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

@@ -1297,10 +1297,10 @@ theorem card_succ (o : Ordinal) : card (succ o) = card o + 1 := by
 #align ordinal.card_succ Ordinal.card_succ
 -/
 
-#print Ordinal.nat_cast_succ /-
-theorem nat_cast_succ (n : ℕ) : ↑n.succ = succ (n : Ordinal) :=
+#print Ordinal.natCast_succ /-
+theorem natCast_succ (n : ℕ) : ↑n.succ = succ (n : Ordinal) :=
   rfl
-#align ordinal.nat_cast_succ Ordinal.nat_cast_succ
+#align ordinal.nat_cast_succ Ordinal.natCast_succ
 -/
 
 #print Ordinal.uniqueIioOne /-

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

@@ -511,7 +511,7 @@ def initialSegOut {α β : Ordinal} (h : α ≤ β) :
     InitialSeg ((· < ·) : α.out.α → α.out.α → Prop) ((· < ·) : β.out.α → β.out.α → Prop) :=
   by
   change α.out.r ≼i β.out.r
-  rw [← Quotient.out_eq α, ← Quotient.out_eq β] at h ; revert h
+  rw [← Quotient.out_eq α, ← Quotient.out_eq β] at h; revert h
   cases Quotient.out α; cases Quotient.out β; exact Classical.choice
 #align ordinal.initial_seg_out Ordinal.initialSegOut
 -/
@@ -523,7 +523,7 @@ def principalSegOut {α β : Ordinal} (h : α < β) :
     PrincipalSeg ((· < ·) : α.out.α → α.out.α → Prop) ((· < ·) : β.out.α → β.out.α → Prop) :=
   by
   change α.out.r ≺i β.out.r
-  rw [← Quotient.out_eq α, ← Quotient.out_eq β] at h ; revert h
+  rw [← Quotient.out_eq α, ← Quotient.out_eq β] at h; revert h
   cases Quotient.out α; cases Quotient.out β; exact Classical.choice
 #align ordinal.principal_seg_out Ordinal.principalSegOut
 -/
@@ -944,12 +944,12 @@ theorem lift_down' {a : Cardinal.{u}} {b : Ordinal.{max u v}} (h : card b ≤ a.
       inductionOn b fun β s _ e' => by
         skip
         rw [card_type, ← Cardinal.lift_id'.{max u v, u} (#β), ← Cardinal.lift_umax.{u, v},
-          lift_mk_eq.{u, max u v, max u v}] at e' 
+          lift_mk_eq.{u, max u v, max u v}] at e'
         cases' e' with f
         have g := RelIso.preimage f s
         haveI := (g : ⇑f ⁻¹'o s ↪r s).IsWellOrder
         have := lift_type_eq.{u, max u v, max u v}.2 ⟨g⟩
-        rw [lift_id, lift_umax.{u, v}] at this 
+        rw [lift_id, lift_umax.{u, v}] at this
         exact ⟨_, this⟩)
     e
 #align ordinal.lift_down' Ordinal.lift_down'
@@ -1578,7 +1578,7 @@ theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=
     Ordinal.inductionOn o fun β s _ => by
       let ⟨r, _, e⟩ := ord_eq α
       skip; simp only [card_type]; constructor <;> intro h
-      · rw [e] at h ;
+      · rw [e] at h;
         exact
           let ⟨f⟩ := h
           ⟨f.toEmbedding⟩
@@ -1792,10 +1792,10 @@ theorem ord_univ : ord univ.{u, v} = Ordinal.univ.{u, v} :=
 theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
   ⟨fun h => by
     have := ord_lt_ord.2 h
-    rw [ord_univ] at this 
+    rw [ord_univ] at this
     cases' lift.principalSeg.{u, u + 1}.down.1 (by simpa only [lift.principal_seg_top]) with o e
     have := card_ord c
-    rw [← e, lift.principal_seg_coe, ← lift_card] at this 
+    rw [← e, lift.principal_seg_coe, ← lift_card] at this
     exact ⟨_, this.symm⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ _⟩
 #align cardinal.lt_univ Cardinal.lt_univ
 -/
@@ -1804,7 +1804,7 @@ theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
 theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c' :=
   ⟨fun h => by
     let ⟨a, e, h'⟩ := lt_lift_iff.1 h
-    rw [← univ_id] at h' 
+    rw [← univ_id] at h'
     rcases lt_univ.{u}.1 h' with ⟨c', rfl⟩
     exact ⟨c', by simp only [e.symm, lift_lift]⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ' _⟩
 #align cardinal.lt_univ' Cardinal.lt_univ'

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

@@ -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: Mario Carneiro, Floris van Doorn
 -/
-import Mathbin.Data.Sum.Order
-import Mathbin.Order.InitialSeg
-import Mathbin.SetTheory.Cardinal.Basic
+import Data.Sum.Order
+import Order.InitialSeg
+import SetTheory.Cardinal.Basic
 
 #align_import set_theory.ordinal.basic from "leanprover-community/mathlib"@"8ea5598db6caeddde6cb734aa179cc2408dbd345"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Floris van Doorn
-
-! This file was ported from Lean 3 source module set_theory.ordinal.basic
-! leanprover-community/mathlib commit 8ea5598db6caeddde6cb734aa179cc2408dbd345
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Sum.Order
 import Mathbin.Order.InitialSeg
 import Mathbin.SetTheory.Cardinal.Basic
 
+#align_import set_theory.ordinal.basic from "leanprover-community/mathlib"@"8ea5598db6caeddde6cb734aa179cc2408dbd345"
+
 /-!
 # Ordinals
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Floris van Doorn
 
 ! This file was ported from Lean 3 source module set_theory.ordinal.basic
-! leanprover-community/mathlib commit 8da9e30545433fdd8fe55a0d3da208e5d9263f03
+! leanprover-community/mathlib commit 8ea5598db6caeddde6cb734aa179cc2408dbd345
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -607,6 +607,24 @@ theorem typein_inj (r : α → α → Prop) [IsWellOrder α r] {a b} : typein r
 #align ordinal.typein_inj Ordinal.typein_inj
 -/
 
+#print Ordinal.typein.principalSeg /-
+/-- Principal segment version of the `typein` function, embedding a well order into
+  ordinals as a principal segment. -/
+def typein.principalSeg (r : α → α → Prop) [IsWellOrder α r] :
+    r ≺i ((· < ·) : Ordinal → Ordinal → Prop) :=
+  ⟨⟨⟨typein r, typein_injective r⟩, fun a b => typein_lt_typein r⟩, type r, fun o =>
+    ⟨typein_surj r, fun ⟨a, h⟩ => h ▸ typein_lt_type r a⟩⟩
+#align ordinal.typein.principal_seg Ordinal.typein.principalSeg
+-/
+
+#print Ordinal.typein.principalSeg_coe /-
+@[simp]
+theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
+    (typein.principalSeg r : α → Ordinal) = typein r :=
+  rfl
+#align ordinal.typein.principal_seg_coe Ordinal.typein.principalSeg_coe
+-/
+
 /-! ### Enumerating elements in a well-order with ordinals. -/
 
 
@@ -614,25 +632,16 @@ theorem typein_inj (r : α → α → Prop) [IsWellOrder α r] {a b} : typein r
 /-- `enum r o h` is the `o`-th element of `α` ordered by `r`.
   That is, `enum` maps an initial segment of the ordinals, those
   less than the order type of `r`, to the elements of `α`. -/
-def enum (r : α → α → Prop) [IsWellOrder α r] (o) : o < type r → α :=
-  Quot.recOn' o (fun ⟨β, s, _⟩ h => (Classical.choice h).top) fun ⟨β, s, _⟩ ⟨γ, t, _⟩ ⟨h⟩ =>
-    by
-    skip; refine' funext fun H₂ : type t < type r => _
-    have H₁ : type s < type r := by rwa [type_eq.2 ⟨h⟩]
-    have :
-      ∀ {o e} (H : o < type r),
-        @Eq.ndrec (fun o : Ordinal => o < type r → α)
-            (fun h : type s < type r => (Classical.choice h).top) e H =
-          (Classical.choice H₁).top :=
-      by intros; subst e
-    exact (this H₂).trans (PrincipalSeg.top_eq h (Classical.choice H₁) (Classical.choice H₂))
+def enum (r : α → α → Prop) [IsWellOrder α r] (o) (h : o < type r) : α :=
+  (typein.principalSeg r).subrelIso ⟨o, h⟩
 #align ordinal.enum Ordinal.enum
 -/
 
 #print Ordinal.enum_type /-
 theorem enum_type {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r] [IsWellOrder β s]
     (f : s ≺i r) {h : type s < type r} : enum r (type s) h = f.top :=
-  PrincipalSeg.top_eq (RelIso.refl _) _ _
+  (typein.principalSeg r).Injective <|
+    ((typein.principalSeg r).apply_subrelIso _).trans (typein_top _).symm
 #align ordinal.enum_type Ordinal.enum_type
 -/
 
@@ -680,18 +689,8 @@ theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β →
 
 #print Ordinal.lt_wf /-
 theorem lt_wf : @WellFounded Ordinal (· < ·) :=
-  ⟨fun a =>
-    inductionOn a fun α r wo =>
-      suffices ∀ a, Acc (· < ·) (typein r a) from
-        ⟨_, fun o h =>
-          let ⟨a, e⟩ := typein_surj r h
-          e ▸ this a⟩
-      fun a =>
-      Acc.recOn (wo.wf.apply a) fun x H IH =>
-        ⟨_, fun o h =>
-          by
-          rcases typein_surj r (lt_trans h (typein_lt_type r _)) with ⟨b, rfl⟩
-          exact IH _ ((typein_lt_typein r).1 h)⟩⟩
+  wellFounded_iff_wellFounded_subrel.mpr fun a =>
+    inductionOn a fun α r wo => RelHomClass.wellFounded (typein.principal_seg r).subrelIso wo.wf
 #align ordinal.lt_wf Ordinal.lt_wf
 -/
 
@@ -707,24 +706,6 @@ theorem induction {p : Ordinal.{u} → Prop} (i : Ordinal.{u}) (h : ∀ j, (∀
 #align ordinal.induction Ordinal.induction
 -/
 
-#print Ordinal.typein.principalSeg /-
-/-- Principal segment version of the `typein` function, embedding a well order into
-  ordinals as a principal segment. -/
-def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r] :
-    @PrincipalSeg α Ordinal.{u} r (· < ·) :=
-  ⟨RelEmbedding.ofMonotone (typein r) fun a b => (typein_lt_typein r).2, type r, fun b =>
-    ⟨fun h => ⟨enum r _ h, typein_enum r h⟩, fun ⟨a, e⟩ => e ▸ typein_lt_type _ _⟩⟩
-#align ordinal.typein.principal_seg Ordinal.typein.principalSeg
--/
-
-#print Ordinal.typein.principalSeg_coe /-
-@[simp]
-theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
-    (typein.principalSeg r : α → Ordinal) = typein r :=
-  rfl
-#align ordinal.typein.principal_seg_coe Ordinal.typein.principalSeg_coe
--/
-
 /-! ### Cardinality of ordinals -/
 
 
@@ -1415,25 +1396,18 @@ theorem le_enum_succ {o : Ordinal} (a : (succ o).out.α) :
 @[simp]
 theorem enum_inj {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordinal} (h₁ : o₁ < type r)
     (h₂ : o₂ < type r) : enum r o₁ h₁ = enum r o₂ h₂ ↔ o₁ = o₂ :=
-  ⟨fun h => by
-    by_contra hne
-    cases' lt_or_gt_of_ne hne with hlt hlt <;> apply (IsWellOrder.isIrrefl r).1
-    · rwa [← @enum_lt_enum α r _ o₁ o₂ h₁ h₂, h] at hlt 
-    · change _ < _ at hlt ; rwa [← @enum_lt_enum α r _ o₂ o₁ h₂ h₁, h] at hlt , fun h => by
-    simp_rw [h]⟩
+  (typein.principalSeg r).subrelIso.Injective.eq_iff.trans Subtype.mk_eq_mk
 #align ordinal.enum_inj Ordinal.enum_inj
 -/
 
 #print Ordinal.enumIso /-
 /-- A well order `r` is order isomorphic to the set of ordinals smaller than `type r`. -/
 @[simps]
-def enumIso (r : α → α → Prop) [IsWellOrder α r] : Subrel (· < ·) (· < type r) ≃r r
-    where
-  toFun x := enum r x.1 x.2
-  invFun x := ⟨typein r x, typein_lt_type r x⟩
-  left_inv := fun ⟨o, h⟩ => Subtype.ext_val (typein_enum _ _)
-  right_inv h := enum_typein _ _
-  map_rel_iff' := by rintro ⟨a, _⟩ ⟨b, _⟩; apply enum_lt_enum
+def enumIso (r : α → α → Prop) [IsWellOrder α r] : Subrel (· < ·) (· < type r) ≃r r :=
+  {
+    (typein.principalSeg r).subrelIso with
+    toFun := fun x => enum r x.1 x.2
+    invFun := fun x => ⟨typein r x, typein_lt_type r x⟩ }
 #align ordinal.enum_iso Ordinal.enumIso
 -/
 

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

@@ -291,10 +291,13 @@ theorem type_empty : type (@EmptyRelation Empty) = 0 :=
 #align ordinal.type_empty Ordinal.type_empty
 -/
 
+#print Ordinal.type_eq_one_of_unique /-
 theorem type_eq_one_of_unique (r) [IsWellOrder α r] [Unique α] : type r = 1 :=
   (RelIso.relIsoOfUniqueOfIrrefl r _).ordinal_type_eq
 #align ordinal.type_eq_one_of_unique Ordinal.type_eq_one_of_unique
+-/
 
+#print Ordinal.type_eq_one_iff_unique /-
 @[simp]
 theorem type_eq_one_iff_unique [IsWellOrder α r] : type r = 1 ↔ Nonempty (Unique α) :=
   ⟨fun h =>
@@ -302,14 +305,19 @@ theorem type_eq_one_iff_unique [IsWellOrder α r] : type r = 1 ↔ Nonempty (Uni
     ⟨s.toEquiv.unique⟩,
     fun ⟨h⟩ => @type_eq_one_of_unique α r _ h⟩
 #align ordinal.type_eq_one_iff_unique Ordinal.type_eq_one_iff_unique
+-/
 
+#print Ordinal.type_pUnit /-
 theorem type_pUnit : type (@EmptyRelation PUnit) = 1 :=
   rfl
 #align ordinal.type_punit Ordinal.type_pUnit
+-/
 
+#print Ordinal.type_unit /-
 theorem type_unit : type (@EmptyRelation Unit) = 1 :=
   rfl
 #align ordinal.type_unit Ordinal.type_unit
+-/
 
 #print Ordinal.out_empty_iff_eq_zero /-
 @[simp]
@@ -343,9 +351,11 @@ theorem ne_zero_of_out_nonempty (o : Ordinal) [h : Nonempty o.out.α] : o ≠ 0
 #align ordinal.ne_zero_of_out_nonempty Ordinal.ne_zero_of_out_nonempty
 -/
 
+#print Ordinal.one_ne_zero /-
 protected theorem one_ne_zero : (1 : Ordinal) ≠ 0 :=
   type_ne_zero_of_nonempty _
 #align ordinal.one_ne_zero Ordinal.one_ne_zero
+-/
 
 instance : Nontrivial Ordinal.{u} :=
   ⟨⟨1, 0, Ordinal.one_ne_zero⟩⟩
@@ -456,10 +466,12 @@ protected theorem zero_le (o : Ordinal) : 0 ≤ o :=
 instance : OrderBot Ordinal :=
   ⟨0, Ordinal.zero_le⟩
 
+#print Ordinal.bot_eq_zero /-
 @[simp]
 theorem bot_eq_zero : (⊥ : Ordinal) = 0 :=
   rfl
 #align ordinal.bot_eq_zero Ordinal.bot_eq_zero
+-/
 
 #print Ordinal.le_zero /-
 @[simp]
@@ -489,9 +501,11 @@ theorem eq_zero_or_pos : ∀ a : Ordinal, a = 0 ∨ 0 < a :=
 instance : ZeroLEOneClass Ordinal :=
   ⟨Ordinal.zero_le _⟩
 
+#print Ordinal.NeZero.one /-
 instance NeZero.one : NeZero (1 : Ordinal) :=
   ⟨Ordinal.one_ne_zero⟩
 #align ordinal.ne_zero.one Ordinal.NeZero.one
+-/
 
 #print Ordinal.initialSegOut /-
 /-- Given two ordinals `α ≤ β`, then `initial_seg_out α β` is the initial segment embedding
@@ -540,6 +554,7 @@ theorem typein_top {α β} {r : α → α → Prop} {s : β → β → Prop} [Is
 #align ordinal.typein_top Ordinal.typein_top
 -/
 
+#print Ordinal.typein_apply /-
 @[simp]
 theorem typein_apply {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r] [IsWellOrder β s]
     (f : r ≼i s) (a : α) : Ordinal.typein s (f a) = Ordinal.typein r a :=
@@ -554,6 +569,7 @@ theorem typein_apply {α β} {r : α → α → Prop} {s : β → β → Prop} [
               ⟨⟨a, f.to_rel_embedding.map_rel_iff.1 h⟩,
                 Subtype.eq <| RelEmbedding.trans_apply _ _ _⟩⟩
 #align ordinal.typein_apply Ordinal.typein_apply
+-/
 
 #print Ordinal.typein_lt_typein /-
 @[simp]
@@ -644,6 +660,7 @@ theorem enum_lt_enum {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Or
 #align ordinal.enum_lt_enum Ordinal.enum_lt_enum
 -/
 
+#print Ordinal.relIso_enum' /-
 theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) :
     ∀ (hr : o < type r) (hs : o < type s), f (enum r o hr) = enum s o hs :=
@@ -651,12 +668,15 @@ theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β 
   refine' induction_on o _; rintro γ t wo ⟨g⟩ ⟨h⟩
   skip; rw [enum_type g, enum_type (PrincipalSeg.ltEquiv g f)]; rfl
 #align ordinal.rel_iso_enum' Ordinal.relIso_enum'
+-/
 
+#print Ordinal.relIso_enum /-
 theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) (hr : o < type r) :
     f (enum r o hr) = enum s o (by convert hr using 1; apply Quotient.sound; exact ⟨f.symm⟩) :=
   relIso_enum' _ _ _ _
 #align ordinal.rel_iso_enum Ordinal.relIso_enum
+-/
 
 #print Ordinal.lt_wf /-
 theorem lt_wf : @WellFounded Ordinal (· < ·) :=
@@ -697,11 +717,13 @@ def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r
 #align ordinal.typein.principal_seg Ordinal.typein.principalSeg
 -/
 
+#print Ordinal.typein.principalSeg_coe /-
 @[simp]
 theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
     (typein.principalSeg r : α → Ordinal) = typein r :=
   rfl
 #align ordinal.typein.principal_seg_coe Ordinal.typein.principalSeg_coe
+-/
 
 /-! ### Cardinality of ordinals -/
 
@@ -752,10 +774,12 @@ theorem card_eq_zero {o} : card o = 0 ↔ o = 0 :=
 #align ordinal.card_eq_zero Ordinal.card_eq_zero
 -/
 
+#print Ordinal.card_one /-
 @[simp]
 theorem card_one : card 1 = 1 :=
   rfl
 #align ordinal.card_one Ordinal.card_one
+-/
 
 /-! ### Lifting ordinals to a higher universe -/
 
@@ -771,11 +795,13 @@ def lift (o : Ordinal.{v}) : Ordinal.{max v u} :=
 #align ordinal.lift Ordinal.lift
 -/
 
+#print Ordinal.type_uLift /-
 @[simp]
 theorem type_uLift (r : α → α → Prop) [IsWellOrder α r] :
     type (ULift.down ⁻¹'o r) = lift.{v} (type r) :=
   rfl
 #align ordinal.type_ulift Ordinal.type_uLift
+-/
 
 #print RelIso.ordinal_lift_type_eq /-
 theorem RelIso.ordinal_lift_type_eq {α : Type u} {β : Type v} {r : α → α → Prop} {s : β → β → Prop}
@@ -813,11 +839,13 @@ theorem lift_umax' : lift.{max v u, u} = lift.{v, u} :=
 #align ordinal.lift_umax' Ordinal.lift_umax'
 -/
 
+#print Ordinal.lift_id' /-
 /-- An ordinal lifted to a lower or equal universe equals itself. -/
 @[simp]
 theorem lift_id' (a : Ordinal) : lift a = a :=
   inductionOn a fun α r _ => Quotient.sound ⟨RelIso.preimage Equiv.ulift r⟩
 #align ordinal.lift_id' Ordinal.lift_id'
+-/
 
 #print Ordinal.lift_id /-
 /-- An ordinal lifted to the same universe equals itself. -/
@@ -835,6 +863,7 @@ theorem lift_uzero (a : Ordinal.{u}) : lift.{0} a = a :=
 #align ordinal.lift_uzero Ordinal.lift_uzero
 -/
 
+#print Ordinal.lift_lift /-
 @[simp]
 theorem lift_lift (a : Ordinal) : lift.{w} (lift.{v} a) = lift.{max v w} a :=
   inductionOn a fun α r _ =>
@@ -842,6 +871,7 @@ theorem lift_lift (a : Ordinal) : lift.{w} (lift.{v} a) = lift.{max v w} a :=
       ⟨(RelIso.preimage Equiv.ulift _).trans <|
           (RelIso.preimage Equiv.ulift _).trans (RelIso.preimage Equiv.ulift _).symm⟩
 #align ordinal.lift_lift Ordinal.lift_lift
+-/
 
 #print Ordinal.lift_type_le /-
 theorem lift_type_le {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWellOrder β s] :
@@ -892,30 +922,40 @@ theorem lift_le {a b : Ordinal} : lift.{u, v} a ≤ lift b ↔ a ≤ b :=
 #align ordinal.lift_le Ordinal.lift_le
 -/
 
+#print Ordinal.lift_inj /-
 @[simp]
 theorem lift_inj {a b : Ordinal} : lift a = lift b ↔ a = b := by
   simp only [le_antisymm_iff, lift_le]
 #align ordinal.lift_inj Ordinal.lift_inj
+-/
 
+#print Ordinal.lift_lt /-
 @[simp]
 theorem lift_lt {a b : Ordinal} : lift a < lift b ↔ a < b := by
   simp only [lt_iff_le_not_le, lift_le]
 #align ordinal.lift_lt Ordinal.lift_lt
+-/
 
+#print Ordinal.lift_zero /-
 @[simp]
 theorem lift_zero : lift 0 = 0 :=
   type_eq_zero_of_empty _
 #align ordinal.lift_zero Ordinal.lift_zero
+-/
 
+#print Ordinal.lift_one /-
 @[simp]
 theorem lift_one : lift 1 = 1 :=
   type_eq_one_of_unique _
 #align ordinal.lift_one Ordinal.lift_one
+-/
 
+#print Ordinal.lift_card /-
 @[simp]
 theorem lift_card (a) : (card a).lift = card (lift a) :=
   inductionOn a fun α r _ => rfl
 #align ordinal.lift_card Ordinal.lift_card
+-/
 
 #print Ordinal.lift_down' /-
 theorem lift_down' {a : Cardinal.{u}} {b : Ordinal.{max u v}} (h : card b ≤ a.lift) :
@@ -971,10 +1011,12 @@ def lift.initialSeg : @InitialSeg Ordinal.{u} Ordinal.{max u v} (· < ·) (· <
 #align ordinal.lift.initial_seg Ordinal.lift.initialSeg
 -/
 
+#print Ordinal.lift.initialSeg_coe /-
 @[simp]
 theorem lift.initialSeg_coe : (lift.initialSeg : Ordinal → Ordinal) = lift :=
   rfl
 #align ordinal.lift.initial_seg_coe Ordinal.lift.initialSeg_coe
+-/
 
 /-! ### The first infinite ordinal `omega` -/
 
@@ -986,7 +1028,6 @@ def omega : Ordinal.{u} :=
 #align ordinal.omega Ordinal.omega
 -/
 
--- mathport name: ordinal.omega
 scoped notation "ω" => Ordinal.omega
 
 #print Ordinal.type_nat_lt /-
@@ -1048,10 +1089,12 @@ instance : AddMonoidWithOne Ordinal.{u}
               simp only [sum_assoc_apply_inl_inl, sum_assoc_apply_inl_inr, sum_assoc_apply_inr,
                 Sum.lex_inl_inl, Sum.lex_inr_inr, Sum.Lex.sep, Sum.lex_inr_inl]⟩⟩
 
+#print Ordinal.card_add /-
 @[simp]
 theorem card_add (o₁ o₂ : Ordinal) : card (o₁ + o₂) = card o₁ + card o₂ :=
   inductionOn o₁ fun α r _ => inductionOn o₂ fun β s _ => rfl
 #align ordinal.card_add Ordinal.card_add
+-/
 
 #print Ordinal.type_sum_lex /-
 @[simp]
@@ -1061,10 +1104,12 @@ theorem type_sum_lex {α β : Type u} (r : α → α → Prop) (s : β → β 
 #align ordinal.type_sum_lex Ordinal.type_sum_lex
 -/
 
+#print Ordinal.card_nat /-
 @[simp]
 theorem card_nat (n : ℕ) : card.{u} n = n := by
   induction n <;> [rfl; simp only [card_add, card_one, Nat.cast_succ, *]]
 #align ordinal.card_nat Ordinal.card_nat
+-/
 
 #print Ordinal.add_covariantClass_le /-
 instance add_covariantClass_le : CovariantClass Ordinal.{u} Ordinal.{u} (· + ·) (· ≤ ·) :=
@@ -1147,25 +1192,33 @@ instance : IsWellOrder Ordinal (· < ·) where
 instance : ConditionallyCompleteLinearOrderBot Ordinal :=
   IsWellOrder.conditionallyCompleteLinearOrderBot _
 
+#print Ordinal.max_zero_left /-
 @[simp]
 theorem max_zero_left : ∀ a : Ordinal, max 0 a = a :=
   max_bot_left
 #align ordinal.max_zero_left Ordinal.max_zero_left
+-/
 
+#print Ordinal.max_zero_right /-
 @[simp]
 theorem max_zero_right : ∀ a : Ordinal, max a 0 = a :=
   max_bot_right
 #align ordinal.max_zero_right Ordinal.max_zero_right
+-/
 
+#print Ordinal.max_eq_zero /-
 @[simp]
 theorem max_eq_zero {a b : Ordinal} : max a b = 0 ↔ a = 0 ∧ b = 0 :=
   max_eq_bot
 #align ordinal.max_eq_zero Ordinal.max_eq_zero
+-/
 
+#print Ordinal.sInf_empty /-
 @[simp]
 theorem sInf_empty : sInf (∅ : Set Ordinal) = 0 :=
   dif_neg not_nonempty_empty
 #align ordinal.Inf_empty Ordinal.sInf_empty
+-/
 
 -- ### Successor order properties
 private theorem succ_le_iff' {a b : Ordinal} : a + 1 ≤ b ↔ a < b :=
@@ -1198,20 +1251,26 @@ instance : NoMaxOrder Ordinal :=
 instance : SuccOrder Ordinal.{u} :=
   SuccOrder.ofSuccLeIff (fun o => o + 1) fun a b => succ_le_iff'
 
+#print Ordinal.add_one_eq_succ /-
 @[simp]
 theorem add_one_eq_succ (o : Ordinal) : o + 1 = succ o :=
   rfl
 #align ordinal.add_one_eq_succ Ordinal.add_one_eq_succ
+-/
 
+#print Ordinal.succ_zero /-
 @[simp]
 theorem succ_zero : succ (0 : Ordinal) = 1 :=
   zero_add 1
 #align ordinal.succ_zero Ordinal.succ_zero
+-/
 
+#print Ordinal.succ_one /-
 @[simp]
 theorem succ_one : succ (1 : Ordinal) = 2 :=
   rfl
 #align ordinal.succ_one Ordinal.succ_one
+-/
 
 #print Ordinal.add_succ /-
 theorem add_succ (o₁ o₂ : Ordinal) : o₁ + succ o₂ = succ (o₁ + o₂) :=
@@ -1219,12 +1278,16 @@ theorem add_succ (o₁ o₂ : Ordinal) : o₁ + succ o₂ = succ (o₁ + o₂) :
 #align ordinal.add_succ Ordinal.add_succ
 -/
 
+#print Ordinal.one_le_iff_pos /-
 theorem one_le_iff_pos {o : Ordinal} : 1 ≤ o ↔ 0 < o := by rw [← succ_zero, succ_le_iff]
 #align ordinal.one_le_iff_pos Ordinal.one_le_iff_pos
+-/
 
+#print Ordinal.one_le_iff_ne_zero /-
 theorem one_le_iff_ne_zero {o : Ordinal} : 1 ≤ o ↔ o ≠ 0 := by
   rw [one_le_iff_pos, Ordinal.pos_iff_ne_zero]
 #align ordinal.one_le_iff_ne_zero Ordinal.one_le_iff_ne_zero
+-/
 
 #print Ordinal.succ_pos /-
 theorem succ_pos (o : Ordinal) : 0 < succ o :=
@@ -1238,17 +1301,23 @@ theorem succ_ne_zero (o : Ordinal) : succ o ≠ 0 :=
 #align ordinal.succ_ne_zero Ordinal.succ_ne_zero
 -/
 
+#print Ordinal.lt_one_iff_zero /-
 theorem lt_one_iff_zero {a : Ordinal} : a < 1 ↔ a = 0 := by simpa using @lt_succ_bot_iff _ _ _ a _ _
 #align ordinal.lt_one_iff_zero Ordinal.lt_one_iff_zero
+-/
 
+#print Ordinal.le_one_iff /-
 theorem le_one_iff {a : Ordinal} : a ≤ 1 ↔ a = 0 ∨ a = 1 := by
   simpa using @le_succ_bot_iff _ _ _ a _
 #align ordinal.le_one_iff Ordinal.le_one_iff
+-/
 
+#print Ordinal.card_succ /-
 @[simp]
 theorem card_succ (o : Ordinal) : card (succ o) = card o + 1 := by
   simp only [← add_one_eq_succ, card_add, card_one]
 #align ordinal.card_succ Ordinal.card_succ
+-/
 
 #print Ordinal.nat_cast_succ /-
 theorem nat_cast_succ (n : ℕ) : ↑n.succ = succ (n : Ordinal) :=
@@ -1256,12 +1325,15 @@ theorem nat_cast_succ (n : ℕ) : ↑n.succ = succ (n : Ordinal) :=
 #align ordinal.nat_cast_succ Ordinal.nat_cast_succ
 -/
 
+#print Ordinal.uniqueIioOne /-
 instance uniqueIioOne : Unique (Iio (1 : Ordinal))
     where
   default := ⟨0, zero_lt_one⟩
   uniq a := Subtype.ext <| lt_one_iff_zero.1 a.Prop
 #align ordinal.unique_Iio_one Ordinal.uniqueIioOne
+-/
 
+#print Ordinal.uniqueOutOne /-
 instance uniqueOutOne : Unique (1 : Ordinal).out.α
     where
   default := enum (· < ·) 0 (by simp)
@@ -1272,18 +1344,23 @@ instance uniqueOutOne : Unique (1 : Ordinal).out.α
     rw [← lt_one_iff_zero]
     apply typein_lt_self
 #align ordinal.unique_out_one Ordinal.uniqueOutOne
+-/
 
+#print Ordinal.one_out_eq /-
 theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :=
   Unique.eq_default x
 #align ordinal.one_out_eq Ordinal.one_out_eq
+-/
 
 /-! ### Extra properties of typein and enum -/
 
 
+#print Ordinal.typein_one_out /-
 @[simp]
 theorem typein_one_out (x : (1 : Ordinal).out.α) : typein (· < ·) x = 0 := by
   rw [one_out_eq x, typein_enum]
 #align ordinal.typein_one_out Ordinal.typein_one_out
+-/
 
 #print Ordinal.typein_le_typein /-
 @[simp]
@@ -1380,12 +1457,14 @@ def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α :=
 #align ordinal.out_order_bot_of_pos Ordinal.outOrderBotOfPos
 -/
 
+#print Ordinal.enum_zero_eq_bot /-
 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
     enum (· < ·) 0 (by rwa [type_lt]) =
       haveI H := out_order_bot_of_pos ho
       ⊥ :=
   rfl
 #align ordinal.enum_zero_eq_bot Ordinal.enum_zero_eq_bot
+-/
 
 /-! ### Universal ordinal -/
 
@@ -1446,11 +1525,13 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
 #align ordinal.lift.principal_seg Ordinal.lift.principalSeg
 -/
 
+#print Ordinal.lift.principalSeg_coe /-
 @[simp]
 theorem lift.principalSeg_coe :
     (lift.principalSeg.{u, v} : Ordinal → Ordinal) = lift.{max (u + 1) v} :=
   rfl
 #align ordinal.lift.principal_seg_coe Ordinal.lift.principalSeg_coe
+-/
 
 #print Ordinal.lift.principalSeg_top /-
 @[simp]
@@ -1501,9 +1582,11 @@ def ord (c : Cardinal) : Ordinal :=
 #align cardinal.ord Cardinal.ord
 -/
 
+#print Cardinal.ord_eq_Inf /-
 theorem ord_eq_Inf (α : Type u) : ord (#α) = ⨅ r : { r // IsWellOrder α r }, @type α r.1 r.2 :=
   rfl
 #align cardinal.ord_eq_Inf Cardinal.ord_eq_Inf
+-/
 
 #print Cardinal.ord_eq /-
 theorem ord_eq (α) : ∃ (r : α → α → Prop) (wo : IsWellOrder α r), ord (#α) = @type α r wo :=
@@ -1568,9 +1651,11 @@ theorem ord_card_le (o : Ordinal) : o.card.ord ≤ o :=
 #align cardinal.ord_card_le Cardinal.ord_card_le
 -/
 
+#print Cardinal.lt_ord_succ_card /-
 theorem lt_ord_succ_card (o : Ordinal) : o < (succ o.card).ord :=
   lt_ord.2 <| lt_succ _
 #align cardinal.lt_ord_succ_card Cardinal.lt_ord_succ_card
+-/
 
 #print Cardinal.ord_strictMono /-
 @[mono]
@@ -1607,6 +1692,7 @@ theorem ord_zero : ord 0 = 0 :=
 #align cardinal.ord_zero Cardinal.ord_zero
 -/
 
+#print Cardinal.ord_nat /-
 @[simp]
 theorem ord_nat (n : ℕ) : ord n = n :=
   (ord_le.2 (card_nat n).ge).antisymm
@@ -1615,11 +1701,15 @@ theorem ord_nat (n : ℕ) : ord n = n :=
       · apply Ordinal.zero_le
       · exact succ_le_of_lt (IH.trans_lt <| ord_lt_ord.2 <| nat_cast_lt.2 (Nat.lt_succ_self n)))
 #align cardinal.ord_nat Cardinal.ord_nat
+-/
 
+#print Cardinal.ord_one /-
 @[simp]
 theorem ord_one : ord 1 = 1 := by simpa using ord_nat 1
 #align cardinal.ord_one Cardinal.ord_one
+-/
 
+#print Cardinal.lift_ord /-
 @[simp]
 theorem lift_ord (c) : (ord c).lift = ord (lift c) :=
   by
@@ -1628,6 +1718,7 @@ theorem lift_ord (c) : (ord c).lift = ord (lift c) :=
     rwa [lt_ord, ← lift_card, lift_lt, ← lt_ord, ← Ordinal.lift_lt]
   · rw [ord_le, ← lift_card, card_ord]
 #align cardinal.lift_ord Cardinal.lift_ord
+-/
 
 #print Cardinal.mk_ord_out /-
 theorem mk_ord_out (c : Cardinal) : (#c.ord.out.α) = c := by simp
@@ -1661,10 +1752,12 @@ def ord.orderEmbedding : Cardinal ↪o Ordinal :=
 #align cardinal.ord.order_embedding Cardinal.ord.orderEmbedding
 -/
 
+#print Cardinal.ord.orderEmbedding_coe /-
 @[simp]
 theorem ord.orderEmbedding_coe : (ord.orderEmbedding : Cardinal → Ordinal) = ord :=
   rfl
 #align cardinal.ord.order_embedding_coe Cardinal.ord.orderEmbedding_coe
+-/
 
 #print Cardinal.univ /-
 -- intended to be used with explicit universe parameters
@@ -1770,30 +1863,40 @@ theorem card_univ : card univ = Cardinal.univ :=
 #align ordinal.card_univ Ordinal.card_univ
 -/
 
+#print Ordinal.nat_le_card /-
 @[simp]
 theorem nat_le_card {o} {n : ℕ} : (n : Cardinal) ≤ card o ↔ (n : Ordinal) ≤ o := by
   rw [← Cardinal.ord_le, Cardinal.ord_nat]
 #align ordinal.nat_le_card Ordinal.nat_le_card
+-/
 
+#print Ordinal.nat_lt_card /-
 @[simp]
 theorem nat_lt_card {o} {n : ℕ} : (n : Cardinal) < card o ↔ (n : Ordinal) < o := by
   rw [← succ_le_iff, ← succ_le_iff, ← nat_succ, nat_le_card]; rfl
 #align ordinal.nat_lt_card Ordinal.nat_lt_card
+-/
 
+#print Ordinal.card_lt_nat /-
 @[simp]
 theorem card_lt_nat {o} {n : ℕ} : card o < n ↔ o < n :=
   lt_iff_lt_of_le_iff_le nat_le_card
 #align ordinal.card_lt_nat Ordinal.card_lt_nat
+-/
 
+#print Ordinal.card_le_nat /-
 @[simp]
 theorem card_le_nat {o} {n : ℕ} : card o ≤ n ↔ o ≤ n :=
   le_iff_le_iff_lt_iff_lt.2 nat_lt_card
 #align ordinal.card_le_nat Ordinal.card_le_nat
+-/
 
+#print Ordinal.card_eq_nat /-
 @[simp]
 theorem card_eq_nat {o} {n : ℕ} : card o = n ↔ o = n := by
   simp only [le_antisymm_iff, card_le_nat, nat_le_card]
 #align ordinal.card_eq_nat Ordinal.card_eq_nat
+-/
 
 #print Ordinal.type_fintype /-
 @[simp]

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

@@ -207,7 +207,7 @@ instance : One Ordinal :=
 /-- The order type of an element inside a well order. For the embedding as a principal segment, see
 `typein.principal_seg`. -/
 def typein (r : α → α → Prop) [IsWellOrder α r] (a : α) : Ordinal :=
-  type (Subrel r { b | r b a })
+  type (Subrel r {b | r b a})
 #align ordinal.typein Ordinal.typein
 -/
 

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

@@ -500,7 +500,7 @@ def initialSegOut {α β : Ordinal} (h : α ≤ β) :
     InitialSeg ((· < ·) : α.out.α → α.out.α → Prop) ((· < ·) : β.out.α → β.out.α → Prop) :=
   by
   change α.out.r ≼i β.out.r
-  rw [← Quotient.out_eq α, ← Quotient.out_eq β] at h; revert h
+  rw [← Quotient.out_eq α, ← Quotient.out_eq β] at h ; revert h
   cases Quotient.out α; cases Quotient.out β; exact Classical.choice
 #align ordinal.initial_seg_out Ordinal.initialSegOut
 -/
@@ -512,7 +512,7 @@ def principalSegOut {α β : Ordinal} (h : α < β) :
     PrincipalSeg ((· < ·) : α.out.α → α.out.α → Prop) ((· < ·) : β.out.α → β.out.α → Prop) :=
   by
   change α.out.r ≺i β.out.r
-  rw [← Quotient.out_eq α, ← Quotient.out_eq β] at h; revert h
+  rw [← Quotient.out_eq α, ← Quotient.out_eq β] at h ; revert h
   cases Quotient.out α; cases Quotient.out β; exact Classical.choice
 #align ordinal.principal_seg_out Ordinal.principalSegOut
 -/
@@ -608,7 +608,7 @@ def enum (r : α → α → Prop) [IsWellOrder α r] (o) : o < type r → α :=
         @Eq.ndrec (fun o : Ordinal => o < type r → α)
             (fun h : type s < type r => (Classical.choice h).top) e H =
           (Classical.choice H₁).top :=
-      by intros ; subst e
+      by intros; subst e
     exact (this H₂).trans (PrincipalSeg.top_eq h (Classical.choice H₁) (Classical.choice H₂))
 #align ordinal.enum Ordinal.enum
 -/
@@ -926,12 +926,12 @@ theorem lift_down' {a : Cardinal.{u}} {b : Ordinal.{max u v}} (h : card b ≤ a.
       inductionOn b fun β s _ e' => by
         skip
         rw [card_type, ← Cardinal.lift_id'.{max u v, u} (#β), ← Cardinal.lift_umax.{u, v},
-          lift_mk_eq.{u, max u v, max u v}] at e'
+          lift_mk_eq.{u, max u v, max u v}] at e' 
         cases' e' with f
         have g := RelIso.preimage f s
         haveI := (g : ⇑f ⁻¹'o s ↪r s).IsWellOrder
         have := lift_type_eq.{u, max u v, max u v}.2 ⟨g⟩
-        rw [lift_id, lift_umax.{u, v}] at this
+        rw [lift_id, lift_umax.{u, v}] at this 
         exact ⟨_, this⟩)
     e
 #align ordinal.lift_down' Ordinal.lift_down'
@@ -1063,7 +1063,7 @@ theorem type_sum_lex {α β : Type u} (r : α → α → Prop) (s : β → β 
 
 @[simp]
 theorem card_nat (n : ℕ) : card.{u} n = n := by
-  induction n <;> [rfl;simp only [card_add, card_one, Nat.cast_succ, *]]
+  induction n <;> [rfl; simp only [card_add, card_one, Nat.cast_succ, *]]
 #align ordinal.card_nat Ordinal.card_nat
 
 #print Ordinal.add_covariantClass_le /-
@@ -1103,8 +1103,8 @@ instance add_swap_covariantClass_le :
                 constructor <;> intro H
                 ·
                   cases' a with a a <;> cases' b with b b <;> cases H <;> constructor <;>
-                    [rwa [← fo];assumption]
-                · cases H <;> constructor <;> [rwa [fo];assumption]⟩⟩
+                    [rwa [← fo]; assumption]
+                · cases H <;> constructor <;> [rwa [fo]; assumption]⟩⟩
 #align ordinal.add_swap_covariant_class_le Ordinal.add_swap_covariantClass_le
 -/
 
@@ -1135,7 +1135,7 @@ instance : LinearOrder Ordinal :=
               rw [← typein_top f, ← typein_top g, le_iff_lt_or_eq, le_iff_lt_or_eq,
                 typein_lt_typein, typein_lt_typein]
               rcases trichotomous_of (Sum.Lex r₁ r₂) g.top f.top with (h | h | h) <;>
-                [exact Or.inl (Or.inl h);· left; right; rw [h];exact Or.inr (Or.inl h)])
+                [exact Or.inl (Or.inl h); · left; right; rw [h]; exact Or.inr (Or.inl h)])
           h₁ h₂
     decidableLe := Classical.decRel _ }
 
@@ -1184,7 +1184,7 @@ private theorem succ_le_iff' {a b : Ordinal} : a + 1 ≤ b ↔ a < b :=
         · exact f; · exact fun _ => t
         · rcases a with (a | _) <;> rcases b with (b | _)
           · simpa only [Sum.lex_inl_inl] using f.map_rel_iff.2
-          · intro ; rw [hf]; exact ⟨_, rfl⟩
+          · intro; rw [hf]; exact ⟨_, rfl⟩
           · exact False.elim ∘ Sum.lex_inr_inl
           · exact False.elim ∘ Sum.lex_inr_inr.1
         · rcases a with (a | _)
@@ -1341,8 +1341,8 @@ theorem enum_inj {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordina
   ⟨fun h => by
     by_contra hne
     cases' lt_or_gt_of_ne hne with hlt hlt <;> apply (IsWellOrder.isIrrefl r).1
-    · rwa [← @enum_lt_enum α r _ o₁ o₂ h₁ h₂, h] at hlt
-    · change _ < _ at hlt; rwa [← @enum_lt_enum α r _ o₂ o₁ h₂ h₁, h] at hlt, fun h => by
+    · rwa [← @enum_lt_enum α r _ o₁ o₂ h₁ h₂, h] at hlt 
+    · change _ < _ at hlt ; rwa [← @enum_lt_enum α r _ o₂ o₁ h₂ h₁, h] at hlt , fun h => by
     simp_rw [h]⟩
 #align ordinal.enum_inj Ordinal.enum_inj
 -/
@@ -1427,7 +1427,7 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
     by
     refine' fun b => induction_on b _; intro β s _
     rw [univ, ← lift_umax]; constructor <;> intro h
-    · rw [← lift_id (type s)] at h⊢
+    · rw [← lift_id (type s)] at h ⊢
       cases' lift_type_lt.1 h with f; cases' f with f a hf
       exists a; revert hf
       apply induction_on a; intro α r _ hf
@@ -1506,7 +1506,7 @@ theorem ord_eq_Inf (α : Type u) : ord (#α) = ⨅ r : { r // IsWellOrder α r }
 #align cardinal.ord_eq_Inf Cardinal.ord_eq_Inf
 
 #print Cardinal.ord_eq /-
-theorem ord_eq (α) : ∃ (r : α → α → Prop)(wo : IsWellOrder α r), ord (#α) = @type α r wo :=
+theorem ord_eq (α) : ∃ (r : α → α → Prop) (wo : IsWellOrder α r), ord (#α) = @type α r wo :=
   let ⟨r, wo⟩ := ciInf_mem fun r : { r // IsWellOrder α r } => @type α r.1 r.2
   ⟨r.1, r.2, wo.symm⟩
 #align cardinal.ord_eq Cardinal.ord_eq
@@ -1524,7 +1524,7 @@ theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=
     Ordinal.inductionOn o fun β s _ => by
       let ⟨r, _, e⟩ := ord_eq α
       skip; simp only [card_type]; constructor <;> intro h
-      · rw [e] at h;
+      · rw [e] at h ;
         exact
           let ⟨f⟩ := h
           ⟨f.toEmbedding⟩
@@ -1728,10 +1728,10 @@ theorem ord_univ : ord univ.{u, v} = Ordinal.univ.{u, v} :=
 theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
   ⟨fun h => by
     have := ord_lt_ord.2 h
-    rw [ord_univ] at this
-    cases' lift.principalSeg.{u, u + 1}.down.1 (by simpa only [lift.principal_seg_top] ) with o e
+    rw [ord_univ] at this 
+    cases' lift.principalSeg.{u, u + 1}.down.1 (by simpa only [lift.principal_seg_top]) with o e
     have := card_ord c
-    rw [← e, lift.principal_seg_coe, ← lift_card] at this
+    rw [← e, lift.principal_seg_coe, ← lift_card] at this 
     exact ⟨_, this.symm⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ _⟩
 #align cardinal.lt_univ Cardinal.lt_univ
 -/
@@ -1740,7 +1740,7 @@ theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
 theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c' :=
   ⟨fun h => by
     let ⟨a, e, h'⟩ := lt_lift_iff.1 h
-    rw [← univ_id] at h'
+    rw [← univ_id] at h' 
     rcases lt_univ.{u}.1 h' with ⟨c', rfl⟩
     exact ⟨c', by simp only [e.symm, lift_lift]⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ' _⟩
 #align cardinal.lt_univ' Cardinal.lt_univ'

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

@@ -64,7 +64,7 @@ noncomputable section
 
 open Function Cardinal Set Equiv Order
 
-open Classical Cardinal InitialSeg
+open scoped Classical Cardinal InitialSeg
 
 universe u v w
 
@@ -178,9 +178,11 @@ instance linearOrderOut (o : Ordinal) : LinearOrder o.out.α :=
 #align linear_order_out linearOrderOut
 -/
 
+#print isWellOrder_out_lt /-
 instance isWellOrder_out_lt (o : Ordinal) : IsWellOrder o.out.α (· < ·) :=
   o.out.wo
 #align is_well_order_out_lt isWellOrder_out_lt
+-/
 
 namespace Ordinal
 
@@ -243,10 +245,12 @@ theorem RelIso.ordinal_type_eq {α β} {r : α → α → Prop} {s : β → β 
 #align rel_iso.ordinal_type_eq RelIso.ordinal_type_eq
 -/
 
+#print Ordinal.type_lt /-
 @[simp]
 theorem type_lt (o : Ordinal) : type ((· < ·) : o.out.α → o.out.α → Prop) = o :=
   (type_def' _).symm.trans <| Quotient.out_eq o
 #align ordinal.type_lt Ordinal.type_lt
+-/
 
 #print Ordinal.type_eq_zero_of_empty /-
 theorem type_eq_zero_of_empty (r) [IsWellOrder α r] [IsEmpty α] : type r = 0 :=
@@ -400,40 +404,54 @@ add_decl_doc ordinal.partial_order.le
   a function embedding `r` as a principal segment of `s`. -/
 add_decl_doc ordinal.partial_order.lt
 
+#print Ordinal.type_le_iff /-
 theorem type_le_iff {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] : type r ≤ type s ↔ Nonempty (r ≼i s) :=
   Iff.rfl
 #align ordinal.type_le_iff Ordinal.type_le_iff
+-/
 
+#print Ordinal.type_le_iff' /-
 theorem type_le_iff' {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] : type r ≤ type s ↔ Nonempty (r ↪r s) :=
   ⟨fun ⟨f⟩ => ⟨f⟩, fun ⟨f⟩ => ⟨f.collapse⟩⟩
 #align ordinal.type_le_iff' Ordinal.type_le_iff'
+-/
 
+#print InitialSeg.ordinal_type_le /-
 theorem InitialSeg.ordinal_type_le {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (h : r ≼i s) : type r ≤ type s :=
   ⟨h⟩
 #align initial_seg.ordinal_type_le InitialSeg.ordinal_type_le
+-/
 
+#print RelEmbedding.ordinal_type_le /-
 theorem RelEmbedding.ordinal_type_le {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (h : r ↪r s) : type r ≤ type s :=
   ⟨h.collapse⟩
 #align rel_embedding.ordinal_type_le RelEmbedding.ordinal_type_le
+-/
 
+#print Ordinal.type_lt_iff /-
 @[simp]
 theorem type_lt_iff {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] : type r < type s ↔ Nonempty (r ≺i s) :=
   Iff.rfl
 #align ordinal.type_lt_iff Ordinal.type_lt_iff
+-/
 
+#print PrincipalSeg.ordinal_type_lt /-
 theorem PrincipalSeg.ordinal_type_lt {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (h : r ≺i s) : type r < type s :=
   ⟨h⟩
 #align principal_seg.ordinal_type_lt PrincipalSeg.ordinal_type_lt
+-/
 
+#print Ordinal.zero_le /-
 protected theorem zero_le (o : Ordinal) : 0 ≤ o :=
   inductionOn o fun α r _ => (InitialSeg.ofIsEmpty _ r).ordinal_type_le
 #align ordinal.zero_le Ordinal.zero_le
+-/
 
 instance : OrderBot Ordinal :=
   ⟨0, Ordinal.zero_le⟩
@@ -443,22 +461,30 @@ theorem bot_eq_zero : (⊥ : Ordinal) = 0 :=
   rfl
 #align ordinal.bot_eq_zero Ordinal.bot_eq_zero
 
+#print Ordinal.le_zero /-
 @[simp]
 protected theorem le_zero {o : Ordinal} : o ≤ 0 ↔ o = 0 :=
   le_bot_iff
 #align ordinal.le_zero Ordinal.le_zero
+-/
 
+#print Ordinal.pos_iff_ne_zero /-
 protected theorem pos_iff_ne_zero {o : Ordinal} : 0 < o ↔ o ≠ 0 :=
   bot_lt_iff_ne_bot
 #align ordinal.pos_iff_ne_zero Ordinal.pos_iff_ne_zero
+-/
 
+#print Ordinal.not_lt_zero /-
 protected theorem not_lt_zero (o : Ordinal) : ¬o < 0 :=
   not_lt_bot
 #align ordinal.not_lt_zero Ordinal.not_lt_zero
+-/
 
+#print Ordinal.eq_zero_or_pos /-
 theorem eq_zero_or_pos : ∀ a : Ordinal, a = 0 ∨ 0 < a :=
   eq_bot_or_bot_lt
 #align ordinal.eq_zero_or_pos Ordinal.eq_zero_or_pos
+-/
 
 instance : ZeroLEOneClass Ordinal :=
   ⟨Ordinal.zero_le _⟩
@@ -467,6 +493,7 @@ instance NeZero.one : NeZero (1 : Ordinal) :=
   ⟨Ordinal.one_ne_zero⟩
 #align ordinal.ne_zero.one Ordinal.NeZero.one
 
+#print Ordinal.initialSegOut /-
 /-- Given two ordinals `α ≤ β`, then `initial_seg_out α β` is the initial segment embedding
 of `α` to `β`, as map from a model type for `α` to a model type for `β`. -/
 def initialSegOut {α β : Ordinal} (h : α ≤ β) :
@@ -476,7 +503,9 @@ def initialSegOut {α β : Ordinal} (h : α ≤ β) :
   rw [← Quotient.out_eq α, ← Quotient.out_eq β] at h; revert h
   cases Quotient.out α; cases Quotient.out β; exact Classical.choice
 #align ordinal.initial_seg_out Ordinal.initialSegOut
+-/
 
+#print Ordinal.principalSegOut /-
 /-- Given two ordinals `α < β`, then `principal_seg_out α β` is the principal segment embedding
 of `α` to `β`, as map from a model type for `α` to a model type for `β`. -/
 def principalSegOut {α β : Ordinal} (h : α < β) :
@@ -486,14 +515,19 @@ def principalSegOut {α β : Ordinal} (h : α < β) :
   rw [← Quotient.out_eq α, ← Quotient.out_eq β] at h; revert h
   cases Quotient.out α; cases Quotient.out β; exact Classical.choice
 #align ordinal.principal_seg_out Ordinal.principalSegOut
+-/
 
+#print Ordinal.typein_lt_type /-
 theorem typein_lt_type (r : α → α → Prop) [IsWellOrder α r] (a : α) : typein r a < type r :=
   ⟨PrincipalSeg.ofElement _ _⟩
 #align ordinal.typein_lt_type Ordinal.typein_lt_type
+-/
 
+#print Ordinal.typein_lt_self /-
 theorem typein_lt_self {o : Ordinal} (i : o.out.α) : typein (· < ·) i < o := by
   simp_rw [← type_lt o]; apply typein_lt_type
 #align ordinal.typein_lt_self Ordinal.typein_lt_self
+-/
 
 #print Ordinal.typein_top /-
 @[simp]
@@ -521,6 +555,7 @@ theorem typein_apply {α β} {r : α → α → Prop} {s : β → β → Prop} [
                 Subtype.eq <| RelEmbedding.trans_apply _ _ _⟩⟩
 #align ordinal.typein_apply Ordinal.typein_apply
 
+#print Ordinal.typein_lt_typein /-
 @[simp]
 theorem typein_lt_typein (r : α → α → Prop) [IsWellOrder α r] {a b : α} :
     typein r a < typein r b ↔ r a b :=
@@ -534,11 +569,14 @@ theorem typein_lt_typein (r : α → α → Prop) [IsWellOrder α r] {a b : α}
     rw [← this]; exact f.top.2, fun h =>
     ⟨PrincipalSeg.codRestrict _ (PrincipalSeg.ofElement r a) (fun x => @trans _ r _ _ _ _ x.2 h) h⟩⟩
 #align ordinal.typein_lt_typein Ordinal.typein_lt_typein
+-/
 
+#print Ordinal.typein_surj /-
 theorem typein_surj (r : α → α → Prop) [IsWellOrder α r] {o} (h : o < type r) :
     ∃ a, typein r a = o :=
   inductionOn o (fun β s _ ⟨f⟩ => ⟨f.top, typein_top _⟩) h
 #align ordinal.typein_surj Ordinal.typein_surj
+-/
 
 #print Ordinal.typein_injective /-
 theorem typein_injective (r : α → α → Prop) [IsWellOrder α r] : Injective (typein r) :=
@@ -556,6 +594,7 @@ theorem typein_inj (r : α → α → Prop) [IsWellOrder α r] {a b} : typein r
 /-! ### Enumerating elements in a well-order with ordinals. -/
 
 
+#print Ordinal.enum /-
 /-- `enum r o h` is the `o`-th element of `α` ordered by `r`.
   That is, `enum` maps an initial segment of the ordinals, those
   less than the order type of `r`, to the elements of `α`. -/
@@ -572,11 +611,14 @@ def enum (r : α → α → Prop) [IsWellOrder α r] (o) : o < type r → α :=
       by intros ; subst e
     exact (this H₂).trans (PrincipalSeg.top_eq h (Classical.choice H₁) (Classical.choice H₂))
 #align ordinal.enum Ordinal.enum
+-/
 
+#print Ordinal.enum_type /-
 theorem enum_type {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r] [IsWellOrder β s]
     (f : s ≺i r) {h : type s < type r} : enum r (type s) h = f.top :=
   PrincipalSeg.top_eq (RelIso.refl _) _ _
 #align ordinal.enum_type Ordinal.enum_type
+-/
 
 #print Ordinal.enum_typein /-
 @[simp]
@@ -586,17 +628,21 @@ theorem enum_typein (r : α → α → Prop) [IsWellOrder α r] (a : α) :
 #align ordinal.enum_typein Ordinal.enum_typein
 -/
 
+#print Ordinal.typein_enum /-
 @[simp]
 theorem typein_enum (r : α → α → Prop) [IsWellOrder α r] {o} (h : o < type r) :
     typein r (enum r o h) = o := by
   let ⟨a, e⟩ := typein_surj r h
   clear _let_match <;> subst e <;> rw [enum_typein]
 #align ordinal.typein_enum Ordinal.typein_enum
+-/
 
+#print Ordinal.enum_lt_enum /-
 theorem enum_lt_enum {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordinal} (h₁ : o₁ < type r)
     (h₂ : o₂ < type r) : r (enum r o₁ h₁) (enum r o₂ h₂) ↔ o₁ < o₂ := by
   rw [← typein_lt_typein r, typein_enum, typein_enum]
 #align ordinal.enum_lt_enum Ordinal.enum_lt_enum
+-/
 
 theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) :
@@ -612,6 +658,7 @@ theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β →
   relIso_enum' _ _ _ _
 #align ordinal.rel_iso_enum Ordinal.relIso_enum
 
+#print Ordinal.lt_wf /-
 theorem lt_wf : @WellFounded Ordinal (· < ·) :=
   ⟨fun a =>
     inductionOn a fun α r wo =>
@@ -626,17 +673,21 @@ theorem lt_wf : @WellFounded Ordinal (· < ·) :=
           rcases typein_surj r (lt_trans h (typein_lt_type r _)) with ⟨b, rfl⟩
           exact IH _ ((typein_lt_typein r).1 h)⟩⟩
 #align ordinal.lt_wf Ordinal.lt_wf
+-/
 
 instance : WellFoundedRelation Ordinal :=
   ⟨(· < ·), lt_wf⟩
 
+#print Ordinal.induction /-
 /-- Reformulation of well founded induction on ordinals as a lemma that works with the
 `induction` tactic, as in `induction i using ordinal.induction with i IH`. -/
 theorem induction {p : Ordinal.{u} → Prop} (i : Ordinal.{u}) (h : ∀ j, (∀ k, k < j → p k) → p j) :
     p i :=
   lt_wf.induction i h
 #align ordinal.induction Ordinal.induction
+-/
 
+#print Ordinal.typein.principalSeg /-
 /-- Principal segment version of the `typein` function, embedding a well order into
   ordinals as a principal segment. -/
 def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r] :
@@ -644,6 +695,7 @@ def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r
   ⟨RelEmbedding.ofMonotone (typein r) fun a b => (typein_lt_typein r).2, type r, fun b =>
     ⟨fun h => ⟨enum r _ h, typein_enum r h⟩, fun ⟨a, e⟩ => e ▸ typein_lt_type _ _⟩⟩
 #align ordinal.typein.principal_seg Ordinal.typein.principalSeg
+-/
 
 @[simp]
 theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
@@ -677,9 +729,11 @@ theorem card_typein {r : α → α → Prop} [wo : IsWellOrder α r] (x : α) :
 #align ordinal.card_typein Ordinal.card_typein
 -/
 
+#print Ordinal.card_le_card /-
 theorem card_le_card {o₁ o₂ : Ordinal} : o₁ ≤ o₂ → card o₁ ≤ card o₂ :=
   inductionOn o₁ fun α r _ => inductionOn o₂ fun β s _ ⟨⟨⟨f, _⟩, _⟩⟩ => ⟨f⟩
 #align ordinal.card_le_card Ordinal.card_le_card
+-/
 
 #print Ordinal.card_zero /-
 @[simp]
@@ -789,6 +843,7 @@ theorem lift_lift (a : Ordinal) : lift.{w} (lift.{v} a) = lift.{max v w} a :=
           (RelIso.preimage Equiv.ulift _).trans (RelIso.preimage Equiv.ulift _).symm⟩
 #align ordinal.lift_lift Ordinal.lift_lift
 
+#print Ordinal.lift_type_le /-
 theorem lift_type_le {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWellOrder β s] :
     lift.{max v w} (type r) ≤ lift.{max u w} (type s) ↔ Nonempty (r ≼i s) :=
   ⟨fun ⟨f⟩ =>
@@ -798,6 +853,7 @@ theorem lift_type_le {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWel
     ⟨(InitialSeg.ofIso (RelIso.preimage Equiv.ulift r)).trans <|
         f.trans (InitialSeg.ofIso (RelIso.preimage Equiv.ulift s).symm)⟩⟩
 #align ordinal.lift_type_le Ordinal.lift_type_le
+-/
 
 #print Ordinal.lift_type_eq /-
 theorem lift_type_eq {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWellOrder β s] :
@@ -810,6 +866,7 @@ theorem lift_type_eq {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWel
 #align ordinal.lift_type_eq Ordinal.lift_type_eq
 -/
 
+#print Ordinal.lift_type_lt /-
 theorem lift_type_lt {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWellOrder β s] :
     lift.{max v w} (type r) < lift.{max u w} (type s) ↔ Nonempty (r ≺i s) := by
   haveI :=
@@ -826,11 +883,14 @@ theorem lift_type_lt {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWel
         ⟨(f.equivLT (RelIso.preimage Equiv.ulift r)).ltLe
             (InitialSeg.ofIso (RelIso.preimage Equiv.ulift s).symm)⟩⟩
 #align ordinal.lift_type_lt Ordinal.lift_type_lt
+-/
 
+#print Ordinal.lift_le /-
 @[simp]
 theorem lift_le {a b : Ordinal} : lift.{u, v} a ≤ lift b ↔ a ≤ b :=
   inductionOn a fun α r _ => inductionOn b fun β s _ => by rw [← lift_umax]; exact lift_type_le
 #align ordinal.lift_le Ordinal.lift_le
+-/
 
 @[simp]
 theorem lift_inj {a b : Ordinal} : lift a = lift b ↔ a = b := by
@@ -877,10 +937,13 @@ theorem lift_down' {a : Cardinal.{u}} {b : Ordinal.{max u v}} (h : card b ≤ a.
 #align ordinal.lift_down' Ordinal.lift_down'
 -/
 
+#print Ordinal.lift_down /-
 theorem lift_down {a : Ordinal.{u}} {b : Ordinal.{max u v}} (h : b ≤ lift a) : ∃ a', lift a' = b :=
   @lift_down' (card a) _ (by rw [lift_card] <;> exact card_le_card h)
 #align ordinal.lift_down Ordinal.lift_down
+-/
 
+#print Ordinal.le_lift_iff /-
 theorem le_lift_iff {a : Ordinal.{u}} {b : Ordinal.{max u v}} :
     b ≤ lift a ↔ ∃ a', lift a' = b ∧ a' ≤ a :=
   ⟨fun h =>
@@ -888,7 +951,9 @@ theorem le_lift_iff {a : Ordinal.{u}} {b : Ordinal.{max u v}} :
     ⟨a', e, lift_le.1 <| e.symm ▸ h⟩,
     fun ⟨a', e, h⟩ => e ▸ lift_le.2 h⟩
 #align ordinal.le_lift_iff Ordinal.le_lift_iff
+-/
 
+#print Ordinal.lt_lift_iff /-
 theorem lt_lift_iff {a : Ordinal.{u}} {b : Ordinal.{max u v}} :
     b < lift a ↔ ∃ a', lift a' = b ∧ a' < a :=
   ⟨fun h =>
@@ -896,12 +961,15 @@ theorem lt_lift_iff {a : Ordinal.{u}} {b : Ordinal.{max u v}} :
     ⟨a', e, lift_lt.1 <| e.symm ▸ h⟩,
     fun ⟨a', e, h⟩ => e ▸ lift_lt.2 h⟩
 #align ordinal.lt_lift_iff Ordinal.lt_lift_iff
+-/
 
+#print Ordinal.lift.initialSeg /-
 /-- Initial segment version of the lift operation on ordinals, embedding `ordinal.{u}` in
   `ordinal.{v}` as an initial segment when `u ≤ v`. -/
 def lift.initialSeg : @InitialSeg Ordinal.{u} Ordinal.{max u v} (· < ·) (· < ·) :=
   ⟨⟨⟨lift.{v}, fun a b => lift_inj.1⟩, fun a b => lift_lt⟩, fun a b h => lift_down (le_of_lt h)⟩
 #align ordinal.lift.initial_seg Ordinal.lift.initialSeg
+-/
 
 @[simp]
 theorem lift.initialSeg_coe : (lift.initialSeg : Ordinal → Ordinal) = lift :=
@@ -998,6 +1066,7 @@ theorem card_nat (n : ℕ) : card.{u} n = n := by
   induction n <;> [rfl;simp only [card_add, card_one, Nat.cast_succ, *]]
 #align ordinal.card_nat Ordinal.card_nat
 
+#print Ordinal.add_covariantClass_le /-
 instance add_covariantClass_le : CovariantClass Ordinal.{u} Ordinal.{u} (· + ·) (· ≤ ·) :=
   ⟨fun c a b h => by revert h c;
     exact
@@ -1018,7 +1087,9 @@ instance add_covariantClass_le : CovariantClass Ordinal.{u} Ordinal.{u} (· + ·
                   let ⟨w, h⟩ := fi _ _ (Sum.lex_inr_inr.1 H)
                   ⟨Sum.inr w, congr_arg Sum.inr h⟩⟩⟩⟩
 #align ordinal.add_covariant_class_le Ordinal.add_covariantClass_le
+-/
 
+#print Ordinal.add_swap_covariantClass_le /-
 instance add_swap_covariantClass_le :
     CovariantClass Ordinal.{u} Ordinal.{u} (swap (· + ·)) (· ≤ ·) :=
   ⟨fun c a b h => by revert h c;
@@ -1035,14 +1106,19 @@ instance add_swap_covariantClass_le :
                     [rwa [← fo];assumption]
                 · cases H <;> constructor <;> [rwa [fo];assumption]⟩⟩
 #align ordinal.add_swap_covariant_class_le Ordinal.add_swap_covariantClass_le
+-/
 
+#print Ordinal.le_add_right /-
 theorem le_add_right (a b : Ordinal) : a ≤ a + b := by
   simpa only [add_zero] using add_le_add_left (Ordinal.zero_le b) a
 #align ordinal.le_add_right Ordinal.le_add_right
+-/
 
+#print Ordinal.le_add_left /-
 theorem le_add_left (a b : Ordinal) : a ≤ b + a := by
   simpa only [zero_add] using add_le_add_right (Ordinal.zero_le b) a
 #align ordinal.le_add_left Ordinal.le_add_left
+-/
 
 instance : LinearOrder Ordinal :=
   {
@@ -1150,9 +1226,11 @@ theorem one_le_iff_ne_zero {o : Ordinal} : 1 ≤ o ↔ o ≠ 0 := by
   rw [one_le_iff_pos, Ordinal.pos_iff_ne_zero]
 #align ordinal.one_le_iff_ne_zero Ordinal.one_le_iff_ne_zero
 
+#print Ordinal.succ_pos /-
 theorem succ_pos (o : Ordinal) : 0 < succ o :=
   bot_lt_succ o
 #align ordinal.succ_pos Ordinal.succ_pos
+-/
 
 #print Ordinal.succ_ne_zero /-
 theorem succ_ne_zero (o : Ordinal) : succ o ≠ 0 :=
@@ -1207,41 +1285,56 @@ theorem typein_one_out (x : (1 : Ordinal).out.α) : typein (· < ·) x = 0 := by
   rw [one_out_eq x, typein_enum]
 #align ordinal.typein_one_out Ordinal.typein_one_out
 
+#print Ordinal.typein_le_typein /-
 @[simp]
 theorem typein_le_typein (r : α → α → Prop) [IsWellOrder α r] {x x' : α} :
     typein r x ≤ typein r x' ↔ ¬r x' x := by rw [← not_lt, typein_lt_typein]
 #align ordinal.typein_le_typein Ordinal.typein_le_typein
+-/
 
+#print Ordinal.typein_le_typein' /-
 @[simp]
 theorem typein_le_typein' (o : Ordinal) {x x' : o.out.α} :
     typein (· < ·) x ≤ typein (· < ·) x' ↔ x ≤ x' := by rw [typein_le_typein]; exact not_lt
 #align ordinal.typein_le_typein' Ordinal.typein_le_typein'
+-/
 
+#print Ordinal.enum_le_enum /-
 @[simp]
 theorem enum_le_enum (r : α → α → Prop) [IsWellOrder α r] {o o' : Ordinal} (ho : o < type r)
     (ho' : o' < type r) : ¬r (enum r o' ho') (enum r o ho) ↔ o ≤ o' := by
   rw [← @not_lt _ _ o' o, enum_lt_enum ho']
 #align ordinal.enum_le_enum Ordinal.enum_le_enum
+-/
 
+#print Ordinal.enum_le_enum' /-
 @[simp]
 theorem enum_le_enum' (a : Ordinal) {o o' : Ordinal} (ho : o < type (· < ·))
     (ho' : o' < type (· < ·)) : enum (· < ·) o ho ≤ @enum a.out.α (· < ·) _ o' ho' ↔ o ≤ o' := by
   rw [← enum_le_enum (· < ·), ← not_lt]
 #align ordinal.enum_le_enum' Ordinal.enum_le_enum'
+-/
 
+#print Ordinal.enum_zero_le /-
 theorem enum_zero_le {r : α → α → Prop} [IsWellOrder α r] (h0 : 0 < type r) (a : α) :
     ¬r a (enum r 0 h0) := by rw [← enum_typein r a, enum_le_enum r]; apply Ordinal.zero_le
 #align ordinal.enum_zero_le Ordinal.enum_zero_le
+-/
 
+#print Ordinal.enum_zero_le' /-
 theorem enum_zero_le' {o : Ordinal} (h0 : 0 < o) (a : o.out.α) :
     @enum o.out.α (· < ·) _ 0 (by rwa [type_lt]) ≤ a := by rw [← not_lt]; apply enum_zero_le
 #align ordinal.enum_zero_le' Ordinal.enum_zero_le'
+-/
 
+#print Ordinal.le_enum_succ /-
 theorem le_enum_succ {o : Ordinal} (a : (succ o).out.α) :
     a ≤ @enum (succ o).out.α (· < ·) _ o (by rw [type_lt]; exact lt_succ o) := by
   rw [← enum_typein (· < ·) a, enum_le_enum', ← lt_succ_iff]; apply typein_lt_self
 #align ordinal.le_enum_succ Ordinal.le_enum_succ
+-/
 
+#print Ordinal.enum_inj /-
 @[simp]
 theorem enum_inj {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordinal} (h₁ : o₁ < type r)
     (h₂ : o₂ < type r) : enum r o₁ h₁ = enum r o₂ h₂ ↔ o₁ = o₂ :=
@@ -1252,7 +1345,9 @@ theorem enum_inj {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordina
     · change _ < _ at hlt; rwa [← @enum_lt_enum α r _ o₂ o₁ h₂ h₁, h] at hlt, fun h => by
     simp_rw [h]⟩
 #align ordinal.enum_inj Ordinal.enum_inj
+-/
 
+#print Ordinal.enumIso /-
 /-- A well order `r` is order isomorphic to the set of ordinals smaller than `type r`. -/
 @[simps]
 def enumIso (r : α → α → Prop) [IsWellOrder α r] : Subrel (· < ·) (· < type r) ≃r r
@@ -1263,7 +1358,9 @@ def enumIso (r : α → α → Prop) [IsWellOrder α r] : Subrel (· < ·) (· <
   right_inv h := enum_typein _ _
   map_rel_iff' := by rintro ⟨a, _⟩ ⟨b, _⟩; apply enum_lt_enum
 #align ordinal.enum_iso Ordinal.enumIso
+-/
 
+#print Ordinal.enumIsoOut /-
 /-- The order isomorphism between ordinals less than `o` and `o.out.α`. -/
 @[simps]
 noncomputable def enumIsoOut (o : Ordinal) : Set.Iio o ≃o o.out.α
@@ -1274,11 +1371,14 @@ noncomputable def enumIsoOut (o : Ordinal) : Set.Iio o ≃o o.out.α
   right_inv h := enum_typein _ _
   map_rel_iff' := by rintro ⟨a, _⟩ ⟨b, _⟩; apply enum_le_enum'
 #align ordinal.enum_iso_out Ordinal.enumIsoOut
+-/
 
+#print Ordinal.outOrderBotOfPos /-
 /-- `o.out.α` is an `order_bot` whenever `0 < o`. -/
 def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α :=
   ⟨_, enum_zero_le' ho⟩
 #align ordinal.out_order_bot_of_pos Ordinal.outOrderBotOfPos
+-/
 
 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
     enum (· < ·) 0 (by rwa [type_lt]) =
@@ -1300,9 +1400,11 @@ def univ : Ordinal.{max (u + 1) v} :=
 #align ordinal.univ Ordinal.univ
 -/
 
+#print Ordinal.univ_id /-
 theorem univ_id : univ.{u, u + 1} = @type Ordinal (· < ·) _ :=
   lift_id _
 #align ordinal.univ_id Ordinal.univ_id
+-/
 
 #print Ordinal.lift_univ /-
 @[simp]
@@ -1317,6 +1419,7 @@ theorem univ_umax : univ.{u, max (u + 1) v} = univ.{u, v} :=
 #align ordinal.univ_umax Ordinal.univ_umax
 -/
 
+#print Ordinal.lift.principalSeg /-
 /-- Principal segment version of the lift operation on ordinals, embedding `ordinal.{u}` in
   `ordinal.{v}` as a principal segment when `u < v`. -/
 def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· < ·) (· < ·) :=
@@ -1341,6 +1444,7 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
       apply induction_on a; intro α r _
       exact lift_type_lt.{u, u + 1, max (u + 1) v}.2 ⟨typein.principal_seg r⟩⟩
 #align ordinal.lift.principal_seg Ordinal.lift.principalSeg
+-/
 
 @[simp]
 theorem lift.principalSeg_coe :
@@ -1355,9 +1459,11 @@ theorem lift.principalSeg_top : lift.principalSeg.top = univ :=
 #align ordinal.lift.principal_seg_top Ordinal.lift.principalSeg_top
 -/
 
+#print Ordinal.lift.principalSeg_top' /-
 theorem lift.principalSeg_top' : lift.principalSeg.{u, u + 1}.top = @type Ordinal (· < ·) _ := by
   simp only [lift.principal_seg_top, univ_id]
 #align ordinal.lift.principal_seg_top' Ordinal.lift.principalSeg_top'
+-/
 
 end Ordinal
 
@@ -1406,10 +1512,13 @@ theorem ord_eq (α) : ∃ (r : α → α → Prop)(wo : IsWellOrder α r), ord (
 #align cardinal.ord_eq Cardinal.ord_eq
 -/
 
+#print Cardinal.ord_le_type /-
 theorem ord_le_type (r : α → α → Prop) [h : IsWellOrder α r] : ord (#α) ≤ type r :=
   ciInf_le' _ (Subtype.mk r h)
 #align cardinal.ord_le_type Cardinal.ord_le_type
+-/
 
+#print Cardinal.ord_le /-
 theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=
   inductionOn c fun α =>
     Ordinal.inductionOn o fun β s _ => by
@@ -1424,15 +1533,18 @@ theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=
         haveI := RelEmbedding.isWellOrder g
         exact le_trans (ord_le_type _) g.ordinal_type_le
 #align cardinal.ord_le Cardinal.ord_le
+-/
 
 #print Cardinal.gc_ord_card /-
 theorem gc_ord_card : GaloisConnection ord card := fun _ _ => ord_le
 #align cardinal.gc_ord_card Cardinal.gc_ord_card
 -/
 
+#print Cardinal.lt_ord /-
 theorem lt_ord {c o} : o < ord c ↔ o.card < c :=
   gc_ord_card.lt_iff_lt
 #align cardinal.lt_ord Cardinal.lt_ord
+-/
 
 #print Cardinal.card_ord /-
 @[simp]
@@ -1450,9 +1562,11 @@ def gciOrdCard : GaloisCoinsertion ord card :=
 #align cardinal.gci_ord_card Cardinal.gciOrdCard
 -/
 
+#print Cardinal.ord_card_le /-
 theorem ord_card_le (o : Ordinal) : o.card.ord ≤ o :=
   gc_ord_card.l_u_le _
 #align cardinal.ord_card_le Cardinal.ord_card_le
+-/
 
 theorem lt_ord_succ_card (o : Ordinal) : o < (succ o.card).ord :=
   lt_ord.2 <| lt_succ _
@@ -1472,15 +1586,19 @@ theorem ord_mono : Monotone ord :=
 #align cardinal.ord_mono Cardinal.ord_mono
 -/
 
+#print Cardinal.ord_le_ord /-
 @[simp]
 theorem ord_le_ord {c₁ c₂} : ord c₁ ≤ ord c₂ ↔ c₁ ≤ c₂ :=
   gciOrdCard.l_le_l_iff
 #align cardinal.ord_le_ord Cardinal.ord_le_ord
+-/
 
+#print Cardinal.ord_lt_ord /-
 @[simp]
 theorem ord_lt_ord {c₁ c₂} : ord c₁ < ord c₂ ↔ c₁ < c₂ :=
   ord_strictMono.lt_iff_lt
 #align cardinal.ord_lt_ord Cardinal.ord_lt_ord
+-/
 
 #print Cardinal.ord_zero /-
 @[simp]
@@ -1516,19 +1634,24 @@ theorem mk_ord_out (c : Cardinal) : (#c.ord.out.α) = c := by simp
 #align cardinal.mk_ord_out Cardinal.mk_ord_out
 -/
 
+#print Cardinal.card_typein_lt /-
 theorem card_typein_lt (r : α → α → Prop) [IsWellOrder α r] (x : α) (h : ord (#α) = type r) :
     card (typein r x) < (#α) := by rw [← lt_ord, h]; apply typein_lt_type
 #align cardinal.card_typein_lt Cardinal.card_typein_lt
+-/
 
+#print Cardinal.card_typein_out_lt /-
 theorem card_typein_out_lt (c : Cardinal) (x : c.ord.out.α) : card (typein (· < ·) x) < c := by
   rw [← lt_ord]; apply typein_lt_self
 #align cardinal.card_typein_out_lt Cardinal.card_typein_out_lt
+-/
 
 #print Cardinal.ord_injective /-
 theorem ord_injective : Injective ord := by intro c c' h; rw [← card_ord c, ← card_ord c', h]
 #align cardinal.ord_injective Cardinal.ord_injective
 -/
 
+#print Cardinal.ord.orderEmbedding /-
 /-- The ordinal corresponding to a cardinal `c` is the least ordinal
   whose cardinal is `c`. This is the order-embedding version. For the regular function, see `ord`.
 -/
@@ -1536,6 +1659,7 @@ def ord.orderEmbedding : Cardinal ↪o Ordinal :=
   RelEmbedding.orderEmbeddingOfLTEmbedding
     (RelEmbedding.ofMonotone Cardinal.ord fun a b => Cardinal.ord_lt_ord.2)
 #align cardinal.ord.order_embedding Cardinal.ord.orderEmbedding
+-/
 
 @[simp]
 theorem ord.orderEmbedding_coe : (ord.orderEmbedding : Cardinal → Ordinal) = ord :=
@@ -1572,14 +1696,18 @@ theorem univ_umax : univ.{u, max (u + 1) v} = univ.{u, v} :=
 #align cardinal.univ_umax Cardinal.univ_umax
 -/
 
+#print Cardinal.lift_lt_univ /-
 theorem lift_lt_univ (c : Cardinal) : lift.{u + 1, u} c < univ.{u, u + 1} := by
   simpa only [lift.principal_seg_coe, lift_ord, lift_succ, ord_le, succ_le_iff] using
     le_of_lt (lift.principalSeg.{u, u + 1}.lt_top (succ c).ord)
 #align cardinal.lift_lt_univ Cardinal.lift_lt_univ
+-/
 
+#print Cardinal.lift_lt_univ' /-
 theorem lift_lt_univ' (c : Cardinal) : lift.{max (u + 1) v, u} c < univ.{u, v} := by
   simpa only [lift_lift, lift_univ, univ_umax] using lift_lt.{_, max (u + 1) v}.2 (lift_lt_univ c)
 #align cardinal.lift_lt_univ' Cardinal.lift_lt_univ'
+-/
 
 #print Cardinal.ord_univ /-
 @[simp]
@@ -1596,6 +1724,7 @@ theorem ord_univ : ord univ.{u, v} = Ordinal.univ.{u, v} :=
 #align cardinal.ord_univ Cardinal.ord_univ
 -/
 
+#print Cardinal.lt_univ /-
 theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
   ⟨fun h => by
     have := ord_lt_ord.2 h
@@ -1605,7 +1734,9 @@ theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
     rw [← e, lift.principal_seg_coe, ← lift_card] at this
     exact ⟨_, this.symm⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ _⟩
 #align cardinal.lt_univ Cardinal.lt_univ
+-/
 
+#print Cardinal.lt_univ' /-
 theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c' :=
   ⟨fun h => by
     let ⟨a, e, h'⟩ := lt_lift_iff.1 h
@@ -1613,7 +1744,9 @@ theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c
     rcases lt_univ.{u}.1 h' with ⟨c', rfl⟩
     exact ⟨c', by simp only [e.symm, lift_lift]⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ' _⟩
 #align cardinal.lt_univ' Cardinal.lt_univ'
+-/
 
+#print Cardinal.small_iff_lift_mk_lt_univ /-
 theorem small_iff_lift_mk_lt_univ {α : Type u} :
     Small.{v} α ↔ Cardinal.lift (#α) < univ.{v, max u (v + 1)} :=
   by
@@ -1624,6 +1757,7 @@ theorem small_iff_lift_mk_lt_univ {α : Type u} :
   · rintro ⟨c, hc⟩
     exact ⟨⟨c.out, lift_mk_eq.{u, _, v + 1}.1 (hc.trans (congr rfl c.mk_out.symm))⟩⟩
 #align cardinal.small_iff_lift_mk_lt_univ Cardinal.small_iff_lift_mk_lt_univ
+-/
 
 end Cardinal
 

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

@@ -178,12 +178,6 @@ instance linearOrderOut (o : Ordinal) : LinearOrder o.out.α :=
 #align linear_order_out linearOrderOut
 -/
 
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 instance isWellOrder_out_lt (o : Ordinal) : IsWellOrder o.out.α (· < ·) :=
   o.out.wo
 #align is_well_order_out_lt isWellOrder_out_lt
@@ -249,12 +243,6 @@ theorem RelIso.ordinal_type_eq {α β} {r : α → α → Prop} {s : β → β 
 #align rel_iso.ordinal_type_eq RelIso.ordinal_type_eq
 -/
 
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 @[simp]
 theorem type_lt (o : Ordinal) : type ((· < ·) : o.out.α → o.out.α → Prop) = o :=
   (type_def' _).symm.trans <| Quotient.out_eq o
@@ -299,22 +287,10 @@ theorem type_empty : type (@EmptyRelation Empty) = 0 :=
 #align ordinal.type_empty Ordinal.type_empty
 -/
 
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 theorem type_eq_one_of_unique (r) [IsWellOrder α r] [Unique α] : type r = 1 :=
   (RelIso.relIsoOfUniqueOfIrrefl r _).ordinal_type_eq
 #align ordinal.type_eq_one_of_unique Ordinal.type_eq_one_of_unique
 
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 @[simp]
 theorem type_eq_one_iff_unique [IsWellOrder α r] : type r = 1 ↔ Nonempty (Unique α) :=
   ⟨fun h =>
@@ -323,22 +299,10 @@ theorem type_eq_one_iff_unique [IsWellOrder α r] : type r = 1 ↔ Nonempty (Uni
     fun ⟨h⟩ => @type_eq_one_of_unique α r _ h⟩
 #align ordinal.type_eq_one_iff_unique Ordinal.type_eq_one_iff_unique
 
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 theorem type_pUnit : type (@EmptyRelation PUnit) = 1 :=
   rfl
 #align ordinal.type_punit Ordinal.type_pUnit
 
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 theorem type_unit : type (@EmptyRelation Unit) = 1 :=
   rfl
 #align ordinal.type_unit Ordinal.type_unit
@@ -375,12 +339,6 @@ theorem ne_zero_of_out_nonempty (o : Ordinal) [h : Nonempty o.out.α] : o ≠ 0
 #align ordinal.ne_zero_of_out_nonempty Ordinal.ne_zero_of_out_nonempty
 -/
 
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 protected theorem one_ne_zero : (1 : Ordinal) ≠ 0 :=
   type_ne_zero_of_nonempty _
 #align ordinal.one_ne_zero Ordinal.one_ne_zero
@@ -442,79 +400,37 @@ add_decl_doc ordinal.partial_order.le
   a function embedding `r` as a principal segment of `s`. -/
 add_decl_doc ordinal.partial_order.lt
 
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 theorem type_le_iff {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] : type r ≤ type s ↔ Nonempty (r ≼i s) :=
   Iff.rfl
 #align ordinal.type_le_iff Ordinal.type_le_iff
 
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 theorem type_le_iff' {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] : type r ≤ type s ↔ Nonempty (r ↪r s) :=
   ⟨fun ⟨f⟩ => ⟨f⟩, fun ⟨f⟩ => ⟨f.collapse⟩⟩
 #align ordinal.type_le_iff' Ordinal.type_le_iff'
 
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 theorem InitialSeg.ordinal_type_le {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (h : r ≼i s) : type r ≤ type s :=
   ⟨h⟩
 #align initial_seg.ordinal_type_le InitialSeg.ordinal_type_le
 
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 theorem RelEmbedding.ordinal_type_le {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (h : r ↪r s) : type r ≤ type s :=
   ⟨h.collapse⟩
 #align rel_embedding.ordinal_type_le RelEmbedding.ordinal_type_le
 
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 @[simp]
 theorem type_lt_iff {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] : type r < type s ↔ Nonempty (r ≺i s) :=
   Iff.rfl
 #align ordinal.type_lt_iff Ordinal.type_lt_iff
 
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 theorem PrincipalSeg.ordinal_type_lt {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (h : r ≺i s) : type r < type s :=
   ⟨h⟩
 #align principal_seg.ordinal_type_lt PrincipalSeg.ordinal_type_lt
 
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 protected theorem zero_le (o : Ordinal) : 0 ≤ o :=
   inductionOn o fun α r _ => (InitialSeg.ofIsEmpty _ r).ordinal_type_le
 #align ordinal.zero_le Ordinal.zero_le
@@ -522,54 +438,24 @@ protected theorem zero_le (o : Ordinal) : 0 ≤ o :=
 instance : OrderBot Ordinal :=
   ⟨0, Ordinal.zero_le⟩
 
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 @[simp]
 theorem bot_eq_zero : (⊥ : Ordinal) = 0 :=
   rfl
 #align ordinal.bot_eq_zero Ordinal.bot_eq_zero
 
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 @[simp]
 protected theorem le_zero {o : Ordinal} : o ≤ 0 ↔ o = 0 :=
   le_bot_iff
 #align ordinal.le_zero Ordinal.le_zero
 
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 protected theorem pos_iff_ne_zero {o : Ordinal} : 0 < o ↔ o ≠ 0 :=
   bot_lt_iff_ne_bot
 #align ordinal.pos_iff_ne_zero Ordinal.pos_iff_ne_zero
 
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 protected theorem not_lt_zero (o : Ordinal) : ¬o < 0 :=
   not_lt_bot
 #align ordinal.not_lt_zero Ordinal.not_lt_zero
 
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 theorem eq_zero_or_pos : ∀ a : Ordinal, a = 0 ∨ 0 < a :=
   eq_bot_or_bot_lt
 #align ordinal.eq_zero_or_pos Ordinal.eq_zero_or_pos
@@ -577,22 +463,10 @@ theorem eq_zero_or_pos : ∀ a : Ordinal, a = 0 ∨ 0 < a :=
 instance : ZeroLEOneClass Ordinal :=
   ⟨Ordinal.zero_le _⟩
 
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 instance NeZero.one : NeZero (1 : Ordinal) :=
   ⟨Ordinal.one_ne_zero⟩
 #align ordinal.ne_zero.one Ordinal.NeZero.one
 
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 /-- Given two ordinals `α ≤ β`, then `initial_seg_out α β` is the initial segment embedding
 of `α` to `β`, as map from a model type for `α` to a model type for `β`. -/
 def initialSegOut {α β : Ordinal} (h : α ≤ β) :
@@ -603,12 +477,6 @@ def initialSegOut {α β : Ordinal} (h : α ≤ β) :
   cases Quotient.out α; cases Quotient.out β; exact Classical.choice
 #align ordinal.initial_seg_out Ordinal.initialSegOut
 
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 /-- Given two ordinals `α < β`, then `principal_seg_out α β` is the principal segment embedding
 of `α` to `β`, as map from a model type for `α` to a model type for `β`. -/
 def principalSegOut {α β : Ordinal} (h : α < β) :
@@ -619,22 +487,10 @@ def principalSegOut {α β : Ordinal} (h : α < β) :
   cases Quotient.out α; cases Quotient.out β; exact Classical.choice
 #align ordinal.principal_seg_out Ordinal.principalSegOut
 
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 theorem typein_lt_type (r : α → α → Prop) [IsWellOrder α r] (a : α) : typein r a < type r :=
   ⟨PrincipalSeg.ofElement _ _⟩
 #align ordinal.typein_lt_type Ordinal.typein_lt_type
 
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 theorem typein_lt_self {o : Ordinal} (i : o.out.α) : typein (· < ·) i < o := by
   simp_rw [← type_lt o]; apply typein_lt_type
 #align ordinal.typein_lt_self Ordinal.typein_lt_self
@@ -650,12 +506,6 @@ theorem typein_top {α β} {r : α → α → Prop} {s : β → β → Prop} [Is
 #align ordinal.typein_top Ordinal.typein_top
 -/
 
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 @[simp]
 theorem typein_apply {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r] [IsWellOrder β s]
     (f : r ≼i s) (a : α) : Ordinal.typein s (f a) = Ordinal.typein r a :=
@@ -671,12 +521,6 @@ theorem typein_apply {α β} {r : α → α → Prop} {s : β → β → Prop} [
                 Subtype.eq <| RelEmbedding.trans_apply _ _ _⟩⟩
 #align ordinal.typein_apply Ordinal.typein_apply
 
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 @[simp]
 theorem typein_lt_typein (r : α → α → Prop) [IsWellOrder α r] {a b : α} :
     typein r a < typein r b ↔ r a b :=
@@ -691,12 +535,6 @@ theorem typein_lt_typein (r : α → α → Prop) [IsWellOrder α r] {a b : α}
     ⟨PrincipalSeg.codRestrict _ (PrincipalSeg.ofElement r a) (fun x => @trans _ r _ _ _ _ x.2 h) h⟩⟩
 #align ordinal.typein_lt_typein Ordinal.typein_lt_typein
 
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 theorem typein_surj (r : α → α → Prop) [IsWellOrder α r] {o} (h : o < type r) :
     ∃ a, typein r a = o :=
   inductionOn o (fun β s _ ⟨f⟩ => ⟨f.top, typein_top _⟩) h
@@ -718,12 +556,6 @@ theorem typein_inj (r : α → α → Prop) [IsWellOrder α r] {a b} : typein r
 /-! ### Enumerating elements in a well-order with ordinals. -/
 
 
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 /-- `enum r o h` is the `o`-th element of `α` ordered by `r`.
   That is, `enum` maps an initial segment of the ordinals, those
   less than the order type of `r`, to the elements of `α`. -/
@@ -741,12 +573,6 @@ def enum (r : α → α → Prop) [IsWellOrder α r] (o) : o < type r → α :=
     exact (this H₂).trans (PrincipalSeg.top_eq h (Classical.choice H₁) (Classical.choice H₂))
 #align ordinal.enum Ordinal.enum
 
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 theorem enum_type {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r] [IsWellOrder β s]
     (f : s ≺i r) {h : type s < type r} : enum r (type s) h = f.top :=
   PrincipalSeg.top_eq (RelIso.refl _) _ _
@@ -760,12 +586,6 @@ theorem enum_typein (r : α → α → Prop) [IsWellOrder α r] (a : α) :
 #align ordinal.enum_typein Ordinal.enum_typein
 -/
 
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 @[simp]
 theorem typein_enum (r : α → α → Prop) [IsWellOrder α r] {o} (h : o < type r) :
     typein r (enum r o h) = o := by
@@ -773,23 +593,11 @@ theorem typein_enum (r : α → α → Prop) [IsWellOrder α r] {o} (h : o < typ
   clear _let_match <;> subst e <;> rw [enum_typein]
 #align ordinal.typein_enum Ordinal.typein_enum
 
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 theorem enum_lt_enum {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordinal} (h₁ : o₁ < type r)
     (h₂ : o₂ < type r) : r (enum r o₁ h₁) (enum r o₂ h₂) ↔ o₁ < o₂ := by
   rw [← typein_lt_typein r, typein_enum, typein_enum]
 #align ordinal.enum_lt_enum Ordinal.enum_lt_enum
 
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 theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) :
     ∀ (hr : o < type r) (hs : o < type s), f (enum r o hr) = enum s o hs :=
@@ -798,21 +606,12 @@ theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β 
   skip; rw [enum_type g, enum_type (PrincipalSeg.ltEquiv g f)]; rfl
 #align ordinal.rel_iso_enum' Ordinal.relIso_enum'
 
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 theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) (hr : o < type r) :
     f (enum r o hr) = enum s o (by convert hr using 1; apply Quotient.sound; exact ⟨f.symm⟩) :=
   relIso_enum' _ _ _ _
 #align ordinal.rel_iso_enum Ordinal.relIso_enum
 
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 theorem lt_wf : @WellFounded Ordinal (· < ·) :=
   ⟨fun a =>
     inductionOn a fun α r wo =>
@@ -831,12 +630,6 @@ theorem lt_wf : @WellFounded Ordinal (· < ·) :=
 instance : WellFoundedRelation Ordinal :=
   ⟨(· < ·), lt_wf⟩
 
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 /-- Reformulation of well founded induction on ordinals as a lemma that works with the
 `induction` tactic, as in `induction i using ordinal.induction with i IH`. -/
 theorem induction {p : Ordinal.{u} → Prop} (i : Ordinal.{u}) (h : ∀ j, (∀ k, k < j → p k) → p j) :
@@ -844,12 +637,6 @@ theorem induction {p : Ordinal.{u} → Prop} (i : Ordinal.{u}) (h : ∀ j, (∀
   lt_wf.induction i h
 #align ordinal.induction Ordinal.induction
 
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 /-- Principal segment version of the `typein` function, embedding a well order into
   ordinals as a principal segment. -/
 def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r] :
@@ -858,12 +645,6 @@ def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r
     ⟨fun h => ⟨enum r _ h, typein_enum r h⟩, fun ⟨a, e⟩ => e ▸ typein_lt_type _ _⟩⟩
 #align ordinal.typein.principal_seg Ordinal.typein.principalSeg
 
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 @[simp]
 theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
     (typein.principalSeg r : α → Ordinal) = typein r :=
@@ -896,12 +677,6 @@ theorem card_typein {r : α → α → Prop} [wo : IsWellOrder α r] (x : α) :
 #align ordinal.card_typein Ordinal.card_typein
 -/
 
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 theorem card_le_card {o₁ o₂ : Ordinal} : o₁ ≤ o₂ → card o₁ ≤ card o₂ :=
   inductionOn o₁ fun α r _ => inductionOn o₂ fun β s _ ⟨⟨⟨f, _⟩, _⟩⟩ => ⟨f⟩
 #align ordinal.card_le_card Ordinal.card_le_card
@@ -923,12 +698,6 @@ theorem card_eq_zero {o} : card o = 0 ↔ o = 0 :=
 #align ordinal.card_eq_zero Ordinal.card_eq_zero
 -/
 
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 @[simp]
 theorem card_one : card 1 = 1 :=
   rfl
@@ -948,12 +717,6 @@ def lift (o : Ordinal.{v}) : Ordinal.{max v u} :=
 #align ordinal.lift Ordinal.lift
 -/
 
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 @[simp]
 theorem type_uLift (r : α → α → Prop) [IsWellOrder α r] :
     type (ULift.down ⁻¹'o r) = lift.{v} (type r) :=
@@ -996,12 +759,6 @@ theorem lift_umax' : lift.{max v u, u} = lift.{v, u} :=
 #align ordinal.lift_umax' Ordinal.lift_umax'
 -/
 
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 /-- An ordinal lifted to a lower or equal universe equals itself. -/
 @[simp]
 theorem lift_id' (a : Ordinal) : lift a = a :=
@@ -1024,12 +781,6 @@ theorem lift_uzero (a : Ordinal.{u}) : lift.{0} a = a :=
 #align ordinal.lift_uzero Ordinal.lift_uzero
 -/
 
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 @[simp]
 theorem lift_lift (a : Ordinal) : lift.{w} (lift.{v} a) = lift.{max v w} a :=
   inductionOn a fun α r _ =>
@@ -1038,12 +789,6 @@ theorem lift_lift (a : Ordinal) : lift.{w} (lift.{v} a) = lift.{max v w} a :=
           (RelIso.preimage Equiv.ulift _).trans (RelIso.preimage Equiv.ulift _).symm⟩
 #align ordinal.lift_lift Ordinal.lift_lift
 
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 theorem lift_type_le {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWellOrder β s] :
     lift.{max v w} (type r) ≤ lift.{max u w} (type s) ↔ Nonempty (r ≼i s) :=
   ⟨fun ⟨f⟩ =>
@@ -1065,12 +810,6 @@ theorem lift_type_eq {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWel
 #align ordinal.lift_type_eq Ordinal.lift_type_eq
 -/
 
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 theorem lift_type_lt {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWellOrder β s] :
     lift.{max v w} (type r) < lift.{max u w} (type s) ↔ Nonempty (r ≺i s) := by
   haveI :=
@@ -1088,67 +827,31 @@ theorem lift_type_lt {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWel
             (InitialSeg.ofIso (RelIso.preimage Equiv.ulift s).symm)⟩⟩
 #align ordinal.lift_type_lt Ordinal.lift_type_lt
 
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 @[simp]
 theorem lift_le {a b : Ordinal} : lift.{u, v} a ≤ lift b ↔ a ≤ b :=
   inductionOn a fun α r _ => inductionOn b fun β s _ => by rw [← lift_umax]; exact lift_type_le
 #align ordinal.lift_le Ordinal.lift_le
 
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 @[simp]
 theorem lift_inj {a b : Ordinal} : lift a = lift b ↔ a = b := by
   simp only [le_antisymm_iff, lift_le]
 #align ordinal.lift_inj Ordinal.lift_inj
 
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 @[simp]
 theorem lift_lt {a b : Ordinal} : lift a < lift b ↔ a < b := by
   simp only [lt_iff_le_not_le, lift_le]
 #align ordinal.lift_lt Ordinal.lift_lt
 
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 @[simp]
 theorem lift_zero : lift 0 = 0 :=
   type_eq_zero_of_empty _
 #align ordinal.lift_zero Ordinal.lift_zero
 
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 @[simp]
 theorem lift_one : lift 1 = 1 :=
   type_eq_one_of_unique _
 #align ordinal.lift_one Ordinal.lift_one
 
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 @[simp]
 theorem lift_card (a) : (card a).lift = card (lift a) :=
   inductionOn a fun α r _ => rfl
@@ -1174,22 +877,10 @@ theorem lift_down' {a : Cardinal.{u}} {b : Ordinal.{max u v}} (h : card b ≤ a.
 #align ordinal.lift_down' Ordinal.lift_down'
 -/
 
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 theorem lift_down {a : Ordinal.{u}} {b : Ordinal.{max u v}} (h : b ≤ lift a) : ∃ a', lift a' = b :=
   @lift_down' (card a) _ (by rw [lift_card] <;> exact card_le_card h)
 #align ordinal.lift_down Ordinal.lift_down
 
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 theorem le_lift_iff {a : Ordinal.{u}} {b : Ordinal.{max u v}} :
     b ≤ lift a ↔ ∃ a', lift a' = b ∧ a' ≤ a :=
   ⟨fun h =>
@@ -1198,12 +889,6 @@ theorem le_lift_iff {a : Ordinal.{u}} {b : Ordinal.{max u v}} :
     fun ⟨a', e, h⟩ => e ▸ lift_le.2 h⟩
 #align ordinal.le_lift_iff Ordinal.le_lift_iff
 
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 theorem lt_lift_iff {a : Ordinal.{u}} {b : Ordinal.{max u v}} :
     b < lift a ↔ ∃ a', lift a' = b ∧ a' < a :=
   ⟨fun h =>
@@ -1212,24 +897,12 @@ theorem lt_lift_iff {a : Ordinal.{u}} {b : Ordinal.{max u v}} :
     fun ⟨a', e, h⟩ => e ▸ lift_lt.2 h⟩
 #align ordinal.lt_lift_iff Ordinal.lt_lift_iff
 
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 /-- Initial segment version of the lift operation on ordinals, embedding `ordinal.{u}` in
   `ordinal.{v}` as an initial segment when `u ≤ v`. -/
 def lift.initialSeg : @InitialSeg Ordinal.{u} Ordinal.{max u v} (· < ·) (· < ·) :=
   ⟨⟨⟨lift.{v}, fun a b => lift_inj.1⟩, fun a b => lift_lt⟩, fun a b h => lift_down (le_of_lt h)⟩
 #align ordinal.lift.initial_seg Ordinal.lift.initialSeg
 
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 @[simp]
 theorem lift.initialSeg_coe : (lift.initialSeg : Ordinal → Ordinal) = lift :=
   rfl
@@ -1307,12 +980,6 @@ instance : AddMonoidWithOne Ordinal.{u}
               simp only [sum_assoc_apply_inl_inl, sum_assoc_apply_inl_inr, sum_assoc_apply_inr,
                 Sum.lex_inl_inl, Sum.lex_inr_inr, Sum.Lex.sep, Sum.lex_inr_inl]⟩⟩
 
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 @[simp]
 theorem card_add (o₁ o₂ : Ordinal) : card (o₁ + o₂) = card o₁ + card o₂ :=
   inductionOn o₁ fun α r _ => inductionOn o₂ fun β s _ => rfl
@@ -1326,23 +993,11 @@ theorem type_sum_lex {α β : Type u} (r : α → α → Prop) (s : β → β 
 #align ordinal.type_sum_lex Ordinal.type_sum_lex
 -/
 
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 @[simp]
 theorem card_nat (n : ℕ) : card.{u} n = n := by
   induction n <;> [rfl;simp only [card_add, card_one, Nat.cast_succ, *]]
 #align ordinal.card_nat Ordinal.card_nat
 
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 instance add_covariantClass_le : CovariantClass Ordinal.{u} Ordinal.{u} (· + ·) (· ≤ ·) :=
   ⟨fun c a b h => by revert h c;
     exact
@@ -1364,12 +1019,6 @@ instance add_covariantClass_le : CovariantClass Ordinal.{u} Ordinal.{u} (· + ·
                   ⟨Sum.inr w, congr_arg Sum.inr h⟩⟩⟩⟩
 #align ordinal.add_covariant_class_le Ordinal.add_covariantClass_le
 
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 instance add_swap_covariantClass_le :
     CovariantClass Ordinal.{u} Ordinal.{u} (swap (· + ·)) (· ≤ ·) :=
   ⟨fun c a b h => by revert h c;
@@ -1387,22 +1036,10 @@ instance add_swap_covariantClass_le :
                 · cases H <;> constructor <;> [rwa [fo];assumption]⟩⟩
 #align ordinal.add_swap_covariant_class_le Ordinal.add_swap_covariantClass_le
 
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 theorem le_add_right (a b : Ordinal) : a ≤ a + b := by
   simpa only [add_zero] using add_le_add_left (Ordinal.zero_le b) a
 #align ordinal.le_add_right Ordinal.le_add_right
 
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 theorem le_add_left (a b : Ordinal) : a ≤ b + a := by
   simpa only [zero_add] using add_le_add_right (Ordinal.zero_le b) a
 #align ordinal.le_add_left Ordinal.le_add_left
@@ -1434,45 +1071,21 @@ instance : IsWellOrder Ordinal (· < ·) where
 instance : ConditionallyCompleteLinearOrderBot Ordinal :=
   IsWellOrder.conditionallyCompleteLinearOrderBot _
 
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 @[simp]
 theorem max_zero_left : ∀ a : Ordinal, max 0 a = a :=
   max_bot_left
 #align ordinal.max_zero_left Ordinal.max_zero_left
 
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 @[simp]
 theorem max_zero_right : ∀ a : Ordinal, max a 0 = a :=
   max_bot_right
 #align ordinal.max_zero_right Ordinal.max_zero_right
 
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 @[simp]
 theorem max_eq_zero {a b : Ordinal} : max a b = 0 ↔ a = 0 ∧ b = 0 :=
   max_eq_bot
 #align ordinal.max_eq_zero Ordinal.max_eq_zero
 
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 @[simp]
 theorem sInf_empty : sInf (∅ : Set Ordinal) = 0 :=
   dif_neg not_nonempty_empty
@@ -1509,34 +1122,16 @@ instance : NoMaxOrder Ordinal :=
 instance : SuccOrder Ordinal.{u} :=
   SuccOrder.ofSuccLeIff (fun o => o + 1) fun a b => succ_le_iff'
 
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 @[simp]
 theorem add_one_eq_succ (o : Ordinal) : o + 1 = succ o :=
   rfl
 #align ordinal.add_one_eq_succ Ordinal.add_one_eq_succ
 
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 @[simp]
 theorem succ_zero : succ (0 : Ordinal) = 1 :=
   zero_add 1
 #align ordinal.succ_zero Ordinal.succ_zero
 
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 @[simp]
 theorem succ_one : succ (1 : Ordinal) = 2 :=
   rfl
@@ -1548,31 +1143,13 @@ theorem add_succ (o₁ o₂ : Ordinal) : o₁ + succ o₂ = succ (o₁ + o₂) :
 #align ordinal.add_succ Ordinal.add_succ
 -/
 
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 theorem one_le_iff_pos {o : Ordinal} : 1 ≤ o ↔ 0 < o := by rw [← succ_zero, succ_le_iff]
 #align ordinal.one_le_iff_pos Ordinal.one_le_iff_pos
 
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 theorem one_le_iff_ne_zero {o : Ordinal} : 1 ≤ o ↔ o ≠ 0 := by
   rw [one_le_iff_pos, Ordinal.pos_iff_ne_zero]
 #align ordinal.one_le_iff_ne_zero Ordinal.one_le_iff_ne_zero
 
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 theorem succ_pos (o : Ordinal) : 0 < succ o :=
   bot_lt_succ o
 #align ordinal.succ_pos Ordinal.succ_pos
@@ -1583,31 +1160,13 @@ theorem succ_ne_zero (o : Ordinal) : succ o ≠ 0 :=
 #align ordinal.succ_ne_zero Ordinal.succ_ne_zero
 -/
 
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 theorem lt_one_iff_zero {a : Ordinal} : a < 1 ↔ a = 0 := by simpa using @lt_succ_bot_iff _ _ _ a _ _
 #align ordinal.lt_one_iff_zero Ordinal.lt_one_iff_zero
 
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 theorem le_one_iff {a : Ordinal} : a ≤ 1 ↔ a = 0 ∨ a = 1 := by
   simpa using @le_succ_bot_iff _ _ _ a _
 #align ordinal.le_one_iff Ordinal.le_one_iff
 
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 @[simp]
 theorem card_succ (o : Ordinal) : card (succ o) = card o + 1 := by
   simp only [← add_one_eq_succ, card_add, card_one]
@@ -1619,24 +1178,12 @@ theorem nat_cast_succ (n : ℕ) : ↑n.succ = succ (n : Ordinal) :=
 #align ordinal.nat_cast_succ Ordinal.nat_cast_succ
 -/
 
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 instance uniqueIioOne : Unique (Iio (1 : Ordinal))
     where
   default := ⟨0, zero_lt_one⟩
   uniq a := Subtype.ext <| lt_one_iff_zero.1 a.Prop
 #align ordinal.unique_Iio_one Ordinal.uniqueIioOne
 
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 instance uniqueOutOne : Unique (1 : Ordinal).out.α
     where
   default := enum (· < ·) 0 (by simp)
@@ -1648,9 +1195,6 @@ instance uniqueOutOne : Unique (1 : Ordinal).out.α
     apply typein_lt_self
 #align ordinal.unique_out_one Ordinal.uniqueOutOne
 
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 theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :=
   Unique.eq_default x
 #align ordinal.one_out_eq Ordinal.one_out_eq
@@ -1658,91 +1202,46 @@ theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :
 /-! ### Extra properties of typein and enum -/
 
 
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 @[simp]
 theorem typein_one_out (x : (1 : Ordinal).out.α) : typein (· < ·) x = 0 := by
   rw [one_out_eq x, typein_enum]
 #align ordinal.typein_one_out Ordinal.typein_one_out
 
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 @[simp]
 theorem typein_le_typein (r : α → α → Prop) [IsWellOrder α r] {x x' : α} :
     typein r x ≤ typein r x' ↔ ¬r x' x := by rw [← not_lt, typein_lt_typein]
 #align ordinal.typein_le_typein Ordinal.typein_le_typein
 
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 @[simp]
 theorem typein_le_typein' (o : Ordinal) {x x' : o.out.α} :
     typein (· < ·) x ≤ typein (· < ·) x' ↔ x ≤ x' := by rw [typein_le_typein]; exact not_lt
 #align ordinal.typein_le_typein' Ordinal.typein_le_typein'
 
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 @[simp]
 theorem enum_le_enum (r : α → α → Prop) [IsWellOrder α r] {o o' : Ordinal} (ho : o < type r)
     (ho' : o' < type r) : ¬r (enum r o' ho') (enum r o ho) ↔ o ≤ o' := by
   rw [← @not_lt _ _ o' o, enum_lt_enum ho']
 #align ordinal.enum_le_enum Ordinal.enum_le_enum
 
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 @[simp]
 theorem enum_le_enum' (a : Ordinal) {o o' : Ordinal} (ho : o < type (· < ·))
     (ho' : o' < type (· < ·)) : enum (· < ·) o ho ≤ @enum a.out.α (· < ·) _ o' ho' ↔ o ≤ o' := by
   rw [← enum_le_enum (· < ·), ← not_lt]
 #align ordinal.enum_le_enum' Ordinal.enum_le_enum'
 
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 theorem enum_zero_le {r : α → α → Prop} [IsWellOrder α r] (h0 : 0 < type r) (a : α) :
     ¬r a (enum r 0 h0) := by rw [← enum_typein r a, enum_le_enum r]; apply Ordinal.zero_le
 #align ordinal.enum_zero_le Ordinal.enum_zero_le
 
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 theorem enum_zero_le' {o : Ordinal} (h0 : 0 < o) (a : o.out.α) :
     @enum o.out.α (· < ·) _ 0 (by rwa [type_lt]) ≤ a := by rw [← not_lt]; apply enum_zero_le
 #align ordinal.enum_zero_le' Ordinal.enum_zero_le'
 
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 theorem le_enum_succ {o : Ordinal} (a : (succ o).out.α) :
     a ≤ @enum (succ o).out.α (· < ·) _ o (by rw [type_lt]; exact lt_succ o) := by
   rw [← enum_typein (· < ·) a, enum_le_enum', ← lt_succ_iff]; apply typein_lt_self
 #align ordinal.le_enum_succ Ordinal.le_enum_succ
 
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 @[simp]
 theorem enum_inj {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordinal} (h₁ : o₁ < type r)
     (h₂ : o₂ < type r) : enum r o₁ h₁ = enum r o₂ h₂ ↔ o₁ = o₂ :=
@@ -1754,12 +1253,6 @@ theorem enum_inj {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordina
     simp_rw [h]⟩
 #align ordinal.enum_inj Ordinal.enum_inj
 
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 /-- A well order `r` is order isomorphic to the set of ordinals smaller than `type r`. -/
 @[simps]
 def enumIso (r : α → α → Prop) [IsWellOrder α r] : Subrel (· < ·) (· < type r) ≃r r
@@ -1771,12 +1264,6 @@ def enumIso (r : α → α → Prop) [IsWellOrder α r] : Subrel (· < ·) (· <
   map_rel_iff' := by rintro ⟨a, _⟩ ⟨b, _⟩; apply enum_lt_enum
 #align ordinal.enum_iso Ordinal.enumIso
 
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 /-- The order isomorphism between ordinals less than `o` and `o.out.α`. -/
 @[simps]
 noncomputable def enumIsoOut (o : Ordinal) : Set.Iio o ≃o o.out.α
@@ -1788,20 +1275,11 @@ noncomputable def enumIsoOut (o : Ordinal) : Set.Iio o ≃o o.out.α
   map_rel_iff' := by rintro ⟨a, _⟩ ⟨b, _⟩; apply enum_le_enum'
 #align ordinal.enum_iso_out Ordinal.enumIsoOut
 
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 /-- `o.out.α` is an `order_bot` whenever `0 < o`. -/
 def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α :=
   ⟨_, enum_zero_le' ho⟩
 #align ordinal.out_order_bot_of_pos Ordinal.outOrderBotOfPos
 
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 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
     enum (· < ·) 0 (by rwa [type_lt]) =
       haveI H := out_order_bot_of_pos ho
@@ -1822,12 +1300,6 @@ def univ : Ordinal.{max (u + 1) v} :=
 #align ordinal.univ Ordinal.univ
 -/
 
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 theorem univ_id : univ.{u, u + 1} = @type Ordinal (· < ·) _ :=
   lift_id _
 #align ordinal.univ_id Ordinal.univ_id
@@ -1845,12 +1317,6 @@ theorem univ_umax : univ.{u, max (u + 1) v} = univ.{u, v} :=
 #align ordinal.univ_umax Ordinal.univ_umax
 -/
 
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 /-- Principal segment version of the lift operation on ordinals, embedding `ordinal.{u}` in
   `ordinal.{v}` as a principal segment when `u < v`. -/
 def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· < ·) (· < ·) :=
@@ -1876,12 +1342,6 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
       exact lift_type_lt.{u, u + 1, max (u + 1) v}.2 ⟨typein.principal_seg r⟩⟩
 #align ordinal.lift.principal_seg Ordinal.lift.principalSeg
 
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 @[simp]
 theorem lift.principalSeg_coe :
     (lift.principalSeg.{u, v} : Ordinal → Ordinal) = lift.{max (u + 1) v} :=
@@ -1895,12 +1355,6 @@ theorem lift.principalSeg_top : lift.principalSeg.top = univ :=
 #align ordinal.lift.principal_seg_top Ordinal.lift.principalSeg_top
 -/
 
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 theorem lift.principalSeg_top' : lift.principalSeg.{u, u + 1}.top = @type Ordinal (· < ·) _ := by
   simp only [lift.principal_seg_top, univ_id]
 #align ordinal.lift.principal_seg_top' Ordinal.lift.principalSeg_top'
@@ -1941,12 +1395,6 @@ def ord (c : Cardinal) : Ordinal :=
 #align cardinal.ord Cardinal.ord
 -/
 
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 theorem ord_eq_Inf (α : Type u) : ord (#α) = ⨅ r : { r // IsWellOrder α r }, @type α r.1 r.2 :=
   rfl
 #align cardinal.ord_eq_Inf Cardinal.ord_eq_Inf
@@ -1958,22 +1406,10 @@ theorem ord_eq (α) : ∃ (r : α → α → Prop)(wo : IsWellOrder α r), ord (
 #align cardinal.ord_eq Cardinal.ord_eq
 -/
 
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 theorem ord_le_type (r : α → α → Prop) [h : IsWellOrder α r] : ord (#α) ≤ type r :=
   ciInf_le' _ (Subtype.mk r h)
 #align cardinal.ord_le_type Cardinal.ord_le_type
 
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 theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=
   inductionOn c fun α =>
     Ordinal.inductionOn o fun β s _ => by
@@ -1994,12 +1430,6 @@ theorem gc_ord_card : GaloisConnection ord card := fun _ _ => ord_le
 #align cardinal.gc_ord_card Cardinal.gc_ord_card
 -/
 
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 theorem lt_ord {c o} : o < ord c ↔ o.card < c :=
   gc_ord_card.lt_iff_lt
 #align cardinal.lt_ord Cardinal.lt_ord
@@ -2020,22 +1450,10 @@ def gciOrdCard : GaloisCoinsertion ord card :=
 #align cardinal.gci_ord_card Cardinal.gciOrdCard
 -/
 
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 theorem ord_card_le (o : Ordinal) : o.card.ord ≤ o :=
   gc_ord_card.l_u_le _
 #align cardinal.ord_card_le Cardinal.ord_card_le
 
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 theorem lt_ord_succ_card (o : Ordinal) : o < (succ o.card).ord :=
   lt_ord.2 <| lt_succ _
 #align cardinal.lt_ord_succ_card Cardinal.lt_ord_succ_card
@@ -2054,23 +1472,11 @@ theorem ord_mono : Monotone ord :=
 #align cardinal.ord_mono Cardinal.ord_mono
 -/
 
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 @[simp]
 theorem ord_le_ord {c₁ c₂} : ord c₁ ≤ ord c₂ ↔ c₁ ≤ c₂ :=
   gciOrdCard.l_le_l_iff
 #align cardinal.ord_le_ord Cardinal.ord_le_ord
 
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 @[simp]
 theorem ord_lt_ord {c₁ c₂} : ord c₁ < ord c₂ ↔ c₁ < c₂ :=
   ord_strictMono.lt_iff_lt
@@ -2083,12 +1489,6 @@ theorem ord_zero : ord 0 = 0 :=
 #align cardinal.ord_zero Cardinal.ord_zero
 -/
 
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 @[simp]
 theorem ord_nat (n : ℕ) : ord n = n :=
   (ord_le.2 (card_nat n).ge).antisymm
@@ -2098,22 +1498,10 @@ theorem ord_nat (n : ℕ) : ord n = n :=
       · exact succ_le_of_lt (IH.trans_lt <| ord_lt_ord.2 <| nat_cast_lt.2 (Nat.lt_succ_self n)))
 #align cardinal.ord_nat Cardinal.ord_nat
 
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 @[simp]
 theorem ord_one : ord 1 = 1 := by simpa using ord_nat 1
 #align cardinal.ord_one Cardinal.ord_one
 
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 @[simp]
 theorem lift_ord (c) : (ord c).lift = ord (lift c) :=
   by
@@ -2128,22 +1516,10 @@ theorem mk_ord_out (c : Cardinal) : (#c.ord.out.α) = c := by simp
 #align cardinal.mk_ord_out Cardinal.mk_ord_out
 -/
 
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 theorem card_typein_lt (r : α → α → Prop) [IsWellOrder α r] (x : α) (h : ord (#α) = type r) :
     card (typein r x) < (#α) := by rw [← lt_ord, h]; apply typein_lt_type
 #align cardinal.card_typein_lt Cardinal.card_typein_lt
 
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 theorem card_typein_out_lt (c : Cardinal) (x : c.ord.out.α) : card (typein (· < ·) x) < c := by
   rw [← lt_ord]; apply typein_lt_self
 #align cardinal.card_typein_out_lt Cardinal.card_typein_out_lt
@@ -2153,12 +1529,6 @@ theorem ord_injective : Injective ord := by intro c c' h; rw [← card_ord c, 
 #align cardinal.ord_injective Cardinal.ord_injective
 -/
 
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 /-- The ordinal corresponding to a cardinal `c` is the least ordinal
   whose cardinal is `c`. This is the order-embedding version. For the regular function, see `ord`.
 -/
@@ -2167,12 +1537,6 @@ def ord.orderEmbedding : Cardinal ↪o Ordinal :=
     (RelEmbedding.ofMonotone Cardinal.ord fun a b => Cardinal.ord_lt_ord.2)
 #align cardinal.ord.order_embedding Cardinal.ord.orderEmbedding
 
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 @[simp]
 theorem ord.orderEmbedding_coe : (ord.orderEmbedding : Cardinal → Ordinal) = ord :=
   rfl
@@ -2208,23 +1572,11 @@ theorem univ_umax : univ.{u, max (u + 1) v} = univ.{u, v} :=
 #align cardinal.univ_umax Cardinal.univ_umax
 -/
 
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 theorem lift_lt_univ (c : Cardinal) : lift.{u + 1, u} c < univ.{u, u + 1} := by
   simpa only [lift.principal_seg_coe, lift_ord, lift_succ, ord_le, succ_le_iff] using
     le_of_lt (lift.principalSeg.{u, u + 1}.lt_top (succ c).ord)
 #align cardinal.lift_lt_univ Cardinal.lift_lt_univ
 
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 theorem lift_lt_univ' (c : Cardinal) : lift.{max (u + 1) v, u} c < univ.{u, v} := by
   simpa only [lift_lift, lift_univ, univ_umax] using lift_lt.{_, max (u + 1) v}.2 (lift_lt_univ c)
 #align cardinal.lift_lt_univ' Cardinal.lift_lt_univ'
@@ -2244,12 +1596,6 @@ theorem ord_univ : ord univ.{u, v} = Ordinal.univ.{u, v} :=
 #align cardinal.ord_univ Cardinal.ord_univ
 -/
 
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 theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
   ⟨fun h => by
     have := ord_lt_ord.2 h
@@ -2260,12 +1606,6 @@ theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
     exact ⟨_, this.symm⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ _⟩
 #align cardinal.lt_univ Cardinal.lt_univ
 
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 theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c' :=
   ⟨fun h => by
     let ⟨a, e, h'⟩ := lt_lift_iff.1 h
@@ -2274,12 +1614,6 @@ theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c
     exact ⟨c', by simp only [e.symm, lift_lift]⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ' _⟩
 #align cardinal.lt_univ' Cardinal.lt_univ'
 
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 theorem small_iff_lift_mk_lt_univ {α : Type u} :
     Small.{v} α ↔ Cardinal.lift (#α) < univ.{v, max u (v + 1)} :=
   by
@@ -2302,56 +1636,26 @@ theorem card_univ : card univ = Cardinal.univ :=
 #align ordinal.card_univ Ordinal.card_univ
 -/
 
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 @[simp]
 theorem nat_le_card {o} {n : ℕ} : (n : Cardinal) ≤ card o ↔ (n : Ordinal) ≤ o := by
   rw [← Cardinal.ord_le, Cardinal.ord_nat]
 #align ordinal.nat_le_card Ordinal.nat_le_card
 
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 @[simp]
 theorem nat_lt_card {o} {n : ℕ} : (n : Cardinal) < card o ↔ (n : Ordinal) < o := by
   rw [← succ_le_iff, ← succ_le_iff, ← nat_succ, nat_le_card]; rfl
 #align ordinal.nat_lt_card Ordinal.nat_lt_card
 
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 @[simp]
 theorem card_lt_nat {o} {n : ℕ} : card o < n ↔ o < n :=
   lt_iff_lt_of_le_iff_le nat_le_card
 #align ordinal.card_lt_nat Ordinal.card_lt_nat
 
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 @[simp]
 theorem card_le_nat {o} {n : ℕ} : card o ≤ n ↔ o ≤ n :=
   le_iff_le_iff_lt_iff_lt.2 nat_lt_card
 #align ordinal.card_le_nat Ordinal.card_le_nat
 
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 @[simp]
 theorem card_eq_nat {o} {n : ℕ} : card o = n ↔ o = n := by
   simp only [le_antisymm_iff, card_le_nat, nat_le_card]

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

@@ -141,10 +141,7 @@ instance : Inhabited WellOrder :=
 
 #print WellOrder.eta /-
 @[simp]
-theorem eta (o : WellOrder) : mk o.α o.R o.wo = o :=
-  by
-  cases o
-  rfl
+theorem eta (o : WellOrder) : mk o.α o.R o.wo = o := by cases o; rfl
 #align Well_order.eta WellOrder.eta
 -/
 
@@ -220,10 +217,7 @@ def typein (r : α → α → Prop) [IsWellOrder α r] (a : α) : Ordinal :=
 
 #print Ordinal.type_def' /-
 @[simp]
-theorem type_def' (w : WellOrder) : ⟦w⟧ = type w.R :=
-  by
-  cases w
-  rfl
+theorem type_def' (w : WellOrder) : ⟦w⟧ = type w.R := by cases w; rfl
 #align ordinal.type_def' Ordinal.type_def'
 -/
 
@@ -641,10 +635,8 @@ lean 3 declaration is
 but is expected to have type
   forall {o : Ordinal.{u1}} (i : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.4069 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.4071 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.4069 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.4071) (isWellOrder_out_lt.{u1} o) i) o
 Case conversion may be inaccurate. Consider using '#align ordinal.typein_lt_self Ordinal.typein_lt_selfₓ'. -/
-theorem typein_lt_self {o : Ordinal} (i : o.out.α) : typein (· < ·) i < o :=
-  by
-  simp_rw [← type_lt o]
-  apply typein_lt_type
+theorem typein_lt_self {o : Ordinal} (i : o.out.α) : typein (· < ·) i < o := by
+  simp_rw [← type_lt o]; apply typein_lt_type
 #align ordinal.typein_lt_self Ordinal.typein_lt_self
 
 #print Ordinal.typein_top /-
@@ -695,8 +687,7 @@ theorem typein_lt_typein (r : α → α → Prop) [IsWellOrder α r] {a b : α}
       let g' := f.trans (PrincipalSeg.ofElement r b)
       have : g'.top = f'.top := by rw [Subsingleton.elim f' g']
       exact this
-    rw [← this]
-    exact f.top.2, fun h =>
+    rw [← this]; exact f.top.2, fun h =>
     ⟨PrincipalSeg.codRestrict _ (PrincipalSeg.ofElement r a) (fun x => @trans _ r _ _ _ _ x.2 h) h⟩⟩
 #align ordinal.typein_lt_typein Ordinal.typein_lt_typein
 
@@ -739,17 +730,14 @@ Case conversion may be inaccurate. Consider using '#align ordinal.enum Ordinal.e
 def enum (r : α → α → Prop) [IsWellOrder α r] (o) : o < type r → α :=
   Quot.recOn' o (fun ⟨β, s, _⟩ h => (Classical.choice h).top) fun ⟨β, s, _⟩ ⟨γ, t, _⟩ ⟨h⟩ =>
     by
-    skip
-    refine' funext fun H₂ : type t < type r => _
+    skip; refine' funext fun H₂ : type t < type r => _
     have H₁ : type s < type r := by rwa [type_eq.2 ⟨h⟩]
     have :
       ∀ {o e} (H : o < type r),
         @Eq.ndrec (fun o : Ordinal => o < type r → α)
             (fun h : type s < type r => (Classical.choice h).top) e H =
           (Classical.choice H₁).top :=
-      by
-      intros
-      subst e
+      by intros ; subst e
     exact (this H₂).trans (PrincipalSeg.top_eq h (Classical.choice H₁) (Classical.choice H₂))
 #align ordinal.enum Ordinal.enum
 
@@ -815,12 +803,7 @@ theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β 
 Case conversion may be inaccurate. Consider using '#align ordinal.rel_iso_enum Ordinal.relIso_enumₓ'. -/
 theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) (hr : o < type r) :
-    f (enum r o hr) =
-      enum s o
-        (by
-          convert hr using 1
-          apply Quotient.sound
-          exact ⟨f.symm⟩) :=
+    f (enum r o hr) = enum s o (by convert hr using 1; apply Quotient.sound; exact ⟨f.symm⟩) :=
   relIso_enum' _ _ _ _
 #align ordinal.rel_iso_enum Ordinal.relIso_enum
 
@@ -1113,10 +1096,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align ordinal.lift_le Ordinal.lift_leₓ'. -/
 @[simp]
 theorem lift_le {a b : Ordinal} : lift.{u, v} a ≤ lift b ↔ a ≤ b :=
-  inductionOn a fun α r _ =>
-    inductionOn b fun β s _ => by
-      rw [← lift_umax]
-      exact lift_type_le
+  inductionOn a fun α r _ => inductionOn b fun β s _ => by rw [← lift_umax]; exact lift_type_le
 #align ordinal.lift_le Ordinal.lift_le
 
 /- warning: ordinal.lift_inj -> Ordinal.lift_inj is a dubious translation:
@@ -1442,10 +1422,7 @@ instance : LinearOrder Ordinal :=
               rw [← typein_top f, ← typein_top g, le_iff_lt_or_eq, le_iff_lt_or_eq,
                 typein_lt_typein, typein_lt_typein]
               rcases trichotomous_of (Sum.Lex r₁ r₂) g.top f.top with (h | h | h) <;>
-                [exact Or.inl (Or.inl h);·
-                  left
-                  right
-                  rw [h];exact Or.inr (Or.inl h)])
+                [exact Or.inl (Or.inl h);· left; right; rw [h];exact Or.inr (Or.inl h)])
           h₁ h₂
     decidableLe := Classical.decRel _ }
 
@@ -1518,19 +1495,13 @@ private theorem succ_le_iff' {a b : Ordinal} : a + 1 ≤ b ↔ a < b :=
         · exact f; · exact fun _ => t
         · rcases a with (a | _) <;> rcases b with (b | _)
           · simpa only [Sum.lex_inl_inl] using f.map_rel_iff.2
-          · intro
-            rw [hf]
-            exact ⟨_, rfl⟩
+          · intro ; rw [hf]; exact ⟨_, rfl⟩
           · exact False.elim ∘ Sum.lex_inr_inl
           · exact False.elim ∘ Sum.lex_inr_inr.1
         · rcases a with (a | _)
-          · intro h
-            have := @PrincipalSeg.init _ _ _ _ _ ⟨f, t, hf⟩ _ _ h
-            cases' this with w h
-            exact ⟨Sum.inl w, h⟩
-          · intro h
-            cases' (hf b).1 h with w h
-            exact ⟨Sum.inl w, h⟩⟩
+          · intro h; have := @PrincipalSeg.init _ _ _ _ _ ⟨f, t, hf⟩ _ _ h
+            cases' this with w h; exact ⟨Sum.inl w, h⟩
+          · intro h; cases' (hf b).1 h with w h; exact ⟨Sum.inl w, h⟩⟩
 
 instance : NoMaxOrder Ordinal :=
   ⟨fun a => ⟨_, succ_le_iff'.1 le_rfl⟩⟩
@@ -1717,10 +1688,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align ordinal.typein_le_typein' Ordinal.typein_le_typein'ₓ'. -/
 @[simp]
 theorem typein_le_typein' (o : Ordinal) {x x' : o.out.α} :
-    typein (· < ·) x ≤ typein (· < ·) x' ↔ x ≤ x' :=
-  by
-  rw [typein_le_typein]
-  exact not_lt
+    typein (· < ·) x ≤ typein (· < ·) x' ↔ x ≤ x' := by rw [typein_le_typein]; exact not_lt
 #align ordinal.typein_le_typein' Ordinal.typein_le_typein'
 
 /- warning: ordinal.enum_le_enum -> Ordinal.enum_le_enum is a dubious translation:
@@ -1751,33 +1719,22 @@ but is expected to have type
   forall {α : Type.{u1}} {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r] (h0 : 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})) (Ordinal.type.{u1} α r _inst_1)) (a : α), Not (r a (Ordinal.enum.{u1} α r _inst_1 (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) h0))
 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_le Ordinal.enum_zero_leₓ'. -/
 theorem enum_zero_le {r : α → α → Prop} [IsWellOrder α r] (h0 : 0 < type r) (a : α) :
-    ¬r a (enum r 0 h0) := by
-  rw [← enum_typein r a, enum_le_enum r]
-  apply Ordinal.zero_le
+    ¬r a (enum r 0 h0) := by rw [← enum_typein r a, enum_le_enum r]; apply Ordinal.zero_le
 #align ordinal.enum_zero_le Ordinal.enum_zero_le
 
 /- warning: ordinal.enum_zero_le' -> Ordinal.enum_zero_le' is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_le' Ordinal.enum_zero_le'ₓ'. -/
 theorem enum_zero_le' {o : Ordinal} (h0 : 0 < o) (a : o.out.α) :
-    @enum o.out.α (· < ·) _ 0 (by rwa [type_lt]) ≤ a :=
-  by
-  rw [← not_lt]
-  apply enum_zero_le
+    @enum o.out.α (· < ·) _ 0 (by rwa [type_lt]) ≤ a := by rw [← not_lt]; apply enum_zero_le
 #align ordinal.enum_zero_le' Ordinal.enum_zero_le'
 
 /- warning: ordinal.le_enum_succ -> Ordinal.le_enum_succ is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align ordinal.le_enum_succ Ordinal.le_enum_succₓ'. -/
 theorem le_enum_succ {o : Ordinal} (a : (succ o).out.α) :
-    a ≤
-      @enum (succ o).out.α (· < ·) _ o
-        (by
-          rw [type_lt]
-          exact lt_succ o) :=
-  by
-  rw [← enum_typein (· < ·) a, enum_le_enum', ← lt_succ_iff]
-  apply typein_lt_self
+    a ≤ @enum (succ o).out.α (· < ·) _ o (by rw [type_lt]; exact lt_succ o) := by
+  rw [← enum_typein (· < ·) a, enum_le_enum', ← lt_succ_iff]; apply typein_lt_self
 #align ordinal.le_enum_succ Ordinal.le_enum_succ
 
 /- warning: ordinal.enum_inj -> Ordinal.enum_inj is a dubious translation:
@@ -1793,8 +1750,8 @@ theorem enum_inj {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordina
     by_contra hne
     cases' lt_or_gt_of_ne hne with hlt hlt <;> apply (IsWellOrder.isIrrefl r).1
     · rwa [← @enum_lt_enum α r _ o₁ o₂ h₁ h₂, h] at hlt
-    · change _ < _ at hlt
-      rwa [← @enum_lt_enum α r _ o₂ o₁ h₂ h₁, h] at hlt, fun h => by simp_rw [h]⟩
+    · change _ < _ at hlt; rwa [← @enum_lt_enum α r _ o₂ o₁ h₂ h₁, h] at hlt, fun h => by
+    simp_rw [h]⟩
 #align ordinal.enum_inj Ordinal.enum_inj
 
 /- warning: ordinal.enum_iso -> Ordinal.enumIso is a dubious translation:
@@ -1811,9 +1768,7 @@ def enumIso (r : α → α → Prop) [IsWellOrder α r] : Subrel (· < ·) (· <
   invFun x := ⟨typein r x, typein_lt_type r x⟩
   left_inv := fun ⟨o, h⟩ => Subtype.ext_val (typein_enum _ _)
   right_inv h := enum_typein _ _
-  map_rel_iff' := by
-    rintro ⟨a, _⟩ ⟨b, _⟩
-    apply enum_lt_enum
+  map_rel_iff' := by rintro ⟨a, _⟩ ⟨b, _⟩; apply enum_lt_enum
 #align ordinal.enum_iso Ordinal.enumIso
 
 /- warning: ordinal.enum_iso_out -> Ordinal.enumIsoOut is a dubious translation:
@@ -1826,16 +1781,11 @@ Case conversion may be inaccurate. Consider using '#align ordinal.enum_iso_out O
 @[simps]
 noncomputable def enumIsoOut (o : Ordinal) : Set.Iio o ≃o o.out.α
     where
-  toFun x :=
-    enum (· < ·) x.1 <| by
-      rw [type_lt]
-      exact x.2
+  toFun x := enum (· < ·) x.1 <| by rw [type_lt]; exact x.2
   invFun x := ⟨typein (· < ·) x, typein_lt_self x⟩
   left_inv := fun ⟨o', h⟩ => Subtype.ext_val (typein_enum _ _)
   right_inv h := enum_typein _ _
-  map_rel_iff' := by
-    rintro ⟨a, _⟩ ⟨b, _⟩
-    apply enum_le_enum'
+  map_rel_iff' := by rintro ⟨a, _⟩ ⟨b, _⟩; apply enum_le_enum'
 #align ordinal.enum_iso_out Ordinal.enumIsoOut
 
 /- warning: ordinal.out_order_bot_of_pos -> Ordinal.outOrderBotOfPos is a dubious translation:
@@ -1909,12 +1859,9 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
     refine' fun b => induction_on b _; intro β s _
     rw [univ, ← lift_umax]; constructor <;> intro h
     · rw [← lift_id (type s)] at h⊢
-      cases' lift_type_lt.1 h with f
-      cases' f with f a hf
-      exists a
-      revert hf
-      apply induction_on a
-      intro α r _ hf
+      cases' lift_type_lt.1 h with f; cases' f with f a hf
+      exists a; revert hf
+      apply induction_on a; intro α r _ hf
       refine'
         lift_type_eq.{u, max (u + 1) v, max (u + 1) v}.2
           ⟨(RelIso.ofSurjective (RelEmbedding.ofMonotone _ _) _).symm⟩
@@ -1922,15 +1869,10 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
       · refine' fun a b h => (typein_lt_typein r).1 _
         rw [typein_enum, typein_enum]
         exact f.map_rel_iff.2 h
-      · intro a'
-        cases' (hf _).1 (typein_lt_type _ a') with b e
-        exists b
-        simp
-        simp [e]
-    · cases' h with a e
-      rw [← e]
-      apply induction_on a
-      intro α r _
+      · intro a'; cases' (hf _).1 (typein_lt_type _ a') with b e
+        exists b; simp; simp [e]
+    · cases' h with a e; rw [← e]
+      apply induction_on a; intro α r _
       exact lift_type_lt.{u, u + 1, max (u + 1) v}.2 ⟨typein.principal_seg r⟩⟩
 #align ordinal.lift.principal_seg Ordinal.lift.principalSeg
 
@@ -2037,7 +1979,7 @@ theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=
     Ordinal.inductionOn o fun β s _ => by
       let ⟨r, _, e⟩ := ord_eq α
       skip; simp only [card_type]; constructor <;> intro h
-      · rw [e] at h
+      · rw [e] at h;
         exact
           let ⟨f⟩ := h
           ⟨f.toEmbedding⟩
@@ -2193,9 +2135,7 @@ but is expected to have type
   forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] (x : α), (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} (Ordinal.typein.{u1} α r _inst_1 x)) (Cardinal.mk.{u1} α))
 Case conversion may be inaccurate. Consider using '#align cardinal.card_typein_lt Cardinal.card_typein_ltₓ'. -/
 theorem card_typein_lt (r : α → α → Prop) [IsWellOrder α r] (x : α) (h : ord (#α) = type r) :
-    card (typein r x) < (#α) := by
-  rw [← lt_ord, h]
-  apply typein_lt_type
+    card (typein r x) < (#α) := by rw [← lt_ord, h]; apply typein_lt_type
 #align cardinal.card_typein_lt Cardinal.card_typein_lt
 
 /- warning: cardinal.card_typein_out_lt -> Cardinal.card_typein_out_lt is a dubious translation:
@@ -2204,16 +2144,12 @@ lean 3 declaration is
 but is expected to have type
   forall (c : Cardinal.{u1}) (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.16644 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.16646 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (linearOrderOut.{u1} (Cardinal.ord.{u1} c)))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.16644 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.16646) (isWellOrder_out_lt.{u1} (Cardinal.ord.{u1} c)) x)) c
 Case conversion may be inaccurate. Consider using '#align cardinal.card_typein_out_lt Cardinal.card_typein_out_ltₓ'. -/
-theorem card_typein_out_lt (c : Cardinal) (x : c.ord.out.α) : card (typein (· < ·) x) < c :=
-  by
-  rw [← lt_ord]
-  apply typein_lt_self
+theorem card_typein_out_lt (c : Cardinal) (x : c.ord.out.α) : card (typein (· < ·) x) < c := by
+  rw [← lt_ord]; apply typein_lt_self
 #align cardinal.card_typein_out_lt Cardinal.card_typein_out_lt
 
 #print Cardinal.ord_injective /-
-theorem ord_injective : Injective ord := by
-  intro c c' h
-  rw [← card_ord c, ← card_ord c', h]
+theorem ord_injective : Injective ord := by intro c c' h; rw [← card_ord c, ← card_ord c', h]
 #align cardinal.ord_injective Cardinal.ord_injective
 -/
 
@@ -2384,10 +2320,8 @@ but is expected to have type
   forall {o : Ordinal.{u1}} {n : Nat}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) (Ordinal.card.{u1} o)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Nat.cast.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1}) n) o)
 Case conversion may be inaccurate. Consider using '#align ordinal.nat_lt_card Ordinal.nat_lt_cardₓ'. -/
 @[simp]
-theorem nat_lt_card {o} {n : ℕ} : (n : Cardinal) < card o ↔ (n : Ordinal) < o :=
-  by
-  rw [← succ_le_iff, ← succ_le_iff, ← nat_succ, nat_le_card]
-  rfl
+theorem nat_lt_card {o} {n : ℕ} : (n : Cardinal) < card o ↔ (n : Ordinal) < o := by
+  rw [← succ_le_iff, ← succ_le_iff, ← nat_succ, nat_le_card]; rfl
 #align ordinal.nat_lt_card Ordinal.nat_lt_card
 
 /- warning: ordinal.card_lt_nat -> Ordinal.card_lt_nat is a dubious translation:

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

@@ -811,10 +811,7 @@ theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β 
 #align ordinal.rel_iso_enum' Ordinal.relIso_enum'
 
 /- warning: ordinal.rel_iso_enum -> Ordinal.relIso_enum is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align ordinal.rel_iso_enum Ordinal.relIso_enumₓ'. -/
 theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) (hr : o < type r) :
@@ -1534,7 +1531,6 @@ private theorem succ_le_iff' {a b : Ordinal} : a + 1 ≤ b ↔ a < b :=
           · intro h
             cases' (hf b).1 h with w h
             exact ⟨Sum.inl w, h⟩⟩
-#align ordinal.succ_le_iff' ordinal.succ_le_iff'
 
 instance : NoMaxOrder Ordinal :=
   ⟨fun a => ⟨_, succ_le_iff'.1 le_rfl⟩⟩
@@ -1682,10 +1678,7 @@ instance uniqueOutOne : Unique (1 : Ordinal).out.α
 #align ordinal.unique_out_one Ordinal.uniqueOutOne
 
 /- warning: ordinal.one_out_eq -> Ordinal.one_out_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ordinal.one_out_eq Ordinal.one_out_eqₓ'. -/
 theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :=
   Unique.eq_default x
@@ -1743,10 +1736,7 @@ theorem enum_le_enum (r : α → α → Prop) [IsWellOrder α r] {o o' : Ordinal
 #align ordinal.enum_le_enum Ordinal.enum_le_enum
 
 /- warning: ordinal.enum_le_enum' -> Ordinal.enum_le_enum' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ordinal.enum_le_enum' Ordinal.enum_le_enum'ₓ'. -/
 @[simp]
 theorem enum_le_enum' (a : Ordinal) {o o' : Ordinal} (ho : o < type (· < ·))
@@ -1767,10 +1757,7 @@ theorem enum_zero_le {r : α → α → Prop} [IsWellOrder α r] (h0 : 0 < type
 #align ordinal.enum_zero_le Ordinal.enum_zero_le
 
 /- warning: ordinal.enum_zero_le' -> Ordinal.enum_zero_le' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_le' Ordinal.enum_zero_le'ₓ'. -/
 theorem enum_zero_le' {o : Ordinal} (h0 : 0 < o) (a : o.out.α) :
     @enum o.out.α (· < ·) _ 0 (by rwa [type_lt]) ≤ a :=
@@ -1780,10 +1767,7 @@ theorem enum_zero_le' {o : Ordinal} (h0 : 0 < o) (a : o.out.α) :
 #align ordinal.enum_zero_le' Ordinal.enum_zero_le'
 
 /- warning: ordinal.le_enum_succ -> Ordinal.le_enum_succ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ordinal.le_enum_succ Ordinal.le_enum_succₓ'. -/
 theorem le_enum_succ {o : Ordinal} (a : (succ o).out.α) :
     a ≤
@@ -1866,10 +1850,7 @@ def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α :=
 #align ordinal.out_order_bot_of_pos Ordinal.outOrderBotOfPos
 
 /- warning: ordinal.enum_zero_eq_bot -> Ordinal.enum_zero_eq_bot is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_eq_bot Ordinal.enum_zero_eq_botₓ'. -/
 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
     enum (· < ·) 0 (by rwa [type_lt]) =

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

@@ -1357,7 +1357,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align ordinal.card_nat Ordinal.card_natₓ'. -/
 @[simp]
 theorem card_nat (n : ℕ) : card.{u} n = n := by
-  induction n <;> [rfl, simp only [card_add, card_one, Nat.cast_succ, *]]
+  induction n <;> [rfl;simp only [card_add, card_one, Nat.cast_succ, *]]
 #align ordinal.card_nat Ordinal.card_nat
 
 /- warning: ordinal.add_covariant_class_le -> Ordinal.add_covariantClass_le is a dubious translation:
@@ -1406,8 +1406,8 @@ instance add_swap_covariantClass_le :
                 constructor <;> intro H
                 ·
                   cases' a with a a <;> cases' b with b b <;> cases H <;> constructor <;>
-                    [rwa [← fo], assumption]
-                · cases H <;> constructor <;> [rwa [fo], assumption]⟩⟩
+                    [rwa [← fo];assumption]
+                · cases H <;> constructor <;> [rwa [fo];assumption]⟩⟩
 #align ordinal.add_swap_covariant_class_le Ordinal.add_swap_covariantClass_le
 
 /- warning: ordinal.le_add_right -> Ordinal.le_add_right is a dubious translation:
@@ -1445,10 +1445,10 @@ instance : LinearOrder Ordinal :=
               rw [← typein_top f, ← typein_top g, le_iff_lt_or_eq, le_iff_lt_or_eq,
                 typein_lt_typein, typein_lt_typein]
               rcases trichotomous_of (Sum.Lex r₁ r₂) g.top f.top with (h | h | h) <;>
-                [exact Or.inl (Or.inl h),
-                · left
+                [exact Or.inl (Or.inl h);·
+                  left
                   right
-                  rw [h], exact Or.inr (Or.inl h)])
+                  rw [h];exact Or.inr (Or.inl h)])
           h₁ h₂
     decidableLe := Classical.decRel _ }
 
@@ -1685,7 +1685,7 @@ instance uniqueOutOne : Unique (1 : Ordinal).out.α
 lean 3 declaration is
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0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1293 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1295 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ 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Ordinal.zero.{u1} Ordinal.one.{u1} Ordinal.partialOrder.{u1} Ordinal.zeroLEOneClass.{u1} Ordinal.NeZero.one.{u1}))))
 Case conversion may be inaccurate. Consider using '#align ordinal.one_out_eq Ordinal.one_out_eqₓ'. -/
 theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :=
   Unique.eq_default x
@@ -1698,7 +1698,7 @@ theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :
 lean 3 declaration is
   forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))))))))) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
 but is expected to have type
-  forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12909 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12911 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12909 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12911) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
+  forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12910 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12912 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12910 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12912) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.typein_one_out Ordinal.typein_one_outₓ'. -/
 @[simp]
 theorem typein_one_out (x : (1 : Ordinal).out.α) : typein (· < ·) x = 0 := by
@@ -1720,7 +1720,7 @@ theorem typein_le_typein (r : α → α → Prop) [IsWellOrder α r] {x x' : α}
 lean 3 declaration is
   forall (o : Ordinal.{u1}) {x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)} {x' : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o) x) (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o) x')) (LE.le.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLe.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o)))))) x x')
 but is expected to have type
-  forall (o : Ordinal.{u1}) {x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)} {x' : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13070 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13072 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13070 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13072) (isWellOrder_out_lt.{u1} o) x) (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13092 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13094 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13092 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13094) (isWellOrder_out_lt.{u1} o) x')) (LE.le.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x x')
+  forall (o : Ordinal.{u1}) {x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)} {x' : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13071 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13073 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13071 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13073) (isWellOrder_out_lt.{u1} o) x) (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13093 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13095 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13093 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13095) (isWellOrder_out_lt.{u1} o) x')) (LE.le.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x x')
 Case conversion may be inaccurate. Consider using '#align ordinal.typein_le_typein' Ordinal.typein_le_typein'ₓ'. -/
 @[simp]
 theorem typein_le_typein' (o : Ordinal) {x x' : o.out.α} :
@@ -1746,7 +1746,7 @@ theorem enum_le_enum (r : α → α → Prop) [IsWellOrder α r] {o o' : Ordinal
 lean 3 declaration is
   forall (a : Ordinal.{u1}) {o : Ordinal.{u1}} {o' : Ordinal.{u1}} (ho : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) (isWellOrder_out_lt.{u1} a))) (ho' : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o' (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) (isWellOrder_out_lt.{u1} a))), Iff (LE.le.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toHasLe.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a)))))) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) (isWellOrder_out_lt.{u1} a) o ho) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) (isWellOrder_out_lt.{u1} a) o' ho')) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o')
 but is expected to have type
-  forall (a : Ordinal.{u1}) {o : Ordinal.{u1}} {o' : Ordinal.{u1}} (ho : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13279 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13281 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13279 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13281) (isWellOrder_out_lt.{u1} a))) (ho' : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o' (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13299 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13301 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13299 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13301) (isWellOrder_out_lt.{u1} a))), Iff (LE.le.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13321 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13323 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13321 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13323) (isWellOrder_out_lt.{u1} a) o ho) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13340 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13342 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13340 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13342) (isWellOrder_out_lt.{u1} a) o' ho')) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o')
+  forall (a : Ordinal.{u1}) {o : Ordinal.{u1}} {o' : Ordinal.{u1}} (ho : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13280 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13282 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13280 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13282) (isWellOrder_out_lt.{u1} a))) (ho' : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o' (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13300 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13302 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13300 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13302) (isWellOrder_out_lt.{u1} a))), Iff (LE.le.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13322 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13324 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13322 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13324) (isWellOrder_out_lt.{u1} a) o ho) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13341 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13343 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} a)) (linearOrderOut.{u1} a))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13341 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13343) (isWellOrder_out_lt.{u1} a) o' ho')) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o')
 Case conversion may be inaccurate. Consider using '#align ordinal.enum_le_enum' Ordinal.enum_le_enum'ₓ'. -/
 @[simp]
 theorem enum_le_enum' (a : Ordinal) {o o' : Ordinal} (ho : o < type (· < ·))
@@ -1770,7 +1770,7 @@ theorem enum_zero_le {r : α → α → Prop} [IsWellOrder α r] (h0 : 0 < type
 lean 3 declaration is
   forall {o : Ordinal.{u1}} (h0 : 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) (a : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)), LE.le.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLe.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o)))))) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (Eq.mpr.{0} (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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)) (Eq.ndrec.{0, succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o)) (fun (_a : Ordinal.{u1}) => Eq.{1} Prop (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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}))) _a)) (rfl.{1} Prop (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o)))) o (Ordinal.type_lt.{u1} o))) h0)) a
 but is expected to have type
-  forall {o : Ordinal.{u1}} (h0 : 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) (a : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)), LE.le.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13527 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13529 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} 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 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_le' Ordinal.enum_zero_le'ₓ'. -/
 theorem enum_zero_le' {o : Ordinal} (h0 : 0 < o) (a : o.out.α) :
     @enum o.out.α (· < ·) _ 0 (by rwa [type_lt]) ≤ a :=
@@ -1783,7 +1783,7 @@ theorem enum_zero_le' {o : Ordinal} (h0 : 0 < o) (a : o.out.α) :
 lean 3 declaration is
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(succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o))) (linearOrderOut.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13653 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.13655) (isWellOrder_out_lt.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o))))) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o) (Ordinal.type_lt.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)))) (Order.lt_succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} Ordinal.noMaxOrder.{u1} o)))
 Case conversion may be inaccurate. Consider using '#align ordinal.le_enum_succ Ordinal.le_enum_succₓ'. -/
 theorem le_enum_succ {o : Ordinal} (a : (succ o).out.α) :
     a ≤
@@ -1817,7 +1817,7 @@ theorem enum_inj {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordina
 lean 3 declaration is
   forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], RelIso.{succ u1, u1} (coeSort.{succ (succ u1), succ (succ (succ u1))} (Set.{succ u1} Ordinal.{u1}) Type.{succ u1} (Set.hasCoeToSort.{succ u1} Ordinal.{u1}) (fun (_x : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _x (Ordinal.type.{u1} α r _inst_1))) α (Subrel.{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}))) (fun (_x : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _x (Ordinal.type.{u1} α r _inst_1))) r
 but is expected to have type
-  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], RelIso.{succ u1, u1} (Set.Elem.{succ u1} Ordinal.{u1} (fun (_x : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _x (Ordinal.type.{u1} α r _inst_1))) α (Subrel.{succ u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14055 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14057 : 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.Ordinal.Basic._hyg.14055 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14057) (fun (_x : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _x (Ordinal.type.{u1} α r _inst_1))) r
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], RelIso.{succ u1, u1} (Set.Elem.{succ u1} Ordinal.{u1} (fun (_x : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _x (Ordinal.type.{u1} α r _inst_1))) α (Subrel.{succ u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14056 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14058 : 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.Ordinal.Basic._hyg.14056 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14058) (fun (_x : Ordinal.{u1}) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) _x (Ordinal.type.{u1} α r _inst_1))) r
 Case conversion may be inaccurate. Consider using '#align ordinal.enum_iso Ordinal.enumIsoₓ'. -/
 /-- A well order `r` is order isomorphic to the set of ordinals smaller than `type r`. -/
 @[simps]
@@ -1869,7 +1869,7 @@ def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α :=
 lean 3 declaration is
   forall {o : Ordinal.{u1}} (ho : 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), Eq.{succ u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (Eq.mpr.{0} (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLt.{u1} 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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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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)) (Eq.ndrec.{0, succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) 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(WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o)))) o (Ordinal.type_lt.{u1} o))) ho)) (Bot.bot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (OrderBot.toHasBot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toHasLe.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} 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 but is expected to have type
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(Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14384 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14386) (isWellOrder_out_lt.{u1} o))) (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)) (Eq.ndrec.{0, succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1293 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1295 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1293 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1295) (isWellOrder_out_lt.{u1} o)) (fun (_a : Ordinal.{u1}) => Eq.{1} Prop (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})) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14384 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14386 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14384 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14386) (isWellOrder_out_lt.{u1} o))) (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})) _a)) (Eq.refl.{1} Prop (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})) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14384 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14386 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14384 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14386) (isWellOrder_out_lt.{u1} o)))) o (Ordinal.type_lt.{u1} o))) ho)) (Bot.bot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (OrderBot.toBot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (Ordinal.outOrderBotOfPos.{u1} o ho)))
 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_eq_bot Ordinal.enum_zero_eq_botₓ'. -/
 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
     enum (· < ·) 0 (by rwa [type_lt]) =
@@ -1895,7 +1895,7 @@ def univ : Ordinal.{max (u + 1) v} :=
 lean 3 declaration is
   Eq.{succ (succ (succ u1))} Ordinal.{succ u1} Ordinal.univ.{u1, succ u1} (Ordinal.type.{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}))) Ordinal.HasLt.Lt.isWellOrder.{u1})
 but is expected to have type
-  Eq.{succ (succ (succ u1))} Ordinal.{succ u1} Ordinal.univ.{u1, succ u1} (Ordinal.type.{succ u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14525 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14527 : 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.Ordinal.Basic._hyg.14525 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14527) Ordinal.isWellOrder.{u1})
+  Eq.{succ (succ (succ u1))} Ordinal.{succ u1} Ordinal.univ.{u1, succ u1} (Ordinal.type.{succ u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14526 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14528 : 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.Ordinal.Basic._hyg.14526 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14528) Ordinal.isWellOrder.{u1})
 Case conversion may be inaccurate. Consider using '#align ordinal.univ_id Ordinal.univ_idₓ'. -/
 theorem univ_id : univ.{u, u + 1} = @type Ordinal (· < ·) _ :=
   lift_id _
@@ -1918,7 +1918,7 @@ theorem univ_umax : univ.{u, max (u + 1) v} = univ.{u, v} :=
 lean 3 declaration is
   PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toHasLt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))
 but is expected to have type
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+  PrincipalSeg.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14625 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627 : 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.Ordinal.Basic._hyg.14625 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642)
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg Ordinal.lift.principalSegₓ'. -/
 /-- Principal segment version of the lift operation on ordinals, embedding `ordinal.{u}` in
   `ordinal.{v}` as a principal segment when `u < v`. -/
@@ -1957,7 +1957,7 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
 lean 3 declaration is
   Eq.{max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} ((fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toHasLt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) Ordinal.lift.principalSeg.{u1, u2}) (coeFn.{max (succ (succ u1)) (succ (succ (max (succ u1) u2))), max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} (PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toHasLt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) (fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toHasLt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) (PrincipalSeg.hasCoeToFun.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toHasLt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) Ordinal.lift.principalSeg.{u1, u2}) Ordinal.lift.{max (succ u1) u2, u1}
 but is expected to have type
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(succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (RelHomClass.toFunLike.{max (succ u1) (succ (succ u1)) (succ u2), succ u1, max (succ (succ u1)) (succ u2)} (RelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641)) Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641))) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641) Ordinal.lift.principalSeg.{u1, u2})) Ordinal.lift.{max (succ u1) u2, u1}
+  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (RelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14625 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627 : 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.Ordinal.Basic._hyg.14625 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (RelHomClass.toFunLike.{max (succ u1) (succ (succ u1)) (succ u2), succ u1, max (succ (succ u1)) (succ u2)} (RelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14625 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627 : 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.Ordinal.Basic._hyg.14625 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642)) Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14625 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627 : 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.Ordinal.Basic._hyg.14625 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14625 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627 : 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.Ordinal.Basic._hyg.14625 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642))) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14625 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627 : 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.Ordinal.Basic._hyg.14625 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642) Ordinal.lift.principalSeg.{u1, u2})) Ordinal.lift.{max (succ u1) u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg_coe Ordinal.lift.principalSeg_coeₓ'. -/
 @[simp]
 theorem lift.principalSeg_coe :
@@ -1976,7 +1976,7 @@ theorem lift.principalSeg_top : lift.principalSeg.top = univ :=
 lean 3 declaration is
   Eq.{succ (succ (succ u1))} Ordinal.{succ u1} (PrincipalSeg.top.{succ u1, succ (succ u1)} Ordinal.{u1} Ordinal.{succ 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 (succ u1)} Ordinal.{succ u1} (Preorder.toHasLt.{succ (succ u1)} Ordinal.{succ u1} (PartialOrder.toPreorder.{succ (succ u1)} Ordinal.{succ u1} Ordinal.partialOrder.{succ u1}))) Ordinal.lift.principalSeg.{u1, succ u1}) (Ordinal.type.{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}))) Ordinal.HasLt.Lt.isWellOrder.{u1})
 but is expected to have type
-  Eq.{succ (succ (succ u1))} Ordinal.{succ u1} (PrincipalSeg.top.{succ u1, succ (succ u1)} Ordinal.{u1} Ordinal.{succ u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{succ u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{succ u1}) => LT.lt.{succ (succ u1)} Ordinal.{succ u1} (Preorder.toLT.{succ (succ u1)} Ordinal.{succ u1} (PartialOrder.toPreorder.{succ (succ u1)} Ordinal.{succ u1} Ordinal.partialOrder.{succ u1})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641) Ordinal.lift.principalSeg.{u1, succ u1}) (Ordinal.type.{succ u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.15121 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.15123 : 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.Ordinal.Basic._hyg.15121 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.15123) Ordinal.isWellOrder.{u1})
+  Eq.{succ (succ (succ u1))} Ordinal.{succ u1} (PrincipalSeg.top.{succ u1, succ (succ u1)} Ordinal.{u1} Ordinal.{succ u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14625 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627 : 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.Ordinal.Basic._hyg.14625 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14627) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 : Ordinal.{succ u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642 : Ordinal.{succ u1}) => LT.lt.{succ (succ u1)} Ordinal.{succ u1} (Preorder.toLT.{succ (succ u1)} Ordinal.{succ u1} (PartialOrder.toPreorder.{succ (succ u1)} Ordinal.{succ u1} Ordinal.partialOrder.{succ u1})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14640 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14642) Ordinal.lift.principalSeg.{u1, succ u1}) (Ordinal.type.{succ u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.15122 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.15124 : 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.Ordinal.Basic._hyg.15122 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.15124) Ordinal.isWellOrder.{u1})
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg_top' Ordinal.lift.principalSeg_top'ₓ'. -/
 theorem lift.principalSeg_top' : lift.principalSeg.{u, u + 1}.top = @type Ordinal (· < ·) _ := by
   simp only [lift.principal_seg_top, univ_id]
@@ -2221,7 +2221,7 @@ theorem card_typein_lt (r : α → α → Prop) [IsWellOrder α r] (x : α) (h :
 lean 3 declaration is
   forall (c : Cardinal.{u1}) (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (linearOrderOut.{u1} (Cardinal.ord.{u1} c)))))))) (isWellOrder_out_lt.{u1} (Cardinal.ord.{u1} c)) x)) c
 but is expected to have type
-  forall (c : Cardinal.{u1}) (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.16643 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.16645 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (linearOrderOut.{u1} (Cardinal.ord.{u1} c)))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.16643 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.16645) (isWellOrder_out_lt.{u1} (Cardinal.ord.{u1} c)) x)) c
+  forall (c : Cardinal.{u1}) (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.16644 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.16646 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (linearOrderOut.{u1} (Cardinal.ord.{u1} c)))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.16644 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.16646) (isWellOrder_out_lt.{u1} (Cardinal.ord.{u1} c)) x)) c
 Case conversion may be inaccurate. Consider using '#align cardinal.card_typein_out_lt Cardinal.card_typein_out_ltₓ'. -/
 theorem card_typein_out_lt (c : Cardinal) (x : c.ord.out.α) : card (typein (· < ·) x) < c :=
   by

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

@@ -882,7 +882,7 @@ def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r
 lean 3 declaration is
   forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} ((fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (coeFn.{succ (succ u1), succ (succ u1)} (PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (PrincipalSeg.hasCoeToFun.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (Ordinal.typein.{u1} α r _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (RelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Ordinal.{u1}) _x) (RelHomClass.toFunLike.{succ u1, u1, succ u1} (RelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003)) α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003) (RelEmbedding.instRelHomClassRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003))) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003) (Ordinal.typein.principalSeg.{u1} α r _inst_1))) (Ordinal.typein.{u1} α r _inst_1)
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (RelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : α) => Ordinal.{u1}) _x) (RelHomClass.toFunLike.{succ u1, u1, succ u1} (RelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003)) α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003) (RelEmbedding.instRelHomClassRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003))) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003) (Ordinal.typein.principalSeg.{u1} α r _inst_1))) (Ordinal.typein.{u1} α r _inst_1)
 Case conversion may be inaccurate. Consider using '#align ordinal.typein.principal_seg_coe Ordinal.typein.principalSeg_coeₓ'. -/
 @[simp]
 theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
@@ -1957,7 +1957,7 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
 lean 3 declaration is
   Eq.{max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} ((fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toHasLt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) Ordinal.lift.principalSeg.{u1, u2}) (coeFn.{max (succ (succ u1)) (succ (succ (max (succ u1) u2))), max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} (PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toHasLt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) (fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toHasLt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) (PrincipalSeg.hasCoeToFun.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toHasLt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) Ordinal.lift.principalSeg.{u1, u2}) Ordinal.lift.{max (succ u1) u2, u1}
 but is expected to have type
-  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (RelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (RelHomClass.toFunLike.{max (succ u1) (succ (succ u1)) (succ u2), succ u1, max (succ (succ u1)) (succ u2)} (RelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641)) Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641))) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641) Ordinal.lift.principalSeg.{u1, u2})) Ordinal.lift.{max (succ u1) u2, u1}
+  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (RelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (RelHomClass.toFunLike.{max (succ u1) (succ (succ u1)) (succ u2), succ u1, max (succ (succ u1)) (succ u2)} (RelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641)) Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641))) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641) Ordinal.lift.principalSeg.{u1, u2})) Ordinal.lift.{max (succ u1) u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg_coe Ordinal.lift.principalSeg_coeₓ'. -/
 @[simp]
 theorem lift.principalSeg_coe :
@@ -2254,7 +2254,7 @@ def ord.orderEmbedding : Cardinal ↪o Ordinal :=
 lean 3 declaration is
   Eq.{succ (succ u1)} ((fun (_x : RelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1}) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.ord.orderEmbedding.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.hasLe.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (fun (_x : RelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1}) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (RelEmbedding.hasCoeToFun.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1}) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.ord.orderEmbedding.{u1}) Cardinal.ord.{u1}
 but is expected to have type
-  Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Cardinal.{u1}) => Ordinal.{u1}) _x) (InfHomClass.toFunLike.{succ u1, succ u1, succ u1} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} Ordinal.{u1} (Lattice.toInf.{succ u1} Cardinal.{u1} (DistribLattice.toLattice.{succ u1} Cardinal.{u1} (instDistribLattice.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1}))) (Lattice.toInf.{succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1})))) (LatticeHomClass.toInfHomClass.{succ u1, succ u1, succ u1} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} Ordinal.{u1} (DistribLattice.toLattice.{succ u1} Cardinal.{u1} (instDistribLattice.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1})) (ConditionallyCompleteLattice.toLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1}))) (OrderHomClass.toLatticeHomClass.{succ u1, succ u1, succ u1} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} Ordinal.{u1} Cardinal.linearOrder.{u1} (ConditionallyCompleteLattice.toLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1}))) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Cardinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Cardinal.{u1}) => LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Ordinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Ordinal.{u1}) => LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) Cardinal.ord.orderEmbedding.{u1}) Cardinal.ord.{u1}
+  Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Cardinal.{u1}) => Ordinal.{u1}) _x) (InfHomClass.toFunLike.{succ u1, succ u1, succ u1} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} Ordinal.{u1} (Lattice.toInf.{succ u1} Cardinal.{u1} (DistribLattice.toLattice.{succ u1} Cardinal.{u1} (instDistribLattice.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1}))) (Lattice.toInf.{succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1})))) (LatticeHomClass.toInfHomClass.{succ u1, succ u1, succ u1} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} Ordinal.{u1} (DistribLattice.toLattice.{succ u1} Cardinal.{u1} (instDistribLattice.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1})) (ConditionallyCompleteLattice.toLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1}))) (OrderHomClass.toLatticeHomClass.{succ u1, succ u1, succ u1} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} Ordinal.{u1} Cardinal.linearOrder.{u1} (ConditionallyCompleteLattice.toLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1}))) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Cardinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : Cardinal.{u1}) => LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Ordinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Ordinal.{u1}) => LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))))) Cardinal.ord.orderEmbedding.{u1}) Cardinal.ord.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.ord.order_embedding_coe Cardinal.ord.orderEmbedding_coeₓ'. -/
 @[simp]
 theorem ord.orderEmbedding_coe : (ord.orderEmbedding : Cardinal → Ordinal) = ord :=

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

@@ -181,11 +181,15 @@ instance linearOrderOut (o : Ordinal) : LinearOrder o.out.α :=
 #align linear_order_out linearOrderOut
 -/
 
-#print isWellOrder_out_lt /-
+/- warning: is_well_order_out_lt -> isWellOrder_out_lt 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 is_well_order_out_lt isWellOrder_out_ltₓ'. -/
 instance isWellOrder_out_lt (o : Ordinal) : IsWellOrder o.out.α (· < ·) :=
   o.out.wo
 #align is_well_order_out_lt isWellOrder_out_lt
--/
 
 namespace Ordinal
 
@@ -251,12 +255,16 @@ theorem RelIso.ordinal_type_eq {α β} {r : α → α → Prop} {s : β → β 
 #align rel_iso.ordinal_type_eq RelIso.ordinal_type_eq
 -/
 
-#print Ordinal.type_lt /-
+/- warning: ordinal.type_lt -> Ordinal.type_lt is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.type_lt Ordinal.type_ltₓ'. -/
 @[simp]
 theorem type_lt (o : Ordinal) : type ((· < ·) : o.out.α → o.out.α → Prop) = o :=
   (type_def' _).symm.trans <| Quotient.out_eq o
 #align ordinal.type_lt Ordinal.type_lt
--/
 
 #print Ordinal.type_eq_zero_of_empty /-
 theorem type_eq_zero_of_empty (r) [IsWellOrder α r] [IsEmpty α] : type r = 0 :=
@@ -440,61 +448,89 @@ add_decl_doc ordinal.partial_order.le
   a function embedding `r` as a principal segment of `s`. -/
 add_decl_doc ordinal.partial_order.lt
 
-#print Ordinal.type_le_iff /-
+/- warning: ordinal.type_le_iff -> Ordinal.type_le_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s], Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} α r _inst_1) (Ordinal.type.{u1} β s _inst_2)) (Nonempty.{succ u1} (InitialSeg.{u1, u1} α β r s))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s], Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} α r _inst_1) (Ordinal.type.{u1} β s _inst_2)) (Nonempty.{succ u1} (InitialSeg.{u1, u1} α β r s))
+Case conversion may be inaccurate. Consider using '#align ordinal.type_le_iff Ordinal.type_le_iffₓ'. -/
 theorem type_le_iff {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] : type r ≤ type s ↔ Nonempty (r ≼i s) :=
   Iff.rfl
 #align ordinal.type_le_iff Ordinal.type_le_iff
--/
 
-#print Ordinal.type_le_iff' /-
+/- warning: ordinal.type_le_iff' -> Ordinal.type_le_iff' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s], Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} α r _inst_1) (Ordinal.type.{u1} β s _inst_2)) (Nonempty.{succ u1} (RelEmbedding.{u1, u1} α β r s))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s], Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} α r _inst_1) (Ordinal.type.{u1} β s _inst_2)) (Nonempty.{succ u1} (RelEmbedding.{u1, u1} α β r s))
+Case conversion may be inaccurate. Consider using '#align ordinal.type_le_iff' Ordinal.type_le_iff'ₓ'. -/
 theorem type_le_iff' {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] : type r ≤ type s ↔ Nonempty (r ↪r s) :=
   ⟨fun ⟨f⟩ => ⟨f⟩, fun ⟨f⟩ => ⟨f.collapse⟩⟩
 #align ordinal.type_le_iff' Ordinal.type_le_iff'
--/
 
-#print InitialSeg.ordinal_type_le /-
+/- warning: initial_seg.ordinal_type_le -> InitialSeg.ordinal_type_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s], (InitialSeg.{u1, u1} α β r s) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} α r _inst_1) (Ordinal.type.{u1} β s _inst_2))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s], (InitialSeg.{u1, u1} α β r s) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} α r _inst_1) (Ordinal.type.{u1} β s _inst_2))
+Case conversion may be inaccurate. Consider using '#align initial_seg.ordinal_type_le InitialSeg.ordinal_type_leₓ'. -/
 theorem InitialSeg.ordinal_type_le {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (h : r ≼i s) : type r ≤ type s :=
   ⟨h⟩
 #align initial_seg.ordinal_type_le InitialSeg.ordinal_type_le
--/
 
-#print RelEmbedding.ordinal_type_le /-
+/- warning: rel_embedding.ordinal_type_le -> RelEmbedding.ordinal_type_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s], (RelEmbedding.{u1, u1} α β r s) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} α r _inst_1) (Ordinal.type.{u1} β s _inst_2))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s], (RelEmbedding.{u1, u1} α β r s) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} α r _inst_1) (Ordinal.type.{u1} β s _inst_2))
+Case conversion may be inaccurate. Consider using '#align rel_embedding.ordinal_type_le RelEmbedding.ordinal_type_leₓ'. -/
 theorem RelEmbedding.ordinal_type_le {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (h : r ↪r s) : type r ≤ type s :=
   ⟨h.collapse⟩
 #align rel_embedding.ordinal_type_le RelEmbedding.ordinal_type_le
--/
 
-#print Ordinal.type_lt_iff /-
+/- warning: ordinal.type_lt_iff -> Ordinal.type_lt_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s], Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} α r _inst_1) (Ordinal.type.{u1} β s _inst_2)) (Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α β r s))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s], Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} α r _inst_1) (Ordinal.type.{u1} β s _inst_2)) (Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α β r s))
+Case conversion may be inaccurate. Consider using '#align ordinal.type_lt_iff Ordinal.type_lt_iffₓ'. -/
 @[simp]
 theorem type_lt_iff {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] : type r < type s ↔ Nonempty (r ≺i s) :=
   Iff.rfl
 #align ordinal.type_lt_iff Ordinal.type_lt_iff
--/
 
-#print PrincipalSeg.ordinal_type_lt /-
+/- warning: principal_seg.ordinal_type_lt -> PrincipalSeg.ordinal_type_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s], (PrincipalSeg.{u1, u1} α β r s) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} α r _inst_1) (Ordinal.type.{u1} β s _inst_2))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s], (PrincipalSeg.{u1, u1} α β r s) -> (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} α r _inst_1) (Ordinal.type.{u1} β s _inst_2))
+Case conversion may be inaccurate. Consider using '#align principal_seg.ordinal_type_lt PrincipalSeg.ordinal_type_ltₓ'. -/
 theorem PrincipalSeg.ordinal_type_lt {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (h : r ≺i s) : type r < type s :=
   ⟨h⟩
 #align principal_seg.ordinal_type_lt PrincipalSeg.ordinal_type_lt
--/
 
-#print Ordinal.zero_le /-
+/- warning: ordinal.zero_le -> Ordinal.zero_le is a dubious translation:
+lean 3 declaration is
+  forall (o : Ordinal.{u1}), LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) o
+but is expected to have type
+  forall (o : Ordinal.{u1}), LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) o
+Case conversion may be inaccurate. Consider using '#align ordinal.zero_le Ordinal.zero_leₓ'. -/
 protected theorem zero_le (o : Ordinal) : 0 ≤ o :=
   inductionOn o fun α r _ => (InitialSeg.ofIsEmpty _ r).ordinal_type_le
 #align ordinal.zero_le Ordinal.zero_le
--/
 
 instance : OrderBot Ordinal :=
   ⟨0, Ordinal.zero_le⟩
 
 /- warning: ordinal.bot_eq_zero -> Ordinal.bot_eq_zero is a dubious translation:
 lean 3 declaration is
-  Eq.{succ (succ u1)} Ordinal.{u1} (Bot.bot.{succ u1} Ordinal.{u1} (OrderBot.toHasBot.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.orderBot.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
+  Eq.{succ (succ u1)} Ordinal.{u1} (Bot.bot.{succ u1} Ordinal.{u1} (OrderBot.toHasBot.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.orderBot.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
 but is expected to have type
   Eq.{succ (succ u1)} Ordinal.{u1} (Bot.bot.{succ u1} Ordinal.{u1} (OrderBot.toBot.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.orderBot.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.bot_eq_zero Ordinal.bot_eq_zeroₓ'. -/
@@ -503,30 +539,46 @@ theorem bot_eq_zero : (⊥ : Ordinal) = 0 :=
   rfl
 #align ordinal.bot_eq_zero Ordinal.bot_eq_zero
 
-#print Ordinal.le_zero /-
+/- warning: ordinal.le_zero -> Ordinal.le_zero is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))) (Eq.{succ (succ u1)} Ordinal.{u1} o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))))
+but is expected to have type
+  forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (Eq.{succ (succ u1)} Ordinal.{u1} o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})))
+Case conversion may be inaccurate. Consider using '#align ordinal.le_zero Ordinal.le_zeroₓ'. -/
 @[simp]
 protected theorem le_zero {o : Ordinal} : o ≤ 0 ↔ o = 0 :=
   le_bot_iff
 #align ordinal.le_zero Ordinal.le_zero
--/
 
-#print Ordinal.pos_iff_ne_zero /-
+/- warning: ordinal.pos_iff_ne_zero -> Ordinal.pos_iff_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, Iff (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) (Ne.{succ (succ u1)} Ordinal.{u1} o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))))
+but is expected to have type
+  forall {o : Ordinal.{u1}}, Iff (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) (Ne.{succ (succ u1)} Ordinal.{u1} o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})))
+Case conversion may be inaccurate. Consider using '#align ordinal.pos_iff_ne_zero Ordinal.pos_iff_ne_zeroₓ'. -/
 protected theorem pos_iff_ne_zero {o : Ordinal} : 0 < o ↔ o ≠ 0 :=
   bot_lt_iff_ne_bot
 #align ordinal.pos_iff_ne_zero Ordinal.pos_iff_ne_zero
--/
 
-#print Ordinal.not_lt_zero /-
+/- warning: ordinal.not_lt_zero -> Ordinal.not_lt_zero is a dubious translation:
+lean 3 declaration is
+  forall (o : Ordinal.{u1}), Not (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))))
+but is expected to have type
+  forall (o : Ordinal.{u1}), Not (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})))
+Case conversion may be inaccurate. Consider using '#align ordinal.not_lt_zero Ordinal.not_lt_zeroₓ'. -/
 protected theorem not_lt_zero (o : Ordinal) : ¬o < 0 :=
   not_lt_bot
 #align ordinal.not_lt_zero Ordinal.not_lt_zero
--/
 
-#print Ordinal.eq_zero_or_pos /-
+/- warning: ordinal.eq_zero_or_pos -> Ordinal.eq_zero_or_pos is a dubious translation:
+lean 3 declaration is
+  forall (a : Ordinal.{u1}), Or (Eq.{succ (succ u1)} Ordinal.{u1} a (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{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}))) a)
+but is expected to have type
+  forall (a : Ordinal.{u1}), Or (Eq.{succ (succ u1)} Ordinal.{u1} a (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{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})) a)
+Case conversion may be inaccurate. Consider using '#align ordinal.eq_zero_or_pos Ordinal.eq_zero_or_posₓ'. -/
 theorem eq_zero_or_pos : ∀ a : Ordinal, a = 0 ∨ 0 < a :=
   eq_bot_or_bot_lt
 #align ordinal.eq_zero_or_pos Ordinal.eq_zero_or_pos
--/
 
 instance : ZeroLEOneClass Ordinal :=
   ⟨Ordinal.zero_le _⟩
@@ -541,7 +593,12 @@ instance NeZero.one : NeZero (1 : Ordinal) :=
   ⟨Ordinal.one_ne_zero⟩
 #align ordinal.ne_zero.one Ordinal.NeZero.one
 
-#print Ordinal.initialSegOut /-
+/- warning: ordinal.initial_seg_out -> Ordinal.initialSegOut is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ordinal.initial_seg_out Ordinal.initialSegOutₓ'. -/
 /-- Given two ordinals `α ≤ β`, then `initial_seg_out α β` is the initial segment embedding
 of `α` to `β`, as map from a model type for `α` to a model type for `β`. -/
 def initialSegOut {α β : Ordinal} (h : α ≤ β) :
@@ -551,9 +608,13 @@ def initialSegOut {α β : Ordinal} (h : α ≤ β) :
   rw [← Quotient.out_eq α, ← Quotient.out_eq β] at h; revert h
   cases Quotient.out α; cases Quotient.out β; exact Classical.choice
 #align ordinal.initial_seg_out Ordinal.initialSegOut
--/
 
-#print Ordinal.principalSegOut /-
+/- warning: ordinal.principal_seg_out -> Ordinal.principalSegOut is a dubious translation:
+lean 3 declaration is
+  forall {α : Ordinal.{u1}} {β : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) α β) -> (PrincipalSeg.{u1, u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} α)) (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} β)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} α)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} α)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} α)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} α)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} α)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} α)) (linearOrderOut.{u1} α))))))) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} β)) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} β)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} β)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} β)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} β)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} β)) (linearOrderOut.{u1} β))))))))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.principal_seg_out Ordinal.principalSegOutₓ'. -/
 /-- Given two ordinals `α < β`, then `principal_seg_out α β` is the principal segment embedding
 of `α` to `β`, as map from a model type for `α` to a model type for `β`. -/
 def principalSegOut {α β : Ordinal} (h : α < β) :
@@ -563,21 +624,28 @@ def principalSegOut {α β : Ordinal} (h : α < β) :
   rw [← Quotient.out_eq α, ← Quotient.out_eq β] at h; revert h
   cases Quotient.out α; cases Quotient.out β; exact Classical.choice
 #align ordinal.principal_seg_out Ordinal.principalSegOut
--/
 
-#print Ordinal.typein_lt_type /-
+/- warning: ordinal.typein_lt_type -> Ordinal.typein_lt_type is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] (a : α), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.typein.{u1} α r _inst_1 a) (Ordinal.type.{u1} α r _inst_1)
+but is expected to have type
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] (a : α), LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.typein.{u1} α r _inst_1 a) (Ordinal.type.{u1} α r _inst_1)
+Case conversion may be inaccurate. Consider using '#align ordinal.typein_lt_type Ordinal.typein_lt_typeₓ'. -/
 theorem typein_lt_type (r : α → α → Prop) [IsWellOrder α r] (a : α) : typein r a < type r :=
   ⟨PrincipalSeg.ofElement _ _⟩
 #align ordinal.typein_lt_type Ordinal.typein_lt_type
--/
 
-#print Ordinal.typein_lt_self /-
+/- warning: ordinal.typein_lt_self -> Ordinal.typein_lt_self is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ordinal.typein_lt_self Ordinal.typein_lt_selfₓ'. -/
 theorem typein_lt_self {o : Ordinal} (i : o.out.α) : typein (· < ·) i < o :=
   by
   simp_rw [← type_lt o]
   apply typein_lt_type
 #align ordinal.typein_lt_self Ordinal.typein_lt_self
--/
 
 #print Ordinal.typein_top /-
 @[simp]
@@ -611,7 +679,12 @@ theorem typein_apply {α β} {r : α → α → Prop} {s : β → β → Prop} [
                 Subtype.eq <| RelEmbedding.trans_apply _ _ _⟩⟩
 #align ordinal.typein_apply Ordinal.typein_apply
 
-#print Ordinal.typein_lt_typein /-
+/- warning: ordinal.typein_lt_typein -> Ordinal.typein_lt_typein is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] {a : α} {b : α}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.typein.{u1} α r _inst_1 a) (Ordinal.typein.{u1} α r _inst_1 b)) (r a b)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.typein_lt_typein Ordinal.typein_lt_typeinₓ'. -/
 @[simp]
 theorem typein_lt_typein (r : α → α → Prop) [IsWellOrder α r] {a b : α} :
     typein r a < typein r b ↔ r a b :=
@@ -626,14 +699,17 @@ theorem typein_lt_typein (r : α → α → Prop) [IsWellOrder α r] {a b : α}
     exact f.top.2, fun h =>
     ⟨PrincipalSeg.codRestrict _ (PrincipalSeg.ofElement r a) (fun x => @trans _ r _ _ _ _ x.2 h) h⟩⟩
 #align ordinal.typein_lt_typein Ordinal.typein_lt_typein
--/
 
-#print Ordinal.typein_surj /-
+/- warning: ordinal.typein_surj -> Ordinal.typein_surj is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] {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 (Ordinal.type.{u1} α r _inst_1)) -> (Exists.{succ u1} α (fun (a : α) => Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} α r _inst_1 a) o))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.typein_surj Ordinal.typein_surjₓ'. -/
 theorem typein_surj (r : α → α → Prop) [IsWellOrder α r] {o} (h : o < type r) :
     ∃ a, typein r a = o :=
   inductionOn o (fun β s _ ⟨f⟩ => ⟨f.top, typein_top _⟩) h
 #align ordinal.typein_surj Ordinal.typein_surj
--/
 
 #print Ordinal.typein_injective /-
 theorem typein_injective (r : α → α → Prop) [IsWellOrder α r] : Injective (typein r) :=
@@ -651,7 +727,12 @@ theorem typein_inj (r : α → α → Prop) [IsWellOrder α r] {a b} : typein r
 /-! ### Enumerating elements in a well-order with ordinals. -/
 
 
-#print Ordinal.enum /-
+/- warning: ordinal.enum -> Ordinal.enum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] (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 (Ordinal.type.{u1} α r _inst_1)) -> α
+but is expected to have type
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] (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 (Ordinal.type.{u1} α r _inst_1)) -> α
+Case conversion may be inaccurate. Consider using '#align ordinal.enum Ordinal.enumₓ'. -/
 /-- `enum r o h` is the `o`-th element of `α` ordered by `r`.
   That is, `enum` maps an initial segment of the ordinals, those
   less than the order type of `r`, to the elements of `α`. -/
@@ -671,14 +752,17 @@ def enum (r : α → α → Prop) [IsWellOrder α r] (o) : o < type r → α :=
       subst e
     exact (this H₂).trans (PrincipalSeg.top_eq h (Classical.choice H₁) (Classical.choice H₂))
 #align ordinal.enum Ordinal.enum
--/
 
-#print Ordinal.enum_type /-
+/- warning: ordinal.enum_type -> Ordinal.enum_type is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : PrincipalSeg.{u1, u1} β α s r) {h : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1)}, Eq.{succ u1} α (Ordinal.enum.{u1} α r _inst_1 (Ordinal.type.{u1} β s _inst_2) h) (PrincipalSeg.top.{u1, u1} β α s r f)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : PrincipalSeg.{u1, u1} β α s r) {h : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1)}, Eq.{succ u1} α (Ordinal.enum.{u1} α r _inst_1 (Ordinal.type.{u1} β s _inst_2) h) (PrincipalSeg.top.{u1, u1} β α s r f)
+Case conversion may be inaccurate. Consider using '#align ordinal.enum_type Ordinal.enum_typeₓ'. -/
 theorem enum_type {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r] [IsWellOrder β s]
     (f : s ≺i r) {h : type s < type r} : enum r (type s) h = f.top :=
   PrincipalSeg.top_eq (RelIso.refl _) _ _
 #align ordinal.enum_type Ordinal.enum_type
--/
 
 #print Ordinal.enum_typein /-
 @[simp]
@@ -688,25 +772,33 @@ theorem enum_typein (r : α → α → Prop) [IsWellOrder α r] (a : α) :
 #align ordinal.enum_typein Ordinal.enum_typein
 -/
 
-#print Ordinal.typein_enum /-
+/- warning: ordinal.typein_enum -> Ordinal.typein_enum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] {o : Ordinal.{u1}} (h : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} α r _inst_1 (Ordinal.enum.{u1} α r _inst_1 o h)) o
+but is expected to have type
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] {o : Ordinal.{u1}} (h : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} α r _inst_1 (Ordinal.enum.{u1} α r _inst_1 o h)) o
+Case conversion may be inaccurate. Consider using '#align ordinal.typein_enum Ordinal.typein_enumₓ'. -/
 @[simp]
 theorem typein_enum (r : α → α → Prop) [IsWellOrder α r] {o} (h : o < type r) :
     typein r (enum r o h) = o := by
   let ⟨a, e⟩ := typein_surj r h
   clear _let_match <;> subst e <;> rw [enum_typein]
 #align ordinal.typein_enum Ordinal.typein_enum
--/
 
-#print Ordinal.enum_lt_enum /-
+/- warning: ordinal.enum_lt_enum -> Ordinal.enum_lt_enum is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r] {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}} (h₁ : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ (Ordinal.type.{u1} α r _inst_1)) (h₂ : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₂ (Ordinal.type.{u1} α r _inst_1)), Iff (r (Ordinal.enum.{u1} α r _inst_1 o₁ h₁) (Ordinal.enum.{u1} α r _inst_1 o₂ h₂)) (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 ordinal.enum_lt_enum Ordinal.enum_lt_enumₓ'. -/
 theorem enum_lt_enum {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordinal} (h₁ : o₁ < type r)
     (h₂ : o₂ < type r) : r (enum r o₁ h₁) (enum r o₂ h₂) ↔ o₁ < o₂ := by
   rw [← typein_lt_typein r, typein_enum, typein_enum]
 #align ordinal.enum_lt_enum Ordinal.enum_lt_enum
--/
 
 /- warning: ordinal.rel_iso_enum' -> Ordinal.relIso_enum' is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align ordinal.rel_iso_enum' Ordinal.relIso_enum'ₓ'. -/
@@ -720,7 +812,7 @@ theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β 
 
 /- warning: ordinal.rel_iso_enum -> Ordinal.relIso_enum is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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a._@.Init.Prelude._hyg.2015 h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5690) e'_4) (Eq.refl.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2015) (HEq.refl.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude._hyg.2015) e'_4)) Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f))))) hr))
 Case conversion may be inaccurate. Consider using '#align ordinal.rel_iso_enum Ordinal.relIso_enumₓ'. -/
@@ -735,7 +827,12 @@ theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β →
   relIso_enum' _ _ _ _
 #align ordinal.rel_iso_enum Ordinal.relIso_enum
 
-#print Ordinal.lt_wf /-
+/- warning: ordinal.lt_wf -> Ordinal.lt_wf is a dubious translation:
+lean 3 declaration is
+  WellFounded.{succ (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})))
+but is expected to have type
+  WellFounded.{succ (succ u1)} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5729 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5731 : 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.Ordinal.Basic._hyg.5729 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5731)
+Case conversion may be inaccurate. Consider using '#align ordinal.lt_wf Ordinal.lt_wfₓ'. -/
 theorem lt_wf : @WellFounded Ordinal (· < ·) :=
   ⟨fun a =>
     inductionOn a fun α r wo =>
@@ -750,21 +847,29 @@ theorem lt_wf : @WellFounded Ordinal (· < ·) :=
           rcases typein_surj r (lt_trans h (typein_lt_type r _)) with ⟨b, rfl⟩
           exact IH _ ((typein_lt_typein r).1 h)⟩⟩
 #align ordinal.lt_wf Ordinal.lt_wf
--/
 
 instance : WellFoundedRelation Ordinal :=
   ⟨(· < ·), lt_wf⟩
 
-#print Ordinal.induction /-
+/- warning: ordinal.induction -> Ordinal.induction is a dubious translation:
+lean 3 declaration is
+  forall {p : Ordinal.{u1} -> Prop} (i : Ordinal.{u1}), (forall (j : Ordinal.{u1}), (forall (k : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) k j) -> (p k)) -> (p j)) -> (p i)
+but is expected to have type
+  forall {p : Ordinal.{u1} -> Prop} (i : Ordinal.{u1}), (forall (j : Ordinal.{u1}), (forall (k : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) k j) -> (p k)) -> (p j)) -> (p i)
+Case conversion may be inaccurate. Consider using '#align ordinal.induction Ordinal.inductionₓ'. -/
 /-- Reformulation of well founded induction on ordinals as a lemma that works with the
 `induction` tactic, as in `induction i using ordinal.induction with i IH`. -/
 theorem induction {p : Ordinal.{u} → Prop} (i : Ordinal.{u}) (h : ∀ j, (∀ k, k < j → p k) → p j) :
     p i :=
   lt_wf.induction i h
 #align ordinal.induction Ordinal.induction
--/
 
-#print Ordinal.typein.principalSeg /-
+/- warning: ordinal.typein.principal_seg -> Ordinal.typein.principalSeg is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (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
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003)
+Case conversion may be inaccurate. Consider using '#align ordinal.typein.principal_seg Ordinal.typein.principalSegₓ'. -/
 /-- Principal segment version of the `typein` function, embedding a well order into
   ordinals as a principal segment. -/
 def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r] :
@@ -772,11 +877,10 @@ def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r
   ⟨RelEmbedding.ofMonotone (typein r) fun a b => (typein_lt_typein r).2, type r, fun b =>
     ⟨fun h => ⟨enum r _ h, typein_enum r h⟩, fun ⟨a, e⟩ => e ▸ typein_lt_type _ _⟩⟩
 #align ordinal.typein.principal_seg Ordinal.typein.principalSeg
--/
 
 /- warning: ordinal.typein.principal_seg_coe -> Ordinal.typein.principalSeg_coe is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} ((fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (coeFn.{succ (succ u1), succ (succ u1)} (PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (PrincipalSeg.hasCoeToFun.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (Ordinal.typein.{u1} α r _inst_1)
 but is expected to have type
   forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (RelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Ordinal.{u1}) _x) (RelHomClass.toFunLike.{succ u1, u1, succ u1} (RelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003)) α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003) (RelEmbedding.instRelHomClassRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003))) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003) (Ordinal.typein.principalSeg.{u1} α r _inst_1))) (Ordinal.typein.{u1} α r _inst_1)
 Case conversion may be inaccurate. Consider using '#align ordinal.typein.principal_seg_coe Ordinal.typein.principalSeg_coeₓ'. -/
@@ -812,11 +916,15 @@ theorem card_typein {r : α → α → Prop} [wo : IsWellOrder α r] (x : α) :
 #align ordinal.card_typein Ordinal.card_typein
 -/
 
-#print Ordinal.card_le_card /-
+/- warning: ordinal.card_le_card -> Ordinal.card_le_card is a dubious translation:
+lean 3 declaration is
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Ordinal.card.{u1} o₁) (Ordinal.card.{u1} o₂))
+but is expected to have type
+  forall {o₁ : Ordinal.{u1}} {o₂ : Ordinal.{u1}}, (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o₁ o₂) -> (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Ordinal.card.{u1} o₁) (Ordinal.card.{u1} o₂))
+Case conversion may be inaccurate. Consider using '#align ordinal.card_le_card Ordinal.card_le_cardₓ'. -/
 theorem card_le_card {o₁ o₂ : Ordinal} : o₁ ≤ o₂ → card o₁ ≤ card o₂ :=
   inductionOn o₁ fun α r _ => inductionOn o₂ fun β s _ ⟨⟨⟨f, _⟩, _⟩⟩ => ⟨f⟩
 #align ordinal.card_le_card Ordinal.card_le_card
--/
 
 #print Ordinal.card_zero /-
 @[simp]
@@ -950,7 +1058,12 @@ theorem lift_lift (a : Ordinal) : lift.{w} (lift.{v} a) = lift.{max v w} a :=
           (RelIso.preimage Equiv.ulift _).trans (RelIso.preimage Equiv.ulift _).symm⟩
 #align ordinal.lift_lift Ordinal.lift_lift
 
-#print Ordinal.lift_type_le /-
+/- warning: ordinal.lift_type_le -> Ordinal.lift_type_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u2} β s], Iff (LE.le.{succ (max u1 u2 u3)} Ordinal.{max u1 u2 u3} (Preorder.toHasLe.{succ (max u1 u2 u3)} Ordinal.{max u1 u2 u3} (PartialOrder.toPreorder.{succ (max u1 u2 u3)} Ordinal.{max u1 u2 u3} Ordinal.partialOrder.{max u1 u2 u3})) (Ordinal.lift.{max u2 u3, u1} (Ordinal.type.{u1} α r _inst_1)) (Ordinal.lift.{max u1 u3, u2} (Ordinal.type.{u2} β s _inst_2))) (Nonempty.{max (succ u1) (succ u2)} (InitialSeg.{u1, u2} α β r s))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u2} β s], Iff (LE.le.{max (max (succ u1) (succ u2)) (succ u3)} Ordinal.{max u1 u2 u3} (Preorder.toLE.{max (max (succ u1) (succ u2)) (succ u3)} Ordinal.{max u1 u2 u3} (PartialOrder.toPreorder.{max (max (succ u1) (succ u2)) (succ u3)} Ordinal.{max u1 u2 u3} Ordinal.partialOrder.{max (max u1 u2) u3})) (Ordinal.lift.{max u2 u3, u1} (Ordinal.type.{u1} α r _inst_1)) (Ordinal.lift.{max u1 u3, u2} (Ordinal.type.{u2} β s _inst_2))) (Nonempty.{max (succ u2) (succ u1)} (InitialSeg.{u1, u2} α β r s))
+Case conversion may be inaccurate. Consider using '#align ordinal.lift_type_le Ordinal.lift_type_leₓ'. -/
 theorem lift_type_le {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWellOrder β s] :
     lift.{max v w} (type r) ≤ lift.{max u w} (type s) ↔ Nonempty (r ≼i s) :=
   ⟨fun ⟨f⟩ =>
@@ -960,7 +1073,6 @@ theorem lift_type_le {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWel
     ⟨(InitialSeg.ofIso (RelIso.preimage Equiv.ulift r)).trans <|
         f.trans (InitialSeg.ofIso (RelIso.preimage Equiv.ulift s).symm)⟩⟩
 #align ordinal.lift_type_le Ordinal.lift_type_le
--/
 
 #print Ordinal.lift_type_eq /-
 theorem lift_type_eq {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWellOrder β s] :
@@ -973,7 +1085,12 @@ theorem lift_type_eq {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWel
 #align ordinal.lift_type_eq Ordinal.lift_type_eq
 -/
 
-#print Ordinal.lift_type_lt /-
+/- warning: ordinal.lift_type_lt -> Ordinal.lift_type_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u2} β s], Iff (LT.lt.{succ (max u1 u2 u3)} Ordinal.{max u1 u2 u3} (Preorder.toHasLt.{succ (max u1 u2 u3)} Ordinal.{max u1 u2 u3} (PartialOrder.toPreorder.{succ (max u1 u2 u3)} Ordinal.{max u1 u2 u3} Ordinal.partialOrder.{max u1 u2 u3})) (Ordinal.lift.{max u2 u3, u1} (Ordinal.type.{u1} α r _inst_1)) (Ordinal.lift.{max u1 u3, u2} (Ordinal.type.{u2} β s _inst_2))) (Nonempty.{max (succ u1) (succ u2)} (PrincipalSeg.{u1, u2} α β r s))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u2} β s], Iff (LT.lt.{max (max (succ u1) (succ u2)) (succ u3)} Ordinal.{max u1 u2 u3} (Preorder.toLT.{max (max (succ u1) (succ u2)) (succ u3)} Ordinal.{max u1 u2 u3} (PartialOrder.toPreorder.{max (max (succ u1) (succ u2)) (succ u3)} Ordinal.{max u1 u2 u3} Ordinal.partialOrder.{max (max u1 u2) u3})) (Ordinal.lift.{max u2 u3, u1} (Ordinal.type.{u1} α r _inst_1)) (Ordinal.lift.{max u1 u3, u2} (Ordinal.type.{u2} β s _inst_2))) (Nonempty.{max (succ u2) (succ u1)} (PrincipalSeg.{u1, u2} α β r s))
+Case conversion may be inaccurate. Consider using '#align ordinal.lift_type_lt Ordinal.lift_type_ltₓ'. -/
 theorem lift_type_lt {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWellOrder β s] :
     lift.{max v w} (type r) < lift.{max u w} (type s) ↔ Nonempty (r ≺i s) := by
   haveI :=
@@ -990,9 +1107,13 @@ theorem lift_type_lt {α : Type u} {β : Type v} {r s} [IsWellOrder α r] [IsWel
         ⟨(f.equivLT (RelIso.preimage Equiv.ulift r)).ltLe
             (InitialSeg.ofIso (RelIso.preimage Equiv.ulift s).symm)⟩⟩
 #align ordinal.lift_type_lt Ordinal.lift_type_lt
--/
 
-#print Ordinal.lift_le /-
+/- warning: ordinal.lift_le -> Ordinal.lift_le is a dubious translation:
+lean 3 declaration is
+  forall {a : Ordinal.{u2}} {b : Ordinal.{u2}}, Iff (LE.le.{succ (max u2 u1)} Ordinal.{max u2 u1} (Preorder.toHasLe.{succ (max u2 u1)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{succ (max u2 u1)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u2 u1})) (Ordinal.lift.{u1, u2} a) (Ordinal.lift.{u1, u2} b)) (LE.le.{succ u2} Ordinal.{u2} (Preorder.toHasLe.{succ u2} Ordinal.{u2} (PartialOrder.toPreorder.{succ u2} Ordinal.{u2} Ordinal.partialOrder.{u2})) a b)
+but is expected to have type
+  forall {a : Ordinal.{u2}} {b : Ordinal.{u2}}, Iff (LE.le.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (Preorder.toLE.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u1 u2})) (Ordinal.lift.{u1, u2} a) (Ordinal.lift.{u1, u2} b)) (LE.le.{succ u2} Ordinal.{u2} (Preorder.toLE.{succ u2} Ordinal.{u2} (PartialOrder.toPreorder.{succ u2} Ordinal.{u2} Ordinal.partialOrder.{u2})) a b)
+Case conversion may be inaccurate. Consider using '#align ordinal.lift_le Ordinal.lift_leₓ'. -/
 @[simp]
 theorem lift_le {a b : Ordinal} : lift.{u, v} a ≤ lift b ↔ a ≤ b :=
   inductionOn a fun α r _ =>
@@ -1000,7 +1121,6 @@ theorem lift_le {a b : Ordinal} : lift.{u, v} a ≤ lift b ↔ a ≤ b :=
       rw [← lift_umax]
       exact lift_type_le
 #align ordinal.lift_le Ordinal.lift_le
--/
 
 /- warning: ordinal.lift_inj -> Ordinal.lift_inj is a dubious translation:
 lean 3 declaration is
@@ -1015,7 +1135,7 @@ theorem lift_inj {a b : Ordinal} : lift a = lift b ↔ a = b := by
 
 /- warning: ordinal.lift_lt -> Ordinal.lift_lt is a dubious translation:
 lean 3 declaration is
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+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (Ordinal.lift.{u2, u1} a) (Ordinal.lift.{u2, u1} b)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a b)
 but is expected to have type
   forall {a : Ordinal.{u2}} {b : Ordinal.{u2}}, Iff (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u1 u2})) (Ordinal.lift.{u1, u2} a) (Ordinal.lift.{u1, u2} b)) (LT.lt.{succ u2} Ordinal.{u2} (Preorder.toLT.{succ u2} Ordinal.{u2} (PartialOrder.toPreorder.{succ u2} Ordinal.{u2} Ordinal.partialOrder.{u2})) a b)
 Case conversion may be inaccurate. Consider using '#align ordinal.lift_lt Ordinal.lift_ltₓ'. -/
@@ -1077,13 +1197,22 @@ theorem lift_down' {a : Cardinal.{u}} {b : Ordinal.{max u v}} (h : card b ≤ a.
 #align ordinal.lift_down' Ordinal.lift_down'
 -/
 
-#print Ordinal.lift_down /-
+/- warning: ordinal.lift_down -> Ordinal.lift_down is a dubious translation:
+lean 3 declaration is
+  forall {a : Ordinal.{u1}} {b : Ordinal.{max u1 u2}}, (LE.le.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLe.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b (Ordinal.lift.{u2, u1} a)) -> (Exists.{succ (succ u1)} Ordinal.{u1} (fun (a' : Ordinal.{u1}) => Eq.{succ (succ (max u1 u2))} Ordinal.{max u1 u2} (Ordinal.lift.{u2, u1} a') b))
+but is expected to have type
+  forall {a : Ordinal.{u1}} {b : Ordinal.{max u1 u2}}, (LE.le.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLE.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b (Ordinal.lift.{u2, u1} a)) -> (Exists.{succ (succ u1)} Ordinal.{u1} (fun (a' : Ordinal.{u1}) => Eq.{max (succ (succ u1)) (succ (succ u2))} Ordinal.{max u1 u2} (Ordinal.lift.{u2, u1} a') b))
+Case conversion may be inaccurate. Consider using '#align ordinal.lift_down Ordinal.lift_downₓ'. -/
 theorem lift_down {a : Ordinal.{u}} {b : Ordinal.{max u v}} (h : b ≤ lift a) : ∃ a', lift a' = b :=
   @lift_down' (card a) _ (by rw [lift_card] <;> exact card_le_card h)
 #align ordinal.lift_down Ordinal.lift_down
--/
 
-#print Ordinal.le_lift_iff /-
+/- warning: ordinal.le_lift_iff -> Ordinal.le_lift_iff is a dubious translation:
+lean 3 declaration is
+  forall {a : Ordinal.{u1}} {b : Ordinal.{max u1 u2}}, Iff (LE.le.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLe.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b (Ordinal.lift.{u2, u1} a)) (Exists.{succ (succ u1)} Ordinal.{u1} (fun (a' : Ordinal.{u1}) => And (Eq.{succ (succ (max u1 u2))} Ordinal.{max u1 u2} (Ordinal.lift.{u2, u1} a') b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a' a)))
+but is expected to have type
+  forall {a : Ordinal.{u1}} {b : Ordinal.{max u1 u2}}, Iff (LE.le.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLE.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b (Ordinal.lift.{u2, u1} a)) (Exists.{succ (succ u1)} Ordinal.{u1} (fun (a' : Ordinal.{u1}) => And (Eq.{max (succ (succ u1)) (succ (succ u2))} Ordinal.{max u1 u2} (Ordinal.lift.{u2, u1} a') b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a' a)))
+Case conversion may be inaccurate. Consider using '#align ordinal.le_lift_iff Ordinal.le_lift_iffₓ'. -/
 theorem le_lift_iff {a : Ordinal.{u}} {b : Ordinal.{max u v}} :
     b ≤ lift a ↔ ∃ a', lift a' = b ∧ a' ≤ a :=
   ⟨fun h =>
@@ -1091,9 +1220,13 @@ theorem le_lift_iff {a : Ordinal.{u}} {b : Ordinal.{max u v}} :
     ⟨a', e, lift_le.1 <| e.symm ▸ h⟩,
     fun ⟨a', e, h⟩ => e ▸ lift_le.2 h⟩
 #align ordinal.le_lift_iff Ordinal.le_lift_iff
--/
 
-#print Ordinal.lt_lift_iff /-
+/- warning: ordinal.lt_lift_iff -> Ordinal.lt_lift_iff is a dubious translation:
+lean 3 declaration is
+  forall {a : Ordinal.{u1}} {b : Ordinal.{max u1 u2}}, Iff (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b (Ordinal.lift.{u2, u1} a)) (Exists.{succ (succ u1)} Ordinal.{u1} (fun (a' : Ordinal.{u1}) => And (Eq.{succ (succ (max u1 u2))} Ordinal.{max u1 u2} (Ordinal.lift.{u2, u1} a') b) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a' a)))
+but is expected to have type
+  forall {a : Ordinal.{u1}} {b : Ordinal.{max u1 u2}}, Iff (LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b (Ordinal.lift.{u2, u1} a)) (Exists.{succ (succ u1)} Ordinal.{u1} (fun (a' : Ordinal.{u1}) => And (Eq.{max (succ (succ u1)) (succ (succ u2))} Ordinal.{max u1 u2} (Ordinal.lift.{u2, u1} a') b) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a' a)))
+Case conversion may be inaccurate. Consider using '#align ordinal.lt_lift_iff Ordinal.lt_lift_iffₓ'. -/
 theorem lt_lift_iff {a : Ordinal.{u}} {b : Ordinal.{max u v}} :
     b < lift a ↔ ∃ a', lift a' = b ∧ a' < a :=
   ⟨fun h =>
@@ -1101,19 +1234,22 @@ theorem lt_lift_iff {a : Ordinal.{u}} {b : Ordinal.{max u v}} :
     ⟨a', e, lift_lt.1 <| e.symm ▸ h⟩,
     fun ⟨a', e, h⟩ => e ▸ lift_lt.2 h⟩
 #align ordinal.lt_lift_iff Ordinal.lt_lift_iff
--/
 
-#print Ordinal.lift.initialSeg /-
+/- warning: ordinal.lift.initial_seg -> Ordinal.lift.initialSeg is a dubious translation:
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+  InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))
+but is expected to have type
+  InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8585 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587 : 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.Ordinal.Basic._hyg.8585 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8600 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8600 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602)
+Case conversion may be inaccurate. Consider using '#align ordinal.lift.initial_seg Ordinal.lift.initialSegₓ'. -/
 /-- Initial segment version of the lift operation on ordinals, embedding `ordinal.{u}` in
   `ordinal.{v}` as an initial segment when `u ≤ v`. -/
 def lift.initialSeg : @InitialSeg Ordinal.{u} Ordinal.{max u v} (· < ·) (· < ·) :=
   ⟨⟨⟨lift.{v}, fun a b => lift_inj.1⟩, fun a b => lift_lt⟩, fun a b h => lift_down (le_of_lt h)⟩
 #align ordinal.lift.initial_seg Ordinal.lift.initialSeg
--/
 
 /- warning: ordinal.lift.initial_seg_coe -> Ordinal.lift.initialSeg_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 ordinal.lift.initial_seg_coe Ordinal.lift.initialSeg_coeₓ'. -/
@@ -1224,7 +1360,12 @@ theorem card_nat (n : ℕ) : card.{u} n = n := by
   induction n <;> [rfl, simp only [card_add, card_one, Nat.cast_succ, *]]
 #align ordinal.card_nat Ordinal.card_nat
 
-#print Ordinal.add_covariantClass_le /-
+/- warning: ordinal.add_covariant_class_le -> Ordinal.add_covariantClass_le is a dubious translation:
+lean 3 declaration is
+  CovariantClass.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1})) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))
+but is expected to have type
+  CovariantClass.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.9972 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.9974 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.9972 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.9974) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.9987 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.9989 : Ordinal.{u1}) => LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.9987 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.9989)
+Case conversion may be inaccurate. Consider using '#align ordinal.add_covariant_class_le Ordinal.add_covariantClass_leₓ'. -/
 instance add_covariantClass_le : CovariantClass Ordinal.{u} Ordinal.{u} (· + ·) (· ≤ ·) :=
   ⟨fun c a b h => by revert h c;
     exact
@@ -1245,9 +1386,13 @@ instance add_covariantClass_le : CovariantClass Ordinal.{u} Ordinal.{u} (· + ·
                   let ⟨w, h⟩ := fi _ _ (Sum.lex_inr_inr.1 H)
                   ⟨Sum.inr w, congr_arg Sum.inr h⟩⟩⟩⟩
 #align ordinal.add_covariant_class_le Ordinal.add_covariantClass_le
--/
 
-#print Ordinal.add_swap_covariantClass_le /-
+/- warning: ordinal.add_swap_covariant_class_le -> Ordinal.add_swap_covariantClass_le is a dubious translation:
+lean 3 declaration is
+  CovariantClass.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} (Function.swap.{succ (succ u1), succ (succ u1), succ (succ u1)} Ordinal.{u1} Ordinal.{u1} (fun (ᾰ : Ordinal.{u1}) (ᾰ : Ordinal.{u1}) => Ordinal.{u1}) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}))) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))
+but is expected to have type
+  CovariantClass.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} (Function.swap.{succ (succ u1), succ (succ u1), succ (succ u1)} Ordinal.{u1} Ordinal.{u1} (fun (ᾰ : Ordinal.{u1}) (ᾰ : Ordinal.{u1}) => Ordinal.{u1}) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.10435 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.10437 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.10435 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.10437)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.10450 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.10452 : Ordinal.{u1}) => LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.10450 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.10452)
+Case conversion may be inaccurate. Consider using '#align ordinal.add_swap_covariant_class_le Ordinal.add_swap_covariantClass_leₓ'. -/
 instance add_swap_covariantClass_le :
     CovariantClass Ordinal.{u} Ordinal.{u} (swap (· + ·)) (· ≤ ·) :=
   ⟨fun c a b h => by revert h c;
@@ -1264,19 +1409,26 @@ instance add_swap_covariantClass_le :
                     [rwa [← fo], assumption]
                 · cases H <;> constructor <;> [rwa [fo], assumption]⟩⟩
 #align ordinal.add_swap_covariant_class_le Ordinal.add_swap_covariantClass_le
--/
 
-#print Ordinal.le_add_right /-
+/- warning: ordinal.le_add_right -> Ordinal.le_add_right is a dubious translation:
+lean 3 declaration is
+  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a b)
+but is expected to have type
+  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a b)
+Case conversion may be inaccurate. Consider using '#align ordinal.le_add_right Ordinal.le_add_rightₓ'. -/
 theorem le_add_right (a b : Ordinal) : a ≤ a + b := by
   simpa only [add_zero] using add_le_add_left (Ordinal.zero_le b) a
 #align ordinal.le_add_right Ordinal.le_add_right
--/
 
-#print Ordinal.le_add_left /-
+/- warning: ordinal.le_add_left -> Ordinal.le_add_left is a dubious translation:
+lean 3 declaration is
+  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) b a)
+but is expected to have type
+  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) b a)
+Case conversion may be inaccurate. Consider using '#align ordinal.le_add_left Ordinal.le_add_leftₓ'. -/
 theorem le_add_left (a b : Ordinal) : a ≤ b + a := by
   simpa only [zero_add] using add_le_add_right (Ordinal.zero_le b) a
 #align ordinal.le_add_left Ordinal.le_add_left
--/
 
 instance : LinearOrder Ordinal :=
   {
@@ -1431,7 +1583,7 @@ theorem add_succ (o₁ o₂ : Ordinal) : o₁ + succ o₂ = succ (o₁ + o₂) :
 
 /- warning: ordinal.one_le_iff_pos -> Ordinal.one_le_iff_pos is a dubious translation:
 lean 3 declaration is
-  forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))) o) (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)
+  forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))) o) (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)
 but is expected to have type
   forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})) o) (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)
 Case conversion may be inaccurate. Consider using '#align ordinal.one_le_iff_pos Ordinal.one_le_iff_posₓ'. -/
@@ -1440,7 +1592,7 @@ theorem one_le_iff_pos {o : Ordinal} : 1 ≤ o ↔ 0 < o := by rw [← succ_zero
 
 /- warning: ordinal.one_le_iff_ne_zero -> Ordinal.one_le_iff_ne_zero is a dubious translation:
 lean 3 declaration is
-  forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))) o) (Ne.{succ (succ u1)} Ordinal.{u1} o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))))
+  forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))) o) (Ne.{succ (succ u1)} Ordinal.{u1} o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))))
 but is expected to have type
   forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})) o) (Ne.{succ (succ u1)} Ordinal.{u1} o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})))
 Case conversion may be inaccurate. Consider using '#align ordinal.one_le_iff_ne_zero Ordinal.one_le_iff_ne_zeroₓ'. -/
@@ -1448,11 +1600,15 @@ theorem one_le_iff_ne_zero {o : Ordinal} : 1 ≤ o ↔ o ≠ 0 := by
   rw [one_le_iff_pos, Ordinal.pos_iff_ne_zero]
 #align ordinal.one_le_iff_ne_zero Ordinal.one_le_iff_ne_zero
 
-#print Ordinal.succ_pos /-
+/- warning: ordinal.succ_pos -> Ordinal.succ_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}))) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)
+but is expected to have type
+  forall (o : Ordinal.{u1}), 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})) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)
+Case conversion may be inaccurate. Consider using '#align ordinal.succ_pos Ordinal.succ_posₓ'. -/
 theorem succ_pos (o : Ordinal) : 0 < succ o :=
   bot_lt_succ o
 #align ordinal.succ_pos Ordinal.succ_pos
--/
 
 #print Ordinal.succ_ne_zero /-
 theorem succ_ne_zero (o : Ordinal) : succ o ≠ 0 :=
@@ -1462,7 +1618,7 @@ theorem succ_ne_zero (o : Ordinal) : succ o ≠ 0 :=
 
 /- warning: ordinal.lt_one_iff_zero -> Ordinal.lt_one_iff_zero is a dubious translation:
 lean 3 declaration is
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+  forall {a : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (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)} Ordinal.{u1} a (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))))
 but is expected to have type
   forall {a : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (Eq.{succ (succ u1)} Ordinal.{u1} a (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})))
 Case conversion may be inaccurate. Consider using '#align ordinal.lt_one_iff_zero Ordinal.lt_one_iff_zeroₓ'. -/
@@ -1471,7 +1627,7 @@ theorem lt_one_iff_zero {a : Ordinal} : a < 1 ↔ a = 0 := by simpa using @lt_su
 
 /- warning: ordinal.le_one_iff -> Ordinal.le_one_iff is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
   forall {a : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (Or (Eq.{succ (succ u1)} Ordinal.{u1} a (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (Eq.{succ (succ u1)} Ordinal.{u1} a (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))
 Case conversion may be inaccurate. Consider using '#align ordinal.le_one_iff Ordinal.le_one_iffₓ'. -/
@@ -1527,9 +1683,9 @@ instance uniqueOutOne : Unique (1 : Ordinal).out.α
 
 /- warning: ordinal.one_out_eq -> Ordinal.one_out_eq is a dubious translation:
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align ordinal.one_out_eq Ordinal.one_out_eqₓ'. -/
 theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :=
   Unique.eq_default x
@@ -1540,23 +1696,32 @@ theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :
 
 /- warning: ordinal.typein_one_out -> Ordinal.typein_one_out is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align ordinal.typein_one_out Ordinal.typein_one_outₓ'. -/
 @[simp]
 theorem typein_one_out (x : (1 : Ordinal).out.α) : typein (· < ·) x = 0 := by
   rw [one_out_eq x, typein_enum]
 #align ordinal.typein_one_out Ordinal.typein_one_out
 
-#print Ordinal.typein_le_typein /-
+/- warning: ordinal.typein_le_typein -> Ordinal.typein_le_typein is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] {x : α} {x' : α}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.typein.{u1} α r _inst_1 x) (Ordinal.typein.{u1} α r _inst_1 x')) (Not (r x' x))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.typein_le_typein Ordinal.typein_le_typeinₓ'. -/
 @[simp]
 theorem typein_le_typein (r : α → α → Prop) [IsWellOrder α r] {x x' : α} :
     typein r x ≤ typein r x' ↔ ¬r x' x := by rw [← not_lt, typein_lt_typein]
 #align ordinal.typein_le_typein Ordinal.typein_le_typein
--/
 
-#print Ordinal.typein_le_typein' /-
+/- warning: ordinal.typein_le_typein' -> Ordinal.typein_le_typein' is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.typein_le_typein' Ordinal.typein_le_typein'ₓ'. -/
 @[simp]
 theorem typein_le_typein' (o : Ordinal) {x x' : o.out.α} :
     typein (· < ·) x ≤ typein (· < ·) x' ↔ x ≤ x' :=
@@ -1564,42 +1729,62 @@ theorem typein_le_typein' (o : Ordinal) {x x' : o.out.α} :
   rw [typein_le_typein]
   exact not_lt
 #align ordinal.typein_le_typein' Ordinal.typein_le_typein'
--/
 
-#print Ordinal.enum_le_enum /-
+/- warning: ordinal.enum_le_enum -> Ordinal.enum_le_enum is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] {o : Ordinal.{u1}} {o' : Ordinal.{u1}} (ho : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) (ho' : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o' (Ordinal.type.{u1} α r _inst_1)), Iff (Not (r (Ordinal.enum.{u1} α r _inst_1 o' ho') (Ordinal.enum.{u1} α r _inst_1 o ho))) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o')
+but is expected to have type
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] {o : Ordinal.{u1}} {o' : Ordinal.{u1}} (ho : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) (ho' : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o' (Ordinal.type.{u1} α r _inst_1)), Iff (Not (r (Ordinal.enum.{u1} α r _inst_1 o' ho') (Ordinal.enum.{u1} α r _inst_1 o ho))) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o')
+Case conversion may be inaccurate. Consider using '#align ordinal.enum_le_enum Ordinal.enum_le_enumₓ'. -/
 @[simp]
 theorem enum_le_enum (r : α → α → Prop) [IsWellOrder α r] {o o' : Ordinal} (ho : o < type r)
     (ho' : o' < type r) : ¬r (enum r o' ho') (enum r o ho) ↔ o ≤ o' := by
   rw [← @not_lt _ _ o' o, enum_lt_enum ho']
 #align ordinal.enum_le_enum Ordinal.enum_le_enum
--/
 
-#print Ordinal.enum_le_enum' /-
+/- warning: ordinal.enum_le_enum' -> Ordinal.enum_le_enum' is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ordinal.enum_le_enum' Ordinal.enum_le_enum'ₓ'. -/
 @[simp]
 theorem enum_le_enum' (a : Ordinal) {o o' : Ordinal} (ho : o < type (· < ·))
     (ho' : o' < type (· < ·)) : enum (· < ·) o ho ≤ @enum a.out.α (· < ·) _ o' ho' ↔ o ≤ o' := by
   rw [← enum_le_enum (· < ·), ← not_lt]
 #align ordinal.enum_le_enum' Ordinal.enum_le_enum'
--/
 
-#print Ordinal.enum_zero_le /-
+/- warning: ordinal.enum_zero_le -> Ordinal.enum_zero_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r] (h0 : 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})) (Ordinal.type.{u1} α r _inst_1)) (a : α), Not (r a (Ordinal.enum.{u1} α r _inst_1 (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) h0))
+Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_le Ordinal.enum_zero_leₓ'. -/
 theorem enum_zero_le {r : α → α → Prop} [IsWellOrder α r] (h0 : 0 < type r) (a : α) :
     ¬r a (enum r 0 h0) := by
   rw [← enum_typein r a, enum_le_enum r]
   apply Ordinal.zero_le
 #align ordinal.enum_zero_le Ordinal.enum_zero_le
--/
 
-#print Ordinal.enum_zero_le' /-
+/- warning: ordinal.enum_zero_le' -> Ordinal.enum_zero_le' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_le' Ordinal.enum_zero_le'ₓ'. -/
 theorem enum_zero_le' {o : Ordinal} (h0 : 0 < o) (a : o.out.α) :
     @enum o.out.α (· < ·) _ 0 (by rwa [type_lt]) ≤ a :=
   by
   rw [← not_lt]
   apply enum_zero_le
 #align ordinal.enum_zero_le' Ordinal.enum_zero_le'
--/
 
-#print Ordinal.le_enum_succ /-
+/- warning: ordinal.le_enum_succ -> Ordinal.le_enum_succ is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align ordinal.le_enum_succ Ordinal.le_enum_succₓ'. -/
 theorem le_enum_succ {o : Ordinal} (a : (succ o).out.α) :
     a ≤
       @enum (succ o).out.α (· < ·) _ o
@@ -1610,9 +1795,13 @@ theorem le_enum_succ {o : Ordinal} (a : (succ o).out.α) :
   rw [← enum_typein (· < ·) a, enum_le_enum', ← lt_succ_iff]
   apply typein_lt_self
 #align ordinal.le_enum_succ Ordinal.le_enum_succ
--/
 
-#print Ordinal.enum_inj /-
+/- warning: ordinal.enum_inj -> Ordinal.enum_inj is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.enum_inj Ordinal.enum_injₓ'. -/
 @[simp]
 theorem enum_inj {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordinal} (h₁ : o₁ < type r)
     (h₂ : o₂ < type r) : enum r o₁ h₁ = enum r o₂ h₂ ↔ o₁ = o₂ :=
@@ -1623,9 +1812,13 @@ theorem enum_inj {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordina
     · change _ < _ at hlt
       rwa [← @enum_lt_enum α r _ o₂ o₁ h₂ h₁, h] at hlt, fun h => by simp_rw [h]⟩
 #align ordinal.enum_inj Ordinal.enum_inj
--/
 
-#print Ordinal.enumIso /-
+/- warning: ordinal.enum_iso -> Ordinal.enumIso is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.enum_iso Ordinal.enumIsoₓ'. -/
 /-- A well order `r` is order isomorphic to the set of ordinals smaller than `type r`. -/
 @[simps]
 def enumIso (r : α → α → Prop) [IsWellOrder α r] : Subrel (· < ·) (· < type r) ≃r r
@@ -1638,9 +1831,13 @@ def enumIso (r : α → α → Prop) [IsWellOrder α r] : Subrel (· < ·) (· <
     rintro ⟨a, _⟩ ⟨b, _⟩
     apply enum_lt_enum
 #align ordinal.enum_iso Ordinal.enumIso
--/
 
-#print Ordinal.enumIsoOut /-
+/- warning: ordinal.enum_iso_out -> Ordinal.enumIsoOut is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.enum_iso_out Ordinal.enumIsoOutₓ'. -/
 /-- The order isomorphism between ordinals less than `o` and `o.out.α`. -/
 @[simps]
 noncomputable def enumIsoOut (o : Ordinal) : Set.Iio o ≃o o.out.α
@@ -1656,20 +1853,23 @@ noncomputable def enumIsoOut (o : Ordinal) : Set.Iio o ≃o o.out.α
     rintro ⟨a, _⟩ ⟨b, _⟩
     apply enum_le_enum'
 #align ordinal.enum_iso_out Ordinal.enumIsoOut
--/
 
-#print Ordinal.outOrderBotOfPos /-
+/- warning: ordinal.out_order_bot_of_pos -> Ordinal.outOrderBotOfPos is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.out_order_bot_of_pos Ordinal.outOrderBotOfPosₓ'. -/
 /-- `o.out.α` is an `order_bot` whenever `0 < o`. -/
 def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α :=
   ⟨_, enum_zero_le' ho⟩
 #align ordinal.out_order_bot_of_pos Ordinal.outOrderBotOfPos
--/
 
 /- warning: ordinal.enum_zero_eq_bot -> Ordinal.enum_zero_eq_bot is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_eq_bot Ordinal.enum_zero_eq_botₓ'. -/
 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
     enum (· < ·) 0 (by rwa [type_lt]) =
@@ -1691,11 +1891,15 @@ def univ : Ordinal.{max (u + 1) v} :=
 #align ordinal.univ Ordinal.univ
 -/
 
-#print Ordinal.univ_id /-
+/- warning: ordinal.univ_id -> Ordinal.univ_id is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.univ_id Ordinal.univ_idₓ'. -/
 theorem univ_id : univ.{u, u + 1} = @type Ordinal (· < ·) _ :=
   lift_id _
 #align ordinal.univ_id Ordinal.univ_id
--/
 
 #print Ordinal.lift_univ /-
 @[simp]
@@ -1710,7 +1914,12 @@ theorem univ_umax : univ.{u, max (u + 1) v} = univ.{u, v} :=
 #align ordinal.univ_umax Ordinal.univ_umax
 -/
 
-#print Ordinal.lift.principalSeg /-
+/- warning: ordinal.lift.principal_seg -> Ordinal.lift.principalSeg is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg Ordinal.lift.principalSegₓ'. -/
 /-- Principal segment version of the lift operation on ordinals, embedding `ordinal.{u}` in
   `ordinal.{v}` as a principal segment when `u < v`. -/
 def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· < ·) (· < ·) :=
@@ -1743,13 +1952,12 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
       intro α r _
       exact lift_type_lt.{u, u + 1, max (u + 1) v}.2 ⟨typein.principal_seg r⟩⟩
 #align ordinal.lift.principal_seg Ordinal.lift.principalSeg
--/
 
 /- warning: ordinal.lift.principal_seg_coe -> Ordinal.lift.principalSeg_coe is a dubious translation:
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(fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641))) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14624 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : 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.Ordinal.Basic._hyg.14624 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14639 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641) Ordinal.lift.principalSeg.{u1, u2})) Ordinal.lift.{max (succ u1) u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg_coe Ordinal.lift.principalSeg_coeₓ'. -/
 @[simp]
 theorem lift.principalSeg_coe :
@@ -1764,11 +1972,15 @@ theorem lift.principalSeg_top : lift.principalSeg.top = univ :=
 #align ordinal.lift.principal_seg_top Ordinal.lift.principalSeg_top
 -/
 
-#print Ordinal.lift.principalSeg_top' /-
+/- warning: ordinal.lift.principal_seg_top' -> Ordinal.lift.principalSeg_top' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg_top' Ordinal.lift.principalSeg_top'ₓ'. -/
 theorem lift.principalSeg_top' : lift.principalSeg.{u, u + 1}.top = @type Ordinal (· < ·) _ := by
   simp only [lift.principal_seg_top, univ_id]
 #align ordinal.lift.principal_seg_top' Ordinal.lift.principalSeg_top'
--/
 
 end Ordinal
 
@@ -1823,13 +2035,22 @@ theorem ord_eq (α) : ∃ (r : α → α → Prop)(wo : IsWellOrder α r), ord (
 #align cardinal.ord_eq Cardinal.ord_eq
 -/
 
-#print Cardinal.ord_le_type /-
+/- warning: cardinal.ord_le_type -> Cardinal.ord_le_type is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [h : IsWellOrder.{u1} α r], LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r h)
+but is expected to have type
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [h : IsWellOrder.{u1} α r], LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r h)
+Case conversion may be inaccurate. Consider using '#align cardinal.ord_le_type Cardinal.ord_le_typeₓ'. -/
 theorem ord_le_type (r : α → α → Prop) [h : IsWellOrder α r] : ord (#α) ≤ type r :=
   ciInf_le' _ (Subtype.mk r h)
 #align cardinal.ord_le_type Cardinal.ord_le_type
--/
 
-#print Cardinal.ord_le /-
+/- warning: cardinal.ord_le -> Cardinal.ord_le is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{u1}} {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} c) o) (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} c (Ordinal.card.{u1} o))
+but is expected to have type
+  forall {c : Cardinal.{u1}} {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} c) o) (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} c (Ordinal.card.{u1} o))
+Case conversion may be inaccurate. Consider using '#align cardinal.ord_le Cardinal.ord_leₓ'. -/
 theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=
   inductionOn c fun α =>
     Ordinal.inductionOn o fun β s _ => by
@@ -1844,18 +2065,21 @@ theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=
         haveI := RelEmbedding.isWellOrder g
         exact le_trans (ord_le_type _) g.ordinal_type_le
 #align cardinal.ord_le Cardinal.ord_le
--/
 
 #print Cardinal.gc_ord_card /-
 theorem gc_ord_card : GaloisConnection ord card := fun _ _ => ord_le
 #align cardinal.gc_ord_card Cardinal.gc_ord_card
 -/
 
-#print Cardinal.lt_ord /-
+/- warning: cardinal.lt_ord -> Cardinal.lt_ord is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{u1}} {o : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Cardinal.ord.{u1} c)) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} o) c)
+but is expected to have type
+  forall {c : Cardinal.{u1}} {o : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Cardinal.ord.{u1} c)) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} o) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.lt_ord Cardinal.lt_ordₓ'. -/
 theorem lt_ord {c o} : o < ord c ↔ o.card < c :=
   gc_ord_card.lt_iff_lt
 #align cardinal.lt_ord Cardinal.lt_ord
--/
 
 #print Cardinal.card_ord /-
 @[simp]
@@ -1873,15 +2097,19 @@ def gciOrdCard : GaloisCoinsertion ord card :=
 #align cardinal.gci_ord_card Cardinal.gciOrdCard
 -/
 
-#print Cardinal.ord_card_le /-
+/- warning: cardinal.ord_card_le -> Cardinal.ord_card_le is a dubious translation:
+lean 3 declaration is
+  forall (o : Ordinal.{u1}), LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.card.{u1} o)) o
+but is expected to have type
+  forall (o : Ordinal.{u1}), LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Cardinal.ord.{u1} (Ordinal.card.{u1} o)) o
+Case conversion may be inaccurate. Consider using '#align cardinal.ord_card_le Cardinal.ord_card_leₓ'. -/
 theorem ord_card_le (o : Ordinal) : o.card.ord ≤ o :=
   gc_ord_card.l_u_le _
 #align cardinal.ord_card_le Cardinal.ord_card_le
--/
 
 /- warning: cardinal.lt_ord_succ_card -> Cardinal.lt_ord_succ_card is a dubious translation:
 lean 3 declaration is
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+  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 (Cardinal.ord.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.succOrder.{u1} (Ordinal.card.{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})) o (Cardinal.ord.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.instSuccOrderCardinalToPreorderPartialOrder.{u1} (Ordinal.card.{u1} o)))
 Case conversion may be inaccurate. Consider using '#align cardinal.lt_ord_succ_card Cardinal.lt_ord_succ_cardₓ'. -/
@@ -1903,19 +2131,27 @@ theorem ord_mono : Monotone ord :=
 #align cardinal.ord_mono Cardinal.ord_mono
 -/
 
-#print Cardinal.ord_le_ord /-
+/- warning: cardinal.ord_le_ord -> Cardinal.ord_le_ord is a dubious translation:
+lean 3 declaration is
+  forall {c₁ : Cardinal.{u1}} {c₂ : 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.ord.{u1} c₁) (Cardinal.ord.{u1} c₂)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} c₁ c₂)
+but is expected to have type
+  forall {c₁ : Cardinal.{u1}} {c₂ : 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.ord.{u1} c₁) (Cardinal.ord.{u1} c₂)) (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} c₁ c₂)
+Case conversion may be inaccurate. Consider using '#align cardinal.ord_le_ord Cardinal.ord_le_ordₓ'. -/
 @[simp]
 theorem ord_le_ord {c₁ c₂} : ord c₁ ≤ ord c₂ ↔ c₁ ≤ c₂ :=
   gciOrdCard.l_le_l_iff
 #align cardinal.ord_le_ord Cardinal.ord_le_ord
--/
 
-#print Cardinal.ord_lt_ord /-
+/- warning: cardinal.ord_lt_ord -> Cardinal.ord_lt_ord is a dubious translation:
+lean 3 declaration is
+  forall {c₁ : Cardinal.{u1}} {c₂ : 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.ord.{u1} c₁) (Cardinal.ord.{u1} c₂)) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c₁ c₂)
+but is expected to have type
+  forall {c₁ : Cardinal.{u1}} {c₂ : 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.ord.{u1} c₁) (Cardinal.ord.{u1} c₂)) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c₁ c₂)
+Case conversion may be inaccurate. Consider using '#align cardinal.ord_lt_ord Cardinal.ord_lt_ordₓ'. -/
 @[simp]
 theorem ord_lt_ord {c₁ c₂} : ord c₁ < ord c₂ ↔ c₁ < c₂ :=
   ord_strictMono.lt_iff_lt
 #align cardinal.ord_lt_ord Cardinal.ord_lt_ord
--/
 
 #print Cardinal.ord_zero /-
 @[simp]
@@ -1969,21 +2205,29 @@ theorem mk_ord_out (c : Cardinal) : (#c.ord.out.α) = c := by simp
 #align cardinal.mk_ord_out Cardinal.mk_ord_out
 -/
 
-#print Cardinal.card_typein_lt /-
+/- warning: cardinal.card_typein_lt -> Cardinal.card_typein_lt is a dubious translation:
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+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] (x : α), (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} (Ordinal.typein.{u1} α r _inst_1 x)) (Cardinal.mk.{u1} α))
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+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] (x : α), (Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (Ordinal.type.{u1} α r _inst_1)) -> (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} (Ordinal.typein.{u1} α r _inst_1 x)) (Cardinal.mk.{u1} α))
+Case conversion may be inaccurate. Consider using '#align cardinal.card_typein_lt Cardinal.card_typein_ltₓ'. -/
 theorem card_typein_lt (r : α → α → Prop) [IsWellOrder α r] (x : α) (h : ord (#α) = type r) :
     card (typein r x) < (#α) := by
   rw [← lt_ord, h]
   apply typein_lt_type
 #align cardinal.card_typein_lt Cardinal.card_typein_lt
--/
 
-#print Cardinal.card_typein_out_lt /-
+/- warning: cardinal.card_typein_out_lt -> Cardinal.card_typein_out_lt is a dubious translation:
+lean 3 declaration is
+  forall (c : Cardinal.{u1}) (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (Preorder.toHasLt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (Cardinal.ord.{u1} c))) (linearOrderOut.{u1} (Cardinal.ord.{u1} c)))))))) (isWellOrder_out_lt.{u1} (Cardinal.ord.{u1} c)) x)) c
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+Case conversion may be inaccurate. Consider using '#align cardinal.card_typein_out_lt Cardinal.card_typein_out_ltₓ'. -/
 theorem card_typein_out_lt (c : Cardinal) (x : c.ord.out.α) : card (typein (· < ·) x) < c :=
   by
   rw [← lt_ord]
   apply typein_lt_self
 #align cardinal.card_typein_out_lt Cardinal.card_typein_out_lt
--/
 
 #print Cardinal.ord_injective /-
 theorem ord_injective : Injective ord := by
@@ -1992,7 +2236,12 @@ theorem ord_injective : Injective ord := by
 #align cardinal.ord_injective Cardinal.ord_injective
 -/
 
-#print Cardinal.ord.orderEmbedding /-
+/- warning: cardinal.ord.order_embedding -> Cardinal.ord.orderEmbedding is a dubious translation:
+lean 3 declaration is
+  OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.hasLe.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align cardinal.ord.order_embedding Cardinal.ord.orderEmbeddingₓ'. -/
 /-- The ordinal corresponding to a cardinal `c` is the least ordinal
   whose cardinal is `c`. This is the order-embedding version. For the regular function, see `ord`.
 -/
@@ -2000,11 +2249,10 @@ def ord.orderEmbedding : Cardinal ↪o Ordinal :=
   RelEmbedding.orderEmbeddingOfLTEmbedding
     (RelEmbedding.ofMonotone Cardinal.ord fun a b => Cardinal.ord_lt_ord.2)
 #align cardinal.ord.order_embedding Cardinal.ord.orderEmbedding
--/
 
 /- warning: cardinal.ord.order_embedding_coe -> Cardinal.ord.orderEmbedding_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.ord.order_embedding_coe Cardinal.ord.orderEmbedding_coeₓ'. -/
@@ -2043,18 +2291,26 @@ theorem univ_umax : univ.{u, max (u + 1) v} = univ.{u, v} :=
 #align cardinal.univ_umax Cardinal.univ_umax
 -/
 
-#print Cardinal.lift_lt_univ /-
+/- warning: cardinal.lift_lt_univ -> Cardinal.lift_lt_univ is a dubious translation:
+lean 3 declaration is
+  forall (c : Cardinal.{u1}), LT.lt.{succ (succ u1)} Cardinal.{succ u1} (Preorder.toHasLt.{succ (succ u1)} Cardinal.{succ u1} (PartialOrder.toPreorder.{succ (succ u1)} Cardinal.{succ u1} Cardinal.partialOrder.{succ u1})) (Cardinal.lift.{succ u1, u1} c) Cardinal.univ.{u1, succ u1}
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align cardinal.lift_lt_univ Cardinal.lift_lt_univₓ'. -/
 theorem lift_lt_univ (c : Cardinal) : lift.{u + 1, u} c < univ.{u, u + 1} := by
   simpa only [lift.principal_seg_coe, lift_ord, lift_succ, ord_le, succ_le_iff] using
     le_of_lt (lift.principalSeg.{u, u + 1}.lt_top (succ c).ord)
 #align cardinal.lift_lt_univ Cardinal.lift_lt_univ
--/
 
-#print Cardinal.lift_lt_univ' /-
+/- warning: cardinal.lift_lt_univ' -> Cardinal.lift_lt_univ' is a dubious translation:
+lean 3 declaration is
+  forall (c : Cardinal.{u1}), LT.lt.{succ (max u1 (succ u1) u2)} Cardinal.{max u1 (succ u1) u2} (Preorder.toHasLt.{succ (max u1 (succ u1) u2)} Cardinal.{max u1 (succ u1) u2} (PartialOrder.toPreorder.{succ (max u1 (succ u1) u2)} Cardinal.{max u1 (succ u1) u2} Cardinal.partialOrder.{max u1 (succ u1) u2})) (Cardinal.lift.{max (succ u1) u2, u1} c) Cardinal.univ.{u1, u2}
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align cardinal.lift_lt_univ' Cardinal.lift_lt_univ'ₓ'. -/
 theorem lift_lt_univ' (c : Cardinal) : lift.{max (u + 1) v, u} c < univ.{u, v} := by
   simpa only [lift_lift, lift_univ, univ_umax] using lift_lt.{_, max (u + 1) v}.2 (lift_lt_univ c)
 #align cardinal.lift_lt_univ' Cardinal.lift_lt_univ'
--/
 
 #print Cardinal.ord_univ /-
 @[simp]
@@ -2071,7 +2327,12 @@ theorem ord_univ : ord univ.{u, v} = Ordinal.univ.{u, v} :=
 #align cardinal.ord_univ Cardinal.ord_univ
 -/
 
-#print Cardinal.lt_univ /-
+/- warning: cardinal.lt_univ -> Cardinal.lt_univ is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{succ u1}}, Iff (LT.lt.{succ (succ u1)} Cardinal.{succ u1} (Preorder.toHasLt.{succ (succ u1)} Cardinal.{succ u1} (PartialOrder.toPreorder.{succ (succ u1)} Cardinal.{succ u1} Cardinal.partialOrder.{succ u1})) c Cardinal.univ.{u1, succ u1}) (Exists.{succ (succ u1)} Cardinal.{u1} (fun (c' : Cardinal.{u1}) => Eq.{succ (succ (succ u1))} Cardinal.{succ u1} c (Cardinal.lift.{succ u1, u1} c')))
+but is expected to have type
+  forall {c : Cardinal.{succ u1}}, Iff (LT.lt.{succ (succ u1)} Cardinal.{succ u1} (Preorder.toLT.{succ (succ u1)} Cardinal.{succ u1} (PartialOrder.toPreorder.{succ (succ u1)} Cardinal.{succ u1} Cardinal.partialOrder.{succ u1})) c Cardinal.univ.{u1, succ u1}) (Exists.{succ (succ u1)} Cardinal.{u1} (fun (c' : Cardinal.{u1}) => Eq.{succ (succ (succ u1))} Cardinal.{succ u1} c (Cardinal.lift.{succ u1, u1} c')))
+Case conversion may be inaccurate. Consider using '#align cardinal.lt_univ Cardinal.lt_univₓ'. -/
 theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
   ⟨fun h => by
     have := ord_lt_ord.2 h
@@ -2081,9 +2342,13 @@ theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
     rw [← e, lift.principal_seg_coe, ← lift_card] at this
     exact ⟨_, this.symm⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ _⟩
 #align cardinal.lt_univ Cardinal.lt_univ
--/
 
-#print Cardinal.lt_univ' /-
+/- warning: cardinal.lt_univ' -> Cardinal.lt_univ' is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{max (succ u1) u2}}, Iff (LT.lt.{succ (max (succ u1) u2)} Cardinal.{max (succ u1) u2} (Preorder.toHasLt.{succ (max (succ u1) u2)} Cardinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Cardinal.{max (succ u1) u2} Cardinal.partialOrder.{max (succ u1) u2})) c Cardinal.univ.{u1, u2}) (Exists.{succ (succ u1)} Cardinal.{u1} (fun (c' : Cardinal.{u1}) => Eq.{succ (succ (max (succ u1) u2))} Cardinal.{max (succ u1) u2} c (Cardinal.lift.{max (succ u1) u2, u1} c')))
+but is expected to have type
+  forall {c : Cardinal.{max (succ u1) u2}}, Iff (LT.lt.{max (succ (succ u1)) (succ u2)} Cardinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Cardinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Cardinal.{max (succ u1) u2} Cardinal.partialOrder.{max (succ u1) u2})) c Cardinal.univ.{u1, u2}) (Exists.{succ (succ u1)} Cardinal.{u1} (fun (c' : Cardinal.{u1}) => Eq.{max (succ (succ (succ u1))) (succ (succ u2))} Cardinal.{max (succ u1) u2} c (Cardinal.lift.{max (succ u1) u2, u1} c')))
+Case conversion may be inaccurate. Consider using '#align cardinal.lt_univ' Cardinal.lt_univ'ₓ'. -/
 theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c' :=
   ⟨fun h => by
     let ⟨a, e, h'⟩ := lt_lift_iff.1 h
@@ -2091,9 +2356,13 @@ theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c
     rcases lt_univ.{u}.1 h' with ⟨c', rfl⟩
     exact ⟨c', by simp only [e.symm, lift_lift]⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ' _⟩
 #align cardinal.lt_univ' Cardinal.lt_univ'
--/
 
-#print Cardinal.small_iff_lift_mk_lt_univ /-
+/- warning: cardinal.small_iff_lift_mk_lt_univ -> Cardinal.small_iff_lift_mk_lt_univ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}}, Iff (Small.{u2, u1} α) (LT.lt.{succ (max u1 (succ u2))} Cardinal.{max u1 (succ u2)} (Preorder.toHasLt.{succ (max u1 (succ u2))} Cardinal.{max u1 (succ u2)} (PartialOrder.toPreorder.{succ (max u1 (succ u2))} Cardinal.{max u1 (succ u2)} Cardinal.partialOrder.{max u1 (succ u2)})) (Cardinal.lift.{succ u2, u1} (Cardinal.mk.{u1} α)) Cardinal.univ.{u2, max u1 (succ u2)})
+but is expected to have type
+  forall {α : Type.{u1}}, Iff (Small.{u2, u1} α) (LT.lt.{max (succ u1) (succ (succ u2))} Cardinal.{max u1 (succ u2)} (Preorder.toLT.{max (succ u1) (succ (succ u2))} Cardinal.{max u1 (succ u2)} (PartialOrder.toPreorder.{max (succ u1) (succ (succ u2))} Cardinal.{max u1 (succ u2)} Cardinal.partialOrder.{max u1 (succ u2)})) (Cardinal.lift.{succ u2, u1} (Cardinal.mk.{u1} α)) Cardinal.univ.{u2, max u1 (succ u2)})
+Case conversion may be inaccurate. Consider using '#align cardinal.small_iff_lift_mk_lt_univ Cardinal.small_iff_lift_mk_lt_univₓ'. -/
 theorem small_iff_lift_mk_lt_univ {α : Type u} :
     Small.{v} α ↔ Cardinal.lift (#α) < univ.{v, max u (v + 1)} :=
   by
@@ -2104,7 +2373,6 @@ theorem small_iff_lift_mk_lt_univ {α : Type u} :
   · rintro ⟨c, hc⟩
     exact ⟨⟨c.out, lift_mk_eq.{u, _, v + 1}.1 (hc.trans (congr rfl c.mk_out.symm))⟩⟩
 #align cardinal.small_iff_lift_mk_lt_univ Cardinal.small_iff_lift_mk_lt_univ
--/
 
 end Cardinal
 
@@ -2119,7 +2387,7 @@ theorem card_univ : card univ = Cardinal.univ :=
 
 /- warning: ordinal.nat_le_card -> Ordinal.nat_le_card is a dubious translation:
 lean 3 declaration is
-  forall {o : Ordinal.{u1}} {n : Nat}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} ((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) (Ordinal.card.{u1} o)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Ordinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Ordinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Ordinal.{u1} (Nat.castCoe.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1})))) n) o)
+  forall {o : Ordinal.{u1}} {n : Nat}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} ((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) (Ordinal.card.{u1} o)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Ordinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Ordinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Ordinal.{u1} (Nat.castCoe.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1})))) n) o)
 but is expected to have type
   forall {o : Ordinal.{u1}} {n : Nat}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) (Ordinal.card.{u1} o)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Nat.cast.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1}) n) o)
 Case conversion may be inaccurate. Consider using '#align ordinal.nat_le_card Ordinal.nat_le_cardₓ'. -/
@@ -2130,7 +2398,7 @@ theorem nat_le_card {o} {n : ℕ} : (n : Cardinal) ≤ card o ↔ (n : Ordinal)
 
 /- warning: ordinal.nat_lt_card -> Ordinal.nat_lt_card is a dubious translation:
 lean 3 declaration is
-  forall {o : Ordinal.{u1}} {n : Nat}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) ((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) (Ordinal.card.{u1} o)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Ordinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Ordinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Ordinal.{u1} (Nat.castCoe.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1})))) n) o)
+  forall {o : Ordinal.{u1}} {n : Nat}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) ((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) (Ordinal.card.{u1} o)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Ordinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Ordinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Ordinal.{u1} (Nat.castCoe.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1})))) n) o)
 but is expected to have type
   forall {o : Ordinal.{u1}} {n : Nat}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) (Ordinal.card.{u1} o)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Nat.cast.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1}) n) o)
 Case conversion may be inaccurate. Consider using '#align ordinal.nat_lt_card Ordinal.nat_lt_cardₓ'. -/
@@ -2143,7 +2411,7 @@ theorem nat_lt_card {o} {n : ℕ} : (n : Cardinal) < card o ↔ (n : Ordinal) <
 
 /- warning: ordinal.card_lt_nat -> Ordinal.card_lt_nat is a dubious translation:
 lean 3 declaration is
-  forall {o : Ordinal.{u1}} {n : Nat}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} o) ((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)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Ordinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Ordinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Ordinal.{u1} (Nat.castCoe.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1})))) n))
+  forall {o : Ordinal.{u1}} {n : Nat}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} o) ((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)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Ordinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Ordinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Ordinal.{u1} (Nat.castCoe.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1})))) n))
 but is expected to have type
   forall {o : Ordinal.{u1}} {n : Nat}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} o) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Nat.cast.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1}) n))
 Case conversion may be inaccurate. Consider using '#align ordinal.card_lt_nat Ordinal.card_lt_natₓ'. -/
@@ -2154,7 +2422,7 @@ theorem card_lt_nat {o} {n : ℕ} : card o < n ↔ o < n :=
 
 /- warning: ordinal.card_le_nat -> Ordinal.card_le_nat is a dubious translation:
 lean 3 declaration is
-  forall {o : Ordinal.{u1}} {n : Nat}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Ordinal.card.{u1} o) ((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)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Ordinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Ordinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Ordinal.{u1} (Nat.castCoe.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1})))) n))
+  forall {o : Ordinal.{u1}} {n : Nat}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Ordinal.card.{u1} o) ((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)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Ordinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Ordinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Ordinal.{u1} (Nat.castCoe.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1})))) n))
 but is expected to have type
   forall {o : Ordinal.{u1}} {n : Nat}, Iff (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Ordinal.card.{u1} o) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Nat.cast.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1}) n))
 Case conversion may be inaccurate. Consider using '#align ordinal.card_le_nat Ordinal.card_le_natₓ'. -/

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

@@ -1341,16 +1341,16 @@ theorem max_eq_zero {a b : Ordinal} : max a b = 0 ↔ a = 0 ∧ b = 0 :=
   max_eq_bot
 #align ordinal.max_eq_zero Ordinal.max_eq_zero
 
-/- warning: ordinal.Inf_empty -> Ordinal.infₛ_empty is a dubious translation:
+/- warning: ordinal.Inf_empty -> Ordinal.sInf_empty is a dubious translation:
 lean 3 declaration is
-  Eq.{succ (succ u1)} Ordinal.{u1} (InfSet.infₛ.{succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toHasInf.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.conditionallyCompleteLinearOrderBot.{u1}))) (EmptyCollection.emptyCollection.{succ u1} (Set.{succ u1} Ordinal.{u1}) (Set.hasEmptyc.{succ u1} Ordinal.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
+  Eq.{succ (succ u1)} Ordinal.{u1} (InfSet.sInf.{succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toHasInf.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.conditionallyCompleteLinearOrderBot.{u1}))) (EmptyCollection.emptyCollection.{succ u1} (Set.{succ u1} Ordinal.{u1}) (Set.hasEmptyc.{succ u1} Ordinal.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
 but is expected to have type
-  Eq.{succ (succ u1)} Ordinal.{u1} (InfSet.infₛ.{succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toInfSet.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1}))) (EmptyCollection.emptyCollection.{succ u1} (Set.{succ u1} Ordinal.{u1}) (Set.instEmptyCollectionSet.{succ u1} Ordinal.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
-Case conversion may be inaccurate. Consider using '#align ordinal.Inf_empty Ordinal.infₛ_emptyₓ'. -/
+  Eq.{succ (succ u1)} Ordinal.{u1} (InfSet.sInf.{succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toInfSet.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1}))) (EmptyCollection.emptyCollection.{succ u1} (Set.{succ u1} Ordinal.{u1}) (Set.instEmptyCollectionSet.{succ u1} Ordinal.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
+Case conversion may be inaccurate. Consider using '#align ordinal.Inf_empty Ordinal.sInf_emptyₓ'. -/
 @[simp]
-theorem infₛ_empty : infₛ (∅ : Set Ordinal) = 0 :=
+theorem sInf_empty : sInf (∅ : Set Ordinal) = 0 :=
   dif_neg not_nonempty_empty
-#align ordinal.Inf_empty Ordinal.infₛ_empty
+#align ordinal.Inf_empty Ordinal.sInf_empty
 
 -- ### Successor order properties
 private theorem succ_le_iff' {a b : Ordinal} : a + 1 ≤ b ↔ a < b :=
@@ -1796,10 +1796,10 @@ def ord (c : Cardinal) : Ordinal :=
       suffices : ∀ {α β}, α ≈ β → F α ≤ F β
       exact fun α β h => (this h).antisymm (this (Setoid.symm h))
       rintro α β ⟨f⟩
-      refine' le_cinfᵢ_iff'.2 fun i => _
+      refine' le_ciInf_iff'.2 fun i => _
       haveI := @RelEmbedding.isWellOrder _ _ (f ⁻¹'o i.1) _ (↑(RelIso.preimage f i.1)) i.2
       exact
-        (cinfᵢ_le' _
+        (ciInf_le' _
               (Subtype.mk (⇑f ⁻¹'o i.val)
                 (@RelEmbedding.isWellOrder _ _ _ _ (↑(RelIso.preimage f i.1)) i.2))).trans_eq
           (Quot.sound ⟨RelIso.preimage f i.1⟩))
@@ -1808,9 +1808,9 @@ def ord (c : Cardinal) : Ordinal :=
 
 /- warning: cardinal.ord_eq_Inf -> Cardinal.ord_eq_Inf is a dubious translation:
 lean 3 declaration is
-  forall (α : Type.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (infᵢ.{succ u1, succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toHasInf.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.conditionallyCompleteLinearOrderBot.{u1}))) (Subtype.{succ u1} (α -> α -> Prop) (fun (r : α -> α -> Prop) => IsWellOrder.{u1} α r)) (fun (r : Subtype.{succ u1} (α -> α -> Prop) (fun (r : α -> α -> Prop) => IsWellOrder.{u1} α r)) => Ordinal.type.{u1} α (Subtype.val.{succ u1} (α -> α -> Prop) (fun (r : α -> α -> Prop) => IsWellOrder.{u1} α r) r) (Subtype.property.{succ u1} (α -> α -> Prop) (fun (r : α -> α -> Prop) => IsWellOrder.{u1} α r) r)))
+  forall (α : Type.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (iInf.{succ u1, succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toHasInf.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.conditionallyCompleteLinearOrderBot.{u1}))) (Subtype.{succ u1} (α -> α -> Prop) (fun (r : α -> α -> Prop) => IsWellOrder.{u1} α r)) (fun (r : Subtype.{succ u1} (α -> α -> Prop) (fun (r : α -> α -> Prop) => IsWellOrder.{u1} α r)) => Ordinal.type.{u1} α (Subtype.val.{succ u1} (α -> α -> Prop) (fun (r : α -> α -> Prop) => IsWellOrder.{u1} α r) r) (Subtype.property.{succ u1} (α -> α -> Prop) (fun (r : α -> α -> Prop) => IsWellOrder.{u1} α r) r)))
 but is expected to have type
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+  forall (α : Type.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (Cardinal.mk.{u1} α)) (iInf.{succ u1, succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toInfSet.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1}))) (Subtype.{succ u1} (α -> α -> Prop) (fun (r : α -> α -> Prop) => IsWellOrder.{u1} α r)) (fun (r : Subtype.{succ u1} (α -> α -> Prop) (fun (r : α -> α -> Prop) => IsWellOrder.{u1} α r)) => Ordinal.type.{u1} α (Subtype.val.{succ u1} (α -> α -> Prop) (fun (r : α -> α -> Prop) => IsWellOrder.{u1} α r) r) (Subtype.property.{succ u1} (α -> α -> Prop) (fun (r : α -> α -> Prop) => IsWellOrder.{u1} α r) r)))
 Case conversion may be inaccurate. Consider using '#align cardinal.ord_eq_Inf Cardinal.ord_eq_Infₓ'. -/
 theorem ord_eq_Inf (α : Type u) : ord (#α) = ⨅ r : { r // IsWellOrder α r }, @type α r.1 r.2 :=
   rfl
@@ -1818,14 +1818,14 @@ theorem ord_eq_Inf (α : Type u) : ord (#α) = ⨅ r : { r // IsWellOrder α r }
 
 #print Cardinal.ord_eq /-
 theorem ord_eq (α) : ∃ (r : α → α → Prop)(wo : IsWellOrder α r), ord (#α) = @type α r wo :=
-  let ⟨r, wo⟩ := cinfᵢ_mem fun r : { r // IsWellOrder α r } => @type α r.1 r.2
+  let ⟨r, wo⟩ := ciInf_mem fun r : { r // IsWellOrder α r } => @type α r.1 r.2
   ⟨r.1, r.2, wo.symm⟩
 #align cardinal.ord_eq Cardinal.ord_eq
 -/
 
 #print Cardinal.ord_le_type /-
 theorem ord_le_type (r : α → α → Prop) [h : IsWellOrder α r] : ord (#α) ≤ type r :=
-  cinfᵢ_le' _ (Subtype.mk r h)
+  ciInf_le' _ (Subtype.mk r h)
 #align cardinal.ord_le_type Cardinal.ord_le_type
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -722,7 +722,7 @@ theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β 
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} β (coeFn.{succ u1, succ u1} (RelIso.{u1, u1} α β r s) (fun (_x : RelIso.{u1, u1} α β r s) => α -> β) (RelIso.hasCoeToFun.{u1, u1} α β r s) f (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) ((fun [self : LT.{succ u1} Ordinal.{u1}] (ᾰ : Ordinal.{u1}) (ᾰ_1 : Ordinal.{u1}) (e_2 : Eq.{succ (succ u1)} Ordinal.{u1} ᾰ ᾰ_1) (ᾰ_2 : Ordinal.{u1}) (ᾰ_3 : Ordinal.{u1}) (e_3 : Eq.{succ (succ u1)} Ordinal.{u1} ᾰ_2 ᾰ_3) => congr.{succ (succ u1), 1} Ordinal.{u1} Prop (LT.lt.{succ u1} Ordinal.{u1} self ᾰ) (LT.lt.{succ u1} Ordinal.{u1} self ᾰ_1) ᾰ_2 ᾰ_3 (congr_arg.{succ (succ u1), succ (succ u1)} Ordinal.{u1} (Ordinal.{u1} -> Prop) ᾰ ᾰ_1 (LT.lt.{succ u1} Ordinal.{u1} self) e_2) e_3) (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o (rfl.{succ (succ u1)} Ordinal.{u1} o) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f)))) hr))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} β (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} α β r s) α (fun (_x : α) => β) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} α β r s) α β r s (RelIso.instRelHomClassRelIso.{u1, u1} α β r s)) f (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} 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+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} β (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} α β r s) α (fun (_x : α) => β) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} α β r s) α β r s (RelIso.instRelHomClassRelIso.{u1, u1} α β r s)) f (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} 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(Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015)) -> (HEq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a._@.Init.Prelude._hyg.2015) Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a'._@.Init.Prelude.2015.Mathlib.SetTheory.Ordinal.Basic._hyg.5688))) (fun (e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5689 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) (h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 : HEq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5689 (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015)) => Eq.ndrec.{0, 0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015) (fun 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a._@.Init.Prelude._hyg.2015 h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5690) e'_4) (Eq.refl.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2015) (HEq.refl.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude._hyg.2015) e'_4)) Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f))))) hr))
 Case conversion may be inaccurate. Consider using '#align ordinal.rel_iso_enum Ordinal.relIso_enumₓ'. -/
 theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) (hr : o < type r) :
@@ -778,7 +778,7 @@ def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r
 lean 3 declaration is
   forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} ((fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (coeFn.{succ (succ u1), succ (succ u1)} (PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (PrincipalSeg.hasCoeToFun.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (Ordinal.typein.{u1} α r _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (RelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Ordinal.{u1}) _x) (RelHomClass.toFunLike.{succ u1, u1, succ u1} (RelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005)) α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005) (RelEmbedding.instRelHomClassRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005))) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005) (Ordinal.typein.principalSeg.{u1} α r _inst_1))) (Ordinal.typein.{u1} α r _inst_1)
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (RelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Ordinal.{u1}) _x) (RelHomClass.toFunLike.{succ u1, u1, succ u1} (RelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003)) α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003) (RelEmbedding.instRelHomClassRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003))) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6001 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : 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.Ordinal.Basic._hyg.6001 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003) (Ordinal.typein.principalSeg.{u1} α r _inst_1))) (Ordinal.typein.{u1} α r _inst_1)
 Case conversion may be inaccurate. Consider using '#align ordinal.typein.principal_seg_coe Ordinal.typein.principalSeg_coeₓ'. -/
 @[simp]
 theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
@@ -1115,7 +1115,7 @@ def lift.initialSeg : @InitialSeg Ordinal.{u} Ordinal.{max u v} (· < ·) (· <
 lean 3 declaration is
   Eq.{max (succ (succ u1)) (succ (succ (max u1 u2)))} ((fun (_x : InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) => Ordinal.{u1} -> Ordinal.{max u1 u2}) Ordinal.lift.initialSeg.{u1, u2}) (coeFn.{max (succ (succ u1)) (succ (succ (max u1 u2))), max (succ (succ u1)) (succ (succ (max u1 u2)))} (InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) (fun (_x : InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) => Ordinal.{u1} -> Ordinal.{max u1 u2}) (FunLike.hasCoeToFun.{max (succ (succ u1)) (succ (succ (max u1 u2))), succ (succ u1), succ (succ (max u1 u2))} (InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => Ordinal.{max u1 u2}) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (succ (max u1 u2))), succ (succ u1), succ (succ (max u1 u2))} (InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) Ordinal.{u1} Ordinal.{max u1 u2} (InitialSeg.embeddingLike.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))))) Ordinal.lift.initialSeg.{u1, u2}) Ordinal.lift.{u2, u1}
 but is expected to have type
-  Eq.{max (succ (succ u1)) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8589 : 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.Ordinal.Basic._hyg.8587 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8589) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8604 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8604)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8589 : 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.Ordinal.Basic._hyg.8587 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8589) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8604 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8604)) Ordinal.{u1} Ordinal.{max u1 u2} (InitialSeg.instEmbeddingLikeInitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8589 : 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.Ordinal.Basic._hyg.8587 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8589) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8604 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8604))) Ordinal.lift.initialSeg.{u1, u2}) Ordinal.lift.{u2, u1}
+  Eq.{max (succ (succ u1)) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8585 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587 : 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.Ordinal.Basic._hyg.8585 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8600 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8600 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8585 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587 : 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.Ordinal.Basic._hyg.8585 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8600 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8600 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602)) Ordinal.{u1} Ordinal.{max u1 u2} (InitialSeg.instEmbeddingLikeInitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8585 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587 : 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.Ordinal.Basic._hyg.8585 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8600 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8600 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602))) Ordinal.lift.initialSeg.{u1, u2}) Ordinal.lift.{u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.initial_seg_coe Ordinal.lift.initialSeg_coeₓ'. -/
 @[simp]
 theorem lift.initialSeg_coe : (lift.initialSeg : Ordinal → Ordinal) = lift :=
@@ -1529,7 +1529,7 @@ instance uniqueOutOne : Unique (1 : Ordinal).out.α
 lean 3 declaration is
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 but is expected to have type
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Ordinal.zero.{u1} Ordinal.one.{u1} Ordinal.partialOrder.{u1} Ordinal.zeroLEOneClass.{u1} Ordinal.NeZero.one.{u1}))))
 Case conversion may be inaccurate. Consider using '#align ordinal.one_out_eq Ordinal.one_out_eqₓ'. -/
 theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :=
   Unique.eq_default x
@@ -1542,7 +1542,7 @@ theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :
 lean 3 declaration is
   forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))))))))) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
 but is expected to have type
-  forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12913 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12915 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12913 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12915) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
+  forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12911 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12913 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12911 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12913) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.typein_one_out Ordinal.typein_one_outₓ'. -/
 @[simp]
 theorem typein_one_out (x : (1 : Ordinal).out.α) : typein (· < ·) x = 0 := by
@@ -1669,7 +1669,7 @@ def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α :=
 lean 3 declaration is
   forall {o : Ordinal.{u1}} (ho : 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), Eq.{succ u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (Eq.mpr.{0} (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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)) (Eq.ndrec.{0, succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o)) (fun (_a : Ordinal.{u1}) => Eq.{1} Prop (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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}))) _a)) (rfl.{1} Prop (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o)))) o (Ordinal.type_lt.{u1} o))) ho)) (Bot.bot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (OrderBot.toHasBot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o)))))) (Ordinal.outOrderBotOfPos.{u1} o ho)))
 but is expected to have type
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(Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14385 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14387) (isWellOrder_out_lt.{u1} o)))) o (Ordinal.type_lt.{u1} o))) ho)) (Bot.bot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (OrderBot.toBot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (Ordinal.outOrderBotOfPos.{u1} o ho)))
 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_eq_bot Ordinal.enum_zero_eq_botₓ'. -/
 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
     enum (· < ·) 0 (by rwa [type_lt]) =
@@ -1749,7 +1749,7 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
 lean 3 declaration is
   Eq.{max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} ((fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) Ordinal.lift.principalSeg.{u1, u2}) (coeFn.{max (succ (succ u1)) (succ (succ (max (succ u1) u2))), max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} (PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) (fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) (PrincipalSeg.hasCoeToFun.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) Ordinal.lift.principalSeg.{u1, u2}) Ordinal.lift.{max (succ u1) u2, u1}
 but is expected to have type
-  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (RelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max 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x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647)) Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647))) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647) Ordinal.lift.principalSeg.{u1, u2})) Ordinal.lift.{max (succ u1) u2, u1}
+  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (RelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14628 : 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.Ordinal.Basic._hyg.14626 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14628) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14643 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14643)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (RelHomClass.toFunLike.{max (succ u1) (succ (succ u1)) (succ u2), succ u1, max (succ (succ u1)) (succ u2)} (RelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14628 : 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.Ordinal.Basic._hyg.14626 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14628) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14643 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14643)) Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14628 : 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.Ordinal.Basic._hyg.14626 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14628) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14643 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14643) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14628 : 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.Ordinal.Basic._hyg.14626 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14628) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14643 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14643))) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14626 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14628 : 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.Ordinal.Basic._hyg.14626 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14628) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14643 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14641 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14643) Ordinal.lift.principalSeg.{u1, u2})) Ordinal.lift.{max (succ u1) u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg_coe Ordinal.lift.principalSeg_coeₓ'. -/
 @[simp]
 theorem lift.principalSeg_coe :

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b8ba04e2f326f3f7cf24ad129beda58531ada61

@@ -2006,7 +2006,7 @@ def ord.orderEmbedding : Cardinal ↪o Ordinal :=
 lean 3 declaration is
   Eq.{succ (succ u1)} ((fun (_x : RelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1}) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.ord.orderEmbedding.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.hasLe.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (fun (_x : RelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1}) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (RelEmbedding.hasCoeToFun.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1}) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.ord.orderEmbedding.{u1}) Cardinal.ord.{u1}
 but is expected to have type
-  Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Cardinal.{u1}) => Ordinal.{u1}) _x) (RelHomClass.toFunLike.{succ u1, succ u1, succ u1} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Cardinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Cardinal.{u1}) => LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Ordinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Ordinal.{u1}) => LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Cardinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Cardinal.{u1}) => LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Ordinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Ordinal.{u1}) => LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) Cardinal.ord.orderEmbedding.{u1}) Cardinal.ord.{u1}
+  Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Order.Hom.Lattice._hyg.494 : Cardinal.{u1}) => Ordinal.{u1}) _x) (InfHomClass.toFunLike.{succ u1, succ u1, succ u1} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} Ordinal.{u1} (Lattice.toInf.{succ u1} Cardinal.{u1} (DistribLattice.toLattice.{succ u1} Cardinal.{u1} (instDistribLattice.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1}))) (Lattice.toInf.{succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1})))) (LatticeHomClass.toInfHomClass.{succ u1, succ u1, succ u1} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} Ordinal.{u1} (DistribLattice.toLattice.{succ u1} Cardinal.{u1} (instDistribLattice.{succ u1} Cardinal.{u1} Cardinal.linearOrder.{u1})) (ConditionallyCompleteLattice.toLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1}))) (OrderHomClass.toLatticeHomClass.{succ u1, succ u1, succ u1} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} Ordinal.{u1} Cardinal.linearOrder.{u1} (ConditionallyCompleteLattice.toLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1}))) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Cardinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Cardinal.{u1}) => LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Ordinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Ordinal.{u1}) => LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))))) Cardinal.ord.orderEmbedding.{u1}) Cardinal.ord.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.ord.order_embedding_coe Cardinal.ord.orderEmbedding_coeₓ'. -/
 @[simp]
 theorem ord.orderEmbedding_coe : (ord.orderEmbedding : Cardinal → Ordinal) = ord :=

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

@@ -708,7 +708,7 @@ theorem enum_lt_enum {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Or
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) (hs : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)), Eq.{succ u1} β (coeFn.{succ u1, succ u1} (RelIso.{u1, u1} α β r s) (fun (_x : RelIso.{u1, u1} α β r s) => α -> β) (RelIso.hasCoeToFun.{u1, u1} α β r s) f (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o hs)
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) (hs : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (Ordinal.enum.{u1} α r _inst_1 o hr)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} α β)) (RelEmbedding.toEmbedding.{u1, u1} α β r s (RelIso.toRelEmbedding.{u1, u1} α β r s f)) (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o hs)
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) (hs : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)), Eq.{succ u1} β (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} α β r s) α (fun (_x : α) => β) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} α β r s) α β r s (RelIso.instRelHomClassRelIso.{u1, u1} α β r s)) f (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o hs)
 Case conversion may be inaccurate. Consider using '#align ordinal.rel_iso_enum' Ordinal.relIso_enum'ₓ'. -/
 theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) :
@@ -722,7 +722,7 @@ theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β 
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} β (coeFn.{succ u1, succ u1} (RelIso.{u1, u1} α β r s) (fun (_x : RelIso.{u1, u1} α β r s) => α -> β) (RelIso.hasCoeToFun.{u1, u1} α β r s) f (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) ((fun [self : LT.{succ u1} Ordinal.{u1}] (ᾰ : Ordinal.{u1}) (ᾰ_1 : Ordinal.{u1}) (e_2 : Eq.{succ (succ u1)} Ordinal.{u1} ᾰ ᾰ_1) (ᾰ_2 : Ordinal.{u1}) (ᾰ_3 : Ordinal.{u1}) (e_3 : Eq.{succ (succ u1)} Ordinal.{u1} ᾰ_2 ᾰ_3) => congr.{succ (succ u1), 1} Ordinal.{u1} Prop (LT.lt.{succ u1} Ordinal.{u1} self ᾰ) (LT.lt.{succ u1} Ordinal.{u1} self ᾰ_1) ᾰ_2 ᾰ_3 (congr_arg.{succ (succ u1), succ (succ u1)} Ordinal.{u1} (Ordinal.{u1} -> Prop) ᾰ ᾰ_1 (LT.lt.{succ u1} Ordinal.{u1} self) e_2) e_3) (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o (rfl.{succ (succ u1)} Ordinal.{u1} o) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f)))) hr))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (Ordinal.enum.{u1} α r _inst_1 o hr)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} α β)) (RelEmbedding.toEmbedding.{u1, u1} α β r s (RelIso.toRelEmbedding.{u1, u1} α β r s f)) (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) (eq_of_heq.{1} Prop (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) ((fun (α : Type.{succ u1}) (self : LT.{succ u1} α) (a._@.Init.Prelude._hyg.2013 : α) (a._@.Init.Prelude._hyg.2015 : α) (a'._@.Init.Prelude._hyg.2015 : α) (e'_4 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude._hyg.2015) => Eq.casesOn.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2015 (fun (a._@.Init.Prelude._hyg.170 : α) (x : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.170) => (Eq.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.170) -> (HEq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude._hyg.2015) e'_4 (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.170) x) -> (HEq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a._@.Init.Prelude._hyg.2015) Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a'._@.Init.Prelude._hyg.2015))) a'._@.Init.Prelude._hyg.2015 e'_4 (fun (h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5692 : Eq.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) => Eq.ndrec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2015 (fun (a'._@.Init.Prelude.2015.Mathlib.SetTheory.Ordinal.Basic._hyg.5690 : α) => forall (e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude.2015.Mathlib.SetTheory.Ordinal.Basic._hyg.5690), (HEq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude.2015.Mathlib.SetTheory.Ordinal.Basic._hyg.5690) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015)) -> (HEq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a._@.Init.Prelude._hyg.2015) Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a'._@.Init.Prelude.2015.Mathlib.SetTheory.Ordinal.Basic._hyg.5690))) (fun (e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) (h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5693 : HEq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015)) => Eq.ndrec.{0, 0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015) (fun (e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) => HEq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a._@.Init.Prelude._hyg.2015) Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a._@.Init.Prelude._hyg.2015)) (HEq.refl.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a._@.Init.Prelude._hyg.2015)) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.symm.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015) (eq_of_heq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015) h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5693))) a'._@.Init.Prelude._hyg.2015 (Eq.symm.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015 h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5692) e'_4) (Eq.refl.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2015) (HEq.refl.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude._hyg.2015) e'_4)) Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f))))) hr))
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} β (FunLike.coe.{succ u1, succ u1, succ u1} (RelIso.{u1, u1} α β r s) α (fun (_x : α) => β) (RelHomClass.toFunLike.{u1, u1, u1} (RelIso.{u1, u1} α β r s) α β r s (RelIso.instRelHomClassRelIso.{u1, u1} α β r s)) f (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) (eq_of_heq.{1} Prop (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) ((fun (α : Type.{succ u1}) (self : LT.{succ u1} α) (a._@.Init.Prelude._hyg.2013 : α) (a._@.Init.Prelude._hyg.2015 : α) (a'._@.Init.Prelude._hyg.2015 : α) (e'_4 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude._hyg.2015) => Eq.casesOn.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2015 (fun (a._@.Init.Prelude._hyg.170 : α) (x : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.170) => (Eq.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.170) -> (HEq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude._hyg.2015) e'_4 (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.170) x) -> (HEq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a._@.Init.Prelude._hyg.2015) Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a'._@.Init.Prelude._hyg.2015))) a'._@.Init.Prelude._hyg.2015 e'_4 (fun (h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5692 : Eq.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) => Eq.ndrec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2015 (fun (a'._@.Init.Prelude.2015.Mathlib.SetTheory.Ordinal.Basic._hyg.5690 : α) => forall (e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude.2015.Mathlib.SetTheory.Ordinal.Basic._hyg.5690), (HEq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude.2015.Mathlib.SetTheory.Ordinal.Basic._hyg.5690) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015)) -> (HEq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a._@.Init.Prelude._hyg.2015) Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a'._@.Init.Prelude.2015.Mathlib.SetTheory.Ordinal.Basic._hyg.5690))) (fun (e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) (h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5693 : HEq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015)) => Eq.ndrec.{0, 0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015) (fun (e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) => HEq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a._@.Init.Prelude._hyg.2015) Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a._@.Init.Prelude._hyg.2015)) (HEq.refl.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2013 a._@.Init.Prelude._hyg.2015)) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.symm.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015) (eq_of_heq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015) h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5693))) a'._@.Init.Prelude._hyg.2015 (Eq.symm.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015 h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5692) e'_4) (Eq.refl.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2015) (HEq.refl.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude._hyg.2015) e'_4)) Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f))))) hr))
 Case conversion may be inaccurate. Consider using '#align ordinal.rel_iso_enum Ordinal.relIso_enumₓ'. -/
 theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) (hr : o < type r) :
@@ -778,7 +778,7 @@ def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r
 lean 3 declaration is
   forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} ((fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (coeFn.{succ (succ u1), succ (succ u1)} (PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (PrincipalSeg.hasCoeToFun.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (Ordinal.typein.{u1} α r _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ u1, succ (succ u1)} α Ordinal.{u1})) (RelEmbedding.toEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005) (Ordinal.typein.principalSeg.{u1} α r _inst_1)))) (Ordinal.typein.{u1} α r _inst_1)
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (RelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005)) α (fun (_x : α) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : α) => Ordinal.{u1}) _x) (RelHomClass.toFunLike.{succ u1, u1, succ u1} (RelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005)) α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005) (RelEmbedding.instRelHomClassRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005))) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005) (Ordinal.typein.principalSeg.{u1} α r _inst_1))) (Ordinal.typein.{u1} α r _inst_1)
 Case conversion may be inaccurate. Consider using '#align ordinal.typein.principal_seg_coe Ordinal.typein.principalSeg_coeₓ'. -/
 @[simp]
 theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
@@ -1749,7 +1749,7 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
 lean 3 declaration is
   Eq.{max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} ((fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) Ordinal.lift.principalSeg.{u1, u2}) (coeFn.{max (succ (succ u1)) (succ (succ (max (succ u1) u2))), max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} (PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) (fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) (PrincipalSeg.hasCoeToFun.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) Ordinal.lift.principalSeg.{u1, u2}) Ordinal.lift.{max (succ u1) u2, u1}
 but is expected to have type
-  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} Ordinal.{max (succ u1) u2} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2})) (RelEmbedding.toEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647) Ordinal.lift.principalSeg.{u1, u2}))) Ordinal.lift.{max (succ u1) u2, u1}
+  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (RelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (RelHomClass.toFunLike.{max (succ u1) (succ (succ u1)) (succ u2), succ u1, max (succ (succ u1)) (succ u2)} (RelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647)) Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647))) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647) Ordinal.lift.principalSeg.{u1, u2})) Ordinal.lift.{max (succ u1) u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg_coe Ordinal.lift.principalSeg_coeₓ'. -/
 @[simp]
 theorem lift.principalSeg_coe :
@@ -2006,7 +2006,7 @@ def ord.orderEmbedding : Cardinal ↪o Ordinal :=
 lean 3 declaration is
   Eq.{succ (succ u1)} ((fun (_x : RelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1}) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) Cardinal.ord.orderEmbedding.{u1}) (coeFn.{succ (succ u1), succ (succ u1)} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.hasLe.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (fun (_x : RelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1}) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => Cardinal.{u1} -> Ordinal.{u1}) (RelEmbedding.hasCoeToFun.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1}) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) Cardinal.ord.orderEmbedding.{u1}) Cardinal.ord.{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.Order.Hom.Basic._hyg.680 : Cardinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Cardinal.{u1}) => LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Ordinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Ordinal.{u1}) => LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) Cardinal.ord.orderEmbedding.{u1})) Cardinal.ord.{u1}
+  Eq.{succ (succ u1)} (forall (a : Cardinal.{u1}), (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Cardinal.{u1}) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ (succ u1), succ (succ u1)} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : Cardinal.{u1}) => Ordinal.{u1}) _x) (RelHomClass.toFunLike.{succ u1, succ u1, succ u1} (OrderEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} Cardinal.instLECardinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Cardinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Cardinal.{u1}) => LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Ordinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Ordinal.{u1}) => LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{succ u1, succ u1} Cardinal.{u1} Ordinal.{u1} (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : Cardinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : Cardinal.{u1}) => LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Ordinal.{u1}) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Ordinal.{u1}) => LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) Cardinal.ord.orderEmbedding.{u1}) Cardinal.ord.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.ord.order_embedding_coe Cardinal.ord.orderEmbedding_coeₓ'. -/
 @[simp]
 theorem ord.orderEmbedding_coe : (ord.orderEmbedding : Cardinal → Ordinal) = ord :=

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

@@ -722,7 +722,7 @@ theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β 
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} β (coeFn.{succ u1, succ u1} (RelIso.{u1, u1} α β r s) (fun (_x : RelIso.{u1, u1} α β r s) => α -> β) (RelIso.hasCoeToFun.{u1, u1} α β r s) f (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) ((fun [self : LT.{succ u1} Ordinal.{u1}] (ᾰ : Ordinal.{u1}) (ᾰ_1 : Ordinal.{u1}) (e_2 : Eq.{succ (succ u1)} Ordinal.{u1} ᾰ ᾰ_1) (ᾰ_2 : Ordinal.{u1}) (ᾰ_3 : Ordinal.{u1}) (e_3 : Eq.{succ (succ u1)} Ordinal.{u1} ᾰ_2 ᾰ_3) => congr.{succ (succ u1), 1} Ordinal.{u1} Prop (LT.lt.{succ u1} Ordinal.{u1} self ᾰ) (LT.lt.{succ u1} Ordinal.{u1} self ᾰ_1) ᾰ_2 ᾰ_3 (congr_arg.{succ (succ u1), succ (succ u1)} Ordinal.{u1} (Ordinal.{u1} -> Prop) ᾰ ᾰ_1 (LT.lt.{succ u1} Ordinal.{u1} self) e_2) e_3) (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o (rfl.{succ (succ u1)} Ordinal.{u1} o) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f)))) hr))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (Ordinal.enum.{u1} α r _inst_1 o hr)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} α β)) (RelEmbedding.toEmbedding.{u1, u1} α β r s (RelIso.toRelEmbedding.{u1, u1} α β r s f)) (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) (eq_of_heq.{1} Prop (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) ((fun (α : Type.{succ u1}) (self : LT.{succ u1} α) (a._@.Init.Prelude._hyg.2009 : α) (a._@.Init.Prelude._hyg.2011 : α) (a'._@.Init.Prelude._hyg.2011 : α) (e'_4 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a'._@.Init.Prelude._hyg.2011) => Eq.casesOn.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2011 (fun (a._@.Init.Prelude._hyg.170 : α) (x : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.170) => (Eq.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.170) -> (HEq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a'._@.Init.Prelude._hyg.2011) e'_4 (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.170) x) -> (HEq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a'._@.Init.Prelude._hyg.2011))) a'._@.Init.Prelude._hyg.2011 e'_4 (fun (h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5692 : Eq.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) => Eq.ndrec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2011 (fun (a'._@.Init.Prelude.2011.Mathlib.SetTheory.Ordinal.Basic._hyg.5690 : α) => forall (e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 : Eq.{succ (succ 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a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011)) => Eq.ndrec.{0, 0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011) (fun (e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) => HEq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011)) (HEq.refl.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011)) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.symm.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011) (eq_of_heq.{0} (Eq.{succ (succ u1)} α 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a._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015) h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5693))) a'._@.Init.Prelude._hyg.2015 (Eq.symm.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2015 a._@.Init.Prelude._hyg.2015 h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5692) e'_4) (Eq.refl.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2015) (HEq.refl.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2015 a'._@.Init.Prelude._hyg.2015) e'_4)) Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f))))) hr))
 Case conversion may be inaccurate. Consider using '#align ordinal.rel_iso_enum Ordinal.relIso_enumₓ'. -/
 theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) (hr : o < type r) :

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

@@ -1881,7 +1881,7 @@ theorem ord_card_le (o : Ordinal) : o.card.ord ≤ o :=
 
 /- warning: cardinal.lt_ord_succ_card -> Cardinal.lt_ord_succ_card is a dubious translation:
 lean 3 declaration is
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+  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 (Cardinal.ord.{u1} (Order.succ.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1}) Cardinal.succOrder.{u1} (Ordinal.card.{u1} o)))
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align cardinal.lt_ord_succ_card Cardinal.lt_ord_succ_cardₓ'. -/
@@ -2130,7 +2130,7 @@ theorem nat_le_card {o} {n : ℕ} : (n : Cardinal) ≤ card o ↔ (n : Ordinal)
 
 /- warning: ordinal.nat_lt_card -> Ordinal.nat_lt_card is a dubious translation:
 lean 3 declaration is
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+  forall {o : Ordinal.{u1}} {n : Nat}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) ((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) (Ordinal.card.{u1} o)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Ordinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Ordinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Ordinal.{u1} (Nat.castCoe.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1})))) n) o)
 but is expected to have type
   forall {o : Ordinal.{u1}} {n : Nat}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) (Ordinal.card.{u1} o)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Nat.cast.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1}) n) o)
 Case conversion may be inaccurate. Consider using '#align ordinal.nat_lt_card Ordinal.nat_lt_cardₓ'. -/
@@ -2143,7 +2143,7 @@ theorem nat_lt_card {o} {n : ℕ} : (n : Cardinal) < card o ↔ (n : Ordinal) <
 
 /- warning: ordinal.card_lt_nat -> Ordinal.card_lt_nat is a dubious translation:
 lean 3 declaration is
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+  forall {o : Ordinal.{u1}} {n : Nat}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} o) ((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)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Ordinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Ordinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Ordinal.{u1} (Nat.castCoe.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1})))) n))
 but is expected to have type
   forall {o : Ordinal.{u1}} {n : Nat}, Iff (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} o) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Nat.cast.{succ u1} Ordinal.{u1} (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1}) n))
 Case conversion may be inaccurate. Consider using '#align ordinal.card_lt_nat Ordinal.card_lt_natₓ'. -/

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

@@ -1846,24 +1846,16 @@ theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=
 #align cardinal.ord_le Cardinal.ord_le
 -/
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align cardinal.gc_ord_card Cardinal.gc_ord_cardₓ'. -/
+#print Cardinal.gc_ord_card /-
 theorem gc_ord_card : GaloisConnection ord card := fun _ _ => ord_le
 #align cardinal.gc_ord_card Cardinal.gc_ord_card
+-/
 
-/- warning: cardinal.lt_ord -> Cardinal.lt_ord is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cardinal.lt_ord Cardinal.lt_ordₓ'. -/
+#print Cardinal.lt_ord /-
 theorem lt_ord {c o} : o < ord c ↔ o.card < c :=
   gc_ord_card.lt_iff_lt
 #align cardinal.lt_ord Cardinal.lt_ord
+-/
 
 #print Cardinal.card_ord /-
 @[simp]
@@ -1874,16 +1866,12 @@ theorem card_ord (c) : (ord c).card = c :=
 #align cardinal.card_ord Cardinal.card_ord
 -/
 
-/- warning: cardinal.gci_ord_card -> Cardinal.gciOrdCard is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cardinal.gci_ord_card Cardinal.gciOrdCardₓ'. -/
+#print Cardinal.gciOrdCard /-
 /-- Galois coinsertion between `cardinal.ord` and `ordinal.card`. -/
 def gciOrdCard : GaloisCoinsertion ord card :=
   gc_ord_card.toGaloisCoinsertion fun c => c.card_ord.le
 #align cardinal.gci_ord_card Cardinal.gciOrdCard
+-/
 
 #print Cardinal.ord_card_le /-
 theorem ord_card_le (o : Ordinal) : o.card.ord ≤ o :=
@@ -1901,27 +1889,19 @@ theorem lt_ord_succ_card (o : Ordinal) : o < (succ o.card).ord :=
   lt_ord.2 <| lt_succ _
 #align cardinal.lt_ord_succ_card Cardinal.lt_ord_succ_card
 
-/- warning: cardinal.ord_strict_mono -> Cardinal.ord_strictMono is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cardinal.ord_strict_mono Cardinal.ord_strictMonoₓ'. -/
+#print Cardinal.ord_strictMono /-
 @[mono]
 theorem ord_strictMono : StrictMono ord :=
   gciOrdCard.strictMono_l
 #align cardinal.ord_strict_mono Cardinal.ord_strictMono
+-/
 
-/- warning: cardinal.ord_mono -> Cardinal.ord_mono is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align cardinal.ord_mono Cardinal.ord_monoₓ'. -/
+#print Cardinal.ord_mono /-
 @[mono]
 theorem ord_mono : Monotone ord :=
   gc_ord_card.monotone_l
 #align cardinal.ord_mono Cardinal.ord_mono
+-/
 
 #print Cardinal.ord_le_ord /-
 @[simp]
@@ -1930,16 +1910,12 @@ theorem ord_le_ord {c₁ c₂} : ord c₁ ≤ ord c₂ ↔ c₁ ≤ c₂ :=
 #align cardinal.ord_le_ord Cardinal.ord_le_ord
 -/
 
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+#print Cardinal.ord_lt_ord /-
 @[simp]
 theorem ord_lt_ord {c₁ c₂} : ord c₁ < ord c₂ ↔ c₁ < c₂ :=
   ord_strictMono.lt_iff_lt
 #align cardinal.ord_lt_ord Cardinal.ord_lt_ord
+-/
 
 #print Cardinal.ord_zero /-
 @[simp]
@@ -1993,29 +1969,21 @@ theorem mk_ord_out (c : Cardinal) : (#c.ord.out.α) = c := by simp
 #align cardinal.mk_ord_out Cardinal.mk_ord_out
 -/
 
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+#print Cardinal.card_typein_lt /-
 theorem card_typein_lt (r : α → α → Prop) [IsWellOrder α r] (x : α) (h : ord (#α) = type r) :
     card (typein r x) < (#α) := by
   rw [← lt_ord, h]
   apply typein_lt_type
 #align cardinal.card_typein_lt Cardinal.card_typein_lt
+-/
 
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+#print Cardinal.card_typein_out_lt /-
 theorem card_typein_out_lt (c : Cardinal) (x : c.ord.out.α) : card (typein (· < ·) x) < c :=
   by
   rw [← lt_ord]
   apply typein_lt_self
 #align cardinal.card_typein_out_lt Cardinal.card_typein_out_lt
+-/
 
 #print Cardinal.ord_injective /-
 theorem ord_injective : Injective ord := by
@@ -2075,26 +2043,18 @@ theorem univ_umax : univ.{u, max (u + 1) v} = univ.{u, v} :=
 #align cardinal.univ_umax Cardinal.univ_umax
 -/
 
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+#print Cardinal.lift_lt_univ /-
 theorem lift_lt_univ (c : Cardinal) : lift.{u + 1, u} c < univ.{u, u + 1} := by
   simpa only [lift.principal_seg_coe, lift_ord, lift_succ, ord_le, succ_le_iff] using
     le_of_lt (lift.principalSeg.{u, u + 1}.lt_top (succ c).ord)
 #align cardinal.lift_lt_univ Cardinal.lift_lt_univ
+-/
 
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+#print Cardinal.lift_lt_univ' /-
 theorem lift_lt_univ' (c : Cardinal) : lift.{max (u + 1) v, u} c < univ.{u, v} := by
   simpa only [lift_lift, lift_univ, univ_umax] using lift_lt.{_, max (u + 1) v}.2 (lift_lt_univ c)
 #align cardinal.lift_lt_univ' Cardinal.lift_lt_univ'
+-/
 
 #print Cardinal.ord_univ /-
 @[simp]
@@ -2111,12 +2071,7 @@ theorem ord_univ : ord univ.{u, v} = Ordinal.univ.{u, v} :=
 #align cardinal.ord_univ Cardinal.ord_univ
 -/
 
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+#print Cardinal.lt_univ /-
 theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
   ⟨fun h => by
     have := ord_lt_ord.2 h
@@ -2126,13 +2081,9 @@ theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
     rw [← e, lift.principal_seg_coe, ← lift_card] at this
     exact ⟨_, this.symm⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ _⟩
 #align cardinal.lt_univ Cardinal.lt_univ
+-/
 
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+#print Cardinal.lt_univ' /-
 theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c' :=
   ⟨fun h => by
     let ⟨a, e, h'⟩ := lt_lift_iff.1 h
@@ -2140,13 +2091,9 @@ theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c
     rcases lt_univ.{u}.1 h' with ⟨c', rfl⟩
     exact ⟨c', by simp only [e.symm, lift_lift]⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ' _⟩
 #align cardinal.lt_univ' Cardinal.lt_univ'
+-/
 
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+#print Cardinal.small_iff_lift_mk_lt_univ /-
 theorem small_iff_lift_mk_lt_univ {α : Type u} :
     Small.{v} α ↔ Cardinal.lift (#α) < univ.{v, max u (v + 1)} :=
   by
@@ -2157,6 +2104,7 @@ theorem small_iff_lift_mk_lt_univ {α : Type u} :
   · rintro ⟨c, hc⟩
     exact ⟨⟨c.out, lift_mk_eq.{u, _, v + 1}.1 (hc.trans (congr rfl c.mk_out.symm))⟩⟩
 #align cardinal.small_iff_lift_mk_lt_univ Cardinal.small_iff_lift_mk_lt_univ
+-/
 
 end Cardinal
 

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

@@ -1846,16 +1846,24 @@ theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=
 #align cardinal.ord_le Cardinal.ord_le
 -/
 
-#print Cardinal.gc_ord_card /-
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+Case conversion may be inaccurate. Consider using '#align cardinal.gc_ord_card Cardinal.gc_ord_cardₓ'. -/
 theorem gc_ord_card : GaloisConnection ord card := fun _ _ => ord_le
 #align cardinal.gc_ord_card Cardinal.gc_ord_card
--/
 
-#print Cardinal.lt_ord /-
+/- warning: cardinal.lt_ord -> Cardinal.lt_ord is a dubious translation:
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+  forall {c : Cardinal.{u1}} {o : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Cardinal.ord.{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})))))) (Ordinal.card.{u1} o) c)
+but is expected to have type
+  forall {c : Cardinal.{u1}} {o : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Cardinal.ord.{u1} c)) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Ordinal.card.{u1} o) c)
+Case conversion may be inaccurate. Consider using '#align cardinal.lt_ord Cardinal.lt_ordₓ'. -/
 theorem lt_ord {c o} : o < ord c ↔ o.card < c :=
   gc_ord_card.lt_iff_lt
 #align cardinal.lt_ord Cardinal.lt_ord
--/
 
 #print Cardinal.card_ord /-
 @[simp]
@@ -1866,12 +1874,16 @@ theorem card_ord (c) : (ord c).card = c :=
 #align cardinal.card_ord Cardinal.card_ord
 -/
 
-#print Cardinal.gciOrdCard /-
+/- warning: cardinal.gci_ord_card -> Cardinal.gciOrdCard is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align cardinal.gci_ord_card Cardinal.gciOrdCardₓ'. -/
 /-- Galois coinsertion between `cardinal.ord` and `ordinal.card`. -/
 def gciOrdCard : GaloisCoinsertion ord card :=
   gc_ord_card.toGaloisCoinsertion fun c => c.card_ord.le
 #align cardinal.gci_ord_card Cardinal.gciOrdCard
--/
 
 #print Cardinal.ord_card_le /-
 theorem ord_card_le (o : Ordinal) : o.card.ord ≤ o :=
@@ -1881,7 +1893,7 @@ theorem ord_card_le (o : Ordinal) : o.card.ord ≤ o :=
 
 /- warning: cardinal.lt_ord_succ_card -> Cardinal.lt_ord_succ_card is a dubious translation:
 lean 3 declaration is
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+  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 (Cardinal.ord.{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} (Ordinal.card.{u1} o)))
 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align cardinal.lt_ord_succ_card Cardinal.lt_ord_succ_cardₓ'. -/
@@ -1889,19 +1901,27 @@ theorem lt_ord_succ_card (o : Ordinal) : o < (succ o.card).ord :=
   lt_ord.2 <| lt_succ _
 #align cardinal.lt_ord_succ_card Cardinal.lt_ord_succ_card
 
-#print Cardinal.ord_strictMono /-
+/- warning: cardinal.ord_strict_mono -> Cardinal.ord_strictMono 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.ord_strict_mono Cardinal.ord_strictMonoₓ'. -/
 @[mono]
 theorem ord_strictMono : StrictMono ord :=
   gciOrdCard.strictMono_l
 #align cardinal.ord_strict_mono Cardinal.ord_strictMono
--/
 
-#print Cardinal.ord_mono /-
+/- warning: cardinal.ord_mono -> Cardinal.ord_mono 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.ord_mono Cardinal.ord_monoₓ'. -/
 @[mono]
 theorem ord_mono : Monotone ord :=
   gc_ord_card.monotone_l
 #align cardinal.ord_mono Cardinal.ord_mono
--/
 
 #print Cardinal.ord_le_ord /-
 @[simp]
@@ -1910,12 +1930,16 @@ theorem ord_le_ord {c₁ c₂} : ord c₁ ≤ ord c₂ ↔ c₁ ≤ c₂ :=
 #align cardinal.ord_le_ord Cardinal.ord_le_ord
 -/
 
-#print Cardinal.ord_lt_ord /-
+/- warning: cardinal.ord_lt_ord -> Cardinal.ord_lt_ord is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.ord_lt_ord Cardinal.ord_lt_ordₓ'. -/
 @[simp]
 theorem ord_lt_ord {c₁ c₂} : ord c₁ < ord c₂ ↔ c₁ < c₂ :=
   ord_strictMono.lt_iff_lt
 #align cardinal.ord_lt_ord Cardinal.ord_lt_ord
--/
 
 #print Cardinal.ord_zero /-
 @[simp]
@@ -1969,21 +1993,29 @@ theorem mk_ord_out (c : Cardinal) : (#c.ord.out.α) = c := by simp
 #align cardinal.mk_ord_out Cardinal.mk_ord_out
 -/
 
-#print Cardinal.card_typein_lt /-
+/- warning: cardinal.card_typein_lt -> Cardinal.card_typein_lt is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.card_typein_lt Cardinal.card_typein_ltₓ'. -/
 theorem card_typein_lt (r : α → α → Prop) [IsWellOrder α r] (x : α) (h : ord (#α) = type r) :
     card (typein r x) < (#α) := by
   rw [← lt_ord, h]
   apply typein_lt_type
 #align cardinal.card_typein_lt Cardinal.card_typein_lt
--/
 
-#print Cardinal.card_typein_out_lt /-
+/- warning: cardinal.card_typein_out_lt -> Cardinal.card_typein_out_lt is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.card_typein_out_lt Cardinal.card_typein_out_ltₓ'. -/
 theorem card_typein_out_lt (c : Cardinal) (x : c.ord.out.α) : card (typein (· < ·) x) < c :=
   by
   rw [← lt_ord]
   apply typein_lt_self
 #align cardinal.card_typein_out_lt Cardinal.card_typein_out_lt
--/
 
 #print Cardinal.ord_injective /-
 theorem ord_injective : Injective ord := by
@@ -2043,18 +2075,26 @@ theorem univ_umax : univ.{u, max (u + 1) v} = univ.{u, v} :=
 #align cardinal.univ_umax Cardinal.univ_umax
 -/
 
-#print Cardinal.lift_lt_univ /-
+/- warning: cardinal.lift_lt_univ -> Cardinal.lift_lt_univ is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.lift_lt_univ Cardinal.lift_lt_univₓ'. -/
 theorem lift_lt_univ (c : Cardinal) : lift.{u + 1, u} c < univ.{u, u + 1} := by
   simpa only [lift.principal_seg_coe, lift_ord, lift_succ, ord_le, succ_le_iff] using
     le_of_lt (lift.principalSeg.{u, u + 1}.lt_top (succ c).ord)
 #align cardinal.lift_lt_univ Cardinal.lift_lt_univ
--/
 
-#print Cardinal.lift_lt_univ' /-
+/- warning: cardinal.lift_lt_univ' -> Cardinal.lift_lt_univ' is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align cardinal.lift_lt_univ' Cardinal.lift_lt_univ'ₓ'. -/
 theorem lift_lt_univ' (c : Cardinal) : lift.{max (u + 1) v, u} c < univ.{u, v} := by
   simpa only [lift_lift, lift_univ, univ_umax] using lift_lt.{_, max (u + 1) v}.2 (lift_lt_univ c)
 #align cardinal.lift_lt_univ' Cardinal.lift_lt_univ'
--/
 
 #print Cardinal.ord_univ /-
 @[simp]
@@ -2071,7 +2111,12 @@ theorem ord_univ : ord univ.{u, v} = Ordinal.univ.{u, v} :=
 #align cardinal.ord_univ Cardinal.ord_univ
 -/
 
-#print Cardinal.lt_univ /-
+/- warning: cardinal.lt_univ -> Cardinal.lt_univ is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{succ u1}}, Iff (LT.lt.{succ (succ u1)} Cardinal.{succ u1} (Preorder.toLT.{succ (succ u1)} Cardinal.{succ u1} (PartialOrder.toPreorder.{succ (succ u1)} Cardinal.{succ u1} (OrderedAddCommMonoid.toPartialOrder.{succ (succ u1)} Cardinal.{succ u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ (succ u1)} Cardinal.{succ u1} (OrderedCommSemiring.toOrderedSemiring.{succ (succ u1)} Cardinal.{succ u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (succ u1)} Cardinal.{succ u1} Cardinal.canonicallyOrderedCommSemiring.{succ u1})))))) c Cardinal.univ.{u1, succ u1}) (Exists.{succ (succ u1)} Cardinal.{u1} (fun (c' : Cardinal.{u1}) => Eq.{succ (succ (succ u1))} Cardinal.{succ u1} c (Cardinal.lift.{succ u1, u1} c')))
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+Case conversion may be inaccurate. Consider using '#align cardinal.lt_univ Cardinal.lt_univₓ'. -/
 theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
   ⟨fun h => by
     have := ord_lt_ord.2 h
@@ -2081,9 +2126,13 @@ theorem lt_univ {c} : c < univ.{u, u + 1} ↔ ∃ c', c = lift.{u + 1, u} c' :=
     rw [← e, lift.principal_seg_coe, ← lift_card] at this
     exact ⟨_, this.symm⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ _⟩
 #align cardinal.lt_univ Cardinal.lt_univ
--/
 
-#print Cardinal.lt_univ' /-
+/- warning: cardinal.lt_univ' -> Cardinal.lt_univ' is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{max (succ u1) u2}}, Iff (LT.lt.{succ (max (succ u1) u2)} Cardinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Cardinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Cardinal.{max (succ u1) u2} (OrderedAddCommMonoid.toPartialOrder.{succ (max (succ u1) u2)} Cardinal.{max (succ u1) u2} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max (succ u1) u2)} Cardinal.{max (succ u1) u2} (OrderedCommSemiring.toOrderedSemiring.{succ (max (succ u1) u2)} Cardinal.{max (succ u1) u2} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max (succ u1) u2)} Cardinal.{max (succ u1) u2} Cardinal.canonicallyOrderedCommSemiring.{max (succ u1) u2})))))) c Cardinal.univ.{u1, u2}) (Exists.{succ (succ u1)} Cardinal.{u1} (fun (c' : Cardinal.{u1}) => Eq.{succ (succ (max (succ u1) u2))} Cardinal.{max (succ u1) u2} c (Cardinal.lift.{max (succ u1) u2, u1} c')))
+but is expected to have type
+  forall {c : Cardinal.{max (succ u1) u2}}, Iff (LT.lt.{max (succ (succ u1)) (succ u2)} Cardinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Cardinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Cardinal.{max (succ u1) u2} Cardinal.partialOrder.{max (succ u1) u2})) c Cardinal.univ.{u1, u2}) (Exists.{succ (succ u1)} Cardinal.{u1} (fun (c' : Cardinal.{u1}) => Eq.{max (succ (succ (succ u1))) (succ (succ u2))} Cardinal.{max (succ u1) u2} c (Cardinal.lift.{max (succ u1) u2, u1} c')))
+Case conversion may be inaccurate. Consider using '#align cardinal.lt_univ' Cardinal.lt_univ'ₓ'. -/
 theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c' :=
   ⟨fun h => by
     let ⟨a, e, h'⟩ := lt_lift_iff.1 h
@@ -2091,9 +2140,13 @@ theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c
     rcases lt_univ.{u}.1 h' with ⟨c', rfl⟩
     exact ⟨c', by simp only [e.symm, lift_lift]⟩, fun ⟨c', e⟩ => e.symm ▸ lift_lt_univ' _⟩
 #align cardinal.lt_univ' Cardinal.lt_univ'
--/
 
-#print Cardinal.small_iff_lift_mk_lt_univ /-
+/- warning: cardinal.small_iff_lift_mk_lt_univ -> Cardinal.small_iff_lift_mk_lt_univ is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}}, Iff (Small.{u2, u1} α) (LT.lt.{succ (max u1 (succ u2))} Cardinal.{max u1 (succ u2)} (Preorder.toLT.{succ (max u1 (succ u2))} Cardinal.{max u1 (succ u2)} (PartialOrder.toPreorder.{succ (max u1 (succ u2))} Cardinal.{max u1 (succ u2)} (OrderedAddCommMonoid.toPartialOrder.{succ (max u1 (succ u2))} Cardinal.{max u1 (succ u2)} (OrderedSemiring.toOrderedAddCommMonoid.{succ (max u1 (succ u2))} Cardinal.{max u1 (succ u2)} (OrderedCommSemiring.toOrderedSemiring.{succ (max u1 (succ u2))} Cardinal.{max u1 (succ u2)} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ (max u1 (succ u2))} Cardinal.{max u1 (succ u2)} Cardinal.canonicallyOrderedCommSemiring.{max u1 (succ u2)})))))) (Cardinal.lift.{succ u2, u1} (Cardinal.mk.{u1} α)) Cardinal.univ.{u2, max u1 (succ u2)})
+but is expected to have type
+  forall {α : Type.{u1}}, Iff (Small.{u2, u1} α) (LT.lt.{max (succ u1) (succ (succ u2))} Cardinal.{max u1 (succ u2)} (Preorder.toLT.{max (succ u1) (succ (succ u2))} Cardinal.{max u1 (succ u2)} (PartialOrder.toPreorder.{max (succ u1) (succ (succ u2))} Cardinal.{max u1 (succ u2)} Cardinal.partialOrder.{max u1 (succ u2)})) (Cardinal.lift.{succ u2, u1} (Cardinal.mk.{u1} α)) Cardinal.univ.{u2, max u1 (succ u2)})
+Case conversion may be inaccurate. Consider using '#align cardinal.small_iff_lift_mk_lt_univ Cardinal.small_iff_lift_mk_lt_univₓ'. -/
 theorem small_iff_lift_mk_lt_univ {α : Type u} :
     Small.{v} α ↔ Cardinal.lift (#α) < univ.{v, max u (v + 1)} :=
   by
@@ -2104,7 +2157,6 @@ theorem small_iff_lift_mk_lt_univ {α : Type u} :
   · rintro ⟨c, hc⟩
     exact ⟨⟨c.out, lift_mk_eq.{u, _, v + 1}.1 (hc.trans (congr rfl c.mk_out.symm))⟩⟩
 #align cardinal.small_iff_lift_mk_lt_univ Cardinal.small_iff_lift_mk_lt_univ
--/
 
 end Cardinal
 
@@ -2130,7 +2182,7 @@ theorem nat_le_card {o} {n : ℕ} : (n : Cardinal) ≤ card o ↔ (n : Ordinal)
 
 /- warning: ordinal.nat_lt_card -> Ordinal.nat_lt_card is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align ordinal.nat_lt_card Ordinal.nat_lt_cardₓ'. -/
@@ -2143,7 +2195,7 @@ theorem nat_lt_card {o} {n : ℕ} : (n : Cardinal) < card o ↔ (n : Ordinal) <
 
 /- warning: ordinal.card_lt_nat -> Ordinal.card_lt_nat is a dubious translation:
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align ordinal.card_lt_nat Ordinal.card_lt_natₓ'. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/728baa2f54e6062c5879a3e397ac6bac323e506f

@@ -1529,7 +1529,7 @@ instance uniqueOutOne : Unique (1 : Ordinal).out.α
 lean 3 declaration is
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0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1293 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1295 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ 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Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1293 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1295) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{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})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) True (congrArg.{succ (succ u1), 1} Ordinal.{u1} Prop (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1293 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1295 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 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Ordinal.zero.{u1} Ordinal.one.{u1} Ordinal.partialOrder.{u1} Ordinal.zeroLEOneClass.{u1} Ordinal.NeZero.one.{u1}))))
 Case conversion may be inaccurate. Consider using '#align ordinal.one_out_eq Ordinal.one_out_eqₓ'. -/
 theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :=
   Unique.eq_default x
@@ -1542,7 +1542,7 @@ theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :
 lean 3 declaration is
   forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))))))))) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
 but is expected to have type
-  forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12881 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12883 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12881 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12883) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
+  forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12913 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12915 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12913 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12915) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.typein_one_out Ordinal.typein_one_outₓ'. -/
 @[simp]
 theorem typein_one_out (x : (1 : Ordinal).out.α) : typein (· < ·) x = 0 := by
@@ -1669,7 +1669,7 @@ def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α :=
 lean 3 declaration is
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Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (Eq.mpr.{0} (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} 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(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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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)) (Eq.ndrec.{0, succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} 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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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o)))) o (Ordinal.type_lt.{u1} o))) ho)) (Bot.bot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (OrderBot.toHasBot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o)))))) (Ordinal.outOrderBotOfPos.{u1} o ho)))
 but is expected to have type
-  forall {o : Ordinal.{u1}} (ho : 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), Eq.{succ u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14357 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14359 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} 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(OrderBot.toBot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (Ordinal.outOrderBotOfPos.{u1} o ho)))
 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_eq_bot Ordinal.enum_zero_eq_botₓ'. -/
 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
     enum (· < ·) 0 (by rwa [type_lt]) =
@@ -1749,7 +1749,7 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
 lean 3 declaration is
   Eq.{max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} ((fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) Ordinal.lift.principalSeg.{u1, u2}) (coeFn.{max (succ (succ u1)) (succ (succ (max (succ u1) u2))), max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} (PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) (fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) (PrincipalSeg.hasCoeToFun.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) Ordinal.lift.principalSeg.{u1, u2}) Ordinal.lift.{max (succ u1) u2, u1}
 but is expected to have type
-  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} Ordinal.{max (succ u1) u2} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2})) (RelEmbedding.toEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14598 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14600 : 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.Ordinal.Basic._hyg.14598 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14600) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14613 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14615 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14613 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14615) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14598 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14600 : 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.Ordinal.Basic._hyg.14598 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14600) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14613 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14615 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14613 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14615) Ordinal.lift.principalSeg.{u1, u2}))) Ordinal.lift.{max (succ u1) u2, u1}
+  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} Ordinal.{max (succ u1) u2} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2})) (RelEmbedding.toEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14630 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632 : 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.Ordinal.Basic._hyg.14630 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14632) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14645 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14647) Ordinal.lift.principalSeg.{u1, u2}))) Ordinal.lift.{max (succ u1) u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg_coe Ordinal.lift.principalSeg_coeₓ'. -/
 @[simp]
 theorem lift.principalSeg_coe :

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -722,7 +722,7 @@ theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β 
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} β (coeFn.{succ u1, succ u1} (RelIso.{u1, u1} α β r s) (fun (_x : RelIso.{u1, u1} α β r s) => α -> β) (RelIso.hasCoeToFun.{u1, u1} α β r s) f (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) ((fun [self : LT.{succ u1} Ordinal.{u1}] (ᾰ : Ordinal.{u1}) (ᾰ_1 : Ordinal.{u1}) (e_2 : Eq.{succ (succ u1)} Ordinal.{u1} ᾰ ᾰ_1) (ᾰ_2 : Ordinal.{u1}) (ᾰ_3 : Ordinal.{u1}) (e_3 : Eq.{succ (succ u1)} Ordinal.{u1} ᾰ_2 ᾰ_3) => congr.{succ (succ u1), 1} Ordinal.{u1} Prop (LT.lt.{succ u1} Ordinal.{u1} self ᾰ) (LT.lt.{succ u1} Ordinal.{u1} self ᾰ_1) ᾰ_2 ᾰ_3 (congr_arg.{succ (succ u1), succ (succ u1)} Ordinal.{u1} (Ordinal.{u1} -> Prop) ᾰ ᾰ_1 (LT.lt.{succ u1} Ordinal.{u1} self) e_2) e_3) (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o (rfl.{succ (succ u1)} Ordinal.{u1} o) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f)))) hr))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (Ordinal.enum.{u1} α r _inst_1 o hr)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} α β)) (RelEmbedding.toEmbedding.{u1, u1} α β r s (RelIso.toRelEmbedding.{u1, u1} α β r s f)) (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (Quot.lift.{succ (succ u1), 1} WellOrder.{u1} (fun (a : WellOrder.{u1}) (b : WellOrder.{u1}) => HasEquiv.Equiv.{succ (succ u1), 0} WellOrder.{u1} (instHasEquiv.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1}) a b) Prop (fun (a₁ : WellOrder.{u1}) => Quotient.lift.{succ (succ u1), 1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} ((fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468.2537 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2550 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469.2555 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2568 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 r s)))) a₁) (Quotient.lift₂.proof_1.{succ (succ u1), 1, succ (succ u1)} WellOrder.{u1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} Ordinal.isEquivalent.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468.2537 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2550 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469.2555 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2568 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 r s)))) Ordinal.partialOrder.proof_2.{u1} a₁) (Ordinal.type.{u1} α r _inst_1)) (Quotient.lift₂.proof_2.{succ (succ u1), 1, succ (succ u1)} WellOrder.{u1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} Ordinal.isEquivalent.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468.2537 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2550 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469.2555 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2568 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 r s)))) Ordinal.partialOrder.proof_2.{u1} (Ordinal.type.{u1} α r _inst_1)) o) ((fun {α : Type.{succ u1}} [self : LT.{succ u1} α] (a._@.Init.Prelude._hyg.2009 : α) (a_1._@.Init.Prelude._hyg.2009 : α) (e_a._@.Init.Prelude._hyg.2009 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2009) => Eq.rec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2009 (fun (a_1._@.Init.Prelude._hyg.2009 : α) (e_a._@.Init.Prelude._hyg.2009 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2009) => forall (a._@.Init.Prelude._hyg.2011 : α) (a_1._@.Init.Prelude._hyg.2011 : α), (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) -> (Eq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) (LT.lt.{succ u1} α self a_1._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2011))) (fun (a._@.Init.Prelude._hyg.2011 : α) (a_1._@.Init.Prelude._hyg.2011 : α) (e_a._@.Init.Prelude._hyg.2011 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) => Eq.rec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2011 (fun (a_1._@.Init.Prelude._hyg.2011 : α) (e_a._@.Init.Prelude._hyg.2011 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) => Eq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2011)) (Eq.refl.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011)) a_1._@.Init.Prelude._hyg.2011 e_a._@.Init.Prelude._hyg.2011) a_1._@.Init.Prelude._hyg.2009 e_a._@.Init.Prelude._hyg.2009) Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o (Eq.refl.{succ (succ u1)} Ordinal.{u1} o) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f)))) hr))
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (Ordinal.enum.{u1} α r _inst_1 o hr)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} α β)) (RelEmbedding.toEmbedding.{u1, u1} α β r s (RelIso.toRelEmbedding.{u1, u1} α β r s f)) (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) (eq_of_heq.{1} Prop (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) ((fun (α : Type.{succ u1}) (self : LT.{succ u1} α) (a._@.Init.Prelude._hyg.2009 : α) (a._@.Init.Prelude._hyg.2011 : α) (a'._@.Init.Prelude._hyg.2011 : α) (e'_4 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a'._@.Init.Prelude._hyg.2011) => Eq.casesOn.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2011 (fun (a._@.Init.Prelude._hyg.170 : α) (x : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.170) => (Eq.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.170) -> (HEq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a'._@.Init.Prelude._hyg.2011) e'_4 (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.170) x) -> (HEq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a'._@.Init.Prelude._hyg.2011))) a'._@.Init.Prelude._hyg.2011 e'_4 (fun (h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5692 : Eq.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) => Eq.ndrec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2011 (fun (a'._@.Init.Prelude.2011.Mathlib.SetTheory.Ordinal.Basic._hyg.5690 : α) => forall (e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a'._@.Init.Prelude.2011.Mathlib.SetTheory.Ordinal.Basic._hyg.5690), (HEq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a'._@.Init.Prelude.2011.Mathlib.SetTheory.Ordinal.Basic._hyg.5690) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011)) -> (HEq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a'._@.Init.Prelude.2011.Mathlib.SetTheory.Ordinal.Basic._hyg.5690))) (fun (e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) (h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5693 : HEq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011)) => Eq.ndrec.{0, 0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011) (fun (e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) => HEq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011)) (HEq.refl.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011)) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.symm.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011) (eq_of_heq.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011) e_4._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5691 (Eq.refl.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011) h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5693))) a'._@.Init.Prelude._hyg.2011 (Eq.symm.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2011 a._@.Init.Prelude._hyg.2011 h._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5692) e'_4) (Eq.refl.{succ (succ u1)} α a'._@.Init.Prelude._hyg.2011) (HEq.refl.{0} (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a'._@.Init.Prelude._hyg.2011) e'_4)) Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f))))) hr))
 Case conversion may be inaccurate. Consider using '#align ordinal.rel_iso_enum Ordinal.relIso_enumₓ'. -/
 theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) (hr : o < type r) :
@@ -778,7 +778,7 @@ def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r
 lean 3 declaration is
   forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} ((fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (coeFn.{succ (succ u1), succ (succ u1)} (PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (PrincipalSeg.hasCoeToFun.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (Ordinal.typein.{u1} α r _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ u1, succ (succ u1)} α Ordinal.{u1})) (RelEmbedding.toEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5885 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5887 : 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.Ordinal.Basic._hyg.5885 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5887) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5885 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5887 : 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.Ordinal.Basic._hyg.5885 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5887) (Ordinal.typein.principalSeg.{u1} α r _inst_1)))) (Ordinal.typein.{u1} α r _inst_1)
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ u1, succ (succ u1)} α Ordinal.{u1})) (RelEmbedding.toEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6003 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005 : 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.Ordinal.Basic._hyg.6003 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.6005) (Ordinal.typein.principalSeg.{u1} α r _inst_1)))) (Ordinal.typein.{u1} α r _inst_1)
 Case conversion may be inaccurate. Consider using '#align ordinal.typein.principal_seg_coe Ordinal.typein.principalSeg_coeₓ'. -/
 @[simp]
 theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
@@ -1115,7 +1115,7 @@ def lift.initialSeg : @InitialSeg Ordinal.{u} Ordinal.{max u v} (· < ·) (· <
 lean 3 declaration is
   Eq.{max (succ (succ u1)) (succ (succ (max u1 u2)))} ((fun (_x : InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) => Ordinal.{u1} -> Ordinal.{max u1 u2}) Ordinal.lift.initialSeg.{u1, u2}) (coeFn.{max (succ (succ u1)) (succ (succ (max u1 u2))), max (succ (succ u1)) (succ (succ (max u1 u2)))} (InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) (fun (_x : InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) => Ordinal.{u1} -> Ordinal.{max u1 u2}) (FunLike.hasCoeToFun.{max (succ (succ u1)) (succ (succ (max u1 u2))), succ (succ u1), succ (succ (max u1 u2))} (InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => Ordinal.{max u1 u2}) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (succ (max u1 u2))), succ (succ u1), succ (succ (max u1 u2))} (InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) Ordinal.{u1} Ordinal.{max u1 u2} (InitialSeg.embeddingLike.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))))) Ordinal.lift.initialSeg.{u1, u2}) Ordinal.lift.{u2, u1}
 but is expected to have type
-  Eq.{max (succ (succ u1)) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8469 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8471 : 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.Ordinal.Basic._hyg.8469 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8471) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8484 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8486 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8484 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8486)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8469 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8471 : 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.Ordinal.Basic._hyg.8469 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8471) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8484 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8486 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8484 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8486)) Ordinal.{u1} Ordinal.{max u1 u2} (InitialSeg.instEmbeddingLikeInitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8469 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8471 : 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.Ordinal.Basic._hyg.8469 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8471) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8484 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8486 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8484 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8486))) Ordinal.lift.initialSeg.{u1, u2}) Ordinal.lift.{u2, u1}
+  Eq.{max (succ (succ u1)) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8589 : 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.Ordinal.Basic._hyg.8587 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8589) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8604 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8604)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8589 : 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.Ordinal.Basic._hyg.8587 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8589) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8604 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8604)) Ordinal.{u1} Ordinal.{max u1 u2} (InitialSeg.instEmbeddingLikeInitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8587 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8589 : 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.Ordinal.Basic._hyg.8587 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8589) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8604 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8602 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8604))) Ordinal.lift.initialSeg.{u1, u2}) Ordinal.lift.{u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.initial_seg_coe Ordinal.lift.initialSeg_coeₓ'. -/
 @[simp]
 theorem lift.initialSeg_coe : (lift.initialSeg : Ordinal → Ordinal) = lift :=
@@ -1529,7 +1529,7 @@ instance uniqueOutOne : Unique (1 : Ordinal).out.α
 lean 3 declaration is
   forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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 u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) x (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))))))))) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (Eq.mpr.{0} (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} 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0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1293 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1295 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ 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Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1293 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1295) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{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})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) True (congrArg.{succ (succ u1), 1} Ordinal.{u1} Prop (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1293 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1295 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 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Ordinal.zero.{u1} Ordinal.one.{u1} Ordinal.partialOrder.{u1} Ordinal.zeroLEOneClass.{u1} Ordinal.NeZero.one.{u1}))))
 Case conversion may be inaccurate. Consider using '#align ordinal.one_out_eq Ordinal.one_out_eqₓ'. -/
 theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :=
   Unique.eq_default x
@@ -1542,7 +1542,7 @@ theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :
 lean 3 declaration is
   forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))))))))) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
 but is expected to have type
-  forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12763 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12765 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12763 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12765) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
+  forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12881 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12883 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12881 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12883) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.typein_one_out Ordinal.typein_one_outₓ'. -/
 @[simp]
 theorem typein_one_out (x : (1 : Ordinal).out.α) : typein (· < ·) x = 0 := by
@@ -1669,7 +1669,7 @@ def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α :=
 lean 3 declaration is
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(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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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)) (Eq.ndrec.{0, succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} 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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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o)))) o (Ordinal.type_lt.{u1} o))) ho)) (Bot.bot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (OrderBot.toHasBot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o)))))) (Ordinal.outOrderBotOfPos.{u1} o ho)))
 but is expected to have type
-  forall {o : Ordinal.{u1}} (ho : 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), Eq.{succ u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14239 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14241 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} 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(OrderBot.toBot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (Ordinal.outOrderBotOfPos.{u1} o ho)))
 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_eq_bot Ordinal.enum_zero_eq_botₓ'. -/
 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
     enum (· < ·) 0 (by rwa [type_lt]) =
@@ -1749,7 +1749,7 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
 lean 3 declaration is
   Eq.{max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} ((fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) Ordinal.lift.principalSeg.{u1, u2}) (coeFn.{max (succ (succ u1)) (succ (succ (max (succ u1) u2))), max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} (PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) (fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) (PrincipalSeg.hasCoeToFun.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) Ordinal.lift.principalSeg.{u1, u2}) Ordinal.lift.{max (succ u1) u2, u1}
 but is expected to have type
-  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} Ordinal.{max (succ u1) u2} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2})) (RelEmbedding.toEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14480 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14482 : 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.Ordinal.Basic._hyg.14480 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14482) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14495 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14497 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14495 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14497) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14480 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14482 : 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.Ordinal.Basic._hyg.14480 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14482) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14495 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14497 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14495 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14497) Ordinal.lift.principalSeg.{u1, u2}))) Ordinal.lift.{max (succ u1) u2, u1}
+  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} Ordinal.{max (succ u1) u2} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2})) (RelEmbedding.toEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14598 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14600 : 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.Ordinal.Basic._hyg.14598 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14600) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14613 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14615 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14613 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14615) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14598 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14600 : 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.Ordinal.Basic._hyg.14598 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14600) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14613 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14615 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14613 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14615) Ordinal.lift.principalSeg.{u1, u2}))) Ordinal.lift.{max (succ u1) u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg_coe Ordinal.lift.principalSeg_coeₓ'. -/
 @[simp]
 theorem lift.principalSeg_coe :

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

@@ -722,7 +722,7 @@ theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β 
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} β (coeFn.{succ u1, succ u1} (RelIso.{u1, u1} α β r s) (fun (_x : RelIso.{u1, u1} α β r s) => α -> β) (RelIso.hasCoeToFun.{u1, u1} α β r s) f (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) ((fun [self : LT.{succ u1} Ordinal.{u1}] (ᾰ : Ordinal.{u1}) (ᾰ_1 : Ordinal.{u1}) (e_2 : Eq.{succ (succ u1)} Ordinal.{u1} ᾰ ᾰ_1) (ᾰ_2 : Ordinal.{u1}) (ᾰ_3 : Ordinal.{u1}) (e_3 : Eq.{succ (succ u1)} Ordinal.{u1} ᾰ_2 ᾰ_3) => congr.{succ (succ u1), 1} Ordinal.{u1} Prop (LT.lt.{succ u1} Ordinal.{u1} self ᾰ) (LT.lt.{succ u1} Ordinal.{u1} self ᾰ_1) ᾰ_2 ᾰ_3 (congr_arg.{succ (succ u1), succ (succ u1)} Ordinal.{u1} (Ordinal.{u1} -> Prop) ᾰ ᾰ_1 (LT.lt.{succ u1} Ordinal.{u1} self) e_2) e_3) (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o (rfl.{succ (succ u1)} Ordinal.{u1} o) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f)))) hr))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (Ordinal.enum.{u1} α r _inst_1 o hr)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} α β)) (RelEmbedding.toEmbedding.{u1, u1} α β r s (RelIso.toRelEmbedding.{u1, u1} α β r s f)) (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (Quot.lift.{succ (succ u1), 1} WellOrder.{u1} (fun (a : WellOrder.{u1}) (b : WellOrder.{u1}) => HasEquiv.Equiv.{succ (succ u1), 0} WellOrder.{u1} (instHasEquiv.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1}) a b) Prop (fun (a₁ : WellOrder.{u1}) => Quotient.lift.{succ (succ u1), 1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} ((fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461.2528 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2541 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462.2546 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2559 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 r s)))) a₁) (Quotient.lift₂.proof_1.{succ (succ u1), 1, succ (succ u1)} WellOrder.{u1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} Ordinal.isEquivalent.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461.2528 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2541 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462.2546 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2559 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 r s)))) Ordinal.partialOrder.proof_2.{u1} a₁) (Ordinal.type.{u1} α r _inst_1)) (Quotient.lift₂.proof_2.{succ (succ u1), 1, succ (succ u1)} WellOrder.{u1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} Ordinal.isEquivalent.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461.2528 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2541 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462.2546 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2559 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 r s)))) Ordinal.partialOrder.proof_2.{u1} (Ordinal.type.{u1} α r _inst_1)) o) ((fun {α : Type.{succ u1}} [self : LT.{succ u1} α] (a._@.Init.Prelude._hyg.2009 : α) (a_1._@.Init.Prelude._hyg.2009 : α) (e_a._@.Init.Prelude._hyg.2009 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2009) => Eq.rec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2009 (fun (a_1._@.Init.Prelude._hyg.2009 : α) (e_a._@.Init.Prelude._hyg.2009 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2009) => forall (a._@.Init.Prelude._hyg.2011 : α) (a_1._@.Init.Prelude._hyg.2011 : α), (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) -> (Eq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) (LT.lt.{succ u1} α self a_1._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2011))) (fun (a._@.Init.Prelude._hyg.2011 : α) (a_1._@.Init.Prelude._hyg.2011 : α) (e_a._@.Init.Prelude._hyg.2011 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) => Eq.rec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2011 (fun (a_1._@.Init.Prelude._hyg.2011 : α) (e_a._@.Init.Prelude._hyg.2011 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) => Eq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2011)) (Eq.refl.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011)) a_1._@.Init.Prelude._hyg.2011 e_a._@.Init.Prelude._hyg.2011) a_1._@.Init.Prelude._hyg.2009 e_a._@.Init.Prelude._hyg.2009) Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o (Eq.refl.{succ (succ u1)} Ordinal.{u1} o) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f)))) hr))
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (Ordinal.enum.{u1} α r _inst_1 o hr)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} α β)) (RelEmbedding.toEmbedding.{u1, u1} α β r s (RelIso.toRelEmbedding.{u1, u1} α β r s f)) (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (Quot.lift.{succ (succ u1), 1} WellOrder.{u1} (fun (a : WellOrder.{u1}) (b : WellOrder.{u1}) => HasEquiv.Equiv.{succ (succ u1), 0} WellOrder.{u1} (instHasEquiv.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1}) a b) Prop (fun (a₁ : WellOrder.{u1}) => Quotient.lift.{succ (succ u1), 1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} ((fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468.2537 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2550 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469.2555 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2568 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 r s)))) a₁) (Quotient.lift₂.proof_1.{succ (succ u1), 1, succ (succ u1)} WellOrder.{u1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} Ordinal.isEquivalent.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468.2537 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2550 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469.2555 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2568 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 r s)))) Ordinal.partialOrder.proof_2.{u1} a₁) (Ordinal.type.{u1} α r _inst_1)) (Quotient.lift₂.proof_2.{succ (succ u1), 1, succ (succ u1)} WellOrder.{u1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} Ordinal.isEquivalent.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468.2537 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2468 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2550 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469.2555 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2469 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2568 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2549 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2567 r s)))) Ordinal.partialOrder.proof_2.{u1} (Ordinal.type.{u1} α r _inst_1)) o) ((fun {α : Type.{succ u1}} [self : LT.{succ u1} α] (a._@.Init.Prelude._hyg.2009 : α) (a_1._@.Init.Prelude._hyg.2009 : α) (e_a._@.Init.Prelude._hyg.2009 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2009) => Eq.rec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2009 (fun (a_1._@.Init.Prelude._hyg.2009 : α) (e_a._@.Init.Prelude._hyg.2009 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2009) => forall (a._@.Init.Prelude._hyg.2011 : α) (a_1._@.Init.Prelude._hyg.2011 : α), (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) -> (Eq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) (LT.lt.{succ u1} α self a_1._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2011))) (fun (a._@.Init.Prelude._hyg.2011 : α) (a_1._@.Init.Prelude._hyg.2011 : α) (e_a._@.Init.Prelude._hyg.2011 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) => Eq.rec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2011 (fun (a_1._@.Init.Prelude._hyg.2011 : α) (e_a._@.Init.Prelude._hyg.2011 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) => Eq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2011)) (Eq.refl.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011)) a_1._@.Init.Prelude._hyg.2011 e_a._@.Init.Prelude._hyg.2011) a_1._@.Init.Prelude._hyg.2009 e_a._@.Init.Prelude._hyg.2009) Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o (Eq.refl.{succ (succ u1)} Ordinal.{u1} o) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f)))) hr))
 Case conversion may be inaccurate. Consider using '#align ordinal.rel_iso_enum Ordinal.relIso_enumₓ'. -/
 theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) (hr : o < type r) :
@@ -778,7 +778,7 @@ def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r
 lean 3 declaration is
   forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} ((fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (coeFn.{succ (succ u1), succ (succ u1)} (PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (PrincipalSeg.hasCoeToFun.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (Ordinal.typein.{u1} α r _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ u1, succ (succ u1)} α Ordinal.{u1})) (RelEmbedding.toEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5873 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5875 : 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.Ordinal.Basic._hyg.5873 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5875) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5873 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5875 : 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.Ordinal.Basic._hyg.5873 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5875) (Ordinal.typein.principalSeg.{u1} α r _inst_1)))) (Ordinal.typein.{u1} α r _inst_1)
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ u1, succ (succ u1)} α Ordinal.{u1})) (RelEmbedding.toEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5885 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5887 : 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.Ordinal.Basic._hyg.5885 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5887) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5885 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5887 : 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.Ordinal.Basic._hyg.5885 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5887) (Ordinal.typein.principalSeg.{u1} α r _inst_1)))) (Ordinal.typein.{u1} α r _inst_1)
 Case conversion may be inaccurate. Consider using '#align ordinal.typein.principal_seg_coe Ordinal.typein.principalSeg_coeₓ'. -/
 @[simp]
 theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
@@ -1115,7 +1115,7 @@ def lift.initialSeg : @InitialSeg Ordinal.{u} Ordinal.{max u v} (· < ·) (· <
 lean 3 declaration is
   Eq.{max (succ (succ u1)) (succ (succ (max u1 u2)))} ((fun (_x : InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) => Ordinal.{u1} -> Ordinal.{max u1 u2}) Ordinal.lift.initialSeg.{u1, u2}) (coeFn.{max (succ (succ u1)) (succ (succ (max u1 u2))), max (succ (succ u1)) (succ (succ (max u1 u2)))} (InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) (fun (_x : InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) => Ordinal.{u1} -> Ordinal.{max u1 u2}) (FunLike.hasCoeToFun.{max (succ (succ u1)) (succ (succ (max u1 u2))), succ (succ u1), succ (succ (max u1 u2))} (InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => Ordinal.{max u1 u2}) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (succ (max u1 u2))), succ (succ u1), succ (succ (max u1 u2))} (InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) Ordinal.{u1} Ordinal.{max u1 u2} (InitialSeg.embeddingLike.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))))) Ordinal.lift.initialSeg.{u1, u2}) Ordinal.lift.{u2, u1}
 but is expected to have type
-  Eq.{max (succ (succ u1)) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8449 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8451 : 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.Ordinal.Basic._hyg.8449 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8451) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8464 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8466 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8464 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8466)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8449 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8451 : 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.Ordinal.Basic._hyg.8449 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8451) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8464 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8466 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8464 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8466)) Ordinal.{u1} Ordinal.{max u1 u2} (InitialSeg.instEmbeddingLikeInitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8449 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8451 : 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.Ordinal.Basic._hyg.8449 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8451) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8464 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8466 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8464 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8466))) Ordinal.lift.initialSeg.{u1, u2}) Ordinal.lift.{u2, u1}
+  Eq.{max (succ (succ u1)) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8469 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8471 : 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.Ordinal.Basic._hyg.8469 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8471) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8484 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8486 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8484 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8486)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8469 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8471 : 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.Ordinal.Basic._hyg.8469 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8471) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8484 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8486 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8484 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8486)) Ordinal.{u1} Ordinal.{max u1 u2} (InitialSeg.instEmbeddingLikeInitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8469 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8471 : 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.Ordinal.Basic._hyg.8469 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8471) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8484 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8486 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8484 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8486))) Ordinal.lift.initialSeg.{u1, u2}) Ordinal.lift.{u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.initial_seg_coe Ordinal.lift.initialSeg_coeₓ'. -/
 @[simp]
 theorem lift.initialSeg_coe : (lift.initialSeg : Ordinal → Ordinal) = lift :=
@@ -1529,7 +1529,7 @@ instance uniqueOutOne : Unique (1 : Ordinal).out.α
 lean 3 declaration is
   forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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 u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) x (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} 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 but is expected to have type
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0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1293 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1295 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ 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Ordinal.zero.{u1} Ordinal.one.{u1} Ordinal.partialOrder.{u1} Ordinal.zeroLEOneClass.{u1} Ordinal.NeZero.one.{u1}))))
 Case conversion may be inaccurate. Consider using '#align ordinal.one_out_eq Ordinal.one_out_eqₓ'. -/
 theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :=
   Unique.eq_default x
@@ -1542,7 +1542,7 @@ theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :
 lean 3 declaration is
   forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))))))))) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
 but is expected to have type
-  forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12740 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12742 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12740 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12742) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
+  forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12763 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12765 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12763 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12765) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.typein_one_out Ordinal.typein_one_outₓ'. -/
 @[simp]
 theorem typein_one_out (x : (1 : Ordinal).out.α) : typein (· < ·) x = 0 := by
@@ -1669,7 +1669,7 @@ def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α :=
 lean 3 declaration is
   forall {o : Ordinal.{u1}} (ho : 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), Eq.{succ u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (Eq.mpr.{0} (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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)) (Eq.ndrec.{0, succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o)) (fun (_a : Ordinal.{u1}) => Eq.{1} Prop (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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}))) _a)) (rfl.{1} Prop (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o)))) o (Ordinal.type_lt.{u1} o))) ho)) (Bot.bot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (OrderBot.toHasBot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o)))))) (Ordinal.outOrderBotOfPos.{u1} o ho)))
 but is expected to have type
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(Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14239 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14241) (isWellOrder_out_lt.{u1} o))) (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)) (Eq.ndrec.{0, succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1293 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1295 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1293 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1295) (isWellOrder_out_lt.{u1} o)) (fun (_a : Ordinal.{u1}) => Eq.{1} Prop (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})) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14239 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14241 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14239 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14241) (isWellOrder_out_lt.{u1} o))) (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})) _a)) (Eq.refl.{1} Prop (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})) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14239 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14241 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14239 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14241) (isWellOrder_out_lt.{u1} o)))) o (Ordinal.type_lt.{u1} o))) ho)) (Bot.bot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (OrderBot.toBot.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLE.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (Ordinal.outOrderBotOfPos.{u1} o ho)))
 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_eq_bot Ordinal.enum_zero_eq_botₓ'. -/
 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
     enum (· < ·) 0 (by rwa [type_lt]) =
@@ -1749,7 +1749,7 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
 lean 3 declaration is
   Eq.{max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} ((fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) Ordinal.lift.principalSeg.{u1, u2}) (coeFn.{max (succ (succ u1)) (succ (succ (max (succ u1) u2))), max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} (PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) (fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) (PrincipalSeg.hasCoeToFun.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) Ordinal.lift.principalSeg.{u1, u2}) Ordinal.lift.{max (succ u1) u2, u1}
 but is expected to have type
-  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} Ordinal.{max (succ u1) u2} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2})) (RelEmbedding.toEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14457 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14459 : 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.Ordinal.Basic._hyg.14457 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14459) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14472 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14474 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14472 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14474) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14457 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14459 : 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.Ordinal.Basic._hyg.14457 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14459) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14472 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14474 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14472 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14474) Ordinal.lift.principalSeg.{u1, u2}))) Ordinal.lift.{max (succ u1) u2, u1}
+  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} Ordinal.{max (succ u1) u2} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2})) (RelEmbedding.toEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14480 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14482 : 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.Ordinal.Basic._hyg.14480 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14482) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14495 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14497 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14495 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14497) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14480 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14482 : 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.Ordinal.Basic._hyg.14480 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14482) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14495 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14497 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14495 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14497) Ordinal.lift.principalSeg.{u1, u2}))) Ordinal.lift.{max (succ u1) u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg_coe Ordinal.lift.principalSeg_coeₓ'. -/
 @[simp]
 theorem lift.principalSeg_coe :

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Floris van Doorn
 
 ! This file was ported from Lean 3 source module set_theory.ordinal.basic
-! leanprover-community/mathlib commit ac34df03f74e6f797efd6991df2e3b7f7d8d33e0
+! leanprover-community/mathlib commit 8da9e30545433fdd8fe55a0d3da208e5d9263f03
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -605,7 +605,7 @@ theorem typein_apply {α β} {r : α → α → Prop} {s : β → β → Prop} [
           (RelEmbedding.codRestrict _ ((Subrel.relEmbedding _ _).trans f) fun ⟨x, h⟩ => by
             rw [RelEmbedding.trans_apply] <;> exact f.to_rel_embedding.map_rel_iff.2 h)
           fun ⟨y, h⟩ => by
-          rcases f.init' h with ⟨a, rfl⟩ <;>
+          rcases f.init h with ⟨a, rfl⟩ <;>
             exact
               ⟨⟨a, f.to_rel_embedding.map_rel_iff.1 h⟩,
                 Subtype.eq <| RelEmbedding.trans_apply _ _ _⟩⟩

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

@@ -722,7 +722,7 @@ theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β 
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} β (coeFn.{succ u1, succ u1} (RelIso.{u1, u1} α β r s) (fun (_x : RelIso.{u1, u1} α β r s) => α -> β) (RelIso.hasCoeToFun.{u1, u1} α β r s) f (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)) ((fun [self : LT.{succ u1} Ordinal.{u1}] (ᾰ : Ordinal.{u1}) (ᾰ_1 : Ordinal.{u1}) (e_2 : Eq.{succ (succ u1)} Ordinal.{u1} ᾰ ᾰ_1) (ᾰ_2 : Ordinal.{u1}) (ᾰ_3 : Ordinal.{u1}) (e_3 : Eq.{succ (succ u1)} Ordinal.{u1} ᾰ_2 ᾰ_3) => congr.{succ (succ u1), 1} Ordinal.{u1} Prop (LT.lt.{succ u1} Ordinal.{u1} self ᾰ) (LT.lt.{succ u1} Ordinal.{u1} self ᾰ_1) ᾰ_2 ᾰ_3 (congr_arg.{succ (succ u1), succ (succ u1)} Ordinal.{u1} (Ordinal.{u1} -> Prop) ᾰ ᾰ_1 (LT.lt.{succ u1} Ordinal.{u1} self) e_2) e_3) (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o (rfl.{succ (succ u1)} Ordinal.{u1} o) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f)))) hr))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (Ordinal.enum.{u1} α r _inst_1 o hr)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} α β)) (RelEmbedding.toEmbedding.{u1, u1} α β r s (RelIso.toRelEmbedding.{u1, u1} α β r s f)) (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (Quot.lift.{succ (succ u1), 1} WellOrder.{u1} (fun (a : WellOrder.{u1}) (b : WellOrder.{u1}) => HasEquiv.Equiv.{succ (succ u1), 0} WellOrder.{u1} (instHasEquiv.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1}) a b) Prop (fun (a₁ : WellOrder.{u1}) => Quotient.lift.{succ (succ u1), 1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} ((fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2458 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2459 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2458.2525 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2458 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2538 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2459.2543 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2459 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2556 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 r s)))) a₁) (Quotient.lift₂.proof_1.{succ (succ u1), 1, succ (succ u1)} WellOrder.{u1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} Ordinal.isEquivalent.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2458 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2459 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2458.2525 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2458 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2538 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2459.2543 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2459 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2556 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 r s)))) Ordinal.partialOrder.proof_2.{u1} a₁) (Ordinal.type.{u1} α r _inst_1)) (Quotient.lift₂.proof_2.{succ (succ u1), 1, succ (succ u1)} WellOrder.{u1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} Ordinal.isEquivalent.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2458 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2459 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2458.2525 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2458 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2538 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2459.2543 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2459 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2556 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2537 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2555 r s)))) Ordinal.partialOrder.proof_2.{u1} (Ordinal.type.{u1} α r _inst_1)) o) ((fun {α : Type.{succ u1}} [self : LT.{succ u1} α] (a._@.Init.Prelude._hyg.2009 : α) (a_1._@.Init.Prelude._hyg.2009 : α) (e_a._@.Init.Prelude._hyg.2009 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2009) => Eq.rec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2009 (fun (a_1._@.Init.Prelude._hyg.2009 : α) (e_a._@.Init.Prelude._hyg.2009 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2009) => forall (a._@.Init.Prelude._hyg.2011 : α) (a_1._@.Init.Prelude._hyg.2011 : α), (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) -> (Eq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) (LT.lt.{succ u1} α self a_1._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2011))) (fun (a._@.Init.Prelude._hyg.2011 : α) (a_1._@.Init.Prelude._hyg.2011 : α) (e_a._@.Init.Prelude._hyg.2011 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) => Eq.rec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2011 (fun (a_1._@.Init.Prelude._hyg.2011 : α) (e_a._@.Init.Prelude._hyg.2011 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) => Eq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2011)) (Eq.refl.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011)) a_1._@.Init.Prelude._hyg.2011 e_a._@.Init.Prelude._hyg.2011) a_1._@.Init.Prelude._hyg.2009 e_a._@.Init.Prelude._hyg.2009) Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o (Eq.refl.{succ (succ u1)} Ordinal.{u1} o) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f)))) hr))
+  forall {α : Type.{u1}} {β : Type.{u1}} {r : α -> α -> Prop} {s : β -> β -> Prop} [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : IsWellOrder.{u1} β s] (f : RelIso.{u1, u1} α β r s) (o : Ordinal.{u1}) (hr : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} α r _inst_1)), Eq.{succ u1} ((fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) (Ordinal.enum.{u1} α r _inst_1 o hr)) (FunLike.coe.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{succ u1, succ u1, succ u1} (Function.Embedding.{succ u1, succ u1} α β) α β (Function.instEmbeddingLikeEmbedding.{succ u1, succ u1} α β)) (RelEmbedding.toEmbedding.{u1, u1} α β r s (RelIso.toRelEmbedding.{u1, u1} α β r s f)) (Ordinal.enum.{u1} α r _inst_1 o hr)) (Ordinal.enum.{u1} β s _inst_2 o (Eq.mpr.{0} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o (Ordinal.type.{u1} β s _inst_2)) (Quot.lift.{succ (succ u1), 1} WellOrder.{u1} (fun (a : WellOrder.{u1}) (b : WellOrder.{u1}) => HasEquiv.Equiv.{succ (succ u1), 0} WellOrder.{u1} (instHasEquiv.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1}) a b) Prop (fun (a₁ : WellOrder.{u1}) => Quotient.lift.{succ (succ u1), 1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} ((fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461.2528 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2541 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462.2546 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2559 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 r s)))) a₁) (Quotient.lift₂.proof_1.{succ (succ u1), 1, succ (succ u1)} WellOrder.{u1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} Ordinal.isEquivalent.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461.2528 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2541 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462.2546 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2559 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 r s)))) Ordinal.partialOrder.proof_2.{u1} a₁) (Ordinal.type.{u1} α r _inst_1)) (Quotient.lift₂.proof_2.{succ (succ u1), 1, succ (succ u1)} WellOrder.{u1} WellOrder.{u1} Prop Ordinal.isEquivalent.{u1} Ordinal.isEquivalent.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461 : WellOrder.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462 : WellOrder.{u1}) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461.2528 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2461 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 : Type.{u1}) (r : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2541 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 r) => Ordinal.isEquivalent.match_1.{u1, 1} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462.2546 : WellOrder.{u1}) => Prop) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2462 (fun (α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 : Type.{u1}) (s : α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 -> α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 -> Prop) (wo._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2559 : IsWellOrder.{u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 s) => Nonempty.{succ u1} (PrincipalSeg.{u1, u1} α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2540 α._@.Mathlib.SetTheory.Ordinal.Basic._hyg.2558 r s)))) Ordinal.partialOrder.proof_2.{u1} (Ordinal.type.{u1} α r _inst_1)) o) ((fun {α : Type.{succ u1}} [self : LT.{succ u1} α] (a._@.Init.Prelude._hyg.2009 : α) (a_1._@.Init.Prelude._hyg.2009 : α) (e_a._@.Init.Prelude._hyg.2009 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2009) => Eq.rec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2009 (fun (a_1._@.Init.Prelude._hyg.2009 : α) (e_a._@.Init.Prelude._hyg.2009 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2009) => forall (a._@.Init.Prelude._hyg.2011 : α) (a_1._@.Init.Prelude._hyg.2011 : α), (Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) -> (Eq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) (LT.lt.{succ u1} α self a_1._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2011))) (fun (a._@.Init.Prelude._hyg.2011 : α) (a_1._@.Init.Prelude._hyg.2011 : α) (e_a._@.Init.Prelude._hyg.2011 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) => Eq.rec.{0, succ (succ u1)} α a._@.Init.Prelude._hyg.2011 (fun (a_1._@.Init.Prelude._hyg.2011 : α) (e_a._@.Init.Prelude._hyg.2011 : Eq.{succ (succ u1)} α a._@.Init.Prelude._hyg.2011 a_1._@.Init.Prelude._hyg.2011) => Eq.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011) (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a_1._@.Init.Prelude._hyg.2011)) (Eq.refl.{1} Prop (LT.lt.{succ u1} α self a._@.Init.Prelude._hyg.2009 a._@.Init.Prelude._hyg.2011)) a_1._@.Init.Prelude._hyg.2011 e_a._@.Init.Prelude._hyg.2011) a_1._@.Init.Prelude._hyg.2009 e_a._@.Init.Prelude._hyg.2009) Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) o o (Eq.refl.{succ (succ u1)} Ordinal.{u1} o) (Ordinal.type.{u1} β s _inst_2) (Ordinal.type.{u1} α r _inst_1) (Quotient.sound.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (WellOrder.mk.{u1} β s _inst_2) (WellOrder.mk.{u1} α r _inst_1) (Nonempty.intro.{succ u1} (RelIso.{u1, u1} β α s r) (RelIso.symm.{u1, u1} α β r s f)))) hr))
 Case conversion may be inaccurate. Consider using '#align ordinal.rel_iso_enum Ordinal.relIso_enumₓ'. -/
 theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) (hr : o < type r) :
@@ -778,7 +778,7 @@ def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r
 lean 3 declaration is
   forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} ((fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (coeFn.{succ (succ u1), succ (succ u1)} (PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (fun (_x : PrincipalSeg.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) => α -> Ordinal.{u1}) (PrincipalSeg.hasCoeToFun.{u1, succ u1} α Ordinal.{u1} r (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})))) (Ordinal.typein.principalSeg.{u1} α r _inst_1)) (Ordinal.typein.{u1} α r _inst_1)
 but is expected to have type
-  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ u1, succ (succ u1)} α Ordinal.{u1})) (RelEmbedding.toEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5870 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5872 : 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.Ordinal.Basic._hyg.5870 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5872) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5870 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5872 : 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.Ordinal.Basic._hyg.5870 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5872) (Ordinal.typein.principalSeg.{u1} α r _inst_1)))) (Ordinal.typein.{u1} α r _inst_1)
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r], Eq.{succ (succ u1)} (forall (a : α), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) a) (FunLike.coe.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => Ordinal.{u1}) _x) (EmbeddingLike.toFunLike.{succ (succ u1), succ u1, succ (succ u1)} (Function.Embedding.{succ u1, succ (succ u1)} α Ordinal.{u1}) α Ordinal.{u1} (Function.instEmbeddingLikeEmbedding.{succ u1, succ (succ u1)} α Ordinal.{u1})) (RelEmbedding.toEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5873 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5875 : 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.Ordinal.Basic._hyg.5873 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5875) (PrincipalSeg.toRelEmbedding.{u1, succ u1} α Ordinal.{u1} r (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5873 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5875 : 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.Ordinal.Basic._hyg.5873 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.5875) (Ordinal.typein.principalSeg.{u1} α r _inst_1)))) (Ordinal.typein.{u1} α r _inst_1)
 Case conversion may be inaccurate. Consider using '#align ordinal.typein.principal_seg_coe Ordinal.typein.principalSeg_coeₓ'. -/
 @[simp]
 theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
@@ -1115,7 +1115,7 @@ def lift.initialSeg : @InitialSeg Ordinal.{u} Ordinal.{max u v} (· < ·) (· <
 lean 3 declaration is
   Eq.{max (succ (succ u1)) (succ (succ (max u1 u2)))} ((fun (_x : InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) => Ordinal.{u1} -> Ordinal.{max u1 u2}) Ordinal.lift.initialSeg.{u1, u2}) (coeFn.{max (succ (succ u1)) (succ (succ (max u1 u2))), max (succ (succ u1)) (succ (succ (max u1 u2)))} (InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) (fun (_x : InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) => Ordinal.{u1} -> Ordinal.{max u1 u2}) (FunLike.hasCoeToFun.{max (succ (succ u1)) (succ (succ (max u1 u2))), succ (succ u1), succ (succ (max u1 u2))} (InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => Ordinal.{max u1 u2}) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (succ (max u1 u2))), succ (succ u1), succ (succ (max u1 u2))} (InitialSeg.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))) Ordinal.{u1} Ordinal.{max u1 u2} (InitialSeg.embeddingLike.{succ u1, succ (max u1 u2)} Ordinal.{u1} Ordinal.{max u1 u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})))))) Ordinal.lift.initialSeg.{u1, u2}) Ordinal.lift.{u2, u1}
 but is expected to have type
-  Eq.{max (succ (succ u1)) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8446 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8448 : 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.Ordinal.Basic._hyg.8446 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8448) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8461 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8463 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8461 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8463)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8446 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8448 : 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.Ordinal.Basic._hyg.8446 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8448) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8461 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8463 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8461 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8463)) Ordinal.{u1} Ordinal.{max u1 u2} (InitialSeg.instEmbeddingLikeInitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8446 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8448 : 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.Ordinal.Basic._hyg.8446 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8448) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8461 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8463 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8461 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8463))) Ordinal.lift.initialSeg.{u1, u2}) Ordinal.lift.{u2, u1}
+  Eq.{max (succ (succ u1)) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8449 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8451 : 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.Ordinal.Basic._hyg.8449 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8451) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8464 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8466 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8464 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8466)) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max u1 u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (succ u2)), succ (succ u1), max (succ (succ u1)) (succ (succ u2))} (InitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8449 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8451 : 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.Ordinal.Basic._hyg.8449 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8451) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8464 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8466 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8464 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8466)) Ordinal.{u1} Ordinal.{max u1 u2} (InitialSeg.instEmbeddingLikeInitialSeg.{succ u1, max (succ u1) (succ u2)} Ordinal.{u1} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8449 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8451 : 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.Ordinal.Basic._hyg.8449 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8451) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8464 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8466 : Ordinal.{max u1 u2}) => LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8464 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.8466))) Ordinal.lift.initialSeg.{u1, u2}) Ordinal.lift.{u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.initial_seg_coe Ordinal.lift.initialSeg_coeₓ'. -/
 @[simp]
 theorem lift.initialSeg_coe : (lift.initialSeg : Ordinal → Ordinal) = lift :=
@@ -1529,7 +1529,7 @@ instance uniqueOutOne : Unique (1 : Ordinal).out.α
 lean 3 declaration is
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Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))))))))) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))))) True (id_tag Tactic.IdTag.simp (Eq.{1} Prop (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} 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u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1292 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.1294) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{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}))) (Ordinal.type_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Mathlib.Algebra.Order.ZeroLEOne._auxLemma.2.{succ u1} Ordinal.{u1} Ordinal.zero.{u1} Ordinal.one.{u1} Ordinal.partialOrder.{u1} Ordinal.zeroLEOneClass.{u1} Ordinal.NeZero.one.{u1}))))
 Case conversion may be inaccurate. Consider using '#align ordinal.one_out_eq Ordinal.one_out_eqₓ'. -/
 theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :=
   Unique.eq_default x
@@ -1542,7 +1542,7 @@ theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :
 lean 3 declaration is
   forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{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.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))))))))) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
 but is expected to have type
-  forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12737 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12739 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12737 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12739) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
+  forall (x : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.typein.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12740 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12742 : WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) => LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (DistribLattice.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (instDistribLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})))) (linearOrderOut.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))))))))) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12740 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.12742) (isWellOrder_out_lt.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) x) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.typein_one_out Ordinal.typein_one_outₓ'. -/
 @[simp]
 theorem typein_one_out (x : (1 : Ordinal).out.α) : typein (· < ·) x = 0 := by
@@ -1669,7 +1669,7 @@ def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α :=
 lean 3 declaration is
   forall {o : Ordinal.{u1}} (ho : 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), Eq.{succ u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Ordinal.enum.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (Eq.mpr.{0} (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}))) (Ordinal.type.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LT.lt.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Preorder.toLT.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (PartialOrder.toPreorder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (SemilatticeInf.toPartialOrder.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Lattice.toSemilatticeInf.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (LinearOrder.toLattice.{u1} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (linearOrderOut.{u1} o))))))) (isWellOrder_out_lt.{u1} o))) (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) (id_tag Tactic.IdTag.rw (Eq.{1} Prop (LT.lt.{succ u1} Ordinal.{u1} 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 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_eq_bot Ordinal.enum_zero_eq_botₓ'. -/
 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
     enum (· < ·) 0 (by rwa [type_lt]) =
@@ -1749,7 +1749,7 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
 lean 3 declaration is
   Eq.{max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} ((fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) Ordinal.lift.principalSeg.{u1, u2}) (coeFn.{max (succ (succ u1)) (succ (succ (max (succ u1) u2))), max (succ (succ u1)) (succ (succ (max (succ u1) u2)))} (PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) (fun (_x : PrincipalSeg.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) => Ordinal.{u1} -> Ordinal.{max (succ u1) u2}) (PrincipalSeg.hasCoeToFun.{succ u1, succ (max (succ u1) u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (LT.lt.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{succ (max (succ u1) u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})))) Ordinal.lift.principalSeg.{u1, u2}) Ordinal.lift.{max (succ u1) u2, u1}
 but is expected to have type
-  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} Ordinal.{max (succ u1) u2} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2})) (RelEmbedding.toEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14454 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14456 : 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.Ordinal.Basic._hyg.14454 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14456) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14469 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14471 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14469 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14471) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14454 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14456 : 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.Ordinal.Basic._hyg.14454 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14456) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14469 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14471 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14469 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14471) Ordinal.lift.principalSeg.{u1, u2}))) Ordinal.lift.{max (succ u1) u2, u1}
+  Eq.{max (succ (succ (succ u1))) (succ (succ u2))} (forall (a : Ordinal.{u1}), (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) a) (FunLike.coe.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} (fun (_x : Ordinal.{u1}) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : Ordinal.{u1}) => Ordinal.{max (succ u1) u2}) _x) (EmbeddingLike.toFunLike.{max (succ (succ u1)) (succ (max (succ (succ u1)) (succ u2))), succ (succ u1), succ (max (succ (succ u1)) (succ u2))} (Function.Embedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2}) Ordinal.{u1} Ordinal.{max (succ u1) u2} (Function.instEmbeddingLikeEmbedding.{succ (succ u1), succ (max (succ (succ u1)) (succ u2))} Ordinal.{u1} Ordinal.{max (succ u1) u2})) (RelEmbedding.toEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14457 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14459 : 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.Ordinal.Basic._hyg.14457 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14459) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14472 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14474 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14472 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14474) (PrincipalSeg.toRelEmbedding.{succ u1, max (succ (succ u1)) (succ u2)} Ordinal.{u1} Ordinal.{max (succ u1) u2} (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14457 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14459 : 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.Ordinal.Basic._hyg.14457 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14459) (fun (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14472 : Ordinal.{max (succ u1) u2}) (x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14474 : Ordinal.{max (succ u1) u2}) => LT.lt.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (Preorder.toLT.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} (PartialOrder.toPreorder.{max (succ (succ u1)) (succ u2)} Ordinal.{max (succ u1) u2} Ordinal.partialOrder.{max (succ u1) u2})) x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14472 x._@.Mathlib.SetTheory.Ordinal.Basic._hyg.14474) Ordinal.lift.principalSeg.{u1, u2}))) Ordinal.lift.{max (succ u1) u2, u1}
 Case conversion may be inaccurate. Consider using '#align ordinal.lift.principal_seg_coe Ordinal.lift.principalSeg_coeₓ'. -/
 @[simp]
 theorem lift.principalSeg_coe :

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

@@ -297,13 +297,22 @@ theorem type_empty : type (@EmptyRelation Empty) = 0 :=
 #align ordinal.type_empty Ordinal.type_empty
 -/
 
-#print Ordinal.type_eq_one_of_unique /-
+/- warning: ordinal.type_eq_one_of_unique -> Ordinal.type_eq_one_of_unique is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : Unique.{succ u1} α], Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} α r _inst_1) (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}} (r : α -> α -> Prop) [_inst_1 : IsWellOrder.{u1} α r] [_inst_2 : Unique.{succ u1} α], Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} α r _inst_1) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))
+Case conversion may be inaccurate. Consider using '#align ordinal.type_eq_one_of_unique Ordinal.type_eq_one_of_uniqueₓ'. -/
 theorem type_eq_one_of_unique (r) [IsWellOrder α r] [Unique α] : type r = 1 :=
   (RelIso.relIsoOfUniqueOfIrrefl r _).ordinal_type_eq
 #align ordinal.type_eq_one_of_unique Ordinal.type_eq_one_of_unique
--/
 
-#print Ordinal.type_eq_one_iff_unique /-
+/- warning: ordinal.type_eq_one_iff_unique -> Ordinal.type_eq_one_iff_unique is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r], Iff (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} α r _inst_1) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) (Nonempty.{succ u1} (Unique.{succ u1} α))
+but is expected to have type
+  forall {α : Type.{u1}} {r : α -> α -> Prop} [_inst_1 : IsWellOrder.{u1} α r], Iff (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} α r _inst_1) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (Nonempty.{succ u1} (Unique.{succ u1} α))
+Case conversion may be inaccurate. Consider using '#align ordinal.type_eq_one_iff_unique Ordinal.type_eq_one_iff_uniqueₓ'. -/
 @[simp]
 theorem type_eq_one_iff_unique [IsWellOrder α r] : type r = 1 ↔ Nonempty (Unique α) :=
   ⟨fun h =>
@@ -311,19 +320,26 @@ theorem type_eq_one_iff_unique [IsWellOrder α r] : type r = 1 ↔ Nonempty (Uni
     ⟨s.toEquiv.unique⟩,
     fun ⟨h⟩ => @type_eq_one_of_unique α r _ h⟩
 #align ordinal.type_eq_one_iff_unique Ordinal.type_eq_one_iff_unique
--/
 
-#print Ordinal.type_pUnit /-
+/- warning: ordinal.type_punit -> Ordinal.type_pUnit is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.type.{u1} PUnit.{succ u1} (EmptyRelation.{succ u1} PUnit.{succ u1}) (EmptyRelation.isWellOrder.{u1} PUnit.{succ u1} PUnit.subsingleton.{succ 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)} Ordinal.{u1} (Ordinal.type.{u1} PUnit.{succ u1} (EmptyRelation.{succ u1} PUnit.{succ u1}) (instIsWellOrderEmptyRelation.{u1} PUnit.{succ u1} instSubsingletonPUnit.{succ 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 ordinal.type_punit Ordinal.type_pUnitₓ'. -/
 theorem type_pUnit : type (@EmptyRelation PUnit) = 1 :=
   rfl
 #align ordinal.type_punit Ordinal.type_pUnit
--/
 
-#print Ordinal.type_unit /-
+/- warning: ordinal.type_unit -> Ordinal.type_unit is a dubious translation:
+lean 3 declaration is
+  Eq.{2} Ordinal.{0} (Ordinal.type.{0} Unit (EmptyRelation.{1} Unit) (EmptyRelation.isWellOrder.{0} Unit PUnit.subsingleton.{1})) (OfNat.ofNat.{1} Ordinal.{0} 1 (OfNat.mk.{1} Ordinal.{0} 1 (One.one.{1} Ordinal.{0} Ordinal.hasOne.{0})))
+but is expected to have type
+  Eq.{2} Ordinal.{0} (Ordinal.type.{0} Unit (EmptyRelation.{1} Unit) (instIsWellOrderEmptyRelation.{0} Unit instSubsingletonPUnit.{1})) (OfNat.ofNat.{1} Ordinal.{0} 1 (One.toOfNat1.{1} Ordinal.{0} Ordinal.one.{0}))
+Case conversion may be inaccurate. Consider using '#align ordinal.type_unit Ordinal.type_unitₓ'. -/
 theorem type_unit : type (@EmptyRelation Unit) = 1 :=
   rfl
 #align ordinal.type_unit Ordinal.type_unit
--/
 
 #print Ordinal.out_empty_iff_eq_zero /-
 @[simp]
@@ -357,11 +373,15 @@ theorem ne_zero_of_out_nonempty (o : Ordinal) [h : Nonempty o.out.α] : o ≠ 0
 #align ordinal.ne_zero_of_out_nonempty Ordinal.ne_zero_of_out_nonempty
 -/
 
-#print Ordinal.one_ne_zero /-
+/- warning: ordinal.one_ne_zero -> Ordinal.one_ne_zero is a dubious translation:
+lean 3 declaration is
+  Ne.{succ (succ u1)} Ordinal.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
+but is expected to have type
+  Ne.{succ (succ u1)} Ordinal.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
+Case conversion may be inaccurate. Consider using '#align ordinal.one_ne_zero Ordinal.one_ne_zeroₓ'. -/
 protected theorem one_ne_zero : (1 : Ordinal) ≠ 0 :=
   type_ne_zero_of_nonempty _
 #align ordinal.one_ne_zero Ordinal.one_ne_zero
--/
 
 instance : Nontrivial Ordinal.{u} :=
   ⟨⟨1, 0, Ordinal.one_ne_zero⟩⟩
@@ -476,7 +496,7 @@ instance : OrderBot Ordinal :=
 lean 3 declaration is
   Eq.{succ (succ u1)} Ordinal.{u1} (Bot.bot.{succ u1} Ordinal.{u1} (OrderBot.toHasBot.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.orderBot.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
 but is expected to have type
-  Eq.{succ (succ u1)} Ordinal.{u1} (Bot.bot.{succ u1} Ordinal.{u1} (OrderBot.toBot.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.orderBot.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))
+  Eq.{succ (succ u1)} Ordinal.{u1} (Bot.bot.{succ u1} Ordinal.{u1} (OrderBot.toBot.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) Ordinal.orderBot.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.bot_eq_zero Ordinal.bot_eq_zeroₓ'. -/
 @[simp]
 theorem bot_eq_zero : (⊥ : Ordinal) = 0 :=
@@ -511,11 +531,15 @@ theorem eq_zero_or_pos : ∀ a : Ordinal, a = 0 ∨ 0 < a :=
 instance : ZeroLEOneClass Ordinal :=
   ⟨Ordinal.zero_le _⟩
 
-#print Ordinal.NeZero.one /-
+/- warning: ordinal.ne_zero.one -> Ordinal.NeZero.one is a dubious translation:
+lean 3 declaration is
+  NeZero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{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
+  NeZero.{succ u1} Ordinal.{u1} Ordinal.zero.{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 ordinal.ne_zero.one Ordinal.NeZero.oneₓ'. -/
 instance NeZero.one : NeZero (1 : Ordinal) :=
   ⟨Ordinal.one_ne_zero⟩
 #align ordinal.ne_zero.one Ordinal.NeZero.one
--/
 
 #print Ordinal.initialSegOut /-
 /-- Given two ordinals `α ≤ β`, then `initial_seg_out α β` is the initial segment embedding
@@ -811,12 +835,16 @@ theorem card_eq_zero {o} : card o = 0 ↔ o = 0 :=
 #align ordinal.card_eq_zero Ordinal.card_eq_zero
 -/
 
-#print Ordinal.card_one /-
+/- warning: ordinal.card_one -> Ordinal.card_one is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Cardinal.{u1} (Ordinal.card.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (OfNat.mk.{succ u1} Cardinal.{u1} 1 (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))
+but is expected to have type
+  Eq.{succ (succ u1)} Cardinal.{u1} (Ordinal.card.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (One.toOfNat1.{succ u1} Cardinal.{u1} Cardinal.instOneCardinal.{u1}))
+Case conversion may be inaccurate. Consider using '#align ordinal.card_one Ordinal.card_oneₓ'. -/
 @[simp]
 theorem card_one : card 1 = 1 :=
   rfl
 #align ordinal.card_one Ordinal.card_one
--/
 
 /-! ### Lifting ordinals to a higher universe -/
 
@@ -1000,7 +1028,7 @@ theorem lift_lt {a b : Ordinal} : lift a < lift b ↔ a < b := by
 lean 3 declaration is
   Eq.{succ (succ (max u1 u2))} Ordinal.{max u1 u2} (Ordinal.lift.{u2, u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))) (OfNat.ofNat.{succ (max u1 u2)} Ordinal.{max u1 u2} 0 (OfNat.mk.{succ (max u1 u2)} Ordinal.{max u1 u2} 0 (Zero.zero.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.hasZero.{max u1 u2})))
 but is expected to have type
-  Eq.{max (succ (succ u2)) (succ (succ u1))} Ordinal.{max u2 u1} (Ordinal.lift.{u1, u2} (OfNat.ofNat.{succ u2} Ordinal.{u2} 0 (Zero.toOfNat0.{succ u2} Ordinal.{u2} Ordinal.hasZero.{u2}))) (OfNat.ofNat.{max (succ u2) (succ u1)} Ordinal.{max u2 u1} 0 (Zero.toOfNat0.{max (succ u2) (succ u1)} Ordinal.{max u2 u1} Ordinal.hasZero.{max u2 u1}))
+  Eq.{max (succ (succ u2)) (succ (succ u1))} Ordinal.{max u2 u1} (Ordinal.lift.{u1, u2} (OfNat.ofNat.{succ u2} Ordinal.{u2} 0 (Zero.toOfNat0.{succ u2} Ordinal.{u2} Ordinal.zero.{u2}))) (OfNat.ofNat.{max (succ u2) (succ u1)} Ordinal.{max u2 u1} 0 (Zero.toOfNat0.{max (succ u2) (succ u1)} Ordinal.{max u2 u1} Ordinal.zero.{max u2 u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.lift_zero Ordinal.lift_zeroₓ'. -/
 @[simp]
 theorem lift_zero : lift 0 = 0 :=
@@ -1011,7 +1039,7 @@ theorem lift_zero : lift 0 = 0 :=
 lean 3 declaration is
   Eq.{succ (succ (max u1 u2))} Ordinal.{max u1 u2} (Ordinal.lift.{u2, u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) (OfNat.ofNat.{succ (max u1 u2)} Ordinal.{max u1 u2} 1 (OfNat.mk.{succ (max u1 u2)} Ordinal.{max u1 u2} 1 (One.one.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.hasOne.{max u1 u2})))
 but is expected to have type
-  Eq.{max (succ (succ u2)) (succ (succ u1))} Ordinal.{max u2 u1} (Ordinal.lift.{u1, u2} (OfNat.ofNat.{succ u2} Ordinal.{u2} 1 (One.toOfNat1.{succ u2} Ordinal.{u2} Ordinal.hasOne.{u2}))) (OfNat.ofNat.{max (succ u2) (succ u1)} Ordinal.{max u2 u1} 1 (One.toOfNat1.{max (succ u2) (succ u1)} Ordinal.{max u2 u1} Ordinal.hasOne.{max u2 u1}))
+  Eq.{max (succ (succ u2)) (succ (succ u1))} Ordinal.{max u2 u1} (Ordinal.lift.{u1, u2} (OfNat.ofNat.{succ u2} Ordinal.{u2} 1 (One.toOfNat1.{succ u2} Ordinal.{u2} Ordinal.one.{u2}))) (OfNat.ofNat.{max (succ u2) (succ u1)} Ordinal.{max u2 u1} 1 (One.toOfNat1.{max (succ u2) (succ u1)} Ordinal.{max u2 u1} Ordinal.one.{max u2 u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.lift_one Ordinal.lift_oneₓ'. -/
 @[simp]
 theorem lift_one : lift 1 = 1 :=
@@ -1170,7 +1198,7 @@ instance : AddMonoidWithOne Ordinal.{u}
 lean 3 declaration is
   forall (o₁ : Ordinal.{u1}) (o₂ : Ordinal.{u1}), Eq.{succ (succ u1)} Cardinal.{u1} (Ordinal.card.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) o₁ o₂)) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) (Ordinal.card.{u1} o₁) (Ordinal.card.{u1} o₂))
 but is expected to have type
-  forall (o₁ : Ordinal.{u1}) (o₂ : Ordinal.{u1}), Eq.{succ (succ u1)} Cardinal.{u1} (Ordinal.card.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) o₁ o₂)) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) (Ordinal.card.{u1} o₁) (Ordinal.card.{u1} o₂))
+  forall (o₁ : Ordinal.{u1}) (o₂ : Ordinal.{u1}), Eq.{succ (succ u1)} Cardinal.{u1} (Ordinal.card.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) o₁ o₂)) (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) (Ordinal.card.{u1} o₁) (Ordinal.card.{u1} o₂))
 Case conversion may be inaccurate. Consider using '#align ordinal.card_add Ordinal.card_addₓ'. -/
 @[simp]
 theorem card_add (o₁ o₂ : Ordinal) : card (o₁ + o₂) = card o₁ + card o₂ :=
@@ -1284,7 +1312,7 @@ instance : ConditionallyCompleteLinearOrderBot Ordinal :=
 lean 3 declaration is
   forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (LinearOrder.max.{succ u1} Ordinal.{u1} Ordinal.linearOrder.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) a
 but is expected to have type
-  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Max.max.{succ u1} Ordinal.{u1} (LinearOrder.toMax.{succ u1} Ordinal.{u1} Ordinal.linearOrder.{u1}) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})) a) a
+  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Max.max.{succ u1} Ordinal.{u1} (LinearOrder.toMax.{succ u1} Ordinal.{u1} Ordinal.linearOrder.{u1}) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) a
 Case conversion may be inaccurate. Consider using '#align ordinal.max_zero_left Ordinal.max_zero_leftₓ'. -/
 @[simp]
 theorem max_zero_left : ∀ a : Ordinal, max 0 a = a :=
@@ -1295,7 +1323,7 @@ theorem max_zero_left : ∀ a : Ordinal, max 0 a = a :=
 lean 3 declaration is
   forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (LinearOrder.max.{succ u1} Ordinal.{u1} Ordinal.linearOrder.{u1} a (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))) a
 but is expected to have type
-  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Max.max.{succ u1} Ordinal.{u1} (LinearOrder.toMax.{succ u1} Ordinal.{u1} Ordinal.linearOrder.{u1}) a (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a
+  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Max.max.{succ u1} Ordinal.{u1} (LinearOrder.toMax.{succ u1} Ordinal.{u1} Ordinal.linearOrder.{u1}) a (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) a
 Case conversion may be inaccurate. Consider using '#align ordinal.max_zero_right Ordinal.max_zero_rightₓ'. -/
 @[simp]
 theorem max_zero_right : ∀ a : Ordinal, max a 0 = a :=
@@ -1306,7 +1334,7 @@ theorem max_zero_right : ∀ a : Ordinal, max a 0 = a :=
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (Eq.{succ (succ u1)} Ordinal.{u1} (LinearOrder.max.{succ u1} Ordinal.{u1} Ordinal.linearOrder.{u1} a b) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))) (And (Eq.{succ (succ u1)} Ordinal.{u1} a (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))) (Eq.{succ (succ u1)} Ordinal.{u1} b (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))))
 but is expected to have type
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (Eq.{succ (succ u1)} Ordinal.{u1} (Max.max.{succ u1} Ordinal.{u1} (LinearOrder.toMax.{succ u1} Ordinal.{u1} Ordinal.linearOrder.{u1}) a b) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (And (Eq.{succ (succ u1)} Ordinal.{u1} a (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (Eq.{succ (succ u1)} Ordinal.{u1} b (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))))
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (Eq.{succ (succ u1)} Ordinal.{u1} (Max.max.{succ u1} Ordinal.{u1} (LinearOrder.toMax.{succ u1} Ordinal.{u1} Ordinal.linearOrder.{u1}) a b) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (And (Eq.{succ (succ u1)} Ordinal.{u1} a (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (Eq.{succ (succ u1)} Ordinal.{u1} b (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))))
 Case conversion may be inaccurate. Consider using '#align ordinal.max_eq_zero Ordinal.max_eq_zeroₓ'. -/
 @[simp]
 theorem max_eq_zero {a b : Ordinal} : max a b = 0 ↔ a = 0 ∧ b = 0 :=
@@ -1317,7 +1345,7 @@ theorem max_eq_zero {a b : Ordinal} : max a b = 0 ↔ a = 0 ∧ b = 0 :=
 lean 3 declaration is
   Eq.{succ (succ u1)} Ordinal.{u1} (InfSet.infₛ.{succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toHasInf.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.conditionallyCompleteLinearOrderBot.{u1}))) (EmptyCollection.emptyCollection.{succ u1} (Set.{succ u1} Ordinal.{u1}) (Set.hasEmptyc.{succ u1} Ordinal.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))
 but is expected to have type
-  Eq.{succ (succ u1)} Ordinal.{u1} (InfSet.infₛ.{succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toInfSet.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1}))) (EmptyCollection.emptyCollection.{succ u1} (Set.{succ u1} Ordinal.{u1}) (Set.instEmptyCollectionSet.{succ u1} Ordinal.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))
+  Eq.{succ (succ u1)} Ordinal.{u1} (InfSet.infₛ.{succ u1} Ordinal.{u1} (ConditionallyCompleteLattice.toInfSet.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{succ u1} Ordinal.{u1} (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{succ u1} Ordinal.{u1} Ordinal.instConditionallyCompleteLinearOrderBotOrdinal.{u1}))) (EmptyCollection.emptyCollection.{succ u1} (Set.{succ u1} Ordinal.{u1}) (Set.instEmptyCollectionSet.{succ u1} Ordinal.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.Inf_empty Ordinal.infₛ_emptyₓ'. -/
 @[simp]
 theorem infₛ_empty : infₛ (∅ : Set Ordinal) = 0 :=
@@ -1362,25 +1390,33 @@ instance : NoMaxOrder Ordinal :=
 instance : SuccOrder Ordinal.{u} :=
   SuccOrder.ofSuccLeIff (fun o => o + 1) fun a b => succ_le_iff'
 
-#print Ordinal.add_one_eq_succ /-
+/- warning: ordinal.add_one_eq_succ -> Ordinal.add_one_eq_succ is a dubious translation:
+lean 3 declaration is
+  forall (o : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) o (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)
+but is expected to have type
+  forall (o : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) o (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} o)
+Case conversion may be inaccurate. Consider using '#align ordinal.add_one_eq_succ Ordinal.add_one_eq_succₓ'. -/
 @[simp]
 theorem add_one_eq_succ (o : Ordinal) : o + 1 = succ o :=
   rfl
 #align ordinal.add_one_eq_succ Ordinal.add_one_eq_succ
--/
 
-#print Ordinal.succ_zero /-
+/- warning: ordinal.succ_zero -> Ordinal.succ_zero is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Ordinal.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 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)} Ordinal.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{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 ordinal.succ_zero Ordinal.succ_zeroₓ'. -/
 @[simp]
 theorem succ_zero : succ (0 : Ordinal) = 1 :=
   zero_add 1
 #align ordinal.succ_zero Ordinal.succ_zero
--/
 
 /- warning: ordinal.succ_one -> Ordinal.succ_one is a dubious translation:
 lean 3 declaration is
   Eq.{succ (succ u1)} Ordinal.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 2 (OfNat.mk.{succ u1} Ordinal.{u1} 2 (bit0.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1} (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))))
 but is expected to have type
-  Eq.{succ (succ u1)} Ordinal.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 2 (instOfNat.{succ u1} Ordinal.{u1} 2 (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1}) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
+  Eq.{succ (succ u1)} Ordinal.{u1} (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 2 (instOfNat.{succ u1} Ordinal.{u1} 2 (AddMonoidWithOne.toNatCast.{succ u1} Ordinal.{u1} Ordinal.addMonoidWithOne.{u1}) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))
 Case conversion may be inaccurate. Consider using '#align ordinal.succ_one Ordinal.succ_oneₓ'. -/
 @[simp]
 theorem succ_one : succ (1 : Ordinal) = 2 :=
@@ -1393,16 +1429,24 @@ theorem add_succ (o₁ o₂ : Ordinal) : o₁ + succ o₂ = succ (o₁ + o₂) :
 #align ordinal.add_succ Ordinal.add_succ
 -/
 
-#print Ordinal.one_le_iff_pos /-
+/- warning: ordinal.one_le_iff_pos -> Ordinal.one_le_iff_pos is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))) o) (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)
+but is expected to have type
+  forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})) o) (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)
+Case conversion may be inaccurate. Consider using '#align ordinal.one_le_iff_pos Ordinal.one_le_iff_posₓ'. -/
 theorem one_le_iff_pos {o : Ordinal} : 1 ≤ o ↔ 0 < o := by rw [← succ_zero, succ_le_iff]
 #align ordinal.one_le_iff_pos Ordinal.one_le_iff_pos
--/
 
-#print Ordinal.one_le_iff_ne_zero /-
+/- warning: ordinal.one_le_iff_ne_zero -> Ordinal.one_le_iff_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))) o) (Ne.{succ (succ u1)} Ordinal.{u1} o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))))
+but is expected to have type
+  forall {o : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1})) o) (Ne.{succ (succ u1)} Ordinal.{u1} o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})))
+Case conversion may be inaccurate. Consider using '#align ordinal.one_le_iff_ne_zero Ordinal.one_le_iff_ne_zeroₓ'. -/
 theorem one_le_iff_ne_zero {o : Ordinal} : 1 ≤ o ↔ o ≠ 0 := by
   rw [one_le_iff_pos, Ordinal.pos_iff_ne_zero]
 #align ordinal.one_le_iff_ne_zero Ordinal.one_le_iff_ne_zero
--/
 
 #print Ordinal.succ_pos /-
 theorem succ_pos (o : Ordinal) : 0 < succ o :=
@@ -1416,16 +1460,24 @@ theorem succ_ne_zero (o : Ordinal) : succ o ≠ 0 :=
 #align ordinal.succ_ne_zero Ordinal.succ_ne_zero
 -/
 
-#print Ordinal.lt_one_iff_zero /-
+/- warning: ordinal.lt_one_iff_zero -> Ordinal.lt_one_iff_zero is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.lt_one_iff_zero Ordinal.lt_one_iff_zeroₓ'. -/
 theorem lt_one_iff_zero {a : Ordinal} : a < 1 ↔ a = 0 := by simpa using @lt_succ_bot_iff _ _ _ a _ _
 #align ordinal.lt_one_iff_zero Ordinal.lt_one_iff_zero
--/
 
-#print Ordinal.le_one_iff /-
+/- warning: ordinal.le_one_iff -> Ordinal.le_one_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.le_one_iff Ordinal.le_one_iffₓ'. -/
 theorem le_one_iff {a : Ordinal} : a ≤ 1 ↔ a = 0 ∨ a = 1 := by
   simpa using @le_succ_bot_iff _ _ _ a _
 #align ordinal.le_one_iff Ordinal.le_one_iff
--/
 
 /- warning: ordinal.card_succ -> Ordinal.card_succ is a dubious translation:
 lean 3 declaration is
@@ -1444,15 +1496,24 @@ theorem nat_cast_succ (n : ℕ) : ↑n.succ = succ (n : Ordinal) :=
 #align ordinal.nat_cast_succ Ordinal.nat_cast_succ
 -/
 
-#print Ordinal.uniqueIioOne /-
+/- warning: ordinal.unique_Iio_one -> Ordinal.uniqueIioOne is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.unique_Iio_one Ordinal.uniqueIioOneₓ'. -/
 instance uniqueIioOne : Unique (Iio (1 : Ordinal))
     where
   default := ⟨0, zero_lt_one⟩
   uniq a := Subtype.ext <| lt_one_iff_zero.1 a.Prop
 #align ordinal.unique_Iio_one Ordinal.uniqueIioOne
--/
 
-#print Ordinal.uniqueOutOne /-
+/- warning: ordinal.unique_out_one -> Ordinal.uniqueOutOne is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.unique_out_one Ordinal.uniqueOutOneₓ'. -/
 instance uniqueOutOne : Unique (1 : Ordinal).out.α
     where
   default := enum (· < ·) 0 (by simp)
@@ -1463,23 +1524,30 @@ instance uniqueOutOne : Unique (1 : Ordinal).out.α
     rw [← lt_one_iff_zero]
     apply typein_lt_self
 #align ordinal.unique_out_one Ordinal.uniqueOutOne
--/
 
-#print Ordinal.one_out_eq /-
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+Case conversion may be inaccurate. Consider using '#align ordinal.one_out_eq Ordinal.one_out_eqₓ'. -/
 theorem one_out_eq (x : (1 : Ordinal).out.α) : x = enum (· < ·) 0 (by simp) :=
   Unique.eq_default x
 #align ordinal.one_out_eq Ordinal.one_out_eq
--/
 
 /-! ### Extra properties of typein and enum -/
 
 
-#print Ordinal.typein_one_out /-
+/- warning: ordinal.typein_one_out -> Ordinal.typein_one_out is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.typein_one_out Ordinal.typein_one_outₓ'. -/
 @[simp]
 theorem typein_one_out (x : (1 : Ordinal).out.α) : typein (· < ·) x = 0 := by
   rw [one_out_eq x, typein_enum]
 #align ordinal.typein_one_out Ordinal.typein_one_out
--/
 
 #print Ordinal.typein_le_typein /-
 @[simp]
@@ -1601,7 +1669,7 @@ def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α :=
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align ordinal.enum_zero_eq_bot Ordinal.enum_zero_eq_botₓ'. -/
 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
     enum (· < ·) 0 (by rwa [type_lt]) =
@@ -1871,11 +1939,15 @@ theorem ord_nat (n : ℕ) : ord n = n :=
       · exact succ_le_of_lt (IH.trans_lt <| ord_lt_ord.2 <| nat_cast_lt.2 (Nat.lt_succ_self n)))
 #align cardinal.ord_nat Cardinal.ord_nat
 
-#print Cardinal.ord_one /-
+/- warning: cardinal.ord_one -> Cardinal.ord_one is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Ordinal.{u1} (Cardinal.ord.{u1} (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (OfNat.mk.{succ u1} Cardinal.{u1} 1 (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{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)} Ordinal.{u1} (Cardinal.ord.{u1} (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (One.toOfNat1.{succ u1} Cardinal.{u1} Cardinal.instOneCardinal.{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.ord_one Cardinal.ord_oneₓ'. -/
 @[simp]
 theorem ord_one : ord 1 = 1 := by simpa using ord_nat 1
 #align cardinal.ord_one Cardinal.ord_one
--/
 
 /- warning: cardinal.lift_ord -> Cardinal.lift_ord is a dubious translation:
 lean 3 declaration is

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

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

@@ -1511,7 +1511,7 @@ theorem lift_lt_univ' (c : Cardinal) : lift.{max (u + 1) v, u} c < univ.{u, v} :
 
 @[simp]
 theorem ord_univ : ord univ.{u, v} = Ordinal.univ.{u, v} := by
-  refine' le_antisymm (ord_card_le _) <| le_of_forall_lt fun o h => lt_ord.2 ?_
+  refine le_antisymm (ord_card_le _) <| le_of_forall_lt fun o h => lt_ord.2 ?_
   have := lift.principalSeg.{u, v}.down.1 (by simpa only [lift.principalSeg_coe] using h)
   rcases this with ⟨o, h'⟩
   rw [← h', lift.principalSeg_coe, ← lift_card]

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

@@ -1093,9 +1093,9 @@ theorem card_succ (o : Ordinal) : card (succ o) = card o + 1 := by
   simp only [← add_one_eq_succ, card_add, card_one]
 #align ordinal.card_succ Ordinal.card_succ
 
-theorem nat_cast_succ (n : ℕ) : ↑n.succ = succ (n : Ordinal) :=
+theorem natCast_succ (n : ℕ) : ↑n.succ = succ (n : Ordinal) :=
   rfl
-#align ordinal.nat_cast_succ Ordinal.nat_cast_succ
+#align ordinal.nat_cast_succ Ordinal.natCast_succ
 
 instance uniqueIioOne : Unique (Iio (1 : Ordinal))
     where

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

@@ -836,7 +836,6 @@ def omega : Ordinal.{u} :=
   lift <| @type ℕ (· < ·) _
 #align ordinal.omega Ordinal.omega
 
--- mathport name: ordinal.omega
 @[inherit_doc]
 scoped notation "ω" => Ordinal.omega
 

@@ -37,10 +37,11 @@ initial segment (or, equivalently, in any way). This total order is well founded
   universe). In some cases the universe level has to be given explicitly.
 
 * `o₁ + o₂` is the order on the disjoint union of `o₁` and `o₂` obtained by declaring that
-  every element of `o₁` is smaller than every element of `o₂`. The main properties of addition
-  (and the other operations on ordinals) are stated and proved in `Ordinal/Arithmetic.lean`. Here,
-  we only introduce it and prove its basic properties to deduce the fact that the order on ordinals
-  is total (and well founded).
+  every element of `o₁` is smaller than every element of `o₂`.
+  The main properties of addition (and the other operations on ordinals) are stated and proved in
+  `Mathlib/SetTheory/Ordinal/Arithmetic.lean`.
+  Here, we only introduce it and prove its basic properties to deduce the fact that the order on
+  ordinals is total (and well founded).
 * `succ o` is the successor of the ordinal `o`.
 * `Cardinal.ord c`: when `c` is a cardinal, `ord c` is the smallest ordinal with this cardinality.
   It is the canonical way to represent a cardinal with an ordinal.
@@ -861,7 +862,7 @@ theorem lift_omega : lift ω = ω :=
 In this paragraph, we introduce the addition on ordinals, and prove just enough properties to
 deduce that the order on ordinals is total (and therefore well-founded). Further properties of
 the addition, together with properties of the other operations, are proved in
-`Ordinal/Arithmetic.lean`.
+`Mathlib/SetTheory/Ordinal/Arithmetic.lean`.
 -/
 
 

The removal of some pointless tactics flagged by #11308.

@@ -550,7 +550,7 @@ theorem relIso_enum' {α β : Type u} {r : α → α → Prop} {s : β → β 
     [IsWellOrder β s] (f : r ≃r s) (o : Ordinal) :
     ∀ (hr : o < type r) (hs : o < type s), f (enum r o hr) = enum s o hs := by
   refine' inductionOn o _; rintro γ t wo ⟨g⟩ ⟨h⟩
-  skip; rw [enum_type g, enum_type (PrincipalSeg.ltEquiv g f)]; rfl
+  rw [enum_type g, enum_type (PrincipalSeg.ltEquiv g f)]; rfl
 #align ordinal.rel_iso_enum' Ordinal.relIso_enum'
 
 theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r]
@@ -1340,7 +1340,7 @@ theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=
   inductionOn c fun α =>
     Ordinal.inductionOn o fun β s _ => by
       let ⟨r, _, e⟩ := ord_eq α
-      skip; simp only [card_type]; constructor <;> intro h
+      simp only [card_type]; constructor <;> intro h
       · rw [e] at h
         exact
           let ⟨f⟩ := h

This PR removes the default values for nsmul and zsmul, forcing the user to populate them manually. The previous behavior can be obtained by writing nsmul := nsmulRec and zsmul := zsmulRec, which is now in the docstring for these fields.

The motivation here is to make it more obvious when module diamonds are being introduced, or at least where they might be hiding; you can now simply search for nsmulRec in the source code.

Arguably we should do the same thing for intCast, natCast, pow, and zpow too, but diamonds are less common in those fields, so I'll leave them to a subsequent PR.

Co-authored-by: Matthew Ballard <matt@mrb.email>

@@ -890,6 +890,7 @@ instance addMonoidWithOne : AddMonoidWithOne Ordinal.{u} where
           rcases a with (⟨a | a⟩ | a) <;> rcases b with (⟨b | b⟩ | b) <;>
             simp only [sumAssoc_apply_inl_inl, sumAssoc_apply_inl_inr, sumAssoc_apply_inr,
               Sum.lex_inl_inl, Sum.lex_inr_inr, Sum.Lex.sep, Sum.lex_inr_inl]⟩⟩
+  nsmul := nsmulRec
 
 @[simp]
 theorem card_add (o₁ o₂ : Ordinal) : card (o₁ + o₂) = card o₁ + card o₂ :=

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.

@@ -59,7 +59,8 @@ noncomputable section
 
 open Function Cardinal Set Equiv Order
 
-open Classical Cardinal InitialSeg
+open scoped Classical
+open Cardinal InitialSeg
 
 universe u v w
 

I loogled for every occurrence of "cast", Nat and "natCast" and where the casted nat was n, and made sure there were corresponding @[simp] lemmas for 0, 1, and OfNat.ofNat n. This is necessary in general for simp confluence. Example:

import Mathlib

variable {α : Type*} [LinearOrderedRing α] (m n : ℕ) [m.AtLeastTwo] [n.AtLeastTwo]

example : ((OfNat.ofNat m : ℕ) : α) ≤ ((OfNat.ofNat n : ℕ) : α) ↔ (OfNat.ofNat m : ℕ) ≤ (OfNat.ofNat n : ℕ) := by
  simp only [Nat.cast_le] -- this `@[simp]` lemma can apply

example : ((OfNat.ofNat m : ℕ) : α) ≤ ((OfNat.ofNat n : ℕ) : α) ↔ (OfNat.ofNat m : α) ≤ (OfNat.ofNat n : α) := by
  simp only [Nat.cast_ofNat] -- and so can this one

example : (OfNat.ofNat m : α) ≤ (OfNat.ofNat n : α) ↔ (OfNat.ofNat m : ℕ) ≤ (OfNat.ofNat n : ℕ) := by
  simp -- fails! `simp` doesn't have a lemma to bridge their results. confluence issue.

As far as I know, the only file this PR leaves with ofNat gaps is PartENat.lean. #8002 is addressing that file in parallel.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -383,6 +383,7 @@ theorem _root_.PrincipalSeg.ordinal_type_lt {α β} {r : α → α → Prop} {s
   ⟨h⟩
 #align principal_seg.ordinal_type_lt PrincipalSeg.ordinal_type_lt
 
+@[simp]
 protected theorem zero_le (o : Ordinal) : 0 ≤ o :=
   inductionOn o fun _ r _ => (InitialSeg.ofIsEmpty _ r).ordinal_type_le
 #align ordinal.zero_le Ordinal.zero_le
@@ -619,14 +620,6 @@ theorem card_le_card {o₁ o₂ : Ordinal} : o₁ ≤ o₂ → card o₁ ≤ car
 theorem card_zero : card 0 = 0 := mk_eq_zero _
 #align ordinal.card_zero Ordinal.card_zero
 
-@[simp]
-theorem card_eq_zero {o} : card o = 0 ↔ o = 0 :=
-  ⟨inductionOn o fun α r _ h => by
-      haveI := Cardinal.mk_eq_zero_iff.1 h
-      apply type_eq_zero_of_empty,
-    fun e => by simp only [e, card_zero]⟩
-#align ordinal.card_eq_zero Ordinal.card_eq_zero
-
 @[simp]
 theorem card_one : card 1 = 1 := mk_eq_one _
 #align ordinal.card_one Ordinal.card_one
@@ -913,6 +906,12 @@ theorem card_nat (n : ℕ) : card.{u} n = n := by
   induction n <;> [simp; simp only [card_add, card_one, Nat.cast_succ, *]]
 #align ordinal.card_nat Ordinal.card_nat
 
+-- See note [no_index around OfNat.ofNat]
+@[simp]
+theorem card_ofNat (n : ℕ) [n.AtLeastTwo] :
+    card.{u} (no_index (OfNat.ofNat n)) = OfNat.ofNat n :=
+  card_nat n
+
 -- Porting note: Rewritten proof of elim, previous version was difficult to debug
 instance add_covariantClass_le : CovariantClass Ordinal.{u} Ordinal.{u} (· + ·) (· ≤ ·) where
   elim := fun c a b h => by
@@ -989,12 +988,10 @@ instance isWellOrder : IsWellOrder Ordinal (· < ·) where
 instance : ConditionallyCompleteLinearOrderBot Ordinal :=
   IsWellOrder.conditionallyCompleteLinearOrderBot _
 
-@[simp]
 theorem max_zero_left : ∀ a : Ordinal, max 0 a = a :=
   max_bot_left
 #align ordinal.max_zero_left Ordinal.max_zero_left
 
-@[simp]
 theorem max_zero_right : ∀ a : Ordinal, max a 0 = a :=
   max_bot_right
 #align ordinal.max_zero_right Ordinal.max_zero_right
@@ -1080,6 +1077,7 @@ theorem succ_ne_zero (o : Ordinal) : succ o ≠ 0 :=
   ne_of_gt <| succ_pos o
 #align ordinal.succ_ne_zero Ordinal.succ_ne_zero
 
+@[simp]
 theorem lt_one_iff_zero {a : Ordinal} : a < 1 ↔ a = 0 := by
   simpa using @lt_succ_bot_iff _ _ _ a _ _
 #align ordinal.lt_one_iff_zero Ordinal.lt_one_iff_zero
@@ -1430,6 +1428,11 @@ theorem ord_nat (n : ℕ) : ord n = n :=
 theorem ord_one : ord 1 = 1 := by simpa using ord_nat 1
 #align cardinal.ord_one Cardinal.ord_one
 
+-- See note [no_index around OfNat.ofNat]
+@[simp]
+theorem ord_ofNat (n : ℕ) [n.AtLeastTwo] : ord (no_index (OfNat.ofNat n)) = OfNat.ofNat n :=
+  ord_nat n
+
 @[simp]
 theorem lift_ord (c) : Ordinal.lift.{u,v} (ord c) = ord (lift.{u,v} c) := by
   refine' le_antisymm (le_of_forall_lt fun a ha => _) _
@@ -1555,27 +1558,82 @@ theorem nat_le_card {o} {n : ℕ} : (n : Cardinal) ≤ card o ↔ (n : Ordinal)
   rw [← Cardinal.ord_le, Cardinal.ord_nat]
 #align ordinal.nat_le_card Ordinal.nat_le_card
 
+@[simp]
+theorem one_le_card {o} : 1 ≤ card o ↔ 1 ≤ o := by
+  simpa using nat_le_card (n := 1)
+
+-- See note [no_index around OfNat.ofNat]
+@[simp]
+theorem ofNat_le_card {o} {n : ℕ} [n.AtLeastTwo] :
+    (no_index (OfNat.ofNat n : Cardinal)) ≤ card o ↔ (OfNat.ofNat n : Ordinal) ≤ o :=
+  nat_le_card
+
 @[simp]
 theorem nat_lt_card {o} {n : ℕ} : (n : Cardinal) < card o ↔ (n : Ordinal) < o := by
   rw [← succ_le_iff, ← succ_le_iff, ← nat_succ, nat_le_card]
   rfl
 #align ordinal.nat_lt_card Ordinal.nat_lt_card
 
+@[simp]
+theorem zero_lt_card {o} : 0 < card o ↔ 0 < o := by
+  simpa using nat_lt_card (n := 0)
+
+@[simp]
+theorem one_lt_card {o} : 1 < card o ↔ 1 < o := by
+  simpa using nat_lt_card (n := 1)
+
+-- See note [no_index around OfNat.ofNat]
+@[simp]
+theorem ofNat_lt_card {o} {n : ℕ} [n.AtLeastTwo] :
+    (no_index (OfNat.ofNat n : Cardinal)) < card o ↔ (OfNat.ofNat n : Ordinal) < o :=
+  nat_lt_card
+
 @[simp]
 theorem card_lt_nat {o} {n : ℕ} : card o < n ↔ o < n :=
   lt_iff_lt_of_le_iff_le nat_le_card
 #align ordinal.card_lt_nat Ordinal.card_lt_nat
 
+-- See note [no_index around OfNat.ofNat]
+@[simp]
+theorem card_lt_ofNat {o} {n : ℕ} [n.AtLeastTwo] :
+    card o < (no_index (OfNat.ofNat n)) ↔ o < OfNat.ofNat n :=
+  card_lt_nat
+
 @[simp]
 theorem card_le_nat {o} {n : ℕ} : card o ≤ n ↔ o ≤ n :=
   le_iff_le_iff_lt_iff_lt.2 nat_lt_card
 #align ordinal.card_le_nat Ordinal.card_le_nat
 
+@[simp]
+theorem card_le_one {o} : card o ≤ 1 ↔ o ≤ 1 := by
+  simpa using card_le_nat (n := 1)
+
+-- See note [no_index around OfNat.ofNat]
+@[simp]
+theorem card_le_ofNat {o} {n : ℕ} [n.AtLeastTwo] :
+    card o ≤ (no_index (OfNat.ofNat n)) ↔ o ≤ OfNat.ofNat n :=
+  card_le_nat
+
 @[simp]
 theorem card_eq_nat {o} {n : ℕ} : card o = n ↔ o = n := by
   simp only [le_antisymm_iff, card_le_nat, nat_le_card]
 #align ordinal.card_eq_nat Ordinal.card_eq_nat
 
+@[simp]
+theorem card_eq_zero {o} : card o = 0 ↔ o = 0 := by
+  simpa using card_eq_nat (n := 0)
+#align ordinal.card_eq_zero Ordinal.card_eq_zero
+
+@[simp]
+theorem card_eq_one {o} : card o = 1 ↔ o = 1 := by
+  simpa using card_eq_nat (n := 1)
+
+-- See note [no_index around OfNat.ofNat]
+@[simp]
+theorem card_eq_ofNat {o} {n : ℕ} [n.AtLeastTwo] :
+    card o = (no_index (OfNat.ofNat n)) ↔ o = OfNat.ofNat n :=
+  card_eq_nat
+
 @[simp]
 theorem type_fintype (r : α → α → Prop) [IsWellOrder α r] [Fintype α] : type r = Fintype.card α :=
   by rw [← card_eq_nat, card_type, mk_fintype]

Classifies by adding issue number (#10675) to porting notes claiming dsimp cannot prove this.

@@ -195,7 +195,7 @@ theorem type_def' (w : WellOrder) : ⟦w⟧ = type w.r := by
   rfl
 #align ordinal.type_def' Ordinal.type_def'
 
-@[simp, nolint simpNF] -- Porting note: dsimp can not prove this
+@[simp, nolint simpNF] -- Porting note (#10675): dsimp can not prove this
 theorem type_def (r) [wo : IsWellOrder α r] : (⟦⟨α, r, wo⟩⟧ : Ordinal) = type r := by
   rfl
 #align ordinal.type_def Ordinal.type_def

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

@@ -1132,7 +1132,7 @@ theorem typein_le_typein (r : α → α → Prop) [IsWellOrder α r] {x x' : α}
     typein r x ≤ typein r x' ↔ ¬r x' x := by rw [← not_lt, typein_lt_typein]
 #align ordinal.typein_le_typein Ordinal.typein_le_typein
 
--- @[simp] -- Porting note: simp can prove this
+-- @[simp] -- Porting note (#10618): simp can prove this
 theorem typein_le_typein' (o : Ordinal) {x x' : o.out.α} :
     @typein _ (· < ·) (isWellOrder_out_lt _) x ≤ @typein _ (· < ·) (isWellOrder_out_lt _) x'
       ↔ x ≤ x' := by

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>

@@ -1311,8 +1311,8 @@ def ord (c : Cardinal) : Ordinal :=
   let F := fun α : Type u => ⨅ r : { r // IsWellOrder α r }, @type α r.1 r.2
   Quot.liftOn c F
     (by
-      suffices : ∀ {α β}, α ≈ β → F α ≤ F β
-      exact fun α β h => (this h).antisymm (this (Setoid.symm h))
+      suffices ∀ {α β}, α ≈ β → F α ≤ F β from
+        fun α β h => (this h).antisymm (this (Setoid.symm h))
       rintro α β ⟨f⟩
       refine' le_ciInf_iff'.2 fun i => _
       haveI := @RelEmbedding.isWellOrder _ _ (f ⁻¹'o i.1) _ (↑(RelIso.preimage f i.1)) i.2

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>

@@ -38,7 +38,7 @@ initial segment (or, equivalently, in any way). This total order is well founded
 
 * `o₁ + o₂` is the order on the disjoint union of `o₁` and `o₂` obtained by declaring that
   every element of `o₁` is smaller than every element of `o₂`. The main properties of addition
-  (and the other operations on ordinals) are stated and proved in `OrdinalArithmetic.lean`. Here,
+  (and the other operations on ordinals) are stated and proved in `Ordinal/Arithmetic.lean`. Here,
   we only introduce it and prove its basic properties to deduce the fact that the order on ordinals
   is total (and well founded).
 * `succ o` is the successor of the ordinal `o`.

docs(SetTheory/Ordinal/Basic.lean): fix file name

Change OrdinalArithmetic.lean to Ordinal/Arithmetic.lean.

@@ -867,7 +867,7 @@ theorem lift_omega : lift ω = ω :=
 In this paragraph, we introduce the addition on ordinals, and prove just enough properties to
 deduce that the order on ordinals is total (and therefore well-founded). Further properties of
 the addition, together with properties of the other operations, are proved in
-`OrdinalArithmetic.lean`.
+`Ordinal/Arithmetic.lean`.
 -/
 
 

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Joachim Breitner <mail@joachim-breitner.de>

@@ -1057,7 +1057,7 @@ theorem succ_zero : succ (0 : Ordinal) = 1 :=
 -- Porting note: Proof used to be rfl
 @[simp]
 theorem succ_one : succ (1 : Ordinal) = 2 := by
-  unfold instOfNat OfNat.ofNat
+  unfold instOfNatAtLeastTwo OfNat.ofNat
   simpa using by rfl
 #align ordinal.succ_one Ordinal.succ_one
 

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

@@ -1509,7 +1509,7 @@ theorem ord_univ : ord univ.{u, v} = Ordinal.univ.{u, v} := by
   refine' le_antisymm (ord_card_le _) <| le_of_forall_lt fun o h => lt_ord.2 ?_
   have := lift.principalSeg.{u, v}.down.1 (by simpa only [lift.principalSeg_coe] using h)
   rcases this with ⟨o, h'⟩
-  rw [←h', lift.principalSeg_coe, ← lift_card]
+  rw [← h', lift.principalSeg_coe, ← lift_card]
   apply lift_lt_univ'
 #align cardinal.ord_univ Cardinal.ord_univ
 

@@ -584,7 +584,7 @@ instance wellFoundedRelation : WellFoundedRelation Ordinal :=
   ⟨(· < ·), lt_wf⟩
 
 /-- Reformulation of well founded induction on ordinals as a lemma that works with the
-`induction` tactic, as in `induction i using Ordinal.induction with i IH`. -/
+`induction` tactic, as in `induction i using Ordinal.induction with | h i IH => ?_`. -/
 theorem induction {p : Ordinal.{u} → Prop} (i : Ordinal.{u}) (h : ∀ j, (∀ k, k < j → p k) → p j) :
     p i :=
   lt_wf.induction i h

Switch from the strong version of UnivLE ∀ α : Type max u v, Small.{v} α to the weaker version ∀ α : Type u, Small.{v} α.

Transfer Has/Preserves/Reflects(Co)limitsOfSize from a larger size (higher universe) to a smaller size.

In a few places it's now necessary to make the type explicit (for Lean to infer the Small instance, I think).

Also prove a characterization of UnivLE and the totality of the UnivLE relation.

A pared down version of #7695.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Junyan Xu <junyanxu.math@gmail.com>

@@ -1224,7 +1224,7 @@ theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :
 -- intended to be used with explicit universe parameters
 /-- `univ.{u v}` is the order type of the ordinals of `Type u` as a member
   of `Ordinal.{v}` (when `u < v`). It is an inaccessible cardinal. -/
- @[nolint checkUnivs]
+@[pp_with_univ, nolint checkUnivs]
 def univ : Ordinal.{max (u + 1) v} :=
   lift.{v, u + 1} (@type Ordinal (· < ·) _)
 #align ordinal.univ Ordinal.univ
@@ -1475,7 +1475,7 @@ theorem ord.orderEmbedding_coe : (ord.orderEmbedding : Cardinal → Ordinal) = o
 /-- The cardinal `univ` is the cardinality of ordinal `univ`, or
   equivalently the cardinal of `Ordinal.{u}`, or `Cardinal.{u}`,
   as an element of `Cardinal.{v}` (when `u < v`). -/
-@[nolint checkUnivs]
+@[pp_with_univ, nolint checkUnivs]
 def univ :=
   lift.{v, u + 1} #Ordinal
 #align cardinal.univ Cardinal.univ

PR contents

This is the supremum of

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

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -648,7 +648,7 @@ def lift (o : Ordinal.{v}) : Ordinal.{max v u} :=
 -- @[simp] -- Porting note: Not in simpnf, added aux lemma below
 theorem type_uLift (r : α → α → Prop) [IsWellOrder α r] :
     type (ULift.down.{v,u} ⁻¹'o r) = lift.{v} (type r) := by
-  simp
+  simp (config := { unfoldPartialApp := true })
   rfl
 #align ordinal.type_ulift Ordinal.type_uLift
 
@@ -921,7 +921,6 @@ instance add_covariantClass_le : CovariantClass Ordinal.{u} Ordinal.{u} (· + ·
     refine inductionOn b (fun α₂ r₂ _ ↦ ?_)
     rintro c ⟨⟨⟨f, fo⟩, fi⟩⟩
     refine inductionOn c (fun β s _ ↦ ?_)
-    have := (Embedding.refl β).sumMap f
     refine ⟨⟨⟨(Embedding.refl.{u+1} _).sumMap f, ?_⟩, ?_⟩⟩
     · intros a b
       match a, b with

This eliminates (fun a ↦ β) α in the type when applying a FunLike.

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -302,10 +302,10 @@ theorem type_preimage {α β : Type u} (r : α → α → Prop) [IsWellOrder α
   (RelIso.preimage f r).ordinal_type_eq
 #align ordinal.type_preimage Ordinal.type_preimage
 
-@[simp]
+@[simp, nolint simpNF] -- `simpNF` incorrectly complains the LHS doesn't simplify.
 theorem type_preimage_aux {α β : Type u} (r : α → α → Prop) [IsWellOrder α r] (f : β ≃ α) :
     @type _ (fun x y => r (f x) (f y)) (inferInstanceAs (IsWellOrder β (↑f ⁻¹'o r))) = type r := by
-    convert (RelIso.preimage f r).ordinal_type_eq
+  convert (RelIso.preimage f r).ordinal_type_eq
 
 @[elab_as_elim]
 theorem inductionOn {C : Ordinal → Prop} (o : Ordinal)

@@ -167,7 +167,8 @@ instance isWellOrder_out_lt (o : Ordinal) : IsWellOrder o.out.α (· < ·) :=
 
 namespace Ordinal
 
--- ### Basic properties of the order type
+/-! ### Basic properties of the order type -/
+
 /-- The order type of a well order is an ordinal. -/
 def type (r : α → α → Prop) [wo : IsWellOrder α r] : Ordinal :=
   ⟦⟨α, r, wo⟩⟧
@@ -1009,7 +1010,8 @@ theorem sInf_empty : sInf (∅ : Set Ordinal) = 0 :=
   dif_neg Set.not_nonempty_empty
 #align ordinal.Inf_empty Ordinal.sInf_empty
 
--- ### Successor order properties
+/-! ### Successor order properties -/
+
 private theorem succ_le_iff' {a b : Ordinal} : a + 1 ≤ b ↔ a < b :=
   ⟨lt_of_lt_of_le
       (inductionOn a fun α r _ =>

@@ -1584,3 +1584,22 @@ theorem type_fin (n : ℕ) : @type (Fin n) (· < ·) _ = n := by simp
 #align ordinal.type_fin Ordinal.type_fin
 
 end Ordinal
+
+/-! ### Sorted lists -/
+
+theorem List.Sorted.lt_ord_of_lt [LinearOrder α] [IsWellOrder α (· < ·)] {l m : List α}
+    {o : Ordinal} (hl : l.Sorted (· > ·)) (hm : m.Sorted (· > ·)) (hmltl : m < l)
+    (hlt : ∀ i ∈ l, Ordinal.typein (· < ·) i < o) : ∀ i ∈ m, Ordinal.typein (· < ·) i < o := by
+  replace hmltl : List.Lex (· < ·) m l := hmltl
+  cases l with
+  | nil => simp at hmltl
+  | cons a as =>
+    cases m with
+    | nil => intro i hi; simp at hi
+    | cons b bs =>
+      intro i hi
+      suffices h : i ≤ a by refine lt_of_le_of_lt ?_ (hlt a (mem_cons_self a as)); simpa
+      cases hi with
+      | head as => exact List.head_le_of_lt hmltl
+      | tail b hi => exact le_of_lt (lt_of_lt_of_le (List.rel_of_sorted_cons hm _ hi)
+          (List.head_le_of_lt hmltl))

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.

@@ -63,7 +63,7 @@ open Classical Cardinal InitialSeg
 
 universe u v w
 
-variable {α : Type _} {β : Type*} {γ : Type*} {r : α → α → Prop} {s : β → β → Prop}
+variable {α : Type u} {β : Type*} {γ : Type*} {r : α → α → Prop} {s : β → β → Prop}
   {t : γ → γ → Prop}
 
 /-! ### Well order on an arbitrary type -/

Fixes the nonterminal simps identified by #7496

@@ -1265,7 +1265,7 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
       · intro a'
         cases' (hf _).1 (typein_lt_type _ a') with b e
         exists b
-        simp
+        simp only [RelEmbedding.ofMonotone_coe]
         simp [e]
     · cases' h with a e
       rw [← e]

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

@@ -378,7 +378,7 @@ theorem type_lt_iff {α β} {r : α → α → Prop} {s : β → β → Prop} [I
 #align ordinal.type_lt_iff Ordinal.type_lt_iff
 
 theorem _root_.PrincipalSeg.ordinal_type_lt {α β} {r : α → α → Prop} {s : β → β → Prop}
-  [IsWellOrder α r] [IsWellOrder β s] (h : r ≺i s) : type r < type s :=
+    [IsWellOrder α r] [IsWellOrder β s] (h : r ≺i s) : type r < type s :=
   ⟨h⟩
 #align principal_seg.ordinal_type_lt PrincipalSeg.ordinal_type_lt
 

• 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>

@@ -1378,6 +1378,19 @@ theorem lt_ord_succ_card (o : Ordinal) : o < (succ o.card).ord :=
   lt_ord.2 <| lt_succ _
 #align cardinal.lt_ord_succ_card Cardinal.lt_ord_succ_card
 
+theorem card_le_iff {o : Ordinal} {c : Cardinal} : o.card ≤ c ↔ o < (succ c).ord := by
+  rw [lt_ord, lt_succ_iff]
+
+/--
+A variation on `Cardinal.lt_ord` using `≤`: If `o` is no greater than the
+initial ordinal of cardinality `c`, then its cardinal is no greater than `c`.
+
+The converse, however, is false (for instance, `o = ω+1` and `c = ℵ₀`).
+-/
+lemma card_le_of_le_ord {o : Ordinal} {c : Cardinal} (ho : o ≤ c.ord) :
+    o.card ≤ c := by
+  rw [← card_ord c]; exact Ordinal.card_le_card ho
+
 @[mono]
 theorem ord_strictMono : StrictMono ord :=
   gciOrdCard.strictMono_l

The docstrings telling you to enable pp.universes are no longer relevant.

@@ -636,6 +636,7 @@ theorem card_one : card 1 = 1 := mk_eq_one _
 /-- The universe lift operation for ordinals, which embeds `Ordinal.{u}` as
   a proper initial segment of `Ordinal.{v}` for `v > u`. For the initial segment version,
   see `lift.initialSeg`. -/
+@[pp_with_univ]
 def lift (o : Ordinal.{v}) : Ordinal.{max v u} :=
   Quotient.liftOn o (fun w => type <| ULift.down.{u} ⁻¹'o w.r) fun ⟨_, r, _⟩ ⟨_, s, _⟩ ⟨f⟩ =>
     Quot.sound
@@ -676,8 +677,7 @@ theorem type_lift_preimage_aux {α : Type u} {β : Type v} (r : α → α → Pr
       (inferInstanceAs (IsWellOrder β (f ⁻¹'o r)))) = lift.{v} (type r) :=
   (RelIso.preimage f r).ordinal_lift_type_eq
 
-/-- `lift.{(max u v) u}` equals `lift.{v u}`. Using `set_option pp.universes true` will make it much
-    easier to understand what's happening when using this lemma. -/
+/-- `lift.{max u v, u}` equals `lift.{v, u}`. -/
 -- @[simp] -- Porting note: simp lemma never applies, tested
 theorem lift_umax : lift.{max u v, u} = lift.{v, u} :=
   funext fun a =>
@@ -685,8 +685,7 @@ theorem lift_umax : lift.{max u v, u} = lift.{v, u} :=
       Quotient.sound ⟨(RelIso.preimage Equiv.ulift r).trans (RelIso.preimage Equiv.ulift r).symm⟩
 #align ordinal.lift_umax Ordinal.lift_umax
 
-/-- `lift.{(max v u) u}` equals `lift.{v u}`. Using `set_option pp.universes true` will make it much
-    easier to understand what's happening when using this lemma. -/
+/-- `lift.{max v u, u}` equals `lift.{v, u}`. -/
 -- @[simp] -- Porting note: simp lemma never applies, tested
 theorem lift_umax' : lift.{max v u, u} = lift.{v, u} :=
   lift_umax

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

@@ -63,7 +63,7 @@ open Classical Cardinal InitialSeg
 
 universe u v w
 
-variable {α : Type _} {β : Type _} {γ : Type _} {r : α → α → Prop} {s : β → β → Prop}
+variable {α : Type _} {β : Type*} {γ : Type*} {r : α → α → Prop} {s : β → β → Prop}
   {t : γ → γ → Prop}
 
 /-! ### Well order on an arbitrary type -/

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.

@@ -615,8 +615,7 @@ theorem card_le_card {o₁ o₂ : Ordinal} : o₁ ≤ o₂ → card o₁ ≤ car
 #align ordinal.card_le_card Ordinal.card_le_card
 
 @[simp]
-theorem card_zero : card 0 = 0 :=
-  rfl
+theorem card_zero : card 0 = 0 := mk_eq_zero _
 #align ordinal.card_zero Ordinal.card_zero
 
 @[simp]
@@ -628,8 +627,7 @@ theorem card_eq_zero {o} : card o = 0 ↔ o = 0 :=
 #align ordinal.card_eq_zero Ordinal.card_eq_zero
 
 @[simp]
-theorem card_one : card 1 = 1 :=
-  rfl
+theorem card_one : card 1 = 1 := mk_eq_one _
 #align ordinal.card_one Ordinal.card_one
 
 /-! ### Lifting ordinals to a higher universe -/
@@ -912,7 +910,7 @@ theorem type_sum_lex {α β : Type u} (r : α → α → Prop) (s : β → β 
 
 @[simp]
 theorem card_nat (n : ℕ) : card.{u} n = n := by
-  induction n <;> [rfl; simp only [card_add, card_one, Nat.cast_succ, *]]
+  induction n <;> [simp; simp only [card_add, card_one, Nat.cast_succ, *]]
 #align ordinal.card_nat Ordinal.card_nat
 
 -- Porting note: Rewritten proof of elim, previous version was difficult to debug

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

@@ -8,7 +8,7 @@ import Mathlib.Order.InitialSeg
 import Mathlib.SetTheory.Cardinal.Basic
 import Mathlib.Tactic.PPWithUniv
 
-#align_import set_theory.ordinal.basic from "leanprover-community/mathlib"@"8da9e30545433fdd8fe55a0d3da208e5d9263f03"
+#align_import set_theory.ordinal.basic from "leanprover-community/mathlib"@"8ea5598db6caeddde6cb734aa179cc2408dbd345"
 
 /-!
 # Ordinals
@@ -498,25 +498,38 @@ theorem typein_inj (r : α → α → Prop) [IsWellOrder α r] {a b} : typein r
   (typein_injective r).eq_iff
 #align ordinal.typein_inj Ordinal.typein_inj
 
+/-- Principal segment version of the `typein` function, embedding a well order into
+  ordinals as a principal segment. -/
+def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r] :
+    @PrincipalSeg α Ordinal.{u} r (· < ·) :=
+  ⟨⟨⟨typein r, typein_injective r⟩, typein_lt_typein r⟩, type r,
+    fun _ ↦ ⟨typein_surj r, fun ⟨a, h⟩ ↦ h ▸ typein_lt_type r a⟩⟩
+#align ordinal.typein.principal_seg Ordinal.typein.principalSeg
+
+@[simp]
+theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
+    (typein.principalSeg r : α → Ordinal) = typein r :=
+  rfl
+#align ordinal.typein.principal_seg_coe Ordinal.typein.principalSeg_coe
+
 /-! ### Enumerating elements in a well-order with ordinals. -/
 
 
 /-- `enum r o h` is the `o`-th element of `α` ordered by `r`.
   That is, `enum` maps an initial segment of the ordinals, those
   less than the order type of `r`, to the elements of `α`. -/
-def enum (r : α → α → Prop) [IsWellOrder α r] (o) : o < type r → α :=
-  Quot.recOn' o (fun ⟨β, s, _⟩ h => (Classical.choice h).top) fun ⟨β, s, _⟩ ⟨γ, t, _⟩ ⟨h⟩ => by
-    refine' funext fun H₂ : type t < type r => _
-    have H₁ : type s < type r := by rwa [type_eq.2 ⟨h⟩]
-    have : ∀ {o : Ordinal} {e : type s = o} (H : o < type r),
-      Eq.rec (fun h : type s < type r => (Classical.choice h).top) e H
-        = (Classical.choice H₁).top := by intros _ e _; subst e; rfl
-    exact (this H₂).trans (PrincipalSeg.top_eq h (Classical.choice H₁) (Classical.choice H₂))
-#align ordinal.enum Ordinal.enum
+def enum (r : α → α → Prop) [IsWellOrder α r] (o) (h : o < type r) : α :=
+  (typein.principalSeg r).subrelIso ⟨o, h⟩
+
+@[simp]
+theorem typein_enum (r : α → α → Prop) [IsWellOrder α r] {o} (h : o < type r) :
+    typein r (enum r o h) = o :=
+  (typein.principalSeg r).apply_subrelIso _
+#align ordinal.typein_enum Ordinal.typein_enum
 
 theorem enum_type {α β} {r : α → α → Prop} {s : β → β → Prop} [IsWellOrder α r] [IsWellOrder β s]
     (f : s ≺i r) {h : type s < type r} : enum r (type s) h = f.top :=
-  PrincipalSeg.top_eq (RelIso.refl _) _ _
+  (typein.principalSeg r).injective <| (typein_enum _ _).trans (typein_top _).symm
 #align ordinal.enum_type Ordinal.enum_type
 
 @[simp]
@@ -525,14 +538,6 @@ theorem enum_typein (r : α → α → Prop) [IsWellOrder α r] (a : α) :
   enum_type (PrincipalSeg.ofElement r a)
 #align ordinal.enum_typein Ordinal.enum_typein
 
-@[simp]
-theorem typein_enum (r : α → α → Prop) [IsWellOrder α r] {o} (h : o < type r) :
-    typein r (enum r o h) = o := by
-  let ⟨a, e⟩ := typein_surj r h
-  subst e
-  rw [enum_typein]
-#align ordinal.typein_enum Ordinal.typein_enum
-
 theorem enum_lt_enum {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordinal} (h₁ : o₁ < type r)
     (h₂ : o₂ < type r) : r (enum r o₁ h₁) (enum r o₂ h₂) ↔ o₁ < o₂ := by
   rw [← typein_lt_typein r, typein_enum, typein_enum]
@@ -557,6 +562,10 @@ theorem relIso_enum {α β : Type u} {r : α → α → Prop} {s : β → β →
 #align ordinal.rel_iso_enum Ordinal.relIso_enum
 
 theorem lt_wf : @WellFounded Ordinal (· < ·) :=
+/-
+  wellFounded_iff_wellFounded_subrel.mpr (·.induction_on fun ⟨_, r, wo⟩ ↦
+    RelHomClass.wellFounded (typein.principalSeg r).subrelIso wo.wf)
+-/
   ⟨fun a =>
     inductionOn a fun α r wo =>
       suffices ∀ a, Acc (· < ·) (typein r a) from
@@ -580,21 +589,6 @@ theorem induction {p : Ordinal.{u} → Prop} (i : Ordinal.{u}) (h : ∀ j, (∀
   lt_wf.induction i h
 #align ordinal.induction Ordinal.induction
 
-/-- Principal segment version of the `typein` function, embedding a well order into
-  ordinals as a principal segment. -/
-def typein.principalSeg {α : Type u} (r : α → α → Prop) [IsWellOrder α r] :
-    @PrincipalSeg α Ordinal.{u} r (· < ·) :=
-  ⟨RelEmbedding.ofMonotone (typein r) fun _ _=> (typein_lt_typein r).2,
-    type r,
-    fun _ => ⟨fun h => ⟨enum r _ h, typein_enum r h⟩, fun ⟨_, e⟩ => e ▸ typein_lt_type _ _⟩⟩
-#align ordinal.typein.principal_seg Ordinal.typein.principalSeg
-
-@[simp]
-theorem typein.principalSeg_coe (r : α → α → Prop) [IsWellOrder α r] :
-    (typein.principalSeg r : α → Ordinal) = typein r :=
-  rfl
-#align ordinal.typein.principal_seg_coe Ordinal.typein.principalSeg_coe
-
 /-! ### Cardinality of ordinals -/
 
 
@@ -1186,26 +1180,16 @@ theorem le_enum_succ {o : Ordinal} (a : (succ o).out.α) :
 @[simp]
 theorem enum_inj {r : α → α → Prop} [IsWellOrder α r] {o₁ o₂ : Ordinal} (h₁ : o₁ < type r)
     (h₂ : o₂ < type r) : enum r o₁ h₁ = enum r o₂ h₂ ↔ o₁ = o₂ :=
-  ⟨fun h => by
-    by_contra hne
-    haveI : IsIrrefl _ r := inferInstance
-    cases' lt_or_gt_of_ne hne with hlt hlt <;> apply (this).1
-    · rwa [← @enum_lt_enum α r _ o₁ o₂ h₁ h₂, h] at hlt
-    · rw [GT.gt] at hlt
-      rwa [← @enum_lt_enum α r _ o₂ o₁ h₂ h₁, h] at hlt, fun h => by simp_rw [h]⟩
+  (typein.principalSeg r).subrelIso.injective.eq_iff.trans Subtype.mk_eq_mk
 #align ordinal.enum_inj Ordinal.enum_inj
 
+-- TODO: Can we remove this definition and just use `(typein.principalSeg r).subrelIso` directly?
 /-- A well order `r` is order isomorphic to the set of ordinals smaller than `type r`. -/
 @[simps]
-def enumIso (r : α → α → Prop) [IsWellOrder α r] : Subrel (· < ·) (· < type r) ≃r r
-    where
-  toFun x := enum r x.1 x.2
-  invFun x := ⟨typein r x, typein_lt_type r x⟩
-  left_inv := fun ⟨o, h⟩ => Subtype.ext_val (typein_enum _ _)
-  right_inv h := enum_typein _ _
-  map_rel_iff' := by
-    rintro ⟨a, _⟩ ⟨b, _⟩
-    apply enum_lt_enum
+def enumIso (r : α → α → Prop) [IsWellOrder α r] : Subrel (· < ·) (· < type r) ≃r r :=
+  { (typein.principalSeg r).subrelIso with
+    toFun := fun x ↦ enum r x.1 x.2
+    invFun := fun x ↦ ⟨typein r x, typein_lt_type r x⟩ }
 #align ordinal.enum_iso Ordinal.enumIso
 
 /-- The order isomorphism between ordinals less than `o` and `o.out.α`. -/

• depends on: #5966

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

@@ -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: Mario Carneiro, Floris van Doorn
-
-! This file was ported from Lean 3 source module set_theory.ordinal.basic
-! leanprover-community/mathlib commit 8da9e30545433fdd8fe55a0d3da208e5d9263f03
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Sum.Order
 import Mathlib.Order.InitialSeg
 import Mathlib.SetTheory.Cardinal.Basic
 import Mathlib.Tactic.PPWithUniv
 
+#align_import set_theory.ordinal.basic from "leanprover-community/mathlib"@"8da9e30545433fdd8fe55a0d3da208e5d9263f03"
+
 /-!
 # Ordinals
 

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

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

@@ -328,7 +328,7 @@ instance partialOrder : PartialOrder Ordinal
           ⟨(InitialSeg.ofIso f).trans <| h.trans (InitialSeg.ofIso g.symm)⟩⟩
   lt a b :=
     Quotient.liftOn₂ a b (fun ⟨_, r, _⟩ ⟨_, s, _⟩ => Nonempty (r ≺i s))
-      fun  _ _ _ _  ⟨f⟩ ⟨g⟩ =>
+      fun _ _ _ _ ⟨f⟩ ⟨g⟩ =>
       propext
         ⟨fun ⟨h⟩ => ⟨PrincipalSeg.equivLT f.symm <| h.ltLe (InitialSeg.ofIso g)⟩, fun ⟨h⟩ =>
           ⟨PrincipalSeg.equivLT f <| h.ltLe (InitialSeg.ofIso g.symm)⟩⟩
@@ -1161,7 +1161,7 @@ theorem enum_le_enum (r : α → α → Prop) [IsWellOrder α r] {o o' : Ordinal
 @[simp]
 theorem enum_le_enum' (a : Ordinal) {o o' : Ordinal} (ho : o < type (· < ·))
     (ho' : o' < type (· < ·)) : enum (· < ·) o ho ≤ @enum a.out.α (· < ·) _ o' ho' ↔ o ≤ o' := by
-  rw [← @enum_le_enum _ (· < ·)  (isWellOrder_out_lt _), ← not_lt]
+  rw [← @enum_le_enum _ (· < ·) (isWellOrder_out_lt _), ← not_lt]
 #align ordinal.enum_le_enum' Ordinal.enum_le_enum'
 
 theorem enum_zero_le {r : α → α → Prop} [IsWellOrder α r] (h0 : 0 < type r) (a : α) :

@@ -151,10 +151,10 @@ instance Ordinal.isEquivalent : Setoid WellOrder
 #align ordinal.is_equivalent Ordinal.isEquivalent
 
 /-- `Ordinal.{u}` is the type of well orders in `Type u`, up to order isomorphism. -/
+@[pp_with_univ]
 def Ordinal : Type (u + 1) :=
   Quotient Ordinal.isEquivalent
 #align ordinal Ordinal
-pp_with_univ Ordinal
 
 instance hasWellFoundedOut (o : Ordinal) : WellFoundedRelation o.out.α :=
   ⟨o.out.r, o.out.wo.wf⟩

@@ -608,14 +608,14 @@ def card : Ordinal → Cardinal :=
 #align ordinal.card Ordinal.card
 
 @[simp]
-theorem card_type (r : α → α → Prop) [IsWellOrder α r] : card (type r) = (#α) :=
+theorem card_type (r : α → α → Prop) [IsWellOrder α r] : card (type r) = #α :=
   rfl
 #align ordinal.card_type Ordinal.card_type
 
 -- Porting note: nolint, simpNF linter falsely claims the lemma never applies
 @[simp, nolint simpNF]
 theorem card_typein {r : α → α → Prop} [IsWellOrder α r] (x : α) :
-    (#{ y // r y x }) = (typein r x).card :=
+    #{ y // r y x } = (typein r x).card :=
   rfl
 #align ordinal.card_typein Ordinal.card_typein
 
@@ -801,7 +801,7 @@ theorem lift_down' {a : Cardinal.{u}} {b : Ordinal.{max u v}}
   Cardinal.inductionOn c
     (fun α =>
       inductionOn b fun β s _ e' => by
-        rw [card_type, ← Cardinal.lift_id'.{max u v, u} (#β), ← Cardinal.lift_umax.{u, v},
+        rw [card_type, ← Cardinal.lift_id'.{max u v, u} #β, ← Cardinal.lift_umax.{u, v},
           lift_mk_eq.{u, max u v, max u v}] at e'
         cases' e' with f
         have g := RelIso.preimage f s
@@ -1322,7 +1322,7 @@ namespace Cardinal
 open Ordinal
 
 @[simp]
-theorem mk_ordinal_out (o : Ordinal) : (#o.out.α) = o.card :=
+theorem mk_ordinal_out (o : Ordinal) : #o.out.α = o.card :=
   (Ordinal.card_type _).symm.trans <| by rw [Ordinal.type_lt]
 #align cardinal.mk_ordinal_out Cardinal.mk_ordinal_out
 
@@ -1344,16 +1344,16 @@ def ord (c : Cardinal) : Ordinal :=
           (Quot.sound ⟨RelIso.preimage f i.1⟩))
 #align cardinal.ord Cardinal.ord
 
-theorem ord_eq_Inf (α : Type u) : ord (#α) = ⨅ r : { r // IsWellOrder α r }, @type α r.1 r.2 :=
+theorem ord_eq_Inf (α : Type u) : ord #α = ⨅ r : { r // IsWellOrder α r }, @type α r.1 r.2 :=
   rfl
 #align cardinal.ord_eq_Inf Cardinal.ord_eq_Inf
 
-theorem ord_eq (α) : ∃ (r : α → α → Prop) (wo : IsWellOrder α r), ord (#α) = @type α r wo :=
+theorem ord_eq (α) : ∃ (r : α → α → Prop) (wo : IsWellOrder α r), ord #α = @type α r wo :=
   let ⟨r, wo⟩ := ciInf_mem fun r : { r // IsWellOrder α r } => @type α r.1 r.2
   ⟨r.1, r.2, wo.symm⟩
 #align cardinal.ord_eq Cardinal.ord_eq
 
-theorem ord_le_type (r : α → α → Prop) [h : IsWellOrder α r] : ord (#α) ≤ type r :=
+theorem ord_le_type (r : α → α → Prop) [h : IsWellOrder α r] : ord #α ≤ type r :=
   ciInf_le' _ (Subtype.mk r h)
 #align cardinal.ord_le_type Cardinal.ord_le_type
 
@@ -1446,11 +1446,11 @@ theorem lift_ord (c) : Ordinal.lift.{u,v} (ord c) = ord (lift.{u,v} c) := by
   · rw [ord_le, ← lift_card, card_ord]
 #align cardinal.lift_ord Cardinal.lift_ord
 
-theorem mk_ord_out (c : Cardinal) : (#c.ord.out.α) = c := by simp
+theorem mk_ord_out (c : Cardinal) : #c.ord.out.α = c := by simp
 #align cardinal.mk_ord_out Cardinal.mk_ord_out
 
-theorem card_typein_lt (r : α → α → Prop) [IsWellOrder α r] (x : α) (h : ord (#α) = type r) :
-    card (typein r x) < (#α) := by
+theorem card_typein_lt (r : α → α → Prop) [IsWellOrder α r] (x : α) (h : ord #α = type r) :
+    card (typein r x) < #α := by
   rw [← lt_ord, h]
   apply typein_lt_type
 #align cardinal.card_typein_lt Cardinal.card_typein_lt
@@ -1485,10 +1485,10 @@ theorem ord.orderEmbedding_coe : (ord.orderEmbedding : Cardinal → Ordinal) = o
   as an element of `Cardinal.{v}` (when `u < v`). -/
 @[nolint checkUnivs]
 def univ :=
-  lift.{v, u + 1} (#Ordinal)
+  lift.{v, u + 1} #Ordinal
 #align cardinal.univ Cardinal.univ
 
-theorem univ_id : univ.{u, u + 1} = (#Ordinal) :=
+theorem univ_id : univ.{u, u + 1} = #Ordinal :=
   lift_id _
 #align cardinal.univ_id Cardinal.univ_id
 
@@ -1540,7 +1540,7 @@ theorem lt_univ' {c} : c < univ.{u, v} ↔ ∃ c', c = lift.{max (u + 1) v, u} c
 #align cardinal.lt_univ' Cardinal.lt_univ'
 
 theorem small_iff_lift_mk_lt_univ {α : Type u} :
-    Small.{v} α ↔ Cardinal.lift.{v+1,_} (#α) < univ.{v, max u (v + 1)} := by
+    Small.{v} α ↔ Cardinal.lift.{v+1,_} #α < univ.{v, max u (v + 1)} := by
   rw [lt_univ']
   constructor
   · rintro ⟨β, e⟩

Adds a pp_with_univ command that pretty-prints the universe parameters for the specified constant by default. Just like Type u, we should include the universe parameter in Ordinal.{u} since you would otherwise have to guess it (and several lemmas require level inequalities, so it's important to know whether you have an Ordinal.{u} or merely an Ordinal.{max u v}).

It might be cute to pretty-print Category.{v} as well, but that is much more involved since the pretty-printer for constants is hardcoded.

@@ -11,6 +11,7 @@ Authors: Mario Carneiro, Floris van Doorn
 import Mathlib.Data.Sum.Order
 import Mathlib.Order.InitialSeg
 import Mathlib.SetTheory.Cardinal.Basic
+import Mathlib.Tactic.PPWithUniv
 
 /-!
 # Ordinals
@@ -153,6 +154,7 @@ instance Ordinal.isEquivalent : Setoid WellOrder
 def Ordinal : Type (u + 1) :=
   Quotient Ordinal.isEquivalent
 #align ordinal Ordinal
+pp_with_univ Ordinal
 
 instance hasWellFoundedOut (o : Ordinal) : WellFoundedRelation o.out.α :=
   ⟨o.out.r, o.out.wo.wf⟩

Changes are of the form

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

@@ -1267,7 +1267,7 @@ def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· <
   ⟨↑lift.initialSeg.{u, max (u + 1) v}, univ.{u, v}, by
     refine' fun b => inductionOn b _; intro β s _
     rw [univ, ← lift_umax]; constructor <;> intro h
-    · rw [← lift_id (type s)] at h⊢
+    · rw [← lift_id (type s)] at h ⊢
       cases' lift_type_lt.{_,_,v}.1 h with f
       cases' f with f a hf
       exists a

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

@@ -1346,7 +1346,7 @@ theorem ord_eq_Inf (α : Type u) : ord (#α) = ⨅ r : { r // IsWellOrder α r }
   rfl
 #align cardinal.ord_eq_Inf Cardinal.ord_eq_Inf
 
-theorem ord_eq (α) : ∃ (r : α → α → Prop)(wo : IsWellOrder α r), ord (#α) = @type α r wo :=
+theorem ord_eq (α) : ∃ (r : α → α → Prop) (wo : IsWellOrder α r), ord (#α) = @type α r wo :=
   let ⟨r, wo⟩ := ciInf_mem fun r : { r // IsWellOrder α r } => @type α r.1 r.2
   ⟨r.1, r.2, wo.symm⟩
 #align cardinal.ord_eq Cardinal.ord_eq

These are all doc fixes

@@ -32,7 +32,7 @@ initial segment (or, equivalently, in any way). This total order is well founded
 * `Ordinal.lift` lifts an ordinal in universe `u` to an ordinal in universe `max u v`.
   For a version registering additionally that this is an initial segment embedding, see
   `Ordinal.lift.initialSeg`.
-  For a version regiserting that it is a principal segment embedding if `u < v`, see
+  For a version registering that it is a principal segment embedding if `u < v`, see
   `Ordinal.lift.principalSeg`.
 * `Ordinal.omega` or `ω` is the order type of `ℕ`. This definition is universe polymorphic:
   `Ordinal.omega.{u} : Ordinal.{u}` (contrast with `ℕ : Type`, which lives in a specific

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

@@ -1225,7 +1225,7 @@ noncomputable def enumIsoOut (o : Ordinal) : Set.Iio o ≃o o.out.α
     apply enum_le_enum'
 #align ordinal.enum_iso_out Ordinal.enumIsoOut
 
-/-- `o.out.α` is an `order_bot` whenever `0 < o`. -/
+/-- `o.out.α` is an `OrderBot` whenever `0 < o`. -/
 def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α where
   bot_le := enum_zero_le' ho
 #align ordinal.out_order_bot_of_pos Ordinal.outOrderBotOfPos

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

@@ -919,7 +919,7 @@ theorem type_sum_lex {α β : Type u} (r : α → α → Prop) (s : β → β 
 
 @[simp]
 theorem card_nat (n : ℕ) : card.{u} n = n := by
-  induction n <;> [rfl, simp only [card_add, card_one, Nat.cast_succ, *]]
+  induction n <;> [rfl; simp only [card_add, card_one, Nat.cast_succ, *]]
 #align ordinal.card_nat Ordinal.card_nat
 
 -- Porting note: Rewritten proof of elim, previous version was difficult to debug
@@ -961,8 +961,8 @@ instance add_swap_covariantClass_le :
                 intro a b
                 constructor <;> intro H
                 · cases' a with a a <;> cases' b with b b <;> cases H <;> constructor <;>
-                    [rwa [← fo], assumption]
-                · cases H <;> constructor <;> [rwa [fo], assumption]⟩
+                    [rwa [← fo]; assumption]
+                · cases H <;> constructor <;> [rwa [fo]; assumption]⟩
 #align ordinal.add_swap_covariant_class_le Ordinal.add_swap_covariantClass_le
 
 theorem le_add_right (a b : Ordinal) : a ≤ a + b := by
@@ -988,11 +988,7 @@ instance linearOrder : LinearOrder Ordinal :=
         rw [← typein_top f, ← typein_top g, le_iff_lt_or_eq, le_iff_lt_or_eq,
                  typein_lt_typein, typein_lt_typein]
         rcases trichotomous_of (Sum.Lex r₁ r₂) g.top f.top with (h | h | h) <;>
-                [exact Or.inl (Or.inl h),
-                · left
-                  right
-                  rw [h],
-                  exact Or.inr (Or.inl h)]
+          [exact Or.inl (Or.inl h); (left; right; rw [h]); exact Or.inr (Or.inl h)]
     decidableLE := Classical.decRel _ }
 
 instance wellFoundedLT : WellFoundedLT Ordinal :=

This renames

• decidable_eq to decidableEq
• decidable_lt to decidableLT
• decidable_le to decidableLE
• decidableLT_of_decidableLE to decidableLTOfDecidableLE
• decidableEq_of_decidableLE to decidableEqOfDecidableLE

These fields are data not proofs, so they should be lowerCamelCased.

@@ -993,7 +993,7 @@ instance linearOrder : LinearOrder Ordinal :=
                   right
                   rw [h],
                   exact Or.inr (Or.inl h)]
-    decidable_le := Classical.decRel _ }
+    decidableLE := Classical.decRel _ }
 
 instance wellFoundedLT : WellFoundedLT Ordinal :=
   ⟨lt_wf⟩

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>

@@ -1019,9 +1019,9 @@ theorem max_eq_zero {a b : Ordinal} : max a b = 0 ↔ a = 0 ∧ b = 0 :=
 #align ordinal.max_eq_zero Ordinal.max_eq_zero
 
 @[simp]
-theorem infₛ_empty : infₛ (∅ : Set Ordinal) = 0 :=
+theorem sInf_empty : sInf (∅ : Set Ordinal) = 0 :=
   dif_neg Set.not_nonempty_empty
-#align ordinal.Inf_empty Ordinal.infₛ_empty
+#align ordinal.Inf_empty Ordinal.sInf_empty
 
 -- ### Successor order properties
 private theorem succ_le_iff' {a b : Ordinal} : a + 1 ≤ b ↔ a < b :=
@@ -1337,10 +1337,10 @@ def ord (c : Cardinal) : Ordinal :=
       suffices : ∀ {α β}, α ≈ β → F α ≤ F β
       exact fun α β h => (this h).antisymm (this (Setoid.symm h))
       rintro α β ⟨f⟩
-      refine' le_cinfᵢ_iff'.2 fun i => _
+      refine' le_ciInf_iff'.2 fun i => _
       haveI := @RelEmbedding.isWellOrder _ _ (f ⁻¹'o i.1) _ (↑(RelIso.preimage f i.1)) i.2
       exact
-        (cinfᵢ_le' _
+        (ciInf_le' _
               (Subtype.mk (f ⁻¹'o i.val)
                 (@RelEmbedding.isWellOrder _ _ _ _ (↑(RelIso.preimage f i.1)) i.2))).trans_eq
           (Quot.sound ⟨RelIso.preimage f i.1⟩))
@@ -1351,12 +1351,12 @@ theorem ord_eq_Inf (α : Type u) : ord (#α) = ⨅ r : { r // IsWellOrder α r }
 #align cardinal.ord_eq_Inf Cardinal.ord_eq_Inf
 
 theorem ord_eq (α) : ∃ (r : α → α → Prop)(wo : IsWellOrder α r), ord (#α) = @type α r wo :=
-  let ⟨r, wo⟩ := cinfᵢ_mem fun r : { r // IsWellOrder α r } => @type α r.1 r.2
+  let ⟨r, wo⟩ := ciInf_mem fun r : { r // IsWellOrder α r } => @type α r.1 r.2
   ⟨r.1, r.2, wo.symm⟩
 #align cardinal.ord_eq Cardinal.ord_eq
 
 theorem ord_le_type (r : α → α → Prop) [h : IsWellOrder α r] : ord (#α) ≤ type r :=
-  cinfᵢ_le' _ (Subtype.mk r h)
+  ciInf_le' _ (Subtype.mk r h)
 #align cardinal.ord_le_type Cardinal.ord_le_type
 
 theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=

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".

@@ -474,8 +474,7 @@ theorem typein_apply {α β} {r : α → α → Prop} {s : β → β → Prop} [
 @[simp]
 theorem typein_lt_typein (r : α → α → Prop) [IsWellOrder α r] {a b : α} :
     typein r a < typein r b ↔ r a b :=
-  ⟨fun ⟨f⟩ =>
-    by
+  ⟨fun ⟨f⟩ => by
     have : f.top.1 = a := by
       let f' := PrincipalSeg.ofElement r a
       let g' := f.trans (PrincipalSeg.ofElement r b)
@@ -507,8 +506,7 @@ theorem typein_inj (r : α → α → Prop) [IsWellOrder α r] {a b} : typein r
   That is, `enum` maps an initial segment of the ordinals, those
   less than the order type of `r`, to the elements of `α`. -/
 def enum (r : α → α → Prop) [IsWellOrder α r] (o) : o < type r → α :=
-  Quot.recOn' o (fun ⟨β, s, _⟩ h => (Classical.choice h).top) fun ⟨β, s, _⟩ ⟨γ, t, _⟩ ⟨h⟩ =>
-    by
+  Quot.recOn' o (fun ⟨β, s, _⟩ h => (Classical.choice h).top) fun ⟨β, s, _⟩ ⟨γ, t, _⟩ ⟨h⟩ => by
     refine' funext fun H₂ : type t < type r => _
     have H₁ : type s < type r := by rwa [type_eq.2 ⟨h⟩]
     have : ∀ {o : Ordinal} {e : type s = o} (H : o < type r),
@@ -568,8 +566,7 @@ theorem lt_wf : @WellFounded Ordinal (· < ·) :=
           e ▸ this a⟩
       fun a =>
       Acc.recOn (wo.wf.apply a) fun x _ IH =>
-        ⟨_, fun o h =>
-          by
+        ⟨_, fun o h => by
           rcases typein_surj r (lt_trans h (typein_lt_type r _)) with ⟨b, rfl⟩
           exact IH _ ((typein_lt_typein r).1 h)⟩⟩
 #align ordinal.lt_wf Ordinal.lt_wf
@@ -1271,8 +1268,7 @@ theorem univ_umax : univ.{u, max (u + 1) v} = univ.{u, v} :=
 /-- Principal segment version of the lift operation on ordinals, embedding `ordinal.{u}` in
   `ordinal.{v}` as a principal segment when `u < v`. -/
 def lift.principalSeg : @PrincipalSeg Ordinal.{u} Ordinal.{max (u + 1) v} (· < ·) (· < ·) :=
-  ⟨↑lift.initialSeg.{u, max (u + 1) v}, univ.{u, v},
-    by
+  ⟨↑lift.initialSeg.{u, max (u + 1) v}, univ.{u, v}, by
     refine' fun b => inductionOn b _; intro β s _
     rw [univ, ← lift_umax]; constructor <;> intro h
     · rw [← lift_id (type s)] at h⊢
@@ -1365,8 +1361,7 @@ theorem ord_le_type (r : α → α → Prop) [h : IsWellOrder α r] : ord (#α)
 
 theorem ord_le {c o} : ord c ≤ o ↔ c ≤ o.card :=
   inductionOn c fun α =>
-    Ordinal.inductionOn o fun β s _ =>
-      by
+    Ordinal.inductionOn o fun β s _ => by
       let ⟨r, _, e⟩ := ord_eq α
       skip; simp only [card_type]; constructor <;> intro h
       · rw [e] at h

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

@@ -948,7 +948,7 @@ instance add_covariantClass_le : CovariantClass Ordinal.{u} Ordinal.{u} (· + ·
       | Sum.inr a, Sum.inr b, H =>
         let ⟨w, h⟩ := fi _ _ (Sum.lex_inr_inr.1 H)
         exact ⟨Sum.inr w, congr_arg Sum.inr h⟩
-  #align ordinal.add_covariant_class_le Ordinal.add_covariantClass_le
+#align ordinal.add_covariant_class_le Ordinal.add_covariantClass_le
 
 -- Porting note: Rewritten proof of elim, previous version was difficult to debug
 instance add_swap_covariantClass_le :

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.)

@@ -1235,7 +1235,6 @@ noncomputable def enumIsoOut (o : Ordinal) : Set.Iio o ≃o o.out.α
 /-- `o.out.α` is an `order_bot` whenever `0 < o`. -/
 def outOrderBotOfPos {o : Ordinal} (ho : 0 < o) : OrderBot o.out.α where
   bot_le := enum_zero_le' ho
-
 #align ordinal.out_order_bot_of_pos Ordinal.outOrderBotOfPos
 
 theorem enum_zero_eq_bot {o : Ordinal} (ho : 0 < o) :

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro, Floris van Doorn
 
 ! This file was ported from Lean 3 source module set_theory.ordinal.basic
-! leanprover-community/mathlib commit dc6c365e751e34d100e80fe6e314c3c3e0fd2988
+! leanprover-community/mathlib commit 8da9e30545433fdd8fe55a0d3da208e5d9263f03
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -466,7 +466,7 @@ theorem typein_apply {α β} {r : α → α → Prop} {s : β → β → Prop} [
         (RelEmbedding.codRestrict _ ((Subrel.relEmbedding _ _).trans f) fun ⟨x, h⟩ => by
           rw [RelEmbedding.trans_apply]; exact f.toRelEmbedding.map_rel_iff.2 h)
           fun ⟨y, h⟩ => by
-            rcases f.init' h with ⟨a, rfl⟩
+            rcases f.init h with ⟨a, rfl⟩
             exact ⟨⟨a, f.toRelEmbedding.map_rel_iff.1 h⟩,
               Subtype.eq <| RelEmbedding.trans_apply _ _ _⟩⟩
 #align ordinal.typein_apply Ordinal.typein_apply

Restore most of the mono attribute now that #1740 is merged.

I think I got all of the monos.

@@ -1408,12 +1408,12 @@ theorem lt_ord_succ_card (o : Ordinal) : o < (succ o.card).ord :=
   lt_ord.2 <| lt_succ _
 #align cardinal.lt_ord_succ_card Cardinal.lt_ord_succ_card
 
--- @[mono] -- Porting note: mono not implemented yet
+@[mono]
 theorem ord_strictMono : StrictMono ord :=
   gciOrdCard.strictMono_l
 #align cardinal.ord_strict_mono Cardinal.ord_strictMono
 
--- @[mono] -- Porting note: mono not implemented yet
+@[mono]
 theorem ord_mono : Monotone ord :=
   gc_ord_card.monotone_l
 #align cardinal.ord_mono Cardinal.ord_mono

@@ -174,13 +174,13 @@ def type (r : α → α → Prop) [wo : IsWellOrder α r] : Ordinal :=
   ⟦⟨α, r, wo⟩⟧
 #align ordinal.type Ordinal.type
 
-instance hasZero : Zero Ordinal :=
+instance zero : Zero Ordinal :=
   ⟨type <| @EmptyRelation PEmpty⟩
 
 instance inhabited : Inhabited Ordinal :=
   ⟨0⟩
 
-instance hasOne : One Ordinal :=
+instance one : One Ordinal :=
   ⟨type <| @EmptyRelation PUnit⟩
 
 /-- The order type of an element inside a well order. For the embedding as a principal segment, see
@@ -885,13 +885,12 @@ the addition, together with properties of the other operations, are proved in
 
 /-- `o₁ + o₂` is the order on the disjoint union of `o₁` and `o₂` obtained by declaring that
   every element of `o₁` is smaller than every element of `o₂`. -/
-instance hasAdd : Add Ordinal.{u} :=
+instance add : Add Ordinal.{u} :=
   ⟨fun o₁ o₂ =>
     Quotient.liftOn₂ o₁ o₂ (fun ⟨_, r, _⟩ ⟨_, s, _⟩ => type (Sum.Lex r s))
       fun _ _ _ _ ⟨f⟩ ⟨g⟩ => Quot.sound ⟨RelIso.sumLexCongr f g⟩⟩
 
-instance addMonoidWithOne : AddMonoidWithOne Ordinal.{u}
-    where
+instance addMonoidWithOne : AddMonoidWithOne Ordinal.{u} where
   add := (· + ·)
   zero := 0
   one := 1

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

@@ -128,7 +128,7 @@ attribute [instance] WellOrder.wo
 
 namespace WellOrder
 
-instance : Inhabited WellOrder :=
+instance inhabited : Inhabited WellOrder :=
   ⟨⟨PEmpty, _, inferInstanceAs (IsWellOrder PEmpty EmptyRelation)⟩⟩
 
 @[simp]
@@ -174,13 +174,13 @@ def type (r : α → α → Prop) [wo : IsWellOrder α r] : Ordinal :=
   ⟦⟨α, r, wo⟩⟧
 #align ordinal.type Ordinal.type
 
-instance : Zero Ordinal :=
+instance hasZero : Zero Ordinal :=
   ⟨type <| @EmptyRelation PEmpty⟩
 
-instance : Inhabited Ordinal :=
+instance inhabited : Inhabited Ordinal :=
   ⟨0⟩
 
-instance : One Ordinal :=
+instance hasOne : One Ordinal :=
   ⟨type <| @EmptyRelation PUnit⟩
 
 /-- The order type of an element inside a well order. For the embedding as a principal segment, see
@@ -293,7 +293,7 @@ protected theorem one_ne_zero : (1 : Ordinal) ≠ 0 :=
   type_ne_zero_of_nonempty _
 #align ordinal.one_ne_zero Ordinal.one_ne_zero
 
-instance : Nontrivial Ordinal.{u} :=
+instance nontrivial : Nontrivial Ordinal.{u} :=
   ⟨⟨1, 0, Ordinal.one_ne_zero⟩⟩
 
 --@[simp] -- Porting note: not in simp nf, added aux lemma below
@@ -316,7 +316,7 @@ theorem inductionOn {C : Ordinal → Prop} (o : Ordinal)
 /-! ### The order on ordinals -/
 
 
-instance : PartialOrder Ordinal
+instance partialOrder : PartialOrder Ordinal
     where
   le a b :=
     Quotient.liftOn₂ a b (fun ⟨_, r, _⟩ ⟨_, s, _⟩ => Nonempty (r ≼i s))
@@ -387,7 +387,7 @@ protected theorem zero_le (o : Ordinal) : 0 ≤ o :=
   inductionOn o fun _ r _ => (InitialSeg.ofIsEmpty _ r).ordinal_type_le
 #align ordinal.zero_le Ordinal.zero_le
 
-instance : OrderBot Ordinal where
+instance orderBot : OrderBot Ordinal where
   bot := 0
   bot_le := Ordinal.zero_le
 
@@ -413,7 +413,7 @@ theorem eq_zero_or_pos : ∀ a : Ordinal, a = 0 ∨ 0 < a :=
   eq_bot_or_bot_lt
 #align ordinal.eq_zero_or_pos Ordinal.eq_zero_or_pos
 
-instance : ZeroLEOneClass Ordinal :=
+instance zeroLEOneClass : ZeroLEOneClass Ordinal :=
   ⟨Ordinal.zero_le _⟩
 
 instance NeZero.one : NeZero (1 : Ordinal) :=
@@ -574,7 +574,7 @@ theorem lt_wf : @WellFounded Ordinal (· < ·) :=
           exact IH _ ((typein_lt_typein r).1 h)⟩⟩
 #align ordinal.lt_wf Ordinal.lt_wf
 
-instance : WellFoundedRelation Ordinal :=
+instance wellFoundedRelation : WellFoundedRelation Ordinal :=
   ⟨(· < ·), lt_wf⟩
 
 /-- Reformulation of well founded induction on ordinals as a lemma that works with the
@@ -885,12 +885,12 @@ the addition, together with properties of the other operations, are proved in
 
 /-- `o₁ + o₂` is the order on the disjoint union of `o₁` and `o₂` obtained by declaring that
   every element of `o₁` is smaller than every element of `o₂`. -/
-instance : Add Ordinal.{u} :=
+instance hasAdd : Add Ordinal.{u} :=
   ⟨fun o₁ o₂ =>
     Quotient.liftOn₂ o₁ o₂ (fun ⟨_, r, _⟩ ⟨_, s, _⟩ => type (Sum.Lex r s))
       fun _ _ _ _ ⟨f⟩ ⟨g⟩ => Quot.sound ⟨RelIso.sumLexCongr f g⟩⟩
 
-instance : AddMonoidWithOne Ordinal.{u}
+instance addMonoidWithOne : AddMonoidWithOne Ordinal.{u}
     where
   add := (· + ·)
   zero := 0
@@ -977,7 +977,7 @@ theorem le_add_left (a b : Ordinal) : a ≤ b + a := by
   simpa only [zero_add] using add_le_add_right (Ordinal.zero_le b) a
 #align ordinal.le_add_left Ordinal.le_add_left
 
-instance : LinearOrder Ordinal :=
+instance linearOrder : LinearOrder Ordinal :=
   {inferInstanceAs (PartialOrder Ordinal) with
     le_total := fun a b =>
       match lt_or_eq_of_le (le_add_left b a), lt_or_eq_of_le (le_add_right a b) with
@@ -999,10 +999,10 @@ instance : LinearOrder Ordinal :=
                   exact Or.inr (Or.inl h)]
     decidable_le := Classical.decRel _ }
 
-instance : WellFoundedLT Ordinal :=
+instance wellFoundedLT : WellFoundedLT Ordinal :=
   ⟨lt_wf⟩
 
-instance : IsWellOrder Ordinal (· < ·) where
+instance isWellOrder : IsWellOrder Ordinal (· < ·) where
 
 instance : ConditionallyCompleteLinearOrderBot Ordinal :=
   IsWellOrder.conditionallyCompleteLinearOrderBot _
@@ -1055,10 +1055,10 @@ private theorem succ_le_iff' {a b : Ordinal} : a + 1 ≤ b ↔ a < b :=
             cases' (hf b).1 h with w h
             exact ⟨Sum.inl w, h⟩⟩
 
-instance : NoMaxOrder Ordinal :=
+instance noMaxOrder : NoMaxOrder Ordinal :=
   ⟨fun _ => ⟨_, succ_le_iff'.1 le_rfl⟩⟩
 
-instance : SuccOrder Ordinal.{u} :=
+instance succOrder : SuccOrder Ordinal.{u} :=
   SuccOrder.ofSuccLeIff (fun o => o + 1) succ_le_iff'
 
 @[simp]

Needed to add some explicit universes here and there, add some _aux simp lemmas, and reformat some funky inductions. What is unfortunate is that succ_one : succ (1 : Ordinal) = 2 is not true by rfl anymore.