set_theory.ordinal.fixed_point | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

0dd4319a

(last sync)

chore(set_theory/ordinal/fixed_point): style + comments (#18322)

We add some missing brackets, and some much-needed comments on various functions.

Diff

@@ -44,6 +44,9 @@ variables {ι : Type u} {f : ι → ordinal.{max u v} → ordinal.{max u v}}
 
 /-- The next common fixed point, at least `a`, for a family of normal functions.
 
+This is defined for any family of functions, as the supremum of all values reachable by applying
+finitely many functions in the family to `a`.
+
 `ordinal.nfp_family_fp` shows this is a fixed point, `ordinal.le_nfp_family` shows it's at
 least `a`, and `ordinal.nfp_family_le_fp` shows this is the least ordinal with these properties. -/
 def nfp_family (f : ι → ordinal → ordinal) (a) : ordinal :=
@@ -78,7 +81,7 @@ let ⟨l, hl⟩ := lt_nfp_family.1 hb in lt_sup.2 ⟨i :: l, (H i).strict_mono h
 
 theorem apply_lt_nfp_family_iff [nonempty ι] (H : ∀ i, is_normal (f i)) {a b} :
   (∀ i, f i b < nfp_family f a) ↔ b < nfp_family f a :=
-⟨λ h, lt_nfp_family.2 $ let ⟨l, hl⟩ := lt_sup.1 (h (classical.arbitrary ι)) in
+⟨λ h, lt_nfp_family.2 $ let ⟨l, hl⟩ := lt_sup.1 $ h $ classical.arbitrary ι in
   ⟨l, ((H _).self_le b).trans_lt hl⟩, apply_lt_nfp_family H⟩
 
 theorem nfp_family_le_apply [nonempty ι] (H : ∀ i, is_normal (f i)) {a b} :
@@ -117,10 +120,11 @@ end
 
 theorem nfp_family_eq_self {f : ι → ordinal → ordinal} {a} (h : ∀ i, f i a = a) :
   nfp_family f a = a :=
-le_antisymm (sup_le (λ l, (by rw list.foldr_fixed' h l))) (le_nfp_family f a)
+le_antisymm (sup_le $ λ l, by rw list.foldr_fixed' h l) $ le_nfp_family f a
 
 /-- A generalization of the fixed point lemma for normal functions: any family of normal functions
     has an unbounded set of common fixed points. -/
+-- Todo: This is actually a special case of the fact the intersection of club sets is a club set.
 theorem fp_family_unbounded (H : ∀ i, is_normal (f i)) :
   (⋂ i, function.fixed_points (f i)).unbounded (<) :=
 λ a, ⟨_, λ s ⟨i, hi⟩, begin
@@ -128,7 +132,10 @@ theorem fp_family_unbounded (H : ∀ i, is_normal (f i)) :
   exact nfp_family_fp (H i) a
 end, (le_nfp_family f a).not_lt⟩
 
-/-- The derivative of a family of normal functions is the sequence of their common fixed points. -/
+/-- The derivative of a family of normal functions is the sequence of their common fixed points.
+
+This is defined for all functions such that `ordinal.deriv_family_zero`,
+`ordinal.deriv_family_succ`, and `ordinal.deriv_family_limit` are satisfied. -/
 def deriv_family (f : ι → ordinal → ordinal) (o : ordinal) : ordinal :=
 limit_rec_on o (nfp_family f 0)
   (λ a IH, nfp_family f (succ IH))
@@ -178,12 +185,13 @@ theorem le_iff_deriv_family (H : ∀ i, is_normal (f i)) {a} :
   { cases eq_or_lt_of_le h₁, {exact ⟨_, h.symm⟩},
     rw [deriv_family_limit _ l, ← not_le, bsup_le_iff, not_ball] at h,
     exact let ⟨o', h, hl⟩ := h in IH o' h (le_of_not_le hl) }
-end, λ ⟨o, e⟩ i, e ▸ le_of_eq (deriv_family_fp (H i) _)⟩
+end, λ ⟨o, e⟩ i, e ▸ (deriv_family_fp (H i) _).le⟩
 
 theorem fp_iff_deriv_family (H : ∀ i, is_normal (f i)) {a} :
   (∀ i, f i a = a) ↔ ∃ o, deriv_family f o = a :=
 iff.trans ⟨λ h i, le_of_eq (h i), λ h i, (H i).le_iff_eq.1 (h i)⟩ (le_iff_deriv_family H)
 
