj_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < aleph0) : α + γ = β + γ ↔ α = β :=
   ⟨fun h => Cardinal.eq_of_add_eq_add_right h γ₀, fun h => congr_fun (congr_arg (· + ·) h) γ⟩
 #align cardinal.add_right_inj_of_lt_aleph_0 Cardinal.add_right_inj_of_lt_aleph0
 
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 @[simp]
 theorem add_nat_inj {α β : Cardinal} (n : ℕ) : α + n = β + n ↔ α = β :=
   add_right_inj_of_lt_aleph0 (nat_lt_aleph0 _)
 #align cardinal.add_nat_inj Cardinal.add_nat_inj
 
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 @[simp]
 theorem add_one_inj {α β : Cardinal} : α + 1 = β + 1 ↔ α = β :=
   add_right_inj_of_lt_aleph0 one_lt_aleph0
 #align cardinal.add_one_inj Cardinal.add_one_inj
 
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 theorem add_le_add_iff_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < Cardinal.aleph0) :
     α + γ ≤ β + γ ↔ α ≤ β :=
   by
@@ -909,11 +1373,23 @@ theorem add_le_add_iff_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < Cardinal
   exact ⟨add_le_add_right h.1 γ, mt (add_right_inj_of_lt_aleph_0 γ₀).1 h.2⟩
 #align cardinal.add_le_add_iff_of_lt_aleph_0 Cardinal.add_le_add_iff_of_lt_aleph0
 
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 @[simp]
 theorem add_nat_le_add_nat_iff_of_lt_aleph_0 {α β : Cardinal} (n : ℕ) : α + n ≤ β + n ↔ α ≤ β :=
   add_le_add_iff_of_lt_aleph0 (nat_lt_aleph0 n)
 #align cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0 Cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0
 
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 @[simp]
 theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β + 1 ↔ α ≤ β :=
   add_le_add_iff_of_lt_aleph0 one_lt_aleph0
@@ -922,6 +1398,7 @@ theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β
 /-! ### Properties about power -/
 
 
+#print Cardinal.pow_le /-
 theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) : κ ^ μ ≤ κ :=
   let ⟨n, H3⟩ := lt_aleph0.1 H2
   H3.symm ▸
@@ -941,11 +1418,20 @@ theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) :
             (mul_eq_self H1))
       H1
 #align cardinal.pow_le Cardinal.pow_le
+-/
 
+#print Cardinal.pow_eq /-
 theorem pow_eq {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : 1 ≤ μ) (H3 : μ < ℵ₀) : κ ^ μ = κ :=
   (pow_le H1 H3).antisymm <| self_le_power κ H2
 #align cardinal.pow_eq Cardinal.pow_eq
+-/
 
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 theorem power_self_eq {c : Cardinal} (h : ℵ₀ ≤ c) : c ^ c = 2 ^ c :=
   by
   apply ((power_le_power_right <| (cantor c).le).trans _).antisymm
@@ -954,6 +1440,12 @@ theorem power_self_eq {c : Cardinal} (h : ℵ₀ ≤ c) : c ^ c = 2 ^ c :=
   · rw [← power_mul, mul_eq_self h]
 #align cardinal.power_self_eq Cardinal.power_self_eq
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.prod_eq_two_power Cardinal.prod_eq_two_powerₓ'. -/
 theorem prod_eq_two_power {ι : Type u} [Infinite ι] {c : ι → Cardinal.{v}} (h₁ : ∀ i, 2 ≤ c i)
     (h₂ : ∀ i, lift.{u} (c i) ≤ lift.{v} (#ι)) : prod c = 2 ^ lift.{v} (#ι) :=
   by
@@ -967,24 +1459,54 @@ theorem prod_eq_two_power {ι : Type u} [Infinite ι] {c : ι → Cardinal.{v}}
     exact h₁ i
 #align cardinal.prod_eq_two_power Cardinal.prod_eq_two_power
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.power_eq_two_power Cardinal.power_eq_two_powerₓ'. -/
 theorem power_eq_two_power {c₁ c₂ : Cardinal} (h₁ : ℵ₀ ≤ c₁) (h₂ : 2 ≤ c₂) (h₂' : c₂ ≤ c₁) :
     c₂ ^ c₁ = 2 ^ c₁ :=
   le_antisymm (power_self_eq h₁ ▸ power_le_power_right h₂') (power_le_power_right h₂)
 #align cardinal.power_eq_two_power Cardinal.power_eq_two_power
 
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 theorem nat_power_eq {c : Cardinal.{u}} (h : ℵ₀ ≤ c) {n : ℕ} (hn : 2 ≤ n) :
     (n : Cardinal.{u}) ^ c = 2 ^ c :=
   power_eq_two_power h (by assumption_mod_cast) ((nat_lt_aleph0 n).le.trans h)
 #align cardinal.nat_power_eq Cardinal.nat_power_eq
 
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 theorem power_nat_le {c : Cardinal.{u}} {n : ℕ} (h : ℵ₀ ≤ c) : c ^ n ≤ c :=
   pow_le h (nat_lt_aleph0 n)
 #align cardinal.power_nat_le Cardinal.power_nat_le
 
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 theorem power_nat_eq {c : Cardinal.{u}} {n : ℕ} (h1 : ℵ₀ ≤ c) (h2 : 1 ≤ n) : c ^ n = c :=
   pow_eq h1 (by exact_mod_cast h2) (nat_lt_aleph0 n)
 #align cardinal.power_nat_eq Cardinal.power_nat_eq
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.power_nat_le_max Cardinal.power_nat_le_maxₓ'. -/
 theorem power_nat_le_max {c : Cardinal.{u}} {n : ℕ} : c ^ (n : Cardinal.{u}) ≤ max c ℵ₀ :=
   by
   cases' le_or_lt ℵ₀ c with hc hc
@@ -992,6 +1514,7 @@ theorem power_nat_le_max {c : Cardinal.{u}} {n : ℕ} : c ^ (n : Cardinal.{u}) 
   · exact le_max_of_le_right (power_lt_aleph_0 hc (nat_lt_aleph_0 _)).le
 #align cardinal.power_nat_le_max Cardinal.power_nat_le_max
 
+#print Cardinal.powerlt_aleph0 /-
 theorem powerlt_aleph0 {c : Cardinal} (h : ℵ₀ ≤ c) : c ^< ℵ₀ = c :=
   by
   apply le_antisymm
@@ -1002,7 +1525,14 @@ theorem powerlt_aleph0 {c : Cardinal} (h : ℵ₀ ≤ c) : c ^< ℵ₀ = c :=
     apply power_nat_le h
   convert le_powerlt c one_lt_aleph_0; rw [power_one]
 #align cardinal.powerlt_aleph_0 Cardinal.powerlt_aleph0
+-/
 
+/- warning: cardinal.powerlt_aleph_0_le -> Cardinal.powerlt_aleph0_le is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.powerlt_aleph_0_le Cardinal.powerlt_aleph0_leₓ'. -/
 theorem powerlt_aleph0_le (c : Cardinal) : c ^< ℵ₀ ≤ max c ℵ₀ :=
   by
   cases le_or_lt ℵ₀ c
@@ -1015,6 +1545,7 @@ theorem powerlt_aleph0_le (c : Cardinal) : c ^< ℵ₀ ≤ max c ℵ₀ :=
 /-! ### Computing cardinality of various types -/
 
 
+#print Cardinal.mk_list_eq_mk /-
 @[simp]
 theorem mk_list_eq_mk (α : Type u) [Infinite α] : (#List α) = (#α) :=
   have H1 : ℵ₀ ≤ (#α) := aleph0_le_mk α
@@ -1026,11 +1557,20 @@ theorem mk_list_eq_mk (α : Type u) [Infinite α] : (#List α) = (#α) :=
         _ = (#α) := by simp [H1]
         
 #align cardinal.mk_list_eq_mk Cardinal.mk_list_eq_mk
+-/
 
+#print Cardinal.mk_list_eq_aleph0 /-
 theorem mk_list_eq_aleph0 (α : Type u) [Countable α] [Nonempty α] : (#List α) = ℵ₀ :=
   mk_le_aleph0.antisymm (aleph0_le_mk _)
 #align cardinal.mk_list_eq_aleph_0 Cardinal.mk_list_eq_aleph0
+-/
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.mk_list_eq_max_mk_aleph_0 Cardinal.mk_list_eq_max_mk_aleph0ₓ'. -/
 theorem mk_list_eq_max_mk_aleph0 (α : Type u) [Nonempty α] : (#List α) = max (#α) ℵ₀ :=
   by
   cases finite_or_infinite α
@@ -1040,6 +1580,12 @@ theorem mk_list_eq_max_mk_aleph0 (α : Type u) [Nonempty α] : (#List α) = max
     exact aleph_0_le_mk α
 #align cardinal.mk_list_eq_max_mk_aleph_0 Cardinal.mk_list_eq_max_mk_aleph0
 
+/- warning: cardinal.mk_list_le_max -> Cardinal.mk_list_le_max is a dubious translation:
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 theorem mk_list_le_max (α : Type u) : (#List α) ≤ max ℵ₀ (#α) :=
   by
   cases finite_or_infinite α
@@ -1048,6 +1594,7 @@ theorem mk_list_le_max (α : Type u) : (#List α) ≤ max ℵ₀ (#α) :=
     apply le_max_right
 #align cardinal.mk_list_le_max Cardinal.mk_list_le_max
 
+#print Cardinal.mk_finset_of_infinite /-
 @[simp]
 theorem mk_finset_of_infinite (α : Type u) [Infinite α] : (#Finset α) = (#α) :=
   Eq.symm <|
@@ -1057,7 +1604,14 @@ theorem mk_finset_of_infinite (α : Type u) [Infinite α] : (#Finset α) = (#α)
         _ = (#α) := mk_list_eq_mk α
         
 #align cardinal.mk_finset_of_infinite Cardinal.mk_finset_of_infinite
+-/
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.mk_finsupp_lift_of_infinite Cardinal.mk_finsupp_lift_of_infiniteₓ'. -/
 @[simp]
 theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Zero β] [Nontrivial β] :
     (#α →₀ β) = max (lift.{v} (#α)) (lift.{u} (#β)) :=
@@ -1077,10 +1631,22 @@ theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Z
       exact lift_mk_le.{v, max u v, u}.2 ⟨⟨_, Finsupp.single_injective default⟩⟩
 #align cardinal.mk_finsupp_lift_of_infinite Cardinal.mk_finsupp_lift_of_infinite
 
+/- warning: cardinal.mk_finsupp_of_infinite -> Cardinal.mk_finsupp_of_infinite is a dubious translation:
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 theorem mk_finsupp_of_infinite (α β : Type u) [Infinite α] [Zero β] [Nontrivial β] :
     (#α →₀ β) = max (#α) (#β) := by simp
 #align cardinal.mk_finsupp_of_infinite Cardinal.mk_finsupp_of_infinite
 
+/- warning: cardinal.mk_finsupp_lift_of_infinite' -> Cardinal.mk_finsupp_lift_of_infinite' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.mk_finsupp_lift_of_infinite' Cardinal.mk_finsupp_lift_of_infinite'ₓ'. -/
 @[simp]
 theorem mk_finsupp_lift_of_infinite' (α : Type u) (β : Type v) [Nonempty α] [Zero β] [Infinite β] :
     (#α →₀ β) = max (lift.{v} (#α)) (lift.{u} (#β)) :=
@@ -1093,30 +1659,55 @@ theorem mk_finsupp_lift_of_infinite' (α : Type u) (β : Type v) [Nonempty α] [
   · apply mk_finsupp_lift_of_infinite
 #align cardinal.mk_finsupp_lift_of_infinite' Cardinal.mk_finsupp_lift_of_infinite'
 
+/- warning: cardinal.mk_finsupp_of_infinite' -> Cardinal.mk_finsupp_of_infinite' is a dubious translation:
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 theorem mk_finsupp_of_infinite' (α β : Type u) [Nonempty α] [Zero β] [Infinite β] :
     (#α →₀ β) = max (#α) (#β) := by simp
 #align cardinal.mk_finsupp_of_infinite' Cardinal.mk_finsupp_of_infinite'
 
+/- warning: cardinal.mk_finsupp_nat -> Cardinal.mk_finsupp_nat is a dubious translation:
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 theorem mk_finsupp_nat (α : Type u) [Nonempty α] : (#α →₀ ℕ) = max (#α) ℵ₀ := by simp
 #align cardinal.mk_finsupp_nat Cardinal.mk_finsupp_nat
 
+/- warning: cardinal.mk_multiset_of_nonempty -> Cardinal.mk_multiset_of_nonempty is a dubious translation:
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 @[simp]
 theorem mk_multiset_of_nonempty (α : Type u) [Nonempty α] : (#Multiset α) = max (#α) ℵ₀ :=
   Multiset.toFinsupp.toEquiv.cardinal_eq.trans (mk_finsupp_nat α)
 #align cardinal.mk_multiset_of_nonempty Cardinal.mk_multiset_of_nonempty
 
+#print Cardinal.mk_multiset_of_infinite /-
 theorem mk_multiset_of_infinite (α : Type u) [Infinite α] : (#Multiset α) = (#α) := by simp
 #align cardinal.mk_multiset_of_infinite Cardinal.mk_multiset_of_infinite
+-/
 
+#print Cardinal.mk_multiset_of_isEmpty /-
 @[simp]
 theorem mk_multiset_of_isEmpty (α : Type u) [IsEmpty α] : (#Multiset α) = 1 :=
   Multiset.toFinsupp.toEquiv.cardinal_eq.trans (by simp)
 #align cardinal.mk_multiset_of_is_empty Cardinal.mk_multiset_of_isEmpty
+-/
 
+#print Cardinal.mk_multiset_of_countable /-
 theorem mk_multiset_of_countable (α : Type u) [Countable α] [Nonempty α] : (#Multiset α) = ℵ₀ :=
   Multiset.toFinsupp.toEquiv.cardinal_eq.trans (by simp)
 #align cardinal.mk_multiset_of_countable Cardinal.mk_multiset_of_countable
+-/
 
+#print Cardinal.mk_bounded_set_le_of_infinite /-
 theorem mk_bounded_set_le_of_infinite (α : Type u) [Infinite α] (c : Cardinal) :
     (#{ t : Set α // (#t) ≤ c }) ≤ (#α) ^ c :=
   by
@@ -1150,7 +1741,14 @@ theorem mk_bounded_set_le_of_infinite (α : Type u) [Infinite α] (c : Cardinal)
     apply g.2
     exact Classical.choose_spec this
 #align cardinal.mk_bounded_set_le_of_infinite Cardinal.mk_bounded_set_le_of_infinite
+-/
 
+/- warning: cardinal.mk_bounded_set_le -> Cardinal.mk_bounded_set_le is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.mk_bounded_set_le Cardinal.mk_bounded_set_leₓ'. -/
 theorem mk_bounded_set_le (α : Type u) (c : Cardinal) :
     (#{ t : Set α // (#t) ≤ c }) ≤ max (#α) ℵ₀ ^ c :=
   by
@@ -1165,6 +1763,12 @@ theorem mk_bounded_set_le (α : Type u) (c : Cardinal) :
   rw [max_comm, ← add_eq_max] <;> rfl
 #align cardinal.mk_bounded_set_le Cardinal.mk_bounded_set_le
 
+/- warning: cardinal.mk_bounded_subset_le -> Cardinal.mk_bounded_subset_le is a dubious translation:
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 theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
     (#{ t : Set α // t ⊆ s ∧ (#t) ≤ c }) ≤ max (#s) ℵ₀ ^ c :=
   by
@@ -1181,6 +1785,12 @@ theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
 /-! ### Properties of `compl` -/
 
 
+/- warning: cardinal.mk_compl_of_infinite -> Cardinal.mk_compl_of_infinite is a dubious translation:
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 theorem mk_compl_of_infinite {α : Type _} [Infinite α] (s : Set α) (h2 : (#s) < (#α)) :
     (#(sᶜ : Set α)) = (#α) :=
   by
@@ -1188,17 +1798,35 @@ theorem mk_compl_of_infinite {α : Type _} [Infinite α] (s : Set α) (h2 : (#s)
   exact mk_sum_compl s
 #align cardinal.mk_compl_of_infinite Cardinal.mk_compl_of_infinite
 
+/- warning: cardinal.mk_compl_finset_of_infinite -> Cardinal.mk_compl_finset_of_infinite is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_finset_of_infinite Cardinal.mk_compl_finset_of_infiniteₓ'. -/
 theorem mk_compl_finset_of_infinite {α : Type _} [Infinite α] (s : Finset α) :
     (#(↑sᶜ : Set α)) = (#α) := by
   apply mk_compl_of_infinite
   exact (finset_card_lt_aleph_0 s).trans_le (aleph_0_le_mk α)
 #align cardinal.mk_compl_finset_of_infinite Cardinal.mk_compl_finset_of_infinite
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_eq_mk_compl_infinite Cardinal.mk_compl_eq_mk_compl_infiniteₓ'. -/
 theorem mk_compl_eq_mk_compl_infinite {α : Type _} [Infinite α] {s t : Set α} (hs : (#s) < (#α))
     (ht : (#t) < (#α)) : (#(sᶜ : Set α)) = (#(tᶜ : Set α)) := by
   rw [mk_compl_of_infinite s hs, mk_compl_of_infinite t ht]
 #align cardinal.mk_compl_eq_mk_compl_infinite Cardinal.mk_compl_eq_mk_compl_infinite
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_eq_mk_compl_finite_lift Cardinal.mk_compl_eq_mk_compl_finite_liftₓ'. -/
 theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α] {s : Set α}
     {t : Set β} (h1 : lift.{max v w} (#α) = lift.{max u w} (#β))
     (h2 : lift.{max v w} (#s) = lift.{max u w} (#t)) :
@@ -1215,6 +1843,12 @@ theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α]
       lift_nat_cast, Nat.cast_inj, h1, h2]
 #align cardinal.mk_compl_eq_mk_compl_finite_lift Cardinal.mk_compl_eq_mk_compl_finite_lift
 
+/- warning: cardinal.mk_compl_eq_mk_compl_finite -> Cardinal.mk_compl_eq_mk_compl_finite is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_eq_mk_compl_finite Cardinal.mk_compl_eq_mk_compl_finiteₓ'. -/
 theorem mk_compl_eq_mk_compl_finite {α β : Type u} [Finite α] {s : Set α} {t : Set β}
     (h1 : (#α) = (#β)) (h : (#s) = (#t)) : (#(sᶜ : Set α)) = (#(tᶜ : Set β)) :=
   by
@@ -1222,6 +1856,12 @@ theorem mk_compl_eq_mk_compl_finite {α β : Type u} [Finite α] {s : Set α} {t
   apply mk_compl_eq_mk_compl_finite_lift <;> rwa [lift_inj]
 #align cardinal.mk_compl_eq_mk_compl_finite Cardinal.mk_compl_eq_mk_compl_finite
 
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+Case conversion may be inaccurate. Consider using '#align cardinal.mk_compl_eq_mk_compl_finite_same Cardinal.mk_compl_eq_mk_compl_finite_sameₓ'. -/
 theorem mk_compl_eq_mk_compl_finite_same {α : Type _} [Finite α] {s t : Set α} (h : (#s) = (#t)) :
     (#(sᶜ : Set α)) = (#(tᶜ : Set α)) :=
   mk_compl_eq_mk_compl_finite rfl h
@@ -1230,6 +1870,12 @@ theorem mk_compl_eq_mk_compl_finite_same {α : Type _} [Finite α] {s t : Set α
 /-! ### Extending an injection to an equiv -/
 
 
+/- warning: cardinal.extend_function -> Cardinal.extend_function is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.extend_function Cardinal.extend_functionₓ'. -/
 theorem extend_function {α β : Type _} {s : Set α} (f : s ↪ β)
     (h : Nonempty ((sᶜ : Set α) ≃ (range fᶜ : Set β))) : ∃ g : α ≃ β, ∀ x : s, g x = f x :=
   by
@@ -1240,6 +1886,7 @@ theorem extend_function {α β : Type _} {s : Set α} (f : s ↪ β)
   refine' ⟨h, _⟩; rintro ⟨x, hx⟩; simp [set.sum_compl_symm_apply_of_mem, hx]
 #align cardinal.extend_function Cardinal.extend_function
 
+#print Cardinal.extend_function_finite /-
 theorem extend_function_finite {α β : Type _} [Finite α] {s : Set α} (f : s ↪ β)
     (h : Nonempty (α ≃ β)) : ∃ g : α ≃ β, ∀ x : s, g x = f x :=
   by
@@ -1249,7 +1896,14 @@ theorem extend_function_finite {α β : Type _} [Finite α] {s : Set α} (f : s
   rw [← lift_mk_eq, mk_compl_eq_mk_compl_finite_lift h]
   rw [mk_range_eq_lift]; exact f.2
 #align cardinal.extend_function_finite Cardinal.extend_function_finite
+-/
 
+/- warning: cardinal.extend_function_of_lt -> Cardinal.extend_function_of_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {s : Set.{u1} α} (f : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) 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} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s)) (Cardinal.mk.{u1} α)) -> (Nonempty.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{succ u1, succ u2} α β)) -> (Exists.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1)} (Equiv.{succ u1, succ u2} α β) (fun (g : Equiv.{succ u1, succ u2} α β) => forall (x : coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s), Eq.{succ u2} β (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) g ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (HasLiftT.mk.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (CoeTCₓ.coe.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeBase.{succ u1, succ u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) α (coeSubtype.{succ u1} α (fun (x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s))))) x)) (coeFn.{max 1 (succ u1) (succ u2), max (succ u1) (succ u2)} (Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) (fun (_x : Function.Embedding.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) => (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) -> β) (Function.Embedding.hasCoeToFun.{succ u1, succ u2} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} α) Type.{u1} (Set.hasCoeToSort.{u1} α) s) β) f x)))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {s : Set.{u2} α} (f : Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β), (LT.lt.{succ u2} Cardinal.{u2} (Preorder.toLT.{succ u2} Cardinal.{u2} (PartialOrder.toPreorder.{succ u2} Cardinal.{u2} Cardinal.partialOrder.{u2})) (Cardinal.mk.{u2} (Set.Elem.{u2} α s)) (Cardinal.mk.{u2} α)) -> (Nonempty.{max (succ u1) (succ u2)} (Equiv.{succ u2, succ u1} α β)) -> (Exists.{max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} α β) (fun (g : Equiv.{succ u2, succ u1} α β) => forall (x : Set.Elem.{u2} α s), Eq.{succ u1} ((fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => β) (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) g (Subtype.val.{succ u2} α (fun (x : α) => Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) x)) (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) (fun (_x : Set.Elem.{u2} α s) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Set.Elem.{u2} α s) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (Function.Embedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β) (Set.Elem.{u2} α s) β (Function.instEmbeddingLikeEmbedding.{succ u2, succ u1} (Set.Elem.{u2} α s) β)) f x)))
+Case conversion may be inaccurate. Consider using '#align cardinal.extend_function_of_lt Cardinal.extend_function_of_ltₓ'. -/
 theorem extend_function_of_lt {α β : Type _} {s : Set α} (f : s ↪ β) (hs : (#s) < (#α))
     (h : Nonempty (α ≃ β)) : ∃ g : α ≃ β, ∀ x : s, g x = f x :=
   by

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore(SetTheory/Ordinal): reduce some open's; add section headers (#11596)

3959ff3c

Diff

@@ -48,10 +48,9 @@ cardinal arithmetic (for infinite cardinals)
 
 noncomputable section
 
-open Function Cardinal Set Equiv Order
+open Function Set Cardinal Equiv Order Ordinal
 
 open scoped Classical
-open Cardinal Ordinal
 
 universe u v w
 
@@ -59,8 +58,6 @@ namespace Cardinal
 
 section UsingOrdinals
 
-open Ordinal
-
 theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit := by
   refine' ⟨fun h => aleph0_ne_zero _, fun a => lt_imp_lt_of_le_imp_le fun h => _⟩
   · rw [← Ordinal.le_zero, ord_le] at h
@@ -73,8 +70,9 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit := by
       exact omega_isLimit
 #align cardinal.ord_is_limit Cardinal.ord_isLimit
 
-/-! ### Aleph cardinals -/
 
+/-! ### Aleph cardinals -/
+section aleph
 
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.
   (The `aleph'` part is because unlike `aleph` this counts also the
@@ -402,8 +400,10 @@ theorem ord_aleph_eq_enum_card :
     exact aleph0_le_aleph _
 #align cardinal.ord_aleph_eq_enum_card Cardinal.ord_aleph_eq_enum_card
 
-/-! ### Beth cardinals -/
+end aleph
 
+/-! ### Beth cardinals -/
+section beth
 
 /-- Beth numbers are defined so that `beth 0 = ℵ₀`, `beth (succ o) = 2 ^ (beth o)`, and when `o` is
 a limit ordinal, `beth o` is the supremum of `beth o'` for `o' < o`.
@@ -489,9 +489,10 @@ theorem beth_normal : IsNormal.{u} fun o => (beth o).ord :=
       exact ciSup_le' fun b => ord_le.1 (ha _ b.2)⟩
 #align cardinal.beth_normal Cardinal.beth_normal
 
-/-! ### Properties of `mul` -/
-
+end beth
 
+/-! ### Properties of `mul` -/
+section mulOrdinals
 
 /-- If `α` is an infinite type, then `α × α` and `α` have the same cardinality. -/
 theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c := by
@@ -541,8 +542,13 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c := by
     apply typein_lt_type
 #align cardinal.mul_eq_self Cardinal.mul_eq_self
 
+end mulOrdinals
+
 end UsingOrdinals
 
+/-! Properties of `mul`, not requiring ordinals -/
+section mul
+
 /-- If `α` and `β` are infinite types, then the cardinality of `α × β` is the maximum
 of the cardinalities of `α` and `β`. -/
 theorem mul_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : ℵ₀ ≤ b) : a * b = max a b :=
@@ -708,8 +714,10 @@ theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧
     all_goals simp
 #align cardinal.mul_eq_left_iff Cardinal.mul_eq_left_iff
 
-/-! ### Properties of `add` -/
+end mul
 
+/-! ### Properties of `add` -/
+section add
 
 /-- If `α` is an infinite type, then `α ⊕ α` and `α` have the same cardinality. -/
 theorem add_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c + c = c :=
@@ -848,6 +856,8 @@ protected theorem eq_of_add_eq_add_right {a b c : Cardinal} (h : a + b = c + b)
   exact Cardinal.eq_of_add_eq_add_left h hb
 #align cardinal.eq_of_add_eq_add_right Cardinal.eq_of_add_eq_add_right
 
+end add
+
 section ciSup
 
 variable {ι : Type u} {ι' : Type w} (f : ι → Cardinal.{v})
@@ -959,6 +969,7 @@ theorem add_one_le_add_one_iff {α β : Cardinal} : α + 1 ≤ β + 1 ↔ α ≤
 alias add_one_le_add_one_iff_of_lt_aleph_0 := add_one_le_add_one_iff  -- deprecated on 2024-02-12
 
 /-! ### Properties about power -/
+section pow
 
 theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) : κ ^ μ ≤ κ :=
   let ⟨n, H3⟩ := lt_aleph0.1 H2
@@ -1044,8 +1055,10 @@ theorem powerlt_aleph0_le (c : Cardinal) : c ^< ℵ₀ ≤ max c ℵ₀ := by
   exact fun c' hc' => (power_lt_aleph0 h hc').le.trans (le_max_right _ _)
 #align cardinal.powerlt_aleph_0_le Cardinal.powerlt_aleph0_le
 
-/-! ### Computing cardinality of various types -/
+end pow
 
+/-! ### Computing cardinality of various types -/
+section computing
 
 section Function
 
@@ -1301,8 +1314,10 @@ theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
   rintro ⟨t, _, h2t⟩; exact (mk_preimage_of_injective _ _ Subtype.val_injective).trans h2t
 #align cardinal.mk_bounded_subset_le Cardinal.mk_bounded_subset_le
 
-/-! ### Properties of `compl` -/
+end computing
 
+/-! ### Properties of `compl` -/
+section compl
 
 theorem mk_compl_of_infinite {α : Type*} [Infinite α] (s : Set α) (h2 : #s < #α) :
     #(sᶜ : Set α) = #α := by
@@ -1348,8 +1363,9 @@ theorem mk_compl_eq_mk_compl_finite_same {α : Type u} [Finite α] {s t : Set α
   mk_compl_eq_mk_compl_finite.{u, u} rfl h
 #align cardinal.mk_compl_eq_mk_compl_finite_same Cardinal.mk_compl_eq_mk_compl_finite_same
 
-/-! ### Extending an injection to an equiv -/
+end compl
 
+/-! ### Extending an injection to an equiv -/
 
 theorem extend_function {α β : Type*} {s : Set α} (f : s ↪ β)
     (h : Nonempty ((sᶜ : Set α) ≃ ((range f)ᶜ : Set β))) : ∃ g : α ≃ β, ∀ x : s, g x = f x := by

chore: classify "simp can prove" porting notes (#11550)

Classifies by adding issue number #10618 to porting notes claiming "simp can prove it".

5befdcb9

Diff

@@ -573,12 +573,12 @@ theorem mul_aleph0_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a * ℵ₀ = a :=
   (mul_eq_max ha le_rfl).trans (max_eq_left ha)
 #align cardinal.mul_aleph_0_eq Cardinal.mul_aleph0_eq
 
--- Porting note: removed `simp`, `simp` can prove it
+-- Porting note (#10618): removed `simp`, `simp` can prove it
 theorem aleph0_mul_mk_eq {α : Type*} [Infinite α] : ℵ₀ * #α = #α :=
   aleph0_mul_eq (aleph0_le_mk α)
 #align cardinal.aleph_0_mul_mk_eq Cardinal.aleph0_mul_mk_eq
 
--- Porting note: removed `simp`, `simp` can prove it
+-- Porting note (#10618): removed `simp`, `simp` can prove it
 theorem mk_mul_aleph0_eq {α : Type*} [Infinite α] : #α * ℵ₀ = #α :=
   mul_aleph0_eq (aleph0_le_mk α)
 #align cardinal.mk_mul_aleph_0_eq Cardinal.mk_mul_aleph0_eq
@@ -816,7 +816,7 @@ theorem add_one_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a + 1 = a :=
   add_one_of_aleph0_le ha
 #align cardinal.add_one_eq Cardinal.add_one_eq
 
--- Porting note: removed `simp`, `simp` can prove it
+-- Porting note (#10618): removed `simp`, `simp` can prove it
 theorem mk_add_one_eq {α : Type*} [Infinite α] : #α + 1 = #α :=
   add_one_eq (aleph0_le_mk α)
 #align cardinal.mk_add_one_eq Cardinal.mk_add_one_eq

chore: remove useless tactics (#11333)

The removal of some pointless tactics flagged by #11308.

ee18bf38

Diff

@@ -500,7 +500,6 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c := by
   refine' Acc.recOn (Cardinal.lt_wf.apply c) (fun c _ => Quotient.inductionOn c fun α IH ol => _) h
   -- consider the minimal well-order `r` on `α` (a type with cardinality `c`).
   rcases ord_eq α with ⟨r, wo, e⟩
-  skip
   letI := linearOrderOfSTO r
   haveI : IsWellOrder α (· < ·) := wo
   -- Define an order `s` on `α × α` by writing `(a, b) < (c, d)` if `max a b < max c d`, or
@@ -1354,7 +1353,7 @@ theorem mk_compl_eq_mk_compl_finite_same {α : Type u} [Finite α] {s t : Set α
 
 theorem extend_function {α β : Type*} {s : Set α} (f : s ↪ β)
     (h : Nonempty ((sᶜ : Set α) ≃ ((range f)ᶜ : Set β))) : ∃ g : α ≃ β, ∀ x : s, g x = f x := by
-  intros; have := h; cases' this with g
+  have := h; cases' this with g
   let h : α ≃ β :=
     (Set.sumCompl (s : Set α)).symm.trans
       ((sumCongr (Equiv.ofInjective f f.2) g).trans (Set.sumCompl (range f)))

chore: Remove ball and bex from lemma names (#10816)

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

c697e040

Diff

@@ -860,7 +860,7 @@ variable [Nonempty ι] [Nonempty ι'] (hf : BddAbove (range f))
 protected theorem ciSup_add (c : Cardinal.{v}) : (⨆ i, f i) + c = ⨆ i, f i + c := by
   have : ∀ i, f i + c ≤ (⨆ i, f i) + c := fun i ↦ add_le_add_right (le_ciSup hf i) c
   refine le_antisymm ?_ (ciSup_le' this)
-  have bdd : BddAbove (range (f · + c)) := ⟨_, forall_range_iff.mpr this⟩
+  have bdd : BddAbove (range (f · + c)) := ⟨_, forall_mem_range.mpr this⟩
   obtain hs | hs := lt_or_le (⨆ i, f i) ℵ₀
   · obtain ⟨i, hi⟩ := exists_eq_of_iSup_eq_of_not_isLimit
       f hf _ (fun h ↦ hs.not_le h.aleph0_le) rfl
@@ -883,11 +883,11 @@ protected theorem ciSup_mul (c : Cardinal.{v}) : (⨆ i, f i) * c = ⨆ i, f i *
   obtain rfl | h0 := eq_or_ne c 0; · simp
   by_cases hf : BddAbove (range f); swap
   · have hfc : ¬ BddAbove (range (f · * c)) := fun bdd ↦ hf
-      ⟨⨆ i, f i * c, forall_range_iff.mpr fun i ↦ (le_mul_right h0).trans (le_ciSup bdd i)⟩
+      ⟨⨆ i, f i * c, forall_mem_range.mpr fun i ↦ (le_mul_right h0).trans (le_ciSup bdd i)⟩
     simp [iSup, csSup_of_not_bddAbove, hf, hfc]
   have : ∀ i, f i * c ≤ (⨆ i, f i) * c := fun i ↦ mul_le_mul_right' (le_ciSup hf i) c
   refine le_antisymm ?_ (ciSup_le' this)
-  have bdd : BddAbove (range (f · * c)) := ⟨_, forall_range_iff.mpr this⟩
+  have bdd : BddAbove (range (f · * c)) := ⟨_, forall_mem_range.mpr this⟩
   obtain hs | hs := lt_or_le (⨆ i, f i) ℵ₀
   · obtain ⟨i, hi⟩ := exists_eq_of_iSup_eq_of_not_isLimit
       f hf _ (fun h ↦ hs.not_le h.aleph0_le) rfl

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

@@ -50,7 +50,8 @@ noncomputable section
 
 open Function Cardinal Set Equiv Order
 
-open Classical Cardinal Ordinal
+open scoped Classical
+open Cardinal Ordinal
 
 universe u v w

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -573,12 +573,12 @@ theorem mul_aleph0_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a * ℵ₀ = a :=
   (mul_eq_max ha le_rfl).trans (max_eq_left ha)
 #align cardinal.mul_aleph_0_eq Cardinal.mul_aleph0_eq
 
---Porting note: removed `simp`, `simp` can prove it
+-- Porting note: removed `simp`, `simp` can prove it
 theorem aleph0_mul_mk_eq {α : Type*} [Infinite α] : ℵ₀ * #α = #α :=
   aleph0_mul_eq (aleph0_le_mk α)
 #align cardinal.aleph_0_mul_mk_eq Cardinal.aleph0_mul_mk_eq
 
---Porting note: removed `simp`, `simp` can prove it
+-- Porting note: removed `simp`, `simp` can prove it
 theorem mk_mul_aleph0_eq {α : Type*} [Infinite α] : #α * ℵ₀ = #α :=
   mul_aleph0_eq (aleph0_le_mk α)
 #align cardinal.mk_mul_aleph_0_eq Cardinal.mk_mul_aleph0_eq
@@ -816,7 +816,7 @@ theorem add_one_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a + 1 = a :=
   add_one_of_aleph0_le ha
 #align cardinal.add_one_eq Cardinal.add_one_eq
 
---Porting note: removed `simp`, `simp` can prove it
+-- Porting note: removed `simp`, `simp` can prove it
 theorem mk_add_one_eq {α : Type*} [Infinite α] : #α + 1 = #α :=
   add_one_eq (aleph0_le_mk α)
 #align cardinal.mk_add_one_eq Cardinal.mk_add_one_eq
@@ -1382,7 +1382,7 @@ theorem extend_function_of_lt {α β : Type*} {s : Set α} (f : s ↪ β) (hs :
 #align cardinal.extend_function_of_lt Cardinal.extend_function_of_lt
 
 
---Porting note: we no longer express literals as `bit0` and `bit1` in Lean 4, so we can't use this
+-- Porting note: we no longer express literals as `bit0` and `bit1` in Lean 4, so we can't use this
 -- section Bit
 
 -- /-!

chore: more backporting of simp changes from #10995 (#11001)

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

d9589c14

Diff

@@ -524,7 +524,7 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c := by
       _
   · have : { q | s q p } ⊆ insert (g p) { x | x < g p } ×ˢ insert (g p) { x | x < g p } := by
       intro q h
-      simp only [Preimage, ge_iff_le, Embedding.coeFn_mk, Prod.lex_def, typein_lt_typein,
+      simp only [s, f, Preimage, ge_iff_le, Embedding.coeFn_mk, Prod.lex_def, typein_lt_typein,
         typein_inj, mem_setOf_eq] at h
       exact max_le_iff.1 (le_iff_lt_or_eq.2 <| h.imp_right And.left)
     suffices H : (insert (g p) { x | r x (g p) } : Set α) ≃ Sum { x | r x (g p) } PUnit from
@@ -1357,7 +1357,7 @@ theorem extend_function {α β : Type*} {s : Set α} (f : s ↪ β)
   let h : α ≃ β :=
     (Set.sumCompl (s : Set α)).symm.trans
       ((sumCongr (Equiv.ofInjective f f.2) g).trans (Set.sumCompl (range f)))
-  refine' ⟨h, _⟩; rintro ⟨x, hx⟩; simp [Set.sumCompl_symm_apply_of_mem, hx]
+  refine' ⟨h, _⟩; rintro ⟨x, hx⟩; simp [h, Set.sumCompl_symm_apply_of_mem, hx]
 #align cardinal.extend_function Cardinal.extend_function
 
 theorem extend_function_finite {α : Type u} {β : Type v} [Finite α] {s : Set α} (f : s ↪ β)

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

@@ -603,7 +603,7 @@ theorem mul_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b
 theorem mul_le_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) : a * b ≤ max a b := by
   convert mul_le_mul' (le_max_left a b) (le_max_right a b) using 1
   rw [mul_eq_self]
-  refine' h.trans (le_max_left a b)
+  exact h.trans (le_max_left a b)
 #align cardinal.mul_le_max_of_aleph_0_le_left Cardinal.mul_le_max_of_aleph0_le_left
 
 theorem mul_eq_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) (h' : b ≠ 0) :

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

@@ -527,16 +527,14 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c := by
       simp only [Preimage, ge_iff_le, Embedding.coeFn_mk, Prod.lex_def, typein_lt_typein,
         typein_inj, mem_setOf_eq] at h
       exact max_le_iff.1 (le_iff_lt_or_eq.2 <| h.imp_right And.left)
-    suffices H : (insert (g p) { x | r x (g p) } : Set α) ≃ Sum { x | r x (g p) } PUnit
-    · exact
-        ⟨(Set.embeddingOfSubset _ _ this).trans
-            ((Equiv.Set.prod _ _).trans (H.prodCongr H)).toEmbedding⟩
+    suffices H : (insert (g p) { x | r x (g p) } : Set α) ≃ Sum { x | r x (g p) } PUnit from
+      ⟨(Set.embeddingOfSubset _ _ this).trans
+        ((Equiv.Set.prod _ _).trans (H.prodCongr H)).toEmbedding⟩
     refine' (Equiv.Set.insert _).trans ((Equiv.refl _).sumCongr punitEquivPUnit)
     apply @irrefl _ r
   cases' lt_or_le (card (succ (typein (· < ·) (g p)))) ℵ₀ with qo qo
   · exact (mul_lt_aleph0 qo qo).trans_le ol
-  · suffices : (succ (typein LT.lt (g p))).card < ⟦α⟧
-    · exact (IH _ this qo).trans_lt this
+  · suffices (succ (typein LT.lt (g p))).card < ⟦α⟧ from (IH _ this qo).trans_lt this
     rw [← lt_ord]
     apply (ord_isLimit ol).2
     rw [mk'_def, e]
@@ -1093,8 +1091,8 @@ variable [Infinite α] {α β'}
 
 theorem mk_perm_eq_self_power : #(Equiv.Perm α) = #α ^ #α :=
   ((mk_equiv_le_embedding α α).trans (mk_embedding_le_arrow α α)).antisymm <| by
-    suffices : Nonempty ((α → Bool) ↪ Equiv.Perm (α × Bool))
-    · obtain ⟨e⟩ : Nonempty (α ≃ α × Bool)
+    suffices Nonempty ((α → Bool) ↪ Equiv.Perm (α × Bool)) by
+      obtain ⟨e⟩ : Nonempty (α ≃ α × Bool)
       · erw [← Cardinal.eq, mk_prod, lift_uzero, mk_bool,
           lift_natCast, mul_two, add_eq_self (aleph0_le_mk α)]
       erw [← le_def, mk_arrow, lift_uzero, mk_bool, lift_natCast 2] at this
@@ -1273,8 +1271,7 @@ theorem mk_bounded_set_le_of_infinite (α : Type u) [Infinite α] (c : Cardinal)
     dsimp only
     rw [dif_pos this]
     congr
-    suffices : Classical.choose this = ⟨x, h⟩
-    exact congr_arg Subtype.val this
+    suffices Classical.choose this = ⟨x, h⟩ from congr_arg Subtype.val this
     apply g.2
     exact Classical.choose_spec this
 #align cardinal.mk_bounded_set_le_of_infinite Cardinal.mk_bounded_set_le_of_infinite

chore(Cardinal/Basic): split (#10466)

Move toNat and toPartENat to new files.

No changes in the code moved to the new files. One lemma remains in Basic but used toNat in the proof, so I changed the proof.

I'm going to redefine them in terms of toENat, so I need to move them out of Basic first.

c2320208

Diff

@@ -5,6 +5,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Floris van Doorn
 -/
 import Mathlib.Data.Finsupp.Multiset
 import Mathlib.Order.Bounded
+import Mathlib.SetTheory.Cardinal.PartENat
 import Mathlib.SetTheory.Ordinal.Principal
 import Mathlib.Tactic.Linarith

fix(Cardinal): fix theorem names (#10465)

Remove unnecessary of_lt_aleph_0 from 2 theorem names. Also fix typos in the comments of 2 other files.

Co-authored-by: damiano <adomani@gmail.com>

a6f14574

Diff

@@ -944,14 +944,20 @@ theorem add_le_add_iff_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < Cardinal
 #align cardinal.add_le_add_iff_of_lt_aleph_0 Cardinal.add_le_add_iff_of_lt_aleph0
 
 @[simp]
-theorem add_nat_le_add_nat_iff_of_lt_aleph_0 {α β : Cardinal} (n : ℕ) : α + n ≤ β + n ↔ α ≤ β :=
+theorem add_nat_le_add_nat_iff {α β : Cardinal} (n : ℕ) : α + n ≤ β + n ↔ α ≤ β :=
   add_le_add_iff_of_lt_aleph0 (nat_lt_aleph0 n)
-#align cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0 Cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0
+#align cardinal.add_nat_le_add_nat_iff_of_lt_aleph_0 Cardinal.add_nat_le_add_nat_iff
+
+@[deprecated]
+alias add_nat_le_add_nat_iff_of_lt_aleph_0 := add_nat_le_add_nat_iff  -- deprecated on 2024-02-12
 
 @[simp]
-theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β + 1 ↔ α ≤ β :=
+theorem add_one_le_add_one_iff {α β : Cardinal} : α + 1 ≤ β + 1 ↔ α ≤ β :=
   add_le_add_iff_of_lt_aleph0 one_lt_aleph0
-#align cardinal.add_one_le_add_one_iff_of_lt_aleph_0 Cardinal.add_one_le_add_one_iff_of_lt_aleph_0
+#align cardinal.add_one_le_add_one_iff_of_lt_aleph_0 Cardinal.add_one_le_add_one_iff
+
+@[deprecated]
+alias add_one_le_add_one_iff_of_lt_aleph_0 := add_one_le_add_one_iff  -- deprecated on 2024-02-12
 
 /-! ### Properties about power -/

chore(*): rename FunLike to DFunLike (#9785)

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

82656743

Diff

@@ -1080,7 +1080,7 @@ variable (α β')
 
 theorem mk_equiv_le_embedding : #(α ≃ β') ≤ #(α ↪ β') := ⟨⟨_, Equiv.toEmbedding_injective⟩⟩
 
-theorem mk_embedding_le_arrow : #(α ↪ β') ≤ #(α → β') := ⟨⟨_, FunLike.coe_injective⟩⟩
+theorem mk_embedding_le_arrow : #(α ↪ β') ≤ #(α → β') := ⟨⟨_, DFunLike.coe_injective⟩⟩
 
 variable [Infinite α] {α β'}

feat(Cardinal): #(α ≃ β) and #(α ↪ β) in the infinite case (#9646)

Main results:

If two types have the same infinite cardinality, then there are as many Equivs between them as there are functions.
If B has infinite cardinality no less than #A, then there are as many embeddings from A into B as there are functions.
If A has infinite cardinality no less than #B, then there are as many surjective functions from A to B as there are functions.

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

d91d6797

Diff

@@ -1042,6 +1042,108 @@ theorem powerlt_aleph0_le (c : Cardinal) : c ^< ℵ₀ ≤ max c ℵ₀ := by
 /-! ### Computing cardinality of various types -/
 
 
+section Function
+
+variable {α β : Type u} {β' : Type v}
+
+theorem mk_equiv_eq_zero_iff_lift_ne : #(α ≃ β') = 0 ↔ lift.{v} #α ≠ lift.{u} #β' := by
+  rw [mk_eq_zero_iff, ← not_nonempty_iff, ← lift_mk_eq']
+
+theorem mk_equiv_eq_zero_iff_ne : #(α ≃ β) = 0 ↔ #α ≠ #β := by
+  rw [mk_equiv_eq_zero_iff_lift_ne, lift_id, lift_id]
+
+/-- This lemma makes lemmas assuming `Infinite α` applicable to the situation where we have
+  `Infinite β` instead. -/
+theorem mk_equiv_comm : #(α ≃ β') = #(β' ≃ α) :=
+  (ofBijective _ symm_bijective).cardinal_eq
+
+theorem mk_embedding_eq_zero_iff_lift_lt : #(α ↪ β') = 0 ↔ lift.{u} #β' < lift.{v} #α := by
+  rw [mk_eq_zero_iff, ← not_nonempty_iff, ← lift_mk_le', not_le]
+
+theorem mk_embedding_eq_zero_iff_lt : #(α ↪ β) = 0 ↔ #β < #α := by
+  rw [mk_embedding_eq_zero_iff_lift_lt, lift_lt]
+
+theorem mk_arrow_eq_zero_iff : #(α → β') = 0 ↔ #α ≠ 0 ∧ #β' = 0 := by
+  simp_rw [mk_eq_zero_iff, mk_ne_zero_iff, isEmpty_fun]
+
+theorem mk_surjective_eq_zero_iff_lift :
+    #{f : α → β' | Surjective f} = 0 ↔ lift.{v} #α < lift.{u} #β' ∨ (#α ≠ 0 ∧ #β' = 0) := by
+  rw [← not_iff_not, not_or, not_lt, lift_mk_le', ← Ne, not_and_or, not_ne_iff, and_comm]
+  simp_rw [mk_ne_zero_iff, mk_eq_zero_iff, nonempty_coe_sort,
+    Set.Nonempty, mem_setOf, exists_surjective_iff, nonempty_fun]
+
+theorem mk_surjective_eq_zero_iff :
+    #{f : α → β | Surjective f} = 0 ↔ #α < #β ∨ (#α ≠ 0 ∧ #β = 0) := by
+  rw [mk_surjective_eq_zero_iff_lift, lift_lt]
+
+variable (α β')
+
+theorem mk_equiv_le_embedding : #(α ≃ β') ≤ #(α ↪ β') := ⟨⟨_, Equiv.toEmbedding_injective⟩⟩
+
+theorem mk_embedding_le_arrow : #(α ↪ β') ≤ #(α → β') := ⟨⟨_, FunLike.coe_injective⟩⟩
+
+variable [Infinite α] {α β'}
+
+theorem mk_perm_eq_self_power : #(Equiv.Perm α) = #α ^ #α :=
+  ((mk_equiv_le_embedding α α).trans (mk_embedding_le_arrow α α)).antisymm <| by
+    suffices : Nonempty ((α → Bool) ↪ Equiv.Perm (α × Bool))
+    · obtain ⟨e⟩ : Nonempty (α ≃ α × Bool)
+      · erw [← Cardinal.eq, mk_prod, lift_uzero, mk_bool,
+          lift_natCast, mul_two, add_eq_self (aleph0_le_mk α)]
+      erw [← le_def, mk_arrow, lift_uzero, mk_bool, lift_natCast 2] at this
+      rwa [← power_def, power_self_eq (aleph0_le_mk α), e.permCongr.cardinal_eq]
+    refine ⟨⟨fun f ↦ Involutive.toPerm (fun x ↦ ⟨x.1, xor (f x.1) x.2⟩) fun x ↦ ?_, fun f g h ↦ ?_⟩⟩
+    · simp_rw [← Bool.xor_assoc, Bool.xor_self, Bool.false_xor]
+    · ext a; rw [← (f a).xor_false, ← (g a).xor_false]; exact congr(($h ⟨a, false⟩).2)
+
+theorem mk_perm_eq_two_power : #(Equiv.Perm α) = 2 ^ #α := by
+  rw [mk_perm_eq_self_power, power_self_eq (aleph0_le_mk α)]
+
+variable (leq : lift.{v} #α = lift.{u} #β') (eq : #α = #β)
+
+theorem mk_equiv_eq_arrow_of_lift_eq : #(α ≃ β') = #(α → β') := by
+  obtain ⟨e⟩ := lift_mk_eq'.mp leq
+  have e₁ := lift_mk_eq'.mpr ⟨.equivCongr (.refl α) e⟩
+  have e₂ := lift_mk_eq'.mpr ⟨.arrowCongr (.refl α) e⟩
+  rw [lift_id'.{u,v}] at e₁ e₂
+  rw [← e₁, ← e₂, lift_inj, mk_perm_eq_self_power, power_def]
+
+theorem mk_equiv_eq_arrow_of_eq : #(α ≃ β) = #(α → β) :=
+  mk_equiv_eq_arrow_of_lift_eq congr(lift $eq)
+
+theorem mk_equiv_of_lift_eq : #(α ≃ β') = 2 ^ lift.{v} #α := by
+  erw [← (lift_mk_eq'.2 ⟨.equivCongr (.refl α) (lift_mk_eq'.1 leq).some⟩).trans (lift_id'.{u,v} _),
+    lift_umax.{u,v}, mk_perm_eq_two_power, lift_power, lift_natCast]; rfl
+
+theorem mk_equiv_of_eq : #(α ≃ β) = 2 ^ #α := by rw [mk_equiv_of_lift_eq (lift_inj.mpr eq), lift_id]
+
+variable (lle : lift.{u} #β' ≤ lift.{v} #α) (le : #β ≤ #α)
+
+theorem mk_embedding_eq_arrow_of_lift_le : #(β' ↪ α) = #(β' → α) :=
+  (mk_embedding_le_arrow _ _).antisymm <| by
+    conv_rhs => rw [← (Equiv.embeddingCongr (.refl _)
+      (Cardinal.eq.mp <| mul_eq_self <| aleph0_le_mk α).some).cardinal_eq]
+    obtain ⟨e⟩ := lift_mk_le'.mp lle
+    exact ⟨⟨fun f ↦ ⟨fun b ↦ ⟨e b, f b⟩, fun _ _ h ↦ e.injective congr(Prod.fst $h)⟩,
+      fun f g h ↦ funext fun b ↦ congr(Prod.snd <| $h b)⟩⟩
+
+theorem mk_embedding_eq_arrow_of_le : #(β ↪ α) = #(β → α) :=
+  mk_embedding_eq_arrow_of_lift_le (lift_le.mpr le)
+
+theorem mk_surjective_eq_arrow_of_lift_le : #{f : α → β' | Surjective f} = #(α → β') :=
+  (mk_set_le _).antisymm <|
+    have ⟨e⟩ : Nonempty (α ≃ α ⊕ β') := by
+      simp_rw [← lift_mk_eq', mk_sum, lift_add, lift_lift]; rw [lift_umax.{u,v}, eq_comm]
+      exact add_eq_left (aleph0_le_lift.mpr <| aleph0_le_mk α) lle
+    ⟨⟨fun f ↦ ⟨fun a ↦ (e a).elim f id, fun b ↦ ⟨e.symm (.inr b), congr_arg _ (e.right_inv _)⟩⟩,
+      fun f g h ↦ funext fun a ↦ by
+        simpa only [e.apply_symm_apply] using congr_fun (Subtype.ext_iff.mp h) (e.symm <| .inl a)⟩⟩
+
+theorem mk_surjective_eq_arrow_of_le : #{f : α → β | Surjective f} = #(α → β) :=
+  mk_surjective_eq_arrow_of_lift_le (lift_le.mpr le)
+
+end Function
+
 @[simp]
 theorem mk_list_eq_mk (α : Type u) [Infinite α] : #(List α) = #α :=
   have H1 : ℵ₀ ≤ #α := aleph0_le_mk α

feat(LinearAlgebra, Cardinal): new cardinal lemmas to generalize some results about Module.rank in #9151 (#9253)

Proves that Sup (ciSup) commutes with cardinal addition (ciSup_add_ciSup) and multiplication. Generalize results in Cardinal/Basic introduced in #8842 to achieve this.
Use ciSup_add_ciSup to prove that the rank of a module is always at least the rank of a submodule plus the rank of the quotient by the submodule. Deduce that the rank of a product module is at least the sum of the ranks of the two factors.
Show that quotienting by a torsion submodule preserves the rank.
Golf rank_zero_iff_forall_zero using a recently added lemma.

Co-authored-by: Andrew Yang <the.erd.one@gmail.com>

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

4ad935a4

Diff

@@ -849,6 +849,63 @@ protected theorem eq_of_add_eq_add_right {a b c : Cardinal} (h : a + b = c + b)
   exact Cardinal.eq_of_add_eq_add_left h hb
 #align cardinal.eq_of_add_eq_add_right Cardinal.eq_of_add_eq_add_right
 
+section ciSup
+
+variable {ι : Type u} {ι' : Type w} (f : ι → Cardinal.{v})
+
+section add
+
+variable [Nonempty ι] [Nonempty ι'] (hf : BddAbove (range f))
+
+protected theorem ciSup_add (c : Cardinal.{v}) : (⨆ i, f i) + c = ⨆ i, f i + c := by
+  have : ∀ i, f i + c ≤ (⨆ i, f i) + c := fun i ↦ add_le_add_right (le_ciSup hf i) c
+  refine le_antisymm ?_ (ciSup_le' this)
+  have bdd : BddAbove (range (f · + c)) := ⟨_, forall_range_iff.mpr this⟩
+  obtain hs | hs := lt_or_le (⨆ i, f i) ℵ₀
+  · obtain ⟨i, hi⟩ := exists_eq_of_iSup_eq_of_not_isLimit
+      f hf _ (fun h ↦ hs.not_le h.aleph0_le) rfl
+    exact hi ▸ le_ciSup bdd i
+  rw [add_eq_max hs, max_le_iff]
+  exact ⟨ciSup_mono bdd fun i ↦ self_le_add_right _ c,
+    (self_le_add_left _ _).trans (le_ciSup bdd <| Classical.arbitrary ι)⟩
+
+protected theorem add_ciSup (c : Cardinal.{v}) : c + (⨆ i, f i) = ⨆ i, c + f i := by
+  rw [add_comm, Cardinal.ciSup_add f hf]; simp_rw [add_comm]
+
+protected theorem ciSup_add_ciSup (g : ι' → Cardinal.{v}) (hg : BddAbove (range g)) :
+    (⨆ i, f i) + (⨆ j, g j) = ⨆ (i) (j), f i + g j := by
+  simp_rw [Cardinal.ciSup_add f hf, Cardinal.add_ciSup g hg]
+
+end add
+
+protected theorem ciSup_mul (c : Cardinal.{v}) : (⨆ i, f i) * c = ⨆ i, f i * c := by
+  cases isEmpty_or_nonempty ι; · simp
+  obtain rfl | h0 := eq_or_ne c 0; · simp
+  by_cases hf : BddAbove (range f); swap
+  · have hfc : ¬ BddAbove (range (f · * c)) := fun bdd ↦ hf
+      ⟨⨆ i, f i * c, forall_range_iff.mpr fun i ↦ (le_mul_right h0).trans (le_ciSup bdd i)⟩
+    simp [iSup, csSup_of_not_bddAbove, hf, hfc]
+  have : ∀ i, f i * c ≤ (⨆ i, f i) * c := fun i ↦ mul_le_mul_right' (le_ciSup hf i) c
+  refine le_antisymm ?_ (ciSup_le' this)
+  have bdd : BddAbove (range (f · * c)) := ⟨_, forall_range_iff.mpr this⟩
+  obtain hs | hs := lt_or_le (⨆ i, f i) ℵ₀
+  · obtain ⟨i, hi⟩ := exists_eq_of_iSup_eq_of_not_isLimit
+      f hf _ (fun h ↦ hs.not_le h.aleph0_le) rfl
+    exact hi ▸ le_ciSup bdd i
+  rw [mul_eq_max_of_aleph0_le_left hs h0, max_le_iff]
+  obtain ⟨i, hi⟩ := exists_lt_of_lt_ciSup' (one_lt_aleph0.trans_le hs)
+  exact ⟨ciSup_mono bdd fun i ↦ le_mul_right h0,
+    (le_mul_left (zero_lt_one.trans hi).ne').trans (le_ciSup bdd i)⟩
+
+protected theorem mul_ciSup (c : Cardinal.{v}) : c * (⨆ i, f i) = ⨆ i, c * f i := by
+  rw [mul_comm, Cardinal.ciSup_mul f]; simp_rw [mul_comm]
+
+protected theorem ciSup_mul_ciSup (g : ι' → Cardinal.{v}) :
+    (⨆ i, f i) * (⨆ j, g j) = ⨆ (i) (j), f i * g j := by
+  simp_rw [Cardinal.ciSup_mul f, Cardinal.mul_ciSup g]
+
+end ciSup
+
 @[simp]
 theorem aleph_add_aleph (o₁ o₂ : Ordinal) : aleph o₁ + aleph o₂ = aleph (max o₁ o₂) := by
   rw [Cardinal.add_eq_max (aleph0_le_aleph o₁), max_aleph_eq]

chore: remove uses of cases' (#9171)

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

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

3fca282c

Diff

@@ -258,7 +258,7 @@ theorem aleph_le {o₁ o₂ : Ordinal} : aleph o₁ ≤ aleph o₂ ↔ o₁ ≤
 
 @[simp]
 theorem max_aleph_eq (o₁ o₂ : Ordinal) : max (aleph o₁) (aleph o₂) = aleph (max o₁ o₂) := by
-  cases' le_total (aleph o₁) (aleph o₂) with h h
+  rcases le_total (aleph o₁) (aleph o₂) with h | h
   · rw [max_eq_right h, max_eq_right (aleph_le.1 h)]
   · rw [max_eq_left h, max_eq_left (aleph_le.1 h)]
 #align cardinal.max_aleph_eq Cardinal.max_aleph_eq
@@ -609,7 +609,7 @@ theorem mul_le_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) : a * b
 
 theorem mul_eq_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) (h' : b ≠ 0) :
     a * b = max a b := by
-  cases' le_or_lt ℵ₀ b with hb hb
+  rcases le_or_lt ℵ₀ b with hb | hb
   · exact mul_eq_max h hb
   refine' (mul_le_max_of_aleph0_le_left h).antisymm _
   have : b ≤ a := hb.le.trans h
@@ -637,10 +637,10 @@ theorem mul_eq_max' {a b : Cardinal} (h : ℵ₀ ≤ a * b) : a * b = max a b :=
 theorem mul_le_max (a b : Cardinal) : a * b ≤ max (max a b) ℵ₀ := by
   rcases eq_or_ne a 0 with (rfl | ha0); · simp
   rcases eq_or_ne b 0 with (rfl | hb0); · simp
-  cases' le_or_lt ℵ₀ a with ha ha
+  rcases le_or_lt ℵ₀ a with ha | ha
   · rw [mul_eq_max_of_aleph0_le_left ha hb0]
     exact le_max_left _ _
-  · cases' le_or_lt ℵ₀ b with hb hb
+  · rcases le_or_lt ℵ₀ b with hb | hb
     · rw [mul_comm, mul_eq_max_of_aleph0_le_left hb ha0, max_comm]
       exact le_max_left _ _
     · exact le_max_of_le_right (mul_lt_aleph0 ha hb).le
@@ -667,7 +667,7 @@ theorem le_mul_right {a b : Cardinal} (h : b ≠ 0) : a ≤ a * b := by
 theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧ b ≠ 0 ∨ b = 1 ∨ a = 0 := by
   rw [max_le_iff]
   refine' ⟨fun h => _, _⟩
-  · cases' le_or_lt ℵ₀ a with ha ha
+  · rcases le_or_lt ℵ₀ a with ha | ha
     · have : a ≠ 0 := by
         rintro rfl
         exact ha.not_lt aleph0_pos
@@ -745,10 +745,10 @@ theorem add_mk_eq_max' {α β : Type u} [Infinite β] : #α + #β = max #α #β
 #align cardinal.add_mk_eq_max' Cardinal.add_mk_eq_max'
 
 theorem add_le_max (a b : Cardinal) : a + b ≤ max (max a b) ℵ₀ := by
-  cases' le_or_lt ℵ₀ a with ha ha
+  rcases le_or_lt ℵ₀ a with ha | ha
   · rw [add_eq_max ha]
     exact le_max_left _ _
-  · cases' le_or_lt ℵ₀ b with hb hb
+  · rcases le_or_lt ℵ₀ b with hb | hb
     · rw [add_comm, add_eq_max hb, max_comm]
       exact le_max_left _ _
     · exact le_max_of_le_right (add_lt_aleph0 ha hb).le
@@ -785,7 +785,7 @@ theorem add_eq_right {a b : Cardinal} (hb : ℵ₀ ≤ b) (ha : a ≤ b) : a + b
 theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨ b = 0 := by
   rw [max_le_iff]
   refine' ⟨fun h => _, _⟩
-  · cases' le_or_lt ℵ₀ a with ha ha
+  · rcases le_or_lt ℵ₀ a with ha | ha
     · left
       use ha
       rw [← not_lt]
@@ -824,7 +824,7 @@ theorem mk_add_one_eq {α : Type*} [Infinite α] : #α + 1 = #α :=
 
 protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (ha : a < ℵ₀) :
     b = c := by
-  cases' le_or_lt ℵ₀ b with hb hb
+  rcases le_or_lt ℵ₀ b with hb | hb
   · have : a < b := ha.trans_le hb
     rw [add_eq_right hb this.le, eq_comm] at h
     rw [eq_of_add_eq_of_aleph0_le h this hb]
@@ -959,7 +959,7 @@ theorem power_nat_eq {c : Cardinal.{u}} {n : ℕ} (h1 : ℵ₀ ≤ c) (h2 : 1 
 #align cardinal.power_nat_eq Cardinal.power_nat_eq
 
 theorem power_nat_le_max {c : Cardinal.{u}} {n : ℕ} : c ^ (n : Cardinal.{u}) ≤ max c ℵ₀ := by
-  cases' le_or_lt ℵ₀ c with hc hc
+  rcases le_or_lt ℵ₀ c with hc | hc
   · exact le_max_of_le_left (power_nat_le hc)
   · exact le_max_of_le_right (power_lt_aleph0 hc (nat_lt_aleph0 _)).le
 #align cardinal.power_nat_le_max Cardinal.power_nat_le_max
@@ -975,7 +975,7 @@ theorem powerlt_aleph0 {c : Cardinal} (h : ℵ₀ ≤ c) : c ^< ℵ₀ = c := by
 #align cardinal.powerlt_aleph_0 Cardinal.powerlt_aleph0
 
 theorem powerlt_aleph0_le (c : Cardinal) : c ^< ℵ₀ ≤ max c ℵ₀ := by
-  cases' le_or_lt ℵ₀ c with h h
+  rcases le_or_lt ℵ₀ c with h | h
   · rw [powerlt_aleph0 h]
     apply le_max_left
   rw [powerlt_le]
@@ -1306,7 +1306,7 @@ theorem extend_function_of_lt {α β : Type*} {s : Set α} (f : s ↪ β) (hs :
 
 -- @[simp]
 -- theorem bit0_le_bit0 {a b : Cardinal} : bit0 a ≤ bit0 b ↔ a ≤ b := by
---   cases' le_or_lt ℵ₀ a with ha ha <;> cases' le_or_lt ℵ₀ b with hb hb
+--   rcases le_or_lt ℵ₀ a with ha | ha <;> rcases le_or_lt ℵ₀ b with hb | hb
 --   · rw [bit0_eq_self ha, bit0_eq_self hb]
 --   · rw [bit0_eq_self ha]
 --     refine' iff_of_false (fun h => _) (hb.trans_le ha).not_le
@@ -1322,7 +1322,7 @@ theorem extend_function_of_lt {α β : Type*} {s : Set α} (f : s ↪ β) (hs :
 
 -- @[simp]
 -- theorem bit0_le_bit1 {a b : Cardinal} : bit0 a ≤ bit1 b ↔ a ≤ b := by
---   cases' le_or_lt ℵ₀ a with ha ha <;> cases' le_or_lt ℵ₀ b with hb hb
+--   rcases le_or_lt ℵ₀ a with ha | ha <;> rcases le_or_lt ℵ₀ b with hb | hb
 --   · rw [bit0_eq_self ha, bit1_eq_self_iff.2 hb]
 --   · rw [bit0_eq_self ha]
 --     refine' iff_of_false (fun h => _) (hb.trans_le ha).not_le
@@ -1344,7 +1344,7 @@ theorem extend_function_of_lt {α β : Type*} {s : Set α} (f : s ↪ β) (hs :
 
 -- @[simp]
 -- theorem bit1_le_bit0 {a b : Cardinal} : bit1 a ≤ bit0 b ↔ a < b ∨ a ≤ b ∧ ℵ₀ ≤ a := by
---   cases' le_or_lt ℵ₀ a with ha ha <;> cases' le_or_lt ℵ₀ b with hb hb
+--   rcases le_or_lt ℵ₀ a with ha | ha <;> rcases le_or_lt ℵ₀ b with hb | hb
 --   · simp only [bit1_eq_self_iff.mpr ha, bit0_eq_self hb, ha, and_true_iff]
 --     refine' ⟨fun h => Or.inr h, fun h => _⟩
 --     cases h
@@ -1365,7 +1365,7 @@ theorem extend_function_of_lt {α β : Type*} {s : Set α} (f : s ↪ β) (hs :
 
 -- @[simp]
 -- theorem bit0_lt_bit0 {a b : Cardinal} : bit0 a < bit0 b ↔ a < b := by
---   cases' le_or_lt ℵ₀ a with ha ha <;> cases' le_or_lt ℵ₀ b with hb hb
+--   rcases le_or_lt ℵ₀ a with ha | ha <;> rcases le_or_lt ℵ₀ b with hb | hb
 --   · rw [bit0_eq_self ha, bit0_eq_self hb]
 --   · rw [bit0_eq_self ha]
 --     refine' iff_of_false (fun h => _) (hb.le.trans ha).not_lt
@@ -1381,7 +1381,7 @@ theorem extend_function_of_lt {α β : Type*} {s : Set α} (f : s ↪ β) (hs :
 
 -- @[simp]
 -- theorem bit1_lt_bit0 {a b : Cardinal} : bit1 a < bit0 b ↔ a < b := by
---   cases' le_or_lt ℵ₀ a with ha ha <;> cases' le_or_lt ℵ₀ b with hb hb
+--   rcases le_or_lt ℵ₀ a with ha | ha <;> rcases le_or_lt ℵ₀ b with hb | hb
 --   · rw [bit1_eq_self_iff.2 ha, bit0_eq_self hb]
 --   · rw [bit1_eq_self_iff.2 ha]
 --     refine' iff_of_false (fun h => _) (hb.le.trans ha).not_lt
@@ -1397,7 +1397,7 @@ theorem extend_function_of_lt {α β : Type*} {s : Set α} (f : s ↪ β) (hs :
 
 -- @[simp]
 -- theorem bit1_lt_bit1 {a b : Cardinal} : bit1 a < bit1 b ↔ a < b := by
---   cases' le_or_lt ℵ₀ a with ha ha <;> cases' le_or_lt ℵ₀ b with hb hb
+--   rcases le_or_lt ℵ₀ a with ha | ha <;> rcases le_or_lt ℵ₀ b with hb | hb
 --   · rw [bit1_eq_self_iff.2 ha, bit1_eq_self_iff.2 hb]
 --   · rw [bit1_eq_self_iff.2 ha]
 --     refine' iff_of_false (fun h => _) (hb.le.trans ha).not_lt
@@ -1413,7 +1413,7 @@ theorem extend_function_of_lt {α β : Type*} {s : Set α} (f : s ↪ β) (hs :
 
 -- @[simp]
 -- theorem bit0_lt_bit1 {a b : Cardinal} : bit0 a < bit1 b ↔ a < b ∨ a ≤ b ∧ a < ℵ₀ := by
---   cases' le_or_lt ℵ₀ a with ha ha <;> cases' le_or_lt ℵ₀ b with hb hb
+--   rcases le_or_lt ℵ₀ a with ha | ha <;> rcases le_or_lt ℵ₀ b with hb | hb
 --   · simp [bit0_eq_self ha, bit1_eq_self_iff.2 hb, not_lt.mpr ha]
 --   · rw [bit0_eq_self ha]
 --     refine' iff_of_false (fun h => _) fun h => _

chore: Replace (· op ·) a by (a op ·) (#8843)

I used the regex $\(· (.) ·$ (.)\), replacing with ($2 $1 ·).

d14658b4

Diff

@@ -865,7 +865,7 @@ theorem principal_add_aleph (o : Ordinal) : Ordinal.Principal (· + ·) (aleph o
 #align cardinal.principal_add_aleph Cardinal.principal_add_aleph
 
 theorem add_right_inj_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < aleph0) : α + γ = β + γ ↔ α = β :=
-  ⟨fun h => Cardinal.eq_of_add_eq_add_right h γ₀, fun h => congr_fun (congr_arg (· + ·) h) γ⟩
+  ⟨fun h => Cardinal.eq_of_add_eq_add_right h γ₀, fun h => congr_arg (· + γ) h⟩
 #align cardinal.add_right_inj_of_lt_aleph_0 Cardinal.add_right_inj_of_lt_aleph0
 
 @[simp]

chore: add some Unique instances (#8500)

The aim is to remove some extraneous Nonempty assumptions in Algebra/DirectLimit.

Co-authored-by: Junyan Xu <junyanxu.math@gmail.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com>

9a4ae4a9

Diff

@@ -1071,7 +1071,6 @@ theorem mk_multiset_of_nonempty (α : Type u) [Nonempty α] : #(Multiset α) = m
 theorem mk_multiset_of_infinite (α : Type u) [Infinite α] : #(Multiset α) = #α := by simp
 #align cardinal.mk_multiset_of_infinite Cardinal.mk_multiset_of_infinite
 
-@[simp]
 theorem mk_multiset_of_isEmpty (α : Type u) [IsEmpty α] : #(Multiset α) = 1 :=
   Multiset.toFinsupp.toEquiv.cardinal_eq.trans (by simp)
 #align cardinal.mk_multiset_of_is_empty Cardinal.mk_multiset_of_isEmpty

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

@@ -955,7 +955,7 @@ theorem power_nat_le {c : Cardinal.{u}} {n : ℕ} (h : ℵ₀ ≤ c) : c ^ n ≤
 #align cardinal.power_nat_le Cardinal.power_nat_le
 
 theorem power_nat_eq {c : Cardinal.{u}} {n : ℕ} (h1 : ℵ₀ ≤ c) (h2 : 1 ≤ n) : c ^ n = c :=
-  pow_eq h1 (by exact_mod_cast h2) (nat_lt_aleph0 n)
+  pow_eq h1 (mod_cast h2) (nat_lt_aleph0 n)
 #align cardinal.power_nat_eq Cardinal.power_nat_eq
 
 theorem power_nat_le_max {c : Cardinal.{u}} {n : ℕ} : c ^ (n : Cardinal.{u}) ≤ max c ℵ₀ := by

fix: remove remaining ^ fixes (#8463)

b0e957dd

Diff

@@ -898,11 +898,6 @@ theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β
 
 /-! ### Properties about power -/
 
---Porting note: Annoying workaround because `c ^ n` when `n` is a `ℕ` coerces `c` for some reason.
-local infixr:80 " ^' " => @HPow.hPow Cardinal Cardinal Cardinal _
--- -- mathport name: cardinal.pow.nat
-local infixr:80 " ^ℕ " => @HPow.hPow Cardinal ℕ Cardinal instHPow
-
 theorem pow_le {κ μ : Cardinal.{u}} (H1 : ℵ₀ ≤ κ) (H2 : μ < ℵ₀) : κ ^ μ ≤ κ :=
   let ⟨n, H3⟩ := lt_aleph0.1 H2
   H3.symm ▸
@@ -955,11 +950,11 @@ theorem nat_power_eq {c : Cardinal.{u}} (h : ℵ₀ ≤ c) {n : ℕ} (hn : 2 ≤
   power_eq_two_power h (by assumption_mod_cast) ((nat_lt_aleph0 n).le.trans h)
 #align cardinal.nat_power_eq Cardinal.nat_power_eq
 
-theorem power_nat_le {c : Cardinal.{u}} {n : ℕ} (h : ℵ₀ ≤ c) : c ^ℕ n ≤ c :=
+theorem power_nat_le {c : Cardinal.{u}} {n : ℕ} (h : ℵ₀ ≤ c) : c ^ n ≤ c :=
   pow_le h (nat_lt_aleph0 n)
 #align cardinal.power_nat_le Cardinal.power_nat_le
 
-theorem power_nat_eq {c : Cardinal.{u}} {n : ℕ} (h1 : ℵ₀ ≤ c) (h2 : 1 ≤ n) : c ^ℕ n = c :=
+theorem power_nat_eq {c : Cardinal.{u}} {n : ℕ} (h1 : ℵ₀ ≤ c) (h2 : 1 ≤ n) : c ^ n = c :=
   pow_eq h1 (by exact_mod_cast h2) (nat_lt_aleph0 n)
 #align cardinal.power_nat_eq Cardinal.power_nat_eq

style(SetTheory): remove useless parentheses (#8279)

These were caused by a bad notation precedence in mathlib3, where the local version of ^ was given precedence 0. We're not using the local notation at all in Mathlib4 (partly because it was broken, which this PR fixes).

a084bd51

Diff

@@ -899,7 +899,7 @@ theorem add_one_le_add_one_iff_of_lt_aleph_0 {α β : Cardinal} : α + 1 ≤ β
 /-! ### Properties about power -/
 
 --Porting note: Annoying workaround because `c ^ n` when `n` is a `ℕ` coerces `c` for some reason.
-local infixr:0 "^'" => @HPow.hPow Cardinal Cardinal Cardinal.instPowCardinal
+local infixr:80 " ^' " => @HPow.hPow Cardinal Cardinal Cardinal _
 -- -- mathport name: cardinal.pow.nat
 local infixr:80 " ^ℕ " => @HPow.hPow Cardinal ℕ Cardinal instHPow

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

@@ -555,7 +555,7 @@ theorem mul_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : ℵ₀ ≤ b) : a
 #align cardinal.mul_eq_max Cardinal.mul_eq_max
 
 @[simp]
-theorem mul_mk_eq_max {α β : Type _} [Infinite α] [Infinite β] : #α * #β = max #α #β :=
+theorem mul_mk_eq_max {α β : Type u} [Infinite α] [Infinite β] : #α * #β = max #α #β :=
   mul_eq_max (aleph0_le_mk α) (aleph0_le_mk β)
 #align cardinal.mul_mk_eq_max Cardinal.mul_mk_eq_max
 
@@ -735,12 +735,12 @@ theorem add_eq_max' {a b : Cardinal} (ha : ℵ₀ ≤ b) : a + b = max a b := by
 #align cardinal.add_eq_max' Cardinal.add_eq_max'
 
 @[simp]
-theorem add_mk_eq_max {α β : Type _} [Infinite α] : #α + #β = max #α #β :=
+theorem add_mk_eq_max {α β : Type u} [Infinite α] : #α + #β = max #α #β :=
   add_eq_max (aleph0_le_mk α)
 #align cardinal.add_mk_eq_max Cardinal.add_mk_eq_max
 
 @[simp]
-theorem add_mk_eq_max' {α β : Type _} [Infinite β] : #α + #β = max #α #β :=
+theorem add_mk_eq_max' {α β : Type u} [Infinite β] : #α + #β = max #α #β :=
   add_eq_max' (aleph0_le_mk β)
 #align cardinal.add_mk_eq_max' Cardinal.add_mk_eq_max'
 
@@ -1482,7 +1482,7 @@ open scoped Cardinal
 /--
 Bounding the cardinal of an ordinal-indexed union of sets.
 -/
-lemma mk_iUnion_Ordinal_le_of_le {β : Type _} {o : Ordinal} {c : Cardinal}
+lemma mk_iUnion_Ordinal_le_of_le {β : Type*} {o : Ordinal} {c : Cardinal}
     (ho : o.card ≤ c) (hc : ℵ₀ ≤ c) (A : Ordinal → Set β)
     (hA : ∀ j < o, #(A j) ≤ c) :
     #(⋃ j < o, A j) ≤ c := by

feat: some simp lemmas to compute more cardinals (#7660)

a577026a

Diff

@@ -810,8 +810,11 @@ theorem add_nat_eq {a : Cardinal} (n : ℕ) (ha : ℵ₀ ≤ a) : a + n = a :=
   add_eq_left ha ((nat_lt_aleph0 _).le.trans ha)
 #align cardinal.add_nat_eq Cardinal.add_nat_eq
 
+theorem nat_add_eq {a : Cardinal} (n : ℕ) (ha : ℵ₀ ≤ a) : n + a = a := by
+  rw [add_comm, add_nat_eq n ha]
+
 theorem add_one_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a + 1 = a :=
-  add_eq_left ha (one_le_aleph0.trans ha)
+  add_one_of_aleph0_le ha
 #align cardinal.add_one_eq Cardinal.add_one_eq
 
 --Porting note: removed `simp`, `simp` can prove it

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

@@ -24,7 +24,9 @@ using ordinals.
   It is an order isomorphism between ordinals and cardinals.
 * The function `Cardinal.aleph` gives the infinite cardinals listed by their
   ordinal index. `aleph 0 = ℵ₀`, `aleph 1 = succ ℵ₀` is the first
-  uncountable cardinal, and so on.
+  uncountable cardinal, and so on. The notation `ω_` combines the latter with `Cardinal.ord`,
+  giving an enumeration of (infinite) initial ordinals.
+  Thus `ω_ 0 = ω` and `ω₁ = ω_ 1` is the first uncountable ordinal.
 * The function `Cardinal.beth` enumerates the Beth cardinals. `beth 0 = ℵ₀`,
   `beth (succ o) = 2 ^ beth o`, and for a limit ordinal `o`, `beth o` is the supremum of `beth a`
   for `a < o`.
@@ -1446,3 +1448,46 @@ theorem extend_function_of_lt {α β : Type*} {s : Set α} (f : s ↪ β) (hs :
 -- end Bit
 
 end Cardinal
+
+section Initial
+
+namespace Ordinal
+
+/--
+`ω_ o` is a notation for the *initial ordinal* of cardinality
+`aleph o`. Thus, for example `ω_ 0 = ω`.
+-/
+scoped notation "ω_" o => ord <| aleph o
+
+/--
+`ω₁` is the first uncountable ordinal.
+-/
+scoped notation "ω₁" => ord <| aleph 1
+
+lemma omega_lt_omega1 : ω < ω₁ := ord_aleph0.symm.trans_lt (ord_lt_ord.mpr (aleph0_lt_aleph_one))
+
+section OrdinalIndices
+/-!
+### Cardinal operations with ordinal indices
+
+Results on cardinality of ordinal-indexed families of sets.
+-/
+namespace Cardinal
+
+open scoped Cardinal
+
+/--
+Bounding the cardinal of an ordinal-indexed union of sets.
+-/
+lemma mk_iUnion_Ordinal_le_of_le {β : Type _} {o : Ordinal} {c : Cardinal}
+    (ho : o.card ≤ c) (hc : ℵ₀ ≤ c) (A : Ordinal → Set β)
+    (hA : ∀ j < o, #(A j) ≤ c) :
+    #(⋃ j < o, A j) ≤ c := by
+  simp_rw [← mem_Iio, biUnion_eq_iUnion, iUnion, iSup, ← o.enumIsoOut.symm.surjective.range_comp]
+  apply ((mk_iUnion_le _).trans _).trans_eq (mul_eq_self hc)
+  rw [mk_ordinal_out]
+  exact mul_le_mul' ho <| ciSup_le' <| (hA _ <| typein_lt_self ·)
+
+end Cardinal
+
+end OrdinalIndices

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

@@ -345,7 +345,7 @@ theorem aleph0_lt_aleph_one : ℵ₀ < aleph 1 := by
   apply lt_succ
 #align cardinal.aleph_0_lt_aleph_one Cardinal.aleph0_lt_aleph_one
 
-theorem countable_iff_lt_aleph_one {α : Type _} (s : Set α) : s.Countable ↔ #s < aleph 1 := by
+theorem countable_iff_lt_aleph_one {α : Type*} (s : Set α) : s.Countable ↔ #s < aleph 1 := by
   rw [← succ_aleph0, lt_succ_iff, le_aleph0_iff_set_countable]
 #align cardinal.countable_iff_lt_aleph_one Cardinal.countable_iff_lt_aleph_one
 
@@ -573,12 +573,12 @@ theorem mul_aleph0_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a * ℵ₀ = a :=
 #align cardinal.mul_aleph_0_eq Cardinal.mul_aleph0_eq
 
 --Porting note: removed `simp`, `simp` can prove it
-theorem aleph0_mul_mk_eq {α : Type _} [Infinite α] : ℵ₀ * #α = #α :=
+theorem aleph0_mul_mk_eq {α : Type*} [Infinite α] : ℵ₀ * #α = #α :=
   aleph0_mul_eq (aleph0_le_mk α)
 #align cardinal.aleph_0_mul_mk_eq Cardinal.aleph0_mul_mk_eq
 
 --Porting note: removed `simp`, `simp` can prove it
-theorem mk_mul_aleph0_eq {α : Type _} [Infinite α] : #α * ℵ₀ = #α :=
+theorem mk_mul_aleph0_eq {α : Type*} [Infinite α] : #α * ℵ₀ = #α :=
   mul_aleph0_eq (aleph0_le_mk α)
 #align cardinal.mk_mul_aleph_0_eq Cardinal.mk_mul_aleph0_eq
 
@@ -813,7 +813,7 @@ theorem add_one_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a + 1 = a :=
 #align cardinal.add_one_eq Cardinal.add_one_eq
 
 --Porting note: removed `simp`, `simp` can prove it
-theorem mk_add_one_eq {α : Type _} [Infinite α] : #α + 1 = #α :=
+theorem mk_add_one_eq {α : Type*} [Infinite α] : #α + 1 = #α :=
   add_one_eq (aleph0_le_mk α)
 #align cardinal.mk_add_one_eq Cardinal.mk_add_one_eq
 
@@ -1142,19 +1142,19 @@ theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
 /-! ### Properties of `compl` -/
 
 
-theorem mk_compl_of_infinite {α : Type _} [Infinite α] (s : Set α) (h2 : #s < #α) :
+theorem mk_compl_of_infinite {α : Type*} [Infinite α] (s : Set α) (h2 : #s < #α) :
     #(sᶜ : Set α) = #α := by
   refine' eq_of_add_eq_of_aleph0_le _ h2 (aleph0_le_mk α)
   exact mk_sum_compl s
 #align cardinal.mk_compl_of_infinite Cardinal.mk_compl_of_infinite
 
-theorem mk_compl_finset_of_infinite {α : Type _} [Infinite α] (s : Finset α) :
+theorem mk_compl_finset_of_infinite {α : Type*} [Infinite α] (s : Finset α) :
     #((↑s)ᶜ : Set α) = #α := by
   apply mk_compl_of_infinite
   exact (finset_card_lt_aleph0 s).trans_le (aleph0_le_mk α)
 #align cardinal.mk_compl_finset_of_infinite Cardinal.mk_compl_finset_of_infinite
 
-theorem mk_compl_eq_mk_compl_infinite {α : Type _} [Infinite α] {s t : Set α} (hs : #s < #α)
+theorem mk_compl_eq_mk_compl_infinite {α : Type*} [Infinite α] {s t : Set α} (hs : #s < #α)
     (ht : #t < #α) : #(sᶜ : Set α) = #(tᶜ : Set α) := by
   rw [mk_compl_of_infinite s hs, mk_compl_of_infinite t ht]
 #align cardinal.mk_compl_eq_mk_compl_infinite Cardinal.mk_compl_eq_mk_compl_infinite
@@ -1189,7 +1189,7 @@ theorem mk_compl_eq_mk_compl_finite_same {α : Type u} [Finite α] {s t : Set α
 /-! ### Extending an injection to an equiv -/
 
 
-theorem extend_function {α β : Type _} {s : Set α} (f : s ↪ β)
+theorem extend_function {α β : Type*} {s : Set α} (f : s ↪ β)
     (h : Nonempty ((sᶜ : Set α) ≃ ((range f)ᶜ : Set β))) : ∃ g : α ≃ β, ∀ x : s, g x = f x := by
   intros; have := h; cases' this with g
   let h : α ≃ β :=
@@ -1207,7 +1207,7 @@ theorem extend_function_finite {α : Type u} {β : Type v} [Finite α] {s : Set
   rw [mk_range_eq_lift.{u, v, max u v}]; exact f.2
 #align cardinal.extend_function_finite Cardinal.extend_function_finite
 
-theorem extend_function_of_lt {α β : Type _} {s : Set α} (f : s ↪ β) (hs : #s < #α)
+theorem extend_function_of_lt {α β : Type*} {s : Set α} (f : s ↪ β) (hs : #s < #α)
     (h : Nonempty (α ≃ β)) : ∃ g : α ≃ β, ∀ x : s, g x = f x := by
   cases fintypeOrInfinite α
   · exact extend_function_finite f h

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

@@ -1090,7 +1090,8 @@ theorem mk_bounded_set_le_of_infinite (α : Type u) [Infinite α] (c : Cardinal)
     refine' le_trans (mk_preimage_of_injective _ _ fun x y => Sum.inl.inj) _
     apply mk_range_le
   rintro ⟨s, ⟨g⟩⟩
-  use fun y => if h : ∃ x : s, g x = y then Sum.inl (Classical.choose h).val else Sum.inr ⟨⟩
+  use fun y => if h : ∃ x : s, g x = y then Sum.inl (Classical.choose h).val
+               else Sum.inr (ULift.up 0)
   apply Subtype.eq; ext x
   constructor
   · rintro ⟨y, h⟩

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

@@ -2,17 +2,14 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Floris van Doorn
-
-! This file was ported from Lean 3 source module set_theory.cardinal.ordinal
-! 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.Data.Finsupp.Multiset
 import Mathlib.Order.Bounded
 import Mathlib.SetTheory.Ordinal.Principal
 import Mathlib.Tactic.Linarith
 
+#align_import set_theory.cardinal.ordinal from "leanprover-community/mathlib"@"7c2ce0c2da15516b4e65d0c9e254bb6dc93abd1f"
+
 /-!
 # Cardinals and ordinals

chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

12343aa5

Diff

@@ -992,7 +992,7 @@ theorem powerlt_aleph0_le (c : Cardinal) : c ^< ℵ₀ ≤ max c ℵ₀ := by
 theorem mk_list_eq_mk (α : Type u) [Infinite α] : #(List α) = #α :=
   have H1 : ℵ₀ ≤ #α := aleph0_le_mk α
   Eq.symm <|
-    le_antisymm ((le_def _ _).2 ⟨⟨fun a => [a], fun _ => by simp⟩⟩)  <|
+    le_antisymm ((le_def _ _).2 ⟨⟨fun a => [a], fun _ => by simp⟩⟩) <|
       calc
         #(List α) = sum fun n : ℕ => #α ^ (n : Cardinal.{u}) := mk_list_eq_sum_pow α
         _ ≤ sum fun _ : ℕ => #α := sum_le_sum _ _ fun n => pow_le H1 <| nat_lt_aleph0 n

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

@@ -459,12 +459,12 @@ theorem beth_le {o₁ o₂ : Ordinal} : beth o₁ ≤ beth o₂ ↔ o₁ ≤ o
 #align cardinal.beth_le Cardinal.beth_le
 
 theorem aleph_le_beth (o : Ordinal) : aleph o ≤ beth o := by
-  apply limitRecOn o
-  · simp
-  · intro o h
+  induction o using limitRecOn with
+  | H₁ => simp
+  | H₂ o h =>
     rw [aleph_succ, beth_succ, succ_le_iff]
     exact (cantor _).trans_le (power_le_power_left two_ne_zero h)
-  · intro o ho IH
+  | H₃ o ho IH =>
     rw [aleph_limit ho, beth_limit ho]
     exact ciSup_mono (bddAbove_of_small _) fun x => IH x.1 x.2
 #align cardinal.aleph_le_beth Cardinal.aleph_le_beth

chore: remove occurrences of semicolon after space (#5713)

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

c795bd35

Diff

@@ -1193,7 +1193,7 @@ theorem mk_compl_eq_mk_compl_finite_same {α : Type u} [Finite α] {s t : Set α
 
 theorem extend_function {α β : Type _} {s : Set α} (f : s ↪ β)
     (h : Nonempty ((sᶜ : Set α) ≃ ((range f)ᶜ : Set β))) : ∃ g : α ≃ β, ∀ x : s, g x = f x := by
-  intros ; have := h; cases' this with g
+  intros; have := h; cases' this with g
   let h : α ≃ β :=
     (Set.sumCompl (s : Set α)).symm.trans
       ((sumCongr (Equiv.ofInjective f f.2) g).trans (Set.sumCompl (range f)))

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

@@ -528,8 +528,7 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c := by
         typein_inj, mem_setOf_eq] at h
       exact max_le_iff.1 (le_iff_lt_or_eq.2 <| h.imp_right And.left)
     suffices H : (insert (g p) { x | r x (g p) } : Set α) ≃ Sum { x | r x (g p) } PUnit
-    ·
-      exact
+    · exact
         ⟨(Set.embeddingOfSubset _ _ this).trans
             ((Equiv.Set.prod _ _).trans (H.prodCongr H)).toEmbedding⟩
     refine' (Equiv.Set.insert _).trans ((Equiv.refl _).sumCongr punitEquivPUnit)
@@ -1032,8 +1031,7 @@ theorem mk_finset_of_infinite (α : Type u) [Infinite α] : #(Finset α) = #α :
 theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Zero β] [Nontrivial β] :
     #(α →₀ β) = max (lift.{v} #α) (lift.{u} #β) := by
   apply le_antisymm
-  ·
-    calc
+  · calc
       #(α →₀ β) ≤ #(Finset (α × β)) := mk_le_of_injective (Finsupp.graph_injective α β)
       _ = #(α × β) := mk_finset_of_infinite _
       _ = max (lift.{v} #α) (lift.{u} #β) :=

fix: precedence of # (#5623)

d450fcd7

Diff

@@ -147,7 +147,7 @@ theorem type_cardinal : @type Cardinal (· < ·) _ = Ordinal.univ.{u, u + 1} :=
 #align cardinal.type_cardinal Cardinal.type_cardinal
 
 @[simp]
-theorem mk_cardinal : (#Cardinal) = univ.{u, u + 1} := by
+theorem mk_cardinal : #Cardinal = univ.{u, u + 1} := by
   simpa only [card_type, card_univ] using congr_arg card type_cardinal
 #align cardinal.mk_cardinal Cardinal.mk_cardinal
 
@@ -348,7 +348,7 @@ theorem aleph0_lt_aleph_one : ℵ₀ < aleph 1 := by
   apply lt_succ
 #align cardinal.aleph_0_lt_aleph_one Cardinal.aleph0_lt_aleph_one
 
-theorem countable_iff_lt_aleph_one {α : Type _} (s : Set α) : s.Countable ↔ (#s) < aleph 1 := by
+theorem countable_iff_lt_aleph_one {α : Type _} (s : Set α) : s.Countable ↔ #s < aleph 1 := by
   rw [← succ_aleph0, lt_succ_iff, le_aleph0_iff_set_countable]
 #align cardinal.countable_iff_lt_aleph_one Cardinal.countable_iff_lt_aleph_one
 
@@ -557,7 +557,7 @@ theorem mul_eq_max {a b : Cardinal} (ha : ℵ₀ ≤ a) (hb : ℵ₀ ≤ b) : a
 #align cardinal.mul_eq_max Cardinal.mul_eq_max
 
 @[simp]
-theorem mul_mk_eq_max {α β : Type _} [Infinite α] [Infinite β] : (#α) * (#β) = max (#α) (#β) :=
+theorem mul_mk_eq_max {α β : Type _} [Infinite α] [Infinite β] : #α * #β = max #α #β :=
   mul_eq_max (aleph0_le_mk α) (aleph0_le_mk β)
 #align cardinal.mul_mk_eq_max Cardinal.mul_mk_eq_max
 
@@ -577,12 +577,12 @@ theorem mul_aleph0_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a * ℵ₀ = a :=
 #align cardinal.mul_aleph_0_eq Cardinal.mul_aleph0_eq
 
 --Porting note: removed `simp`, `simp` can prove it
-theorem aleph0_mul_mk_eq {α : Type _} [Infinite α] : ℵ₀ * (#α) = (#α) :=
+theorem aleph0_mul_mk_eq {α : Type _} [Infinite α] : ℵ₀ * #α = #α :=
   aleph0_mul_eq (aleph0_le_mk α)
 #align cardinal.aleph_0_mul_mk_eq Cardinal.aleph0_mul_mk_eq
 
 --Porting note: removed `simp`, `simp` can prove it
-theorem mk_mul_aleph0_eq {α : Type _} [Infinite α] : (#α) * ℵ₀ = (#α) :=
+theorem mk_mul_aleph0_eq {α : Type _} [Infinite α] : #α * ℵ₀ = #α :=
   mul_aleph0_eq (aleph0_le_mk α)
 #align cardinal.mk_mul_aleph_0_eq Cardinal.mk_mul_aleph0_eq
 
@@ -737,12 +737,12 @@ theorem add_eq_max' {a b : Cardinal} (ha : ℵ₀ ≤ b) : a + b = max a b := by
 #align cardinal.add_eq_max' Cardinal.add_eq_max'
 
 @[simp]
-theorem add_mk_eq_max {α β : Type _} [Infinite α] : (#α) + (#β) = max (#α) (#β) :=
+theorem add_mk_eq_max {α β : Type _} [Infinite α] : #α + #β = max #α #β :=
   add_eq_max (aleph0_le_mk α)
 #align cardinal.add_mk_eq_max Cardinal.add_mk_eq_max
 
 @[simp]
-theorem add_mk_eq_max' {α β : Type _} [Infinite β] : (#α) + (#β) = max (#α) (#β) :=
+theorem add_mk_eq_max' {α β : Type _} [Infinite β] : #α + #β = max #α #β :=
   add_eq_max' (aleph0_le_mk β)
 #align cardinal.add_mk_eq_max' Cardinal.add_mk_eq_max'
 
@@ -817,7 +817,7 @@ theorem add_one_eq {a : Cardinal} (ha : ℵ₀ ≤ a) : a + 1 = a :=
 #align cardinal.add_one_eq Cardinal.add_one_eq
 
 --Porting note: removed `simp`, `simp` can prove it
-theorem mk_add_one_eq {α : Type _} [Infinite α] : (#α) + 1 = (#α) :=
+theorem mk_add_one_eq {α : Type _} [Infinite α] : #α + 1 = #α :=
   add_one_eq (aleph0_le_mk α)
 #align cardinal.mk_add_one_eq Cardinal.mk_add_one_eq
 
@@ -933,7 +933,7 @@ theorem power_self_eq {c : Cardinal} (h : ℵ₀ ≤ c) : c ^ c = 2 ^ c := by
 #align cardinal.power_self_eq Cardinal.power_self_eq
 
 theorem prod_eq_two_power {ι : Type u} [Infinite ι] {c : ι → Cardinal.{v}} (h₁ : ∀ i, 2 ≤ c i)
-    (h₂ : ∀ i, lift.{u} (c i) ≤ lift.{v} (#ι)) : prod c = 2 ^ lift.{v} (#ι) := by
+    (h₂ : ∀ i, lift.{u} (c i) ≤ lift.{v} #ι) : prod c = 2 ^ lift.{v} #ι := by
   rw [← lift_id'.{u, v} (prod.{u, v} c), lift_prod, ← lift_two_power]
   apply le_antisymm
   · refine' (prod_le_prod _ _ h₂).trans_eq _
@@ -990,21 +990,21 @@ theorem powerlt_aleph0_le (c : Cardinal) : c ^< ℵ₀ ≤ max c ℵ₀ := by
 
 
 @[simp]
-theorem mk_list_eq_mk (α : Type u) [Infinite α] : (#List α) = (#α) :=
-  have H1 : ℵ₀ ≤ (#α) := aleph0_le_mk α
+theorem mk_list_eq_mk (α : Type u) [Infinite α] : #(List α) = #α :=
+  have H1 : ℵ₀ ≤ #α := aleph0_le_mk α
   Eq.symm <|
     le_antisymm ((le_def _ _).2 ⟨⟨fun a => [a], fun _ => by simp⟩⟩)  <|
       calc
-        (#List α) = sum fun n : ℕ => (#α) ^ (n : Cardinal.{u}) := mk_list_eq_sum_pow α
+        #(List α) = sum fun n : ℕ => #α ^ (n : Cardinal.{u}) := mk_list_eq_sum_pow α
         _ ≤ sum fun _ : ℕ => #α := sum_le_sum _ _ fun n => pow_le H1 <| nat_lt_aleph0 n
-        _ = (#α) := by simp [H1]
+        _ = #α := by simp [H1]
 #align cardinal.mk_list_eq_mk Cardinal.mk_list_eq_mk
 
-theorem mk_list_eq_aleph0 (α : Type u) [Countable α] [Nonempty α] : (#List α) = ℵ₀ :=
+theorem mk_list_eq_aleph0 (α : Type u) [Countable α] [Nonempty α] : #(List α) = ℵ₀ :=
   mk_le_aleph0.antisymm (aleph0_le_mk _)
 #align cardinal.mk_list_eq_aleph_0 Cardinal.mk_list_eq_aleph0
 
-theorem mk_list_eq_max_mk_aleph0 (α : Type u) [Nonempty α] : (#List α) = max (#α) ℵ₀ := by
+theorem mk_list_eq_max_mk_aleph0 (α : Type u) [Nonempty α] : #(List α) = max #α ℵ₀ := by
   cases finite_or_infinite α
   · rw [mk_list_eq_aleph0, eq_comm, max_eq_right]
     exact mk_le_aleph0
@@ -1012,7 +1012,7 @@ theorem mk_list_eq_max_mk_aleph0 (α : Type u) [Nonempty α] : (#List α) = max
     exact aleph0_le_mk α
 #align cardinal.mk_list_eq_max_mk_aleph_0 Cardinal.mk_list_eq_max_mk_aleph0
 
-theorem mk_list_le_max (α : Type u) : (#List α) ≤ max ℵ₀ (#α) := by
+theorem mk_list_le_max (α : Type u) : #(List α) ≤ max ℵ₀ #α := by
   cases finite_or_infinite α
   · exact mk_le_aleph0.trans (le_max_left _ _)
   · rw [mk_list_eq_mk]
@@ -1020,26 +1020,26 @@ theorem mk_list_le_max (α : Type u) : (#List α) ≤ max ℵ₀ (#α) := by
 #align cardinal.mk_list_le_max Cardinal.mk_list_le_max
 
 @[simp]
-theorem mk_finset_of_infinite (α : Type u) [Infinite α] : (#Finset α) = (#α) :=
+theorem mk_finset_of_infinite (α : Type u) [Infinite α] : #(Finset α) = #α :=
   Eq.symm <|
     le_antisymm (mk_le_of_injective fun _ _ => Finset.singleton_inj.1) <|
       calc
-        (#Finset α) ≤ (#List α) := mk_le_of_surjective List.toFinset_surjective
-        _ = (#α) := mk_list_eq_mk α
+        #(Finset α) ≤ #(List α) := mk_le_of_surjective List.toFinset_surjective
+        _ = #α := mk_list_eq_mk α
 #align cardinal.mk_finset_of_infinite Cardinal.mk_finset_of_infinite
 
 @[simp]
 theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Zero β] [Nontrivial β] :
-    (#α →₀ β) = max (lift.{v} (#α)) (lift.{u} (#β)) := by
+    #(α →₀ β) = max (lift.{v} #α) (lift.{u} #β) := by
   apply le_antisymm
   ·
     calc
-      (#α →₀ β) ≤ (#Finset (α × β)) := mk_le_of_injective (Finsupp.graph_injective α β)
-      _ = (#α × β) := mk_finset_of_infinite _
-      _ = max (lift.{v} (#α)) (lift.{u} (#β)) :=
+      #(α →₀ β) ≤ #(Finset (α × β)) := mk_le_of_injective (Finsupp.graph_injective α β)
+      _ = #(α × β) := mk_finset_of_infinite _
+      _ = max (lift.{v} #α) (lift.{u} #β) :=
         by rw [mk_prod, mul_eq_max_of_aleph0_le_left] <;> simp
 
-  · apply max_le <;> rw [← lift_id (#α →₀ β), ← lift_umax]
+  · apply max_le <;> rw [← lift_id #(α →₀ β), ← lift_umax]
     · cases' exists_ne (0 : β) with b hb
       exact lift_mk_le.{v}.2 ⟨⟨_, Finsupp.single_left_injective hb⟩⟩
     · inhabit α
@@ -1047,12 +1047,12 @@ theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Z
 #align cardinal.mk_finsupp_lift_of_infinite Cardinal.mk_finsupp_lift_of_infinite
 
 theorem mk_finsupp_of_infinite (α β : Type u) [Infinite α] [Zero β] [Nontrivial β] :
-    (#α →₀ β) = max (#α) (#β) := by simp
+    #(α →₀ β) = max #α #β := by simp
 #align cardinal.mk_finsupp_of_infinite Cardinal.mk_finsupp_of_infinite
 
 @[simp]
 theorem mk_finsupp_lift_of_infinite' (α : Type u) (β : Type v) [Nonempty α] [Zero β] [Infinite β] :
-    (#α →₀ β) = max (lift.{v} (#α)) (lift.{u} (#β)) := by
+    #(α →₀ β) = max (lift.{v} #α) (lift.{u} #β) := by
   cases fintypeOrInfinite α
   · rw [mk_finsupp_lift_of_fintype]
     have : ℵ₀ ≤ (#β).lift := aleph0_le_lift.2 (aleph0_le_mk β)
@@ -1062,31 +1062,31 @@ theorem mk_finsupp_lift_of_infinite' (α : Type u) (β : Type v) [Nonempty α] [
 #align cardinal.mk_finsupp_lift_of_infinite' Cardinal.mk_finsupp_lift_of_infinite'
 
 theorem mk_finsupp_of_infinite' (α β : Type u) [Nonempty α] [Zero β] [Infinite β] :
-    (#α →₀ β) = max (#α) (#β) := by simp
+    #(α →₀ β) = max #α #β := by simp
 #align cardinal.mk_finsupp_of_infinite' Cardinal.mk_finsupp_of_infinite'
 
-theorem mk_finsupp_nat (α : Type u) [Nonempty α] : (#α →₀ ℕ) = max (#α) ℵ₀ := by simp
+theorem mk_finsupp_nat (α : Type u) [Nonempty α] : #(α →₀ ℕ) = max #α ℵ₀ := by simp
 #align cardinal.mk_finsupp_nat Cardinal.mk_finsupp_nat
 
 @[simp]
-theorem mk_multiset_of_nonempty (α : Type u) [Nonempty α] : (#Multiset α) = max (#α) ℵ₀ :=
+theorem mk_multiset_of_nonempty (α : Type u) [Nonempty α] : #(Multiset α) = max #α ℵ₀ :=
   Multiset.toFinsupp.toEquiv.cardinal_eq.trans (mk_finsupp_nat α)
 #align cardinal.mk_multiset_of_nonempty Cardinal.mk_multiset_of_nonempty
 
-theorem mk_multiset_of_infinite (α : Type u) [Infinite α] : (#Multiset α) = (#α) := by simp
+theorem mk_multiset_of_infinite (α : Type u) [Infinite α] : #(Multiset α) = #α := by simp
 #align cardinal.mk_multiset_of_infinite Cardinal.mk_multiset_of_infinite
 
 @[simp]
-theorem mk_multiset_of_isEmpty (α : Type u) [IsEmpty α] : (#Multiset α) = 1 :=
+theorem mk_multiset_of_isEmpty (α : Type u) [IsEmpty α] : #(Multiset α) = 1 :=
   Multiset.toFinsupp.toEquiv.cardinal_eq.trans (by simp)
 #align cardinal.mk_multiset_of_is_empty Cardinal.mk_multiset_of_isEmpty
 
-theorem mk_multiset_of_countable (α : Type u) [Countable α] [Nonempty α] : (#Multiset α) = ℵ₀ :=
+theorem mk_multiset_of_countable (α : Type u) [Countable α] [Nonempty α] : #(Multiset α) = ℵ₀ :=
   Multiset.toFinsupp.toEquiv.cardinal_eq.trans (by simp)
 #align cardinal.mk_multiset_of_countable Cardinal.mk_multiset_of_countable
 
 theorem mk_bounded_set_le_of_infinite (α : Type u) [Infinite α] (c : Cardinal) :
-    (#{ t : Set α // (#t) ≤ c }) ≤ (#α) ^ c := by
+    #{ t : Set α // #t ≤ c } ≤ #α ^ c := by
   refine' le_trans _ (by rw [← add_one_eq (aleph0_le_mk α)])
   induction' c using Cardinal.inductionOn with β
   fapply mk_le_of_surjective
@@ -1119,8 +1119,8 @@ theorem mk_bounded_set_le_of_infinite (α : Type u) [Infinite α] (c : Cardinal)
 #align cardinal.mk_bounded_set_le_of_infinite Cardinal.mk_bounded_set_le_of_infinite
 
 theorem mk_bounded_set_le (α : Type u) (c : Cardinal) :
-    (#{ t : Set α // (#t) ≤ c }) ≤ max (#α) ℵ₀ ^ c := by
-  trans #{ t : Set (Sum (ULift.{u} ℕ) α) // (#t) ≤ c }
+    #{ t : Set α // #t ≤ c } ≤ max #α ℵ₀ ^ c := by
+  trans #{ t : Set (Sum (ULift.{u} ℕ) α) // #t ≤ c }
   · refine' ⟨Embedding.subtypeMap _ _⟩
     apply Embedding.image
     use Sum.inr
@@ -1132,7 +1132,7 @@ theorem mk_bounded_set_le (α : Type u) (c : Cardinal) :
 #align cardinal.mk_bounded_set_le Cardinal.mk_bounded_set_le
 
 theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
-    (#{ t : Set α // t ⊆ s ∧ (#t) ≤ c }) ≤ max (#s) ℵ₀ ^ c := by
+    #{ t : Set α // t ⊆ s ∧ #t ≤ c } ≤ max #s ℵ₀ ^ c := by
   refine' le_trans _ (mk_bounded_set_le s c)
   refine' ⟨Embedding.codRestrict _ _ _⟩
   use fun t => (↑) ⁻¹' t.1
@@ -1146,27 +1146,27 @@ theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
 /-! ### Properties of `compl` -/
 
 
-theorem mk_compl_of_infinite {α : Type _} [Infinite α] (s : Set α) (h2 : (#s) < (#α)) :
-    (#(sᶜ : Set α)) = (#α) := by
+theorem mk_compl_of_infinite {α : Type _} [Infinite α] (s : Set α) (h2 : #s < #α) :
+    #(sᶜ : Set α) = #α := by
   refine' eq_of_add_eq_of_aleph0_le _ h2 (aleph0_le_mk α)
   exact mk_sum_compl s
 #align cardinal.mk_compl_of_infinite Cardinal.mk_compl_of_infinite
 
 theorem mk_compl_finset_of_infinite {α : Type _} [Infinite α] (s : Finset α) :
-    (#((↑s)ᶜ : Set α)) = (#α) := by
+    #((↑s)ᶜ : Set α) = #α := by
   apply mk_compl_of_infinite
   exact (finset_card_lt_aleph0 s).trans_le (aleph0_le_mk α)
 #align cardinal.mk_compl_finset_of_infinite Cardinal.mk_compl_finset_of_infinite
 
-theorem mk_compl_eq_mk_compl_infinite {α : Type _} [Infinite α] {s t : Set α} (hs : (#s) < (#α))
-    (ht : (#t) < (#α)) : (#(sᶜ : Set α)) = (#(tᶜ : Set α)) := by
+theorem mk_compl_eq_mk_compl_infinite {α : Type _} [Infinite α] {s t : Set α} (hs : #s < #α)
+    (ht : #t < #α) : #(sᶜ : Set α) = #(tᶜ : Set α) := by
   rw [mk_compl_of_infinite s hs, mk_compl_of_infinite t ht]
 #align cardinal.mk_compl_eq_mk_compl_infinite Cardinal.mk_compl_eq_mk_compl_infinite
 
 theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α] {s : Set α}
-    {t : Set β} (h1 : (lift.{max v w, u} (#α)) = (lift.{max u w, v} (#β)))
-    (h2 : lift.{max v w, u} (#s) = lift.{max u w, v} (#t)) :
-    lift.{max v w} (#(sᶜ : Set α)) = lift.{max u w} (#(tᶜ : Set β)) := by
+    {t : Set β} (h1 : (lift.{max v w, u} #α) = (lift.{max u w, v} #β))
+    (h2 : lift.{max v w, u} #s = lift.{max u w, v} #t) :
+    lift.{max v w} #(sᶜ : Set α) = lift.{max u w} #(tᶜ : Set β) := by
   cases nonempty_fintype α
   rcases lift_mk_eq.{u, v, w}.1 h1 with ⟨e⟩; letI : Fintype β := Fintype.ofEquiv α e
   replace h1 : Fintype.card α = Fintype.card β := (Fintype.ofEquiv_card _).symm
@@ -1179,14 +1179,14 @@ theorem mk_compl_eq_mk_compl_finite_lift {α : Type u} {β : Type v} [Finite α]
 #align cardinal.mk_compl_eq_mk_compl_finite_lift Cardinal.mk_compl_eq_mk_compl_finite_lift
 
 theorem mk_compl_eq_mk_compl_finite {α β : Type u} [Finite α] {s : Set α} {t : Set β}
-    (h1 : (#α) = (#β)) (h : (#s) = (#t)) : (#(sᶜ : Set α)) = (#(tᶜ : Set β)) := by
+    (h1 : #α = #β) (h : #s = #t) : #(sᶜ : Set α) = #(tᶜ : Set β) := by
   rw [← lift_inj.{u, max u v}]
   apply mk_compl_eq_mk_compl_finite_lift.{u, u, max u v}
   <;> rwa [lift_inj]
 #align cardinal.mk_compl_eq_mk_compl_finite Cardinal.mk_compl_eq_mk_compl_finite
 
-theorem mk_compl_eq_mk_compl_finite_same {α : Type u} [Finite α] {s t : Set α} (h : (#s) = (#t)) :
-    (#(sᶜ : Set α)) = (#(tᶜ : Set α)) :=
+theorem mk_compl_eq_mk_compl_finite_same {α : Type u} [Finite α] {s t : Set α} (h : #s = #t) :
+    #(sᶜ : Set α) = #(tᶜ : Set α) :=
   mk_compl_eq_mk_compl_finite.{u, u} rfl h
 #align cardinal.mk_compl_eq_mk_compl_finite_same Cardinal.mk_compl_eq_mk_compl_finite_same
 
@@ -1211,7 +1211,7 @@ theorem extend_function_finite {α : Type u} {β : Type v} [Finite α] {s : Set
   rw [mk_range_eq_lift.{u, v, max u v}]; exact f.2
 #align cardinal.extend_function_finite Cardinal.extend_function_finite
 
-theorem extend_function_of_lt {α β : Type _} {s : Set α} (f : s ↪ β) (hs : (#s) < (#α))
+theorem extend_function_of_lt {α β : Type _} {s : Set α} (f : s ↪ β) (hs : #s < #α)
     (h : Nonempty (α ≃ β)) : ∃ g : α ≃ β, ∀ x : s, g x = f x := by
   cases fintypeOrInfinite α
   · exact extend_function_finite f h

fix: change compl precedence (#5586)

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

4d4f0f25

Diff

@@ -1153,7 +1153,7 @@ theorem mk_compl_of_infinite {α : Type _} [Infinite α] (s : Set α) (h2 : (#s)
 #align cardinal.mk_compl_of_infinite Cardinal.mk_compl_of_infinite
 
 theorem mk_compl_finset_of_infinite {α : Type _} [Infinite α] (s : Finset α) :
-    (#(↑sᶜ : Set α)) = (#α) := by
+    (#((↑s)ᶜ : Set α)) = (#α) := by
   apply mk_compl_of_infinite
   exact (finset_card_lt_aleph0 s).trans_le (aleph0_le_mk α)
 #align cardinal.mk_compl_finset_of_infinite Cardinal.mk_compl_finset_of_infinite
@@ -1194,7 +1194,7 @@ theorem mk_compl_eq_mk_compl_finite_same {α : Type u} [Finite α] {s t : Set α
 
 
 theorem extend_function {α β : Type _} {s : Set α} (f : s ↪ β)
-    (h : Nonempty ((sᶜ : Set α) ≃ (range fᶜ : Set β))) : ∃ g : α ≃ β, ∀ x : s, g x = f x := by
+    (h : Nonempty ((sᶜ : Set α) ≃ ((range f)ᶜ : Set β))) : ∃ g : α ≃ β, ∀ x : s, g x = f x := by
   intros ; have := h; cases' this with g
   let h : α ≃ β :=
     (Set.sumCompl (s : Set α)).symm.trans

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

@@ -64,7 +64,7 @@ theorem ord_isLimit {c} (co : ℵ₀ ≤ c) : (ord c).IsLimit := by
   refine' ⟨fun h => aleph0_ne_zero _, fun a => lt_imp_lt_of_le_imp_le fun h => _⟩
   · rw [← Ordinal.le_zero, ord_le] at h
     simpa only [card_zero, nonpos_iff_eq_zero] using co.trans h
-  · rw [ord_le] at h⊢
+  · rw [ord_le] at h ⊢
     rwa [← @add_one_of_aleph0_le (card a), ← card_succ]
     rw [← ord_le, ← le_succ_of_isLimit, ord_le]
     · exact co.trans h
@@ -698,7 +698,7 @@ theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧
     contradiction
     rw [← Ne] at h2a
     rw [← one_le_iff_ne_zero] at h2a hb
-    norm_cast  at h2a hb h⊢
+    norm_cast at h2a hb h ⊢
     apply le_antisymm _ hb
     rw [← not_lt]
     apply fun h2b => ne_of_gt _ h
@@ -797,7 +797,7 @@ theorem add_eq_left_iff {a b : Cardinal} : a + b = a ↔ max ℵ₀ b ≤ a ∨
     right
     rw [← h, add_lt_aleph0_iff, lt_aleph0, lt_aleph0] at ha
     rcases ha with ⟨⟨n, rfl⟩, ⟨m, rfl⟩⟩
-    norm_cast  at h⊢
+    norm_cast at h ⊢
     rw [← add_right_inj, h, add_zero]
   · rintro (⟨h1, h2⟩ | h3)
     · rw [add_eq_max h1, max_eq_left h2]
@@ -838,7 +838,7 @@ protected theorem eq_of_add_eq_add_left {a b c : Cardinal} (h : a + b = a + c) (
     rcases ha with ⟨n, rfl⟩
     rcases hb with ⟨m, rfl⟩
     rcases hc with ⟨k, rfl⟩
-    norm_cast  at h⊢
+    norm_cast at h ⊢
     apply add_left_cancel h
 #align cardinal.eq_of_add_eq_add_left Cardinal.eq_of_add_eq_add_left
 
@@ -881,7 +881,7 @@ theorem add_le_add_iff_of_lt_aleph0 {α β γ : Cardinal} (γ₀ : γ < Cardinal
     α + γ ≤ β + γ ↔ α ≤ β := by
   refine' ⟨fun h => _, fun h => add_le_add_right h γ⟩
   contrapose h
-  rw [not_le, lt_iff_le_and_ne, Ne] at h⊢
+  rw [not_le, lt_iff_le_and_ne, Ne] at h ⊢
   exact ⟨add_le_add_right h.1 γ, mt (add_right_inj_of_lt_aleph0 γ₀).1 h.2⟩
 #align cardinal.add_le_add_iff_of_lt_aleph_0 Cardinal.add_le_add_iff_of_lt_aleph0
 
@@ -1138,7 +1138,7 @@ theorem mk_bounded_subset_le {α : Type u} (s : Set α) (c : Cardinal.{u}) :
   use fun t => (↑) ⁻¹' t.1
   · rintro ⟨t, ht1, ht2⟩ ⟨t', h1t', h2t'⟩ h
     apply Subtype.eq
-    dsimp only at h⊢
+    dsimp only at h ⊢
     refine' (preimage_eq_preimage' _ _).1 h <;> rw [Subtype.range_coe] <;> assumption
   rintro ⟨t, _, h2t⟩; exact (mk_preimage_of_injective _ _ Subtype.val_injective).trans h2t
 #align cardinal.mk_bounded_subset_le Cardinal.mk_bounded_subset_le
@@ -1218,7 +1218,7 @@ theorem extend_function_of_lt {α β : Type _} {s : Set α} (f : s ↪ β) (hs :
   · apply extend_function f
     cases' id h with g
     haveI := Infinite.of_injective _ g.injective
-    rw [← lift_mk_eq'] at h⊢
+    rw [← lift_mk_eq'] at h ⊢
     rwa [mk_compl_of_infinite s hs, mk_compl_of_infinite]
     rwa [← lift_lt, mk_range_eq_of_injective f.injective, ← h, lift_lt]
 #align cardinal.extend_function_of_lt Cardinal.extend_function_of_lt

chore: reorder universe variables in Cardinal.lift_le and Cardinal.lift_mk_le (#5325)

Cardinal.lift_le and Cardinal.lift_mk_le have their universes out of order, in the sense that persistently through the rest of the library we need to specify the 2nd universe (resp 3rd), while the others are solved by unification.

This PR reorders the universes so it's easier to specify the thing you need to specify!

(This PR doesn't get rid of all the occurrences of \.\{_, in the library, but I'd like to do that later.)

I do have a hidden agenda here, which is that I've been experimenting with solutions to the dreaded "Can't solve max u v = max v ?u" universe unification issue (which is making life hellish forward porting https://github.com/leanprover-community/mathlib/pull/19153), and my favourite (but still hacky) solution doesn't like some of the occasions where we reference a lemma filling in some of its universe arguments with _ but then fully specify a later one. (e.g. rw [← lift_le.{_, max u v}, lift_lift, lift_mk_le.{_, _, v}] in ModelTheory/Skolem.lean). Hence the cleanup proposed in this PR makes my life easier working on these experiments. :-)

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

719a2170

Diff

@@ -1041,9 +1041,9 @@ theorem mk_finsupp_lift_of_infinite (α : Type u) (β : Type v) [Infinite α] [Z
 
   · apply max_le <;> rw [← lift_id (#α →₀ β), ← lift_umax]
     · cases' exists_ne (0 : β) with b hb
-      exact lift_mk_le.{u, max u v, v}.2 ⟨⟨_, Finsupp.single_left_injective hb⟩⟩
+      exact lift_mk_le.{v}.2 ⟨⟨_, Finsupp.single_left_injective hb⟩⟩
     · inhabit α
-      exact lift_mk_le.{v, max u v, u}.2 ⟨⟨_, Finsupp.single_injective default⟩⟩
+      exact lift_mk_le.{u}.2 ⟨⟨_, Finsupp.single_injective default⟩⟩
 #align cardinal.mk_finsupp_lift_of_infinite Cardinal.mk_finsupp_lift_of_infinite
 
 theorem mk_finsupp_of_infinite (α β : Type u) [Infinite α] [Zero β] [Nontrivial β] :

chore: add space after exacts (#4945)

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

bf799bb9

Diff

@@ -1057,7 +1057,7 @@ theorem mk_finsupp_lift_of_infinite' (α : Type u) (β : Type v) [Nonempty α] [
   · rw [mk_finsupp_lift_of_fintype]
     have : ℵ₀ ≤ (#β).lift := aleph0_le_lift.2 (aleph0_le_mk β)
     rw [max_eq_right (le_trans _ this), power_nat_eq this]
-    exacts[Fintype.card_pos, lift_le_aleph0.2 (lt_aleph0_of_finite _).le]
+    exacts [Fintype.card_pos, lift_le_aleph0.2 (lt_aleph0_of_finite _).le]
   · apply mk_finsupp_lift_of_infinite
 #align cardinal.mk_finsupp_lift_of_infinite' Cardinal.mk_finsupp_lift_of_infinite'

chore: fix upper/lowercase in comments (#4360)

Run a non-interactive version of fix-comments.py on all files.
Go through the diff and manually add/discard/edit chunks.

27d257fc

Diff

@@ -234,7 +234,7 @@ theorem aleph'_omega : aleph' ω = ℵ₀ :=
     exact forall_swap.trans (forall_congr' fun n => by simp only [forall_eq, aleph'_nat])
 #align cardinal.aleph'_omega Cardinal.aleph'_omega
 
-/-- `aleph'` and `aleph_idx` form an equivalence between `ordinal` and `cardinal` -/
+/-- `aleph'` and `aleph_idx` form an equivalence between `Ordinal` and `Cardinal` -/
 @[simp]
 def aleph'Equiv : Ordinal ≃ Cardinal :=
   ⟨aleph', alephIdx, alephIdx_aleph', aleph'_alephIdx⟩

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

@@ -131,7 +131,7 @@ def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
       apply (lt_succ s).not_le
       have I : Injective.{u+2, u+2} alephIdx := alephIdx.initialSeg.toEmbedding.injective
       simpa only [typein_enum, leftInverse_invFun I (succ s)] using
-        le_csupᵢ
+        le_ciSup
           (Cardinal.bddAbove_range.{u, u} fun a : α => invFun alephIdx (Ordinal.typein r a))
           (Ordinal.enum r _ (h (succ s)))
 #align cardinal.aleph_idx.rel_iso Cardinal.alephIdx.relIso
@@ -222,9 +222,9 @@ theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
 #align cardinal.aleph'_le_of_limit Cardinal.aleph'_le_of_limit
 
 theorem aleph'_limit {o : Ordinal} (ho : o.IsLimit) : aleph' o = ⨆ a : Iio o, aleph' a := by
-  refine' le_antisymm _ (csupᵢ_le' fun i => aleph'_le.2 (le_of_lt i.2))
+  refine' le_antisymm _ (ciSup_le' fun i => aleph'_le.2 (le_of_lt i.2))
   rw [aleph'_le_of_limit ho]
-  exact fun a ha => le_csupᵢ (bddAbove_of_small _) (⟨a, ha⟩ : Iio o)
+  exact fun a ha => le_ciSup (bddAbove_of_small _) (⟨a, ha⟩ : Iio o)
 #align cardinal.aleph'_limit Cardinal.aleph'_limit
 
 @[simp]
@@ -274,9 +274,9 @@ theorem aleph_zero : aleph 0 = ℵ₀ := by rw [aleph, add_zero, aleph'_omega]
 #align cardinal.aleph_zero Cardinal.aleph_zero
 
 theorem aleph_limit {o : Ordinal} (ho : o.IsLimit) : aleph o = ⨆ a : Iio o, aleph a := by
-  apply le_antisymm _ (csupᵢ_le' _)
+  apply le_antisymm _ (ciSup_le' _)
   · rw [aleph, aleph'_limit (ho.add _)]
-    refine' csupᵢ_mono' (bddAbove_of_small _) _
+    refine' ciSup_mono' (bddAbove_of_small _) _
     rintro ⟨i, hi⟩
     cases' lt_or_le i ω with h h
     · rcases lt_omega.1 h with ⟨n, rfl⟩
@@ -441,7 +441,7 @@ theorem beth_strictMono : StrictMono beth := by
     exact (IH c (lt_succ c) h).le
   · apply (cantor _).trans_le
     rw [beth_limit hb, ← beth_succ]
-    exact le_csupᵢ (bddAbove_of_small _) (⟨_, hb.succ_lt h⟩ : Iio b)
+    exact le_ciSup (bddAbove_of_small _) (⟨_, hb.succ_lt h⟩ : Iio b)
 #align cardinal.beth_strict_mono Cardinal.beth_strictMono
 
 theorem beth_mono : Monotone beth :=
@@ -466,7 +466,7 @@ theorem aleph_le_beth (o : Ordinal) : aleph o ≤ beth o := by
     exact (cantor _).trans_le (power_le_power_left two_ne_zero h)
   · intro o ho IH
     rw [aleph_limit ho, beth_limit ho]
-    exact csupᵢ_mono (bddAbove_of_small _) fun x => IH x.1 x.2
+    exact ciSup_mono (bddAbove_of_small _) fun x => IH x.1 x.2
 #align cardinal.aleph_le_beth Cardinal.aleph_le_beth
 
 theorem aleph0_le_beth (o : Ordinal) : ℵ₀ ≤ beth o :=
@@ -485,7 +485,7 @@ theorem beth_normal : IsNormal.{u} fun o => (beth o).ord :=
   (isNormal_iff_strictMono_limit _).2
     ⟨ord_strictMono.comp beth_strictMono, fun o ho a ha => by
       rw [beth_limit ho, ord_le]
-      exact csupᵢ_le' fun b => ord_le.1 (ha _ b.2)⟩
+      exact ciSup_le' fun b => ord_le.1 (ha _ b.2)⟩
 #align cardinal.beth_normal Cardinal.beth_normal
 
 /-! ### Properties of `mul` -/

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

@@ -124,8 +124,7 @@ theorem alephIdx.init {a b} : b < alephIdx a → ∃ c, alephIdx c = b :=
   For the basic function version, see `alephIdx`. -/
 def alephIdx.relIso : @RelIso Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) :=
   @RelIso.ofSurjective Cardinal.{u} Ordinal.{u} (· < ·) (· < ·) alephIdx.initialSeg.{u} <|
-    (InitialSeg.eq_or_principal alephIdx.initialSeg.{u}).resolve_right fun ⟨o, e⟩ =>
-      by
+    (InitialSeg.eq_or_principal alephIdx.initialSeg.{u}).resolve_right fun ⟨o, e⟩ => by
       have : ∀ c, alephIdx c < o := fun c => (e _).2 ⟨_, rfl⟩
       refine' Ordinal.inductionOn o _ this; intro α r _ h
       let s := ⨆ a, invFun alephIdx (Ordinal.typein r a)
@@ -215,8 +214,7 @@ theorem aleph'_nat : ∀ n : ℕ, aleph' n = n
 
 theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
     aleph' o ≤ c ↔ ∀ o' < o, aleph' o' ≤ c :=
-  ⟨fun h o' h' => (aleph'_le.2 <| h'.le).trans h, fun h =>
-    by
+  ⟨fun h o' h' => (aleph'_le.2 <| h'.le).trans h, fun h => by
     rw [← aleph'_alephIdx c, aleph'_le, limit_le l]
     intro x h'
     rw [← aleph'_le, aleph'_alephIdx]
@@ -231,8 +229,7 @@ theorem aleph'_limit {o : Ordinal} (ho : o.IsLimit) : aleph' o = ⨆ a : Iio o,
 
 @[simp]
 theorem aleph'_omega : aleph' ω = ℵ₀ :=
-  eq_of_forall_ge_iff fun c =>
-    by
+  eq_of_forall_ge_iff fun c => by
     simp only [aleph'_le_of_limit omega_isLimit, lt_omega, exists_imp, aleph0_le]
     exact forall_swap.trans (forall_congr' fun n => by simp only [forall_eq, aleph'_nat])
 #align cardinal.aleph'_omega Cardinal.aleph'_omega
@@ -393,8 +390,8 @@ theorem eq_aleph_of_eq_card_ord {o : Ordinal} (ho : o.card.ord = o) (ho' : ω 
 #align cardinal.eq_aleph_of_eq_card_ord Cardinal.eq_aleph_of_eq_card_ord
 
 /-- `ord ∘ aleph` enumerates the infinite ordinals that are cardinals. -/
-theorem ord_aleph_eq_enum_card : ord ∘ aleph = enumOrd { b : Ordinal | b.card.ord = b ∧ ω ≤ b } :=
-  by
+theorem ord_aleph_eq_enum_card :
+    ord ∘ aleph = enumOrd { b : Ordinal | b.card.ord = b ∧ ω ≤ b } := by
   rw [← eq_enumOrd _ ord_card_unbounded']
   use aleph_isNormal.strictMono
   rw [range_eq_iff]
@@ -486,8 +483,7 @@ theorem beth_ne_zero (o : Ordinal) : beth o ≠ 0 :=
 
 theorem beth_normal : IsNormal.{u} fun o => (beth o).ord :=
   (isNormal_iff_strictMono_limit _).2
-    ⟨ord_strictMono.comp beth_strictMono, fun o ho a ha =>
-      by
+    ⟨ord_strictMono.comp beth_strictMono, fun o ho a ha => by
       rw [beth_limit ho, ord_le]
       exact csupᵢ_le' fun b => ord_le.1 (ha _ b.2)⟩
 #align cardinal.beth_normal Cardinal.beth_normal
@@ -526,8 +522,7 @@ theorem mul_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c * c = c := by
   refine'
     lt_of_le_of_lt (_ : _ ≤ card (succ (typein (· < ·) (g p))) * card (succ (typein (· < ·) (g p))))
       _
-  · have : { q | s q p } ⊆ insert (g p) { x | x < g p } ×ˢ insert (g p) { x | x < g p } :=
-      by
+  · have : { q | s q p } ⊆ insert (g p) { x | x < g p } ×ˢ insert (g p) { x | x < g p } := by
       intro q h
       simp only [Preimage, ge_iff_le, Embedding.coeFn_mk, Prod.lex_def, typein_lt_typein,
         typein_inj, mem_setOf_eq] at h
@@ -603,8 +598,7 @@ theorem aleph_mul_aleph0 (o : Ordinal) : aleph o * ℵ₀ = aleph o :=
 
 theorem mul_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b < c) : a * b < c :=
   (mul_le_mul' (le_max_left a b) (le_max_right a b)).trans_lt <|
-    (lt_or_le (max a b) ℵ₀).elim (fun h => (mul_lt_aleph0 h h).trans_le hc) fun h =>
-      by
+    (lt_or_le (max a b) ℵ₀).elim (fun h => (mul_lt_aleph0 h h).trans_le hc) fun h => by
       rw [mul_eq_self h]
       exact max_lt h1 h2
 #align cardinal.mul_lt_of_lt Cardinal.mul_lt_of_lt

chore: fix #align lines (#3640)

This PR fixes two things:

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

2b42dc7c

Diff

@@ -1004,7 +1004,6 @@ theorem mk_list_eq_mk (α : Type u) [Infinite α] : (#List α) = (#α) :=
         (#List α) = sum fun n : ℕ => (#α) ^ (n : Cardinal.{u}) := mk_list_eq_sum_pow α
         _ ≤ sum fun _ : ℕ => #α := sum_le_sum _ _ fun n => pow_le H1 <| nat_lt_aleph0 n
         _ = (#α) := by simp [H1]
-
 #align cardinal.mk_list_eq_mk Cardinal.mk_list_eq_mk
 
 theorem mk_list_eq_aleph0 (α : Type u) [Countable α] [Nonempty α] : (#List α) = ℵ₀ :=
@@ -1033,7 +1032,6 @@ theorem mk_finset_of_infinite (α : Type u) [Infinite α] : (#Finset α) = (#α)
       calc
         (#Finset α) ≤ (#List α) := mk_le_of_surjective List.toFinset_surjective
         _ = (#α) := mk_list_eq_mk α
-
 #align cardinal.mk_finset_of_infinite Cardinal.mk_finset_of_infinite
 
 @[simp]

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: Johannes Hölzl, Mario Carneiro, Floris van Doorn
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.ordinal
-! leanprover-community/mathlib commit 8da9e30545433fdd8fe55a0d3da208e5d9263f03
+! leanprover-community/mathlib commit 7c2ce0c2da15516b4e65d0c9e254bb6dc93abd1f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -223,7 +223,7 @@ theorem aleph'_le_of_limit {o : Ordinal} (l : o.IsLimit) {c} :
     exact h _ h'⟩
 #align cardinal.aleph'_le_of_limit Cardinal.aleph'_le_of_limit
 
-theorem aleph'_limit {o : Ordinal} (ho : IsLimit o) : aleph' o = ⨆ a : Iio o, aleph' a := by
+theorem aleph'_limit {o : Ordinal} (ho : o.IsLimit) : aleph' o = ⨆ a : Iio o, aleph' a := by
   refine' le_antisymm _ (csupᵢ_le' fun i => aleph'_le.2 (le_of_lt i.2))
   rw [aleph'_le_of_limit ho]
   exact fun a ha => le_csupᵢ (bddAbove_of_small _) (⟨a, ha⟩ : Iio o)
@@ -276,7 +276,7 @@ theorem aleph_succ {o : Ordinal} : aleph (succ o) = succ (aleph o) := by
 theorem aleph_zero : aleph 0 = ℵ₀ := by rw [aleph, add_zero, aleph'_omega]
 #align cardinal.aleph_zero Cardinal.aleph_zero
 
-theorem aleph_limit {o : Ordinal} (ho : IsLimit o) : aleph o = ⨆ a : Iio o, aleph a := by
+theorem aleph_limit {o : Ordinal} (ho : o.IsLimit) : aleph o = ⨆ a : Iio o, aleph a := by
   apply le_antisymm _ (csupᵢ_le' _)
   · rw [aleph, aleph'_limit (ho.add _)]
     refine' csupᵢ_mono' (bddAbove_of_small _) _
@@ -319,7 +319,7 @@ instance nonempty_out_aleph (o : Ordinal) : Nonempty (aleph o).ord.out.α := by
   exact fun h => (ord_injective h).not_gt (aleph_pos o)
 #align cardinal.nonempty_out_aleph Cardinal.nonempty_out_aleph
 
-theorem ord_aleph_isLimit (o : Ordinal) : IsLimit (aleph o).ord :=
+theorem ord_aleph_isLimit (o : Ordinal) : (aleph o).ord.IsLimit :=
   ord_isLimit <| aleph0_le_aleph _
 #align cardinal.ord_aleph_is_limit Cardinal.ord_aleph_isLimit
 
@@ -426,7 +426,7 @@ theorem beth_succ (o : Ordinal) : beth (succ o) = 2 ^ beth o :=
   limitRecOn_succ _ _ _ _
 #align cardinal.beth_succ Cardinal.beth_succ
 
-theorem beth_limit {o : Ordinal} : IsLimit o → beth o = ⨆ a : Iio o, beth a :=
+theorem beth_limit {o : Ordinal} : o.IsLimit → beth o = ⨆ a : Iio o, beth a :=
   limitRecOn_limit _ _ _ _
 #align cardinal.beth_limit Cardinal.beth_limit

feat: improvements to congr! and convert (#2606)

There is now configuration for congr!, convert, and convert_to to control parts of the congruence algorithm, in particular transparency settings when applying congruence lemmas.
congr! now applies congruence lemmas with reducible transparency by default. This prevents it from unfolding definitions when applying congruence lemmas. It also now tries both the LHS-biased and RHS-biased simp congruence lemmas, with a configuration option to set which it should try first.
There is now a new HEq congruence lemma generator that gives each hypothesis access to the proofs of previous hypotheses. This means that if you have an equality ⊢ ⟨a, x⟩ = ⟨b, y⟩ of sigma types, congr! turns this into goals ⊢ a = b and ⊢ a = b → HEq x y (note that congr! will also auto-introduce a = b for you in the second goal). This congruence lemma generator applies to more cases than the simp congruence lemma generator does.
congr! (and hence convert) are more careful about applying lemmas that don't force definitions to unfold. There were a number of cases in mathlib where the implementation of congr was being abused to unfold definitions.
With set_option trace.congr! true you can see what congr! sees when it is deciding on congruence lemmas.
There is also a bug fix in convert_to to do using 1 when there is no using clause, to match its documentation.

Note that congr! is more capable than congr at finding a way to equate left-hand sides and right-hand sides, so you will frequently need to limit its depth with a using clause. However, there is also a new heuristic to prevent considering unlikely-to-be-provable type equalities (controlled by the typeEqs option), which can help limit the depth automatically.

There is also a predefined configuration that you can invoke with, for example, convert (config := .unfoldSameFun) h, that causes it to behave more like congr, including using default transparency when unfolding.

61ca0ea8

Diff

@@ -610,7 +610,7 @@ theorem mul_lt_of_lt {a b c : Cardinal} (hc : ℵ₀ ≤ c) (h1 : a < c) (h2 : b
 #align cardinal.mul_lt_of_lt Cardinal.mul_lt_of_lt
 
 theorem mul_le_max_of_aleph0_le_left {a b : Cardinal} (h : ℵ₀ ≤ a) : a * b ≤ max a b := by
-  convert mul_le_mul' (le_max_left a b) (le_max_right a b)
+  convert mul_le_mul' (le_max_left a b) (le_max_right a b) using 1
   rw [mul_eq_self]
   refine' h.trans (le_max_left a b)
 #align cardinal.mul_le_max_of_aleph_0_le_left Cardinal.mul_le_max_of_aleph0_le_left
@@ -724,7 +724,7 @@ theorem mul_eq_left_iff {a b : Cardinal} : a * b = a ↔ max ℵ₀ b ≤ a ∧
 theorem add_eq_self {c : Cardinal} (h : ℵ₀ ≤ c) : c + c = c :=
   le_antisymm
     (by
-      convert mul_le_mul_right' ((nat_lt_aleph0 2).le.trans h) c
+      convert mul_le_mul_right' ((nat_lt_aleph0 2).le.trans h) c using 1
       <;> simp [two_mul, mul_eq_self h])
     (self_le_add_left c c)
 #align cardinal.add_eq_self Cardinal.add_eq_self

chore: swap the names of InitialSeg.init and InitialSeg.init' (#2581)

mathlib3 PR: https://github.com/leanprover-community/mathlib/pull/18534

591e208d

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Floris van Doorn
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.ordinal
-! leanprover-community/mathlib commit 40494fe75ecbd6d2ec61711baa630cf0a7b7d064
+! leanprover-community/mathlib commit 8da9e30545433fdd8fe55a0d3da208e5d9263f03
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -112,7 +112,7 @@ theorem alephIdx_le {a b} : alephIdx a ≤ alephIdx b ↔ a ≤ b := by
 #align cardinal.aleph_idx_le Cardinal.alephIdx_le
 
 theorem alephIdx.init {a b} : b < alephIdx a → ∃ c, alephIdx c = b :=
-  alephIdx.initialSeg.init _ _
+  alephIdx.initialSeg.init
 #align cardinal.aleph_idx.init Cardinal.alephIdx.init
 
 /-- The `aleph'` index function, which gives the ordinal index of a cardinal.