+/-- For a family of normal functions, `ordinal.deriv_family` enumerates the common fixed points. -/
 theorem deriv_family_eq_enum_ord (H : ∀ i, is_normal (f i)) :
   deriv_family f = enum_ord (⋂ i, function.fixed_points (f i)) :=
 begin
@@ -206,6 +214,8 @@ section
 variables {o : ordinal.{u}} {f : Π b < o, ordinal.{max u v} → ordinal.{max u v}}
 
 /-- The next common fixed point, at least `a`, for a family of normal functions indexed by ordinals.
+
+This is defined as `ordinal.nfp_family` of the type-indexed family associated to `f`.
 -/
 def nfp_bfamily (o : ordinal) (f : Π b < o, ordinal → ordinal) : ordinal → ordinal :=
 nfp_family (family_of_bfamily o f)
@@ -271,8 +281,8 @@ begin
   refine ⟨λ h, _, λ h i hi, _⟩,
   { have ho' : 0 < o := ordinal.pos_iff_ne_zero.2 ho,
     exact ((H 0 ho').self_le b).trans (h 0 ho') },
-  rw ←nfp_bfamily_fp (H i hi),
-  exact (H i hi).monotone h
+  { rw ←nfp_bfamily_fp (H i hi),
+    exact (H i hi).monotone h }
 end
 
 theorem nfp_bfamily_eq_self {a} (h : ∀ i hi, f i hi a = a) : nfp_bfamily o f a = a :=
@@ -285,7 +295,9 @@ theorem fp_bfamily_unbounded (H : ∀ i hi, is_normal (f i hi)) :
 λ a, ⟨_, by { rw set.mem_Inter₂, exact λ i hi, nfp_bfamily_fp (H i hi) _ },
   (le_nfp_bfamily f a).not_lt⟩
 
-/-- The derivative of a family of normal functions is the sequence of their common fixed points. -/
+/-- The derivative of a family of normal functions is the sequence of their common fixed points.
+
+This is defined as `ordinal.deriv_family` of the type-indexed family associated to `f`. -/
 def deriv_bfamily (o : ordinal) (f : Π b < o, ordinal → ordinal) : ordinal → ordinal :=
 deriv_family (family_of_bfamily o f)
 
@@ -309,7 +321,7 @@ begin
   { refine ⟨λ h i, h _ _, λ h i hi, _⟩,
     rw ←family_of_bfamily_enum o f,
     apply h },
-  exact λ _, H _ _
+  { exact λ _, H _ _ }
 end
 
 theorem fp_iff_deriv_bfamily (H : ∀ i hi, is_normal (f i hi)) {a} :
@@ -321,6 +333,7 @@ begin
   exact h i hi
 end
 
+/-- For a family of normal functions, `ordinal.deriv_bfamily` enumerates the common fixed points. -/
 theorem deriv_bfamily_eq_enum_ord (H : ∀ i hi, is_normal (f i hi)) :
   deriv_bfamily o f = enum_ord (⋂ i hi, function.fixed_points (f i hi)) :=
 begin
@@ -340,7 +353,8 @@ section
 variable {f : ordinal.{u} → ordinal.{u}}
 
 /-- The next fixed point function, the least fixed point of the normal function `f`, at least `a`.
--/
+
+This is defined as `ordinal.nfp_family` applied to a family consisting only of `f`. -/
 def nfp (f : ordinal → ordinal) : ordinal → ordinal :=
 nfp_family (λ _ : unit, f)
 
@@ -371,8 +385,7 @@ by { rw ←sup_iterate_eq_nfp, exact lt_sup }
 theorem nfp_le_iff {a b} : nfp f a ≤ b ↔ ∀ n, (f^[n]) a ≤ b :=
 by { rw ←sup_iterate_eq_nfp, exact sup_le_iff }
 
-theorem nfp_le {a b} : (∀ n, (f^[n]) a ≤ b) → nfp f a ≤ b :=
-nfp_le_iff.2
+theorem nfp_le {a b} : (∀ n, (f^[n]) a ≤ b) → nfp f a ≤ b := nfp_le_iff.2
 
 @[simp] theorem nfp_id : nfp id = id :=
 funext (λ a, begin
@@ -412,7 +425,9 @@ fixed points. -/
 theorem fp_unbounded (H : is_normal f) : (function.fixed_points f).unbounded (<) :=
 by { convert fp_family_unbounded (λ _ : unit, H), exact (set.Inter_const _).symm }
 
-/-- The derivative of a normal function `f` is the sequence of fixed points of `f`. -/
+/-- The derivative of a normal function `f` is the sequence of fixed points of `f`.
+
+This is defined as `ordinal.deriv_family` applied to a trivial family consisting only of `f`. -/
 def deriv (f : ordinal → ordinal) : ordinal → ordinal :=
 deriv_family (λ _ : unit, f)
 
@@ -447,11 +462,12 @@ end
 theorem is_normal.fp_iff_deriv {f} (H : is_normal f) {a} : f a = a ↔ ∃ o, deriv f o = a :=
 by rw [←H.le_iff_eq, H.le_iff_deriv]
 
+/-- `ordinal.deriv` enumerates the fixed points of a normal function. -/
 theorem deriv_eq_enum_ord (H : is_normal f) : deriv f = enum_ord (function.fixed_points f) :=
 by { convert deriv_family_eq_enum_ord (λ _ : unit, H), exact (set.Inter_const _).symm }
 
 theorem deriv_eq_id_of_nfp_eq_id {f : ordinal → ordinal} (h : nfp f = id) : deriv f = id :=
-(is_normal.eq_iff_zero_and_succ (deriv_is_normal _) is_normal.refl).2 (by simp [h])
+(is_normal.eq_iff_zero_and_succ (deriv_is_normal _) is_normal.refl).2 $ by simp [h]
 
 end

c6b53304

feat(set_theory/ordinal/fixed_point): add missing theorem (#18323)

We add apply_lt_nfp_bfamily matching apply_lt_nfp_family, and rename the existing theorem with that name to apply_lt_nfp_bfamily_iff, matching apply_lt_nfp_family_iff.

Diff

@@ -237,20 +237,25 @@ sup_le
 theorem nfp_bfamily_monotone (hf : ∀ i hi, monotone (f i hi)) : monotone (nfp_bfamily o f) :=
 nfp_family_monotone (λ i, hf _ _)
 
-theorem apply_lt_nfp_bfamily (ho : o ≠ 0) (H : ∀ i hi, is_normal (f i hi)) {a b} :
-  (∀ i hi, f i hi b < nfp_bfamily o f a) ↔ b < nfp_bfamily o f a :=
+theorem apply_lt_nfp_bfamily (H : ∀ i hi, is_normal (f i hi)) {a b} (hb : b < nfp_bfamily o f a)
+  (i hi) : f i hi b < nfp_bfamily o f a :=
 begin
-  unfold nfp_bfamily,
-  rw ←@apply_lt_nfp_family_iff _ (family_of_bfamily o f) (out_nonempty_iff_ne_zero.2 ho)
-    (λ i, H _ _),
-  refine ⟨λ h i, h _ (typein_lt_self i), λ h i hio, _⟩,
   rw ←family_of_bfamily_enum o f,
-  apply h
+  apply apply_lt_nfp_family _ hb,
+  exact λ _, H _ _
 end
 
+theorem apply_lt_nfp_bfamily_iff (ho : o ≠ 0) (H : ∀ i hi, is_normal (f i hi)) {a b} :
+  (∀ i hi, f i hi b < nfp_bfamily o f a) ↔ b < nfp_bfamily o f a :=
+⟨λ h, begin
+  haveI := out_nonempty_iff_ne_zero.2 ho,
+  refine (apply_lt_nfp_family_iff _).1 (λ _, h _ _),
+  exact λ _, H _ _,
+end, apply_lt_nfp_bfamily H⟩
+
 theorem nfp_bfamily_le_apply (ho : o ≠ 0) (H : ∀ i hi, is_normal (f i hi)) {a b} :
   (∃ i hi, nfp_bfamily o f a ≤ f i hi b) ↔ nfp_bfamily o f a ≤ b :=
-by { rw ←not_iff_not, push_neg, convert apply_lt_nfp_bfamily ho H, simp only [not_le] }
+by { rw ←not_iff_not, push_neg, convert apply_lt_nfp_bfamily_iff ho H, simp only [not_le] }
 
 theorem nfp_bfamily_le_fp (H : ∀ i hi, monotone (f i hi)) {a b} (ab : a ≤ b)
   (h : ∀ i hi, f i hi b ≤ b) : nfp_bfamily o f a ≤ b :=

bd9851ca

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

0dd4319a

bump to nightly-2024-04-10-08

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

cd0c1af5

Diff

@@ -252,7 +252,7 @@ theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
       rw [deriv_family_succ]
       exact nfp_family_le_fp (fun i => (H i).Monotone) (succ_le_of_lt h) ha
     · cases eq_or_lt_of_le h₁; · exact ⟨_, h.symm⟩
-      rw [deriv_family_limit _ l, ← not_le, bsup_le_iff, not_ball] at h
+      rw [deriv_family_limit _ l, ← not_le, bsup_le_iff, not_forall₂] at h
       exact
         let ⟨o', h, hl⟩ := h
         IH o' h (le_of_not_le hl),

0dd4319a

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -252,7 +252,7 @@ theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
       rw [deriv_family_succ]
       exact nfp_family_le_fp (fun i => (H i).Monotone) (succ_le_of_lt h) ha
     · cases eq_or_lt_of_le h₁; · exact ⟨_, h.symm⟩
-      rw [deriv_family_limit _ l, ← not_le, bsup_le_iff, not_ball] at h 
+      rw [deriv_family_limit _ l, ← not_le, bsup_le_iff, not_ball] at h
       exact
         let ⟨o', h, hl⟩ := h
         IH o' h (le_of_not_le hl),
@@ -279,7 +279,7 @@ theorem derivFamily_eq_enumOrd (H : ∀ i, IsNormal (f i)) :
   · rintro a S ⟨i, hi⟩
     rw [← hi]
     exact deriv_family_fp (H i) a
-  rw [Set.mem_iInter] at ha 
+  rw [Set.mem_iInter] at ha
   rwa [← fp_iff_deriv_family H]
 #align ordinal.deriv_family_eq_enum_ord Ordinal.derivFamily_eq_enumOrd
 -/
@@ -484,7 +484,7 @@ theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
   use(deriv_bfamily_is_normal f).StrictMono
   rw [Set.range_eq_iff]
   refine' ⟨fun a => Set.mem_iInter₂.2 fun i hi => deriv_bfamily_fp (H i hi) a, fun a ha => _⟩
-  rw [Set.mem_iInter₂] at ha 
+  rw [Set.mem_iInter₂] at ha
   rwa [← fp_iff_deriv_bfamily H]
 #align ordinal.deriv_bfamily_eq_enum_ord Ordinal.derivBFamily_eq_enumOrd
 -/
@@ -838,9 +838,9 @@ theorem eq_zero_or_opow_omega_le_of_mul_eq_right {a b : Ordinal} (hab : a * b =
     exact Or.inr (Ordinal.zero_le b)
   rw [Classical.or_iff_not_imp_left]
   intro hb
-  change b ≠ 0 at hb 
+  change b ≠ 0 at hb
   rw [← nfp_mul_one ha]
-  rw [← one_le_iff_ne_zero] at hb 
+  rw [← one_le_iff_ne_zero] at hb
   exact nfp_le_fp (mul_is_normal ha).Monotone hb (le_of_eq hab)
 #align ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right Ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right
 -/
@@ -854,7 +854,7 @@ theorem mul_eq_right_iff_opow_omega_dvd {a b : Ordinal} : a * b = b ↔ (a^omega
   refine' ⟨fun hab => _, fun h => _⟩
   · rw [dvd_iff_mod_eq_zero]
     rw [← div_add_mod b (a^omega), mul_add, ← mul_assoc, ← opow_one_add, one_add_omega,
-      add_left_cancel] at hab 
+      add_left_cancel] at hab
     cases' eq_zero_or_opow_omega_le_of_mul_eq_right hab with hab hab
     · exact hab
     refine' (not_lt_of_le hab (mod_lt b (opow_ne_zero omega _))).elim
@@ -884,9 +884,9 @@ theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hc
     rw [hd]
     apply mul_le_mul_left'
     have := le_nfp (Mul.mul a) ((a^omega) * b + c)
-    rw [hd] at this 
+    rw [hd] at this
     have := (add_lt_add_left hc ((a^omega) * b)).trans_le this
-    rw [add_zero, mul_lt_mul_iff_left (opow_pos omega ha)] at this 
+    rw [add_zero, mul_lt_mul_iff_left (opow_pos omega ha)] at this
     rwa [succ_le_iff]
 #align ordinal.nfp_mul_opow_omega_add Ordinal.nfp_mul_opow_omega_add
 -/

0dd4319a

bump to nightly-2023-11-05-06

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

acc3325f

Diff

@@ -836,7 +836,7 @@ theorem eq_zero_or_opow_omega_le_of_mul_eq_right {a b : Ordinal} (hab : a * b =
   cases' eq_zero_or_pos a with ha ha
   · rw [ha, zero_opow omega_ne_zero]
     exact Or.inr (Ordinal.zero_le b)
-  rw [or_iff_not_imp_left]
+  rw [Classical.or_iff_not_imp_left]
   intro hb
   change b ≠ 0 at hb 
   rw [← nfp_mul_one ha]

0dd4319a

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2018 Violeta Hernández Palacios, Mario Carneiro. All rights reser
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios, Mario Carneiro
 -/
-import Mathbin.SetTheory.Ordinal.Arithmetic
-import Mathbin.SetTheory.Ordinal.Exponential
+import SetTheory.Ordinal.Arithmetic
+import SetTheory.Ordinal.Exponential
 
 #align_import set_theory.ordinal.fixed_point from "leanprover-community/mathlib"@"0dd4319a17376eda5763cd0a7e0d35bbaaa50e83"

0dd4319a

bump to nightly-2023-08-02-01

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

7aca3f15

Diff

@@ -273,7 +273,7 @@ theorem derivFamily_eq_enumOrd (H : ∀ i, IsNormal (f i)) :
     derivFamily f = enumOrd (⋂ i, Function.fixedPoints (f i)) :=
   by
   rw [← eq_enum_ord _ (fp_family_unbounded H)]
-  use (deriv_family_is_normal f).StrictMono
+  use(deriv_family_is_normal f).StrictMono
   rw [Set.range_eq_iff]
   refine' ⟨_, fun a ha => _⟩
   · rintro a S ⟨i, hi⟩
@@ -481,7 +481,7 @@ theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
     derivBFamily o f = enumOrd (⋂ (i) (hi), Function.fixedPoints (f i hi)) :=
   by
   rw [← eq_enum_ord _ (fp_bfamily_unbounded H)]
-  use (deriv_bfamily_is_normal f).StrictMono
+  use(deriv_bfamily_is_normal f).StrictMono
   rw [Set.range_eq_iff]
   refine' ⟨fun a => Set.mem_iInter₂.2 fun i hi => deriv_bfamily_fp (H i hi) a, fun a ha => _⟩
   rw [Set.mem_iInter₂] at ha

0dd4319a

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Violeta Hernández Palacios, Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios, Mario Carneiro
-
-! This file was ported from Lean 3 source module set_theory.ordinal.fixed_point
-! leanprover-community/mathlib commit 0dd4319a17376eda5763cd0a7e0d35bbaaa50e83
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.SetTheory.Ordinal.Arithmetic
 import Mathbin.SetTheory.Ordinal.Exponential
 
+#align_import set_theory.ordinal.fixed_point from "leanprover-community/mathlib"@"0dd4319a17376eda5763cd0a7e0d35bbaaa50e83"
+
 /-!
 # Fixed points of normal functions

0dd4319a

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -74,9 +74,11 @@ theorem foldr_le_nfpFamily (f : ι → Ordinal → Ordinal) (a l) : List.foldr f
 #align ordinal.foldr_le_nfp_family Ordinal.foldr_le_nfpFamily
 -/
 
+#print Ordinal.le_nfpFamily /-
 theorem le_nfpFamily (f : ι → Ordinal → Ordinal) (a) : a ≤ nfpFamily f a :=
   le_sup _ []
 #align ordinal.le_nfp_family Ordinal.le_nfpFamily
+-/
 
 #print Ordinal.lt_nfpFamily /-
 theorem lt_nfpFamily {a b} : a < nfpFamily f b ↔ ∃ l, a < List.foldr f b l :=
@@ -165,10 +167,12 @@ theorem apply_le_nfpFamily [hι : Nonempty ι] {f : ι → Ordinal → Ordinal}
 #align ordinal.apply_le_nfp_family Ordinal.apply_le_nfpFamily
 -/
 
+#print Ordinal.nfpFamily_eq_self /-
 theorem nfpFamily_eq_self {f : ι → Ordinal → Ordinal} {a} (h : ∀ i, f i a = a) :
     nfpFamily f a = a :=
   le_antisymm (sup_le fun l => by rw [List.foldr_fixed' h l]) <| le_nfpFamily f a
 #align ordinal.nfp_family_eq_self Ordinal.nfpFamily_eq_self
+-/
 
 #print Ordinal.fp_family_unbounded /-
 -- Todo: This is actually a special case of the fact the intersection of club sets is a club set.
@@ -214,10 +218,12 @@ theorem derivFamily_limit (f : ι → Ordinal → Ordinal) {o} :
 #align ordinal.deriv_family_limit Ordinal.derivFamily_limit
 -/
 
+#print Ordinal.derivFamily_isNormal /-
 theorem derivFamily_isNormal (f : ι → Ordinal → Ordinal) : IsNormal (derivFamily f) :=
   ⟨fun o => by rw [deriv_family_succ, ← succ_le_iff] <;> apply le_nfp_family, fun o l a => by
     rw [deriv_family_limit _ l, bsup_le_iff]⟩
 #align ordinal.deriv_family_is_normal Ordinal.derivFamily_isNormal
+-/
 
 #print Ordinal.derivFamily_fp /-
 theorem derivFamily_fp {i} (H : IsNormal (f i)) (o : Ordinal.{max u v}) :
@@ -433,10 +439,12 @@ theorem derivBFamily_eq_derivFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Or
 #align ordinal.deriv_bfamily_eq_deriv_family Ordinal.derivBFamily_eq_derivFamily
 -/
 
+#print Ordinal.derivBFamily_isNormal /-
 theorem derivBFamily_isNormal {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) :
     IsNormal (derivBFamily o f) :=
   derivFamily_isNormal _
 #align ordinal.deriv_bfamily_is_normal Ordinal.derivBFamily_isNormal
+-/
 
 #print Ordinal.derivBFamily_fp /-
 theorem derivBFamily_fp {i hi} (H : IsNormal (f i hi)) (a : Ordinal) :
@@ -701,6 +709,7 @@ end
 /-! ### Fixed points of addition -/
 
 
+#print Ordinal.nfp_add_zero /-
 @[simp]
 theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
   by
@@ -711,7 +720,9 @@ theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
   · nth_rw 2 [Nat.succ_eq_one_add]
     rw [Nat.cast_add, Nat.cast_one, mul_one_add, iterate_succ_apply', hn]
 #align ordinal.nfp_add_zero Ordinal.nfp_add_zero
+-/
 
+#print Ordinal.nfp_add_eq_mul_omega /-
 theorem nfp_add_eq_mul_omega {a b} (hba : b ≤ a * omega) : nfp ((· + ·) a) b = a * omega :=
   by
   apply le_antisymm (nfp_le_fp (add_is_normal a).Monotone hba _)
@@ -719,7 +730,9 @@ theorem nfp_add_eq_mul_omega {a b} (hba : b ≤ a * omega) : nfp ((· + ·) a) b
     exact nfp_monotone (add_is_normal a).Monotone (Ordinal.zero_le b)
   · rw [← mul_one_add, one_add_omega]
 #align ordinal.nfp_add_eq_mul_omega Ordinal.nfp_add_eq_mul_omega
+-/
 
+#print Ordinal.add_eq_right_iff_mul_omega_le /-
 theorem add_eq_right_iff_mul_omega_le {a b : Ordinal} : a + b = b ↔ a * omega ≤ b :=
   by
   refine' ⟨fun h => _, fun h => _⟩
@@ -731,11 +744,15 @@ theorem add_eq_right_iff_mul_omega_le {a b : Ordinal} : a + b = b ↔ a * omega
     nth_rw 1 [← this]
     rwa [← add_assoc, ← mul_one_add, one_add_omega]
 #align ordinal.add_eq_right_iff_mul_omega_le Ordinal.add_eq_right_iff_mul_omega_le
+-/
 
+#print Ordinal.add_le_right_iff_mul_omega_le /-
 theorem add_le_right_iff_mul_omega_le {a b : Ordinal} : a + b ≤ b ↔ a * omega ≤ b := by
   rw [← add_eq_right_iff_mul_omega_le]; exact (add_is_normal a).le_iff_eq
 #align ordinal.add_le_right_iff_mul_omega_le Ordinal.add_le_right_iff_mul_omega_le
+-/
 
+#print Ordinal.deriv_add_eq_mul_omega_add /-
 theorem deriv_add_eq_mul_omega_add (a b : Ordinal.{u}) : deriv ((· + ·) a) b = a * omega + b :=
   by
   revert b
@@ -746,13 +763,14 @@ theorem deriv_add_eq_mul_omega_add (a b : Ordinal.{u}) : deriv ((· + ·) a) b =
   · rw [deriv_succ, h, add_succ]
     exact nfp_eq_self (add_eq_right_iff_mul_omega_le.2 ((le_add_right _ _).trans (le_succ _)))
 #align ordinal.deriv_add_eq_mul_omega_add Ordinal.deriv_add_eq_mul_omega_add
+-/
 
 /-! ### Fixed points of multiplication -/
 
 
--- mathport name: ordinal.pow
 local infixr:0 "^" => @pow Ordinal Ordinal Ordinal.hasPow
 
+#print Ordinal.nfp_mul_one /-
 @[simp]
 theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega) :=
   by
@@ -764,7 +782,9 @@ theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega)
     rw [Nat.cast_add, Nat.cast_one, opow_add, opow_one, iterate_succ_apply', hn]
   · exact ha
 #align ordinal.nfp_mul_one Ordinal.nfp_mul_one
+-/
 
+#print Ordinal.nfp_mul_zero /-
 @[simp]
 theorem nfp_mul_zero (a : Ordinal) : nfp ((· * ·) a) 0 = 0 :=
   by
@@ -773,7 +793,9 @@ theorem nfp_mul_zero (a : Ordinal) : nfp ((· * ·) a) 0 = 0 :=
   induction' n with n hn; · rfl
   rwa [iterate_succ_apply, MulZeroClass.mul_zero]
 #align ordinal.nfp_mul_zero Ordinal.nfp_mul_zero
+-/
 
+#print Ordinal.nfp_zero_mul /-
 @[simp]
 theorem nfp_zero_mul : nfp ((· * ·) 0) = id :=
   by
@@ -785,12 +807,16 @@ theorem nfp_zero_mul : nfp ((· * ·) 0) = id :=
   rw [MulZeroClass.zero_mul]
   exact Ordinal.zero_le a
 #align ordinal.nfp_zero_mul Ordinal.nfp_zero_mul
+-/
 
+#print Ordinal.deriv_mul_zero /-
 @[simp]
 theorem deriv_mul_zero : deriv ((· * ·) 0) = id :=
   deriv_eq_id_of_nfp_eq_id nfp_zero_mul
 #align ordinal.deriv_mul_zero Ordinal.deriv_mul_zero
+-/
 
+#print Ordinal.nfp_mul_eq_opow_omega /-
 theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega)) :
     nfp ((· * ·) a) b = (a^omega.{u}) :=
   by
@@ -804,7 +830,9 @@ theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega
   rw [← nfp_mul_one ha]
   exact nfp_monotone (mul_is_normal ha).Monotone (one_le_iff_pos.2 hb)
 #align ordinal.nfp_mul_eq_opow_omega Ordinal.nfp_mul_eq_opow_omega
+-/
 
+#print Ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right /-
 theorem eq_zero_or_opow_omega_le_of_mul_eq_right {a b : Ordinal} (hab : a * b = b) :
     b = 0 ∨ (a^omega.{u}) ≤ b :=
   by
@@ -818,7 +846,9 @@ theorem eq_zero_or_opow_omega_le_of_mul_eq_right {a b : Ordinal} (hab : a * b =
   rw [← one_le_iff_ne_zero] at hb 
   exact nfp_le_fp (mul_is_normal ha).Monotone hb (le_of_eq hab)
 #align ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right Ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right
+-/
 
+#print Ordinal.mul_eq_right_iff_opow_omega_dvd /-
 theorem mul_eq_right_iff_opow_omega_dvd {a b : Ordinal} : a * b = b ↔ (a^omega) ∣ b :=
   by
   cases' eq_zero_or_pos a with ha ha
@@ -835,11 +865,15 @@ theorem mul_eq_right_iff_opow_omega_dvd {a b : Ordinal} : a * b = b ↔ (a^omega
   cases' h with c hc
   rw [hc, ← mul_assoc, ← opow_one_add, one_add_omega]
 #align ordinal.mul_eq_right_iff_opow_omega_dvd Ordinal.mul_eq_right_iff_opow_omega_dvd
+-/
 
+#print Ordinal.mul_le_right_iff_opow_omega_dvd /-
 theorem mul_le_right_iff_opow_omega_dvd {a b : Ordinal} (ha : 0 < a) : a * b ≤ b ↔ (a^omega) ∣ b :=
   by rw [← mul_eq_right_iff_opow_omega_dvd]; exact (mul_is_normal ha).le_iff_eq
 #align ordinal.mul_le_right_iff_opow_omega_dvd Ordinal.mul_le_right_iff_opow_omega_dvd
+-/
 
+#print Ordinal.nfp_mul_opow_omega_add /-
 theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hca : c ≤ (a^omega)) :
     nfp ((· * ·) a) ((a^omega) * b + c) = (a^omega.{u}) * succ b :=
   by
@@ -858,7 +892,9 @@ theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hc
     rw [add_zero, mul_lt_mul_iff_left (opow_pos omega ha)] at this 
     rwa [succ_le_iff]
 #align ordinal.nfp_mul_opow_omega_add Ordinal.nfp_mul_opow_omega_add
+-/
 
+#print Ordinal.deriv_mul_eq_opow_omega_mul /-
 theorem deriv_mul_eq_opow_omega_mul {a : Ordinal.{u}} (ha : 0 < a) (b) :
     deriv ((· * ·) a) b = (a^omega) * b := by
   revert b
@@ -869,6 +905,7 @@ theorem deriv_mul_eq_opow_omega_mul {a : Ordinal.{u}} (ha : 0 < a) (b) :
   · rw [deriv_succ, h]
     exact nfp_mul_opow_omega_add c ha zero_lt_one (one_le_iff_pos.2 (opow_pos _ ha))
 #align ordinal.deriv_mul_eq_opow_omega_mul Ordinal.deriv_mul_eq_opow_omega_mul
+-/
 
 end Ordinal

0dd4319a

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -848,8 +848,8 @@ theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hc
     · rw [mul_succ]
       apply add_le_add_left hca
     · rw [← mul_assoc, ← opow_one_add, one_add_omega]
-  · cases' mul_eq_right_iff_opow_omega_dvd.1 ((mul_is_normal ha).nfp_fp ((a^omega) * b + c)) with
-      d hd
+  · cases' mul_eq_right_iff_opow_omega_dvd.1 ((mul_is_normal ha).nfp_fp ((a^omega) * b + c)) with d
+      hd
     rw [hd]
     apply mul_le_mul_left'
     have := le_nfp (Mul.mul a) ((a^omega) * b + c)

0dd4319a

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -249,7 +249,7 @@ theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
       rw [deriv_family_succ]
       exact nfp_family_le_fp (fun i => (H i).Monotone) (succ_le_of_lt h) ha
     · cases eq_or_lt_of_le h₁; · exact ⟨_, h.symm⟩
-      rw [deriv_family_limit _ l, ← not_le, bsup_le_iff, not_ball] at h
+      rw [deriv_family_limit _ l, ← not_le, bsup_le_iff, not_ball] at h 
       exact
         let ⟨o', h, hl⟩ := h
         IH o' h (le_of_not_le hl),
@@ -276,7 +276,7 @@ theorem derivFamily_eq_enumOrd (H : ∀ i, IsNormal (f i)) :
   · rintro a S ⟨i, hi⟩
     rw [← hi]
     exact deriv_family_fp (H i) a
-  rw [Set.mem_iInter] at ha
+  rw [Set.mem_iInter] at ha 
   rwa [← fp_iff_deriv_family H]
 #align ordinal.deriv_family_eq_enum_ord Ordinal.derivFamily_eq_enumOrd
 -/
@@ -479,7 +479,7 @@ theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
   use (deriv_bfamily_is_normal f).StrictMono
   rw [Set.range_eq_iff]
   refine' ⟨fun a => Set.mem_iInter₂.2 fun i hi => deriv_bfamily_fp (H i hi) a, fun a ha => _⟩
-  rw [Set.mem_iInter₂] at ha
+  rw [Set.mem_iInter₂] at ha 
   rwa [← fp_iff_deriv_bfamily H]
 #align ordinal.deriv_bfamily_eq_enum_ord Ordinal.derivBFamily_eq_enumOrd
 -/
@@ -705,7 +705,7 @@ end
 theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
   by
   simp_rw [← sup_iterate_eq_nfp, ← sup_mul_nat]
-  congr ; funext
+  congr; funext
   induction' n with n hn
   · rw [Nat.cast_zero, MulZeroClass.mul_zero, iterate_zero_apply]
   · nth_rw 2 [Nat.succ_eq_one_add]
@@ -757,7 +757,7 @@ local infixr:0 "^" => @pow Ordinal Ordinal Ordinal.hasPow
 theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega) :=
   by
   rw [← sup_iterate_eq_nfp, ← sup_opow_nat]
-  · dsimp; congr ; funext
+  · dsimp; congr; funext
     induction' n with n hn
     · rw [Nat.cast_zero, opow_zero, iterate_zero_apply]
     nth_rw 2 [Nat.succ_eq_one_add]
@@ -813,9 +813,9 @@ theorem eq_zero_or_opow_omega_le_of_mul_eq_right {a b : Ordinal} (hab : a * b =
     exact Or.inr (Ordinal.zero_le b)
   rw [or_iff_not_imp_left]
   intro hb
-  change b ≠ 0 at hb
+  change b ≠ 0 at hb 
   rw [← nfp_mul_one ha]
-  rw [← one_le_iff_ne_zero] at hb
+  rw [← one_le_iff_ne_zero] at hb 
   exact nfp_le_fp (mul_is_normal ha).Monotone hb (le_of_eq hab)
 #align ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right Ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right
 
@@ -827,7 +827,7 @@ theorem mul_eq_right_iff_opow_omega_dvd {a b : Ordinal} : a * b = b ↔ (a^omega
   refine' ⟨fun hab => _, fun h => _⟩
   · rw [dvd_iff_mod_eq_zero]
     rw [← div_add_mod b (a^omega), mul_add, ← mul_assoc, ← opow_one_add, one_add_omega,
-      add_left_cancel] at hab
+      add_left_cancel] at hab 
     cases' eq_zero_or_opow_omega_le_of_mul_eq_right hab with hab hab
     · exact hab
     refine' (not_lt_of_le hab (mod_lt b (opow_ne_zero omega _))).elim
@@ -853,9 +853,9 @@ theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hc
     rw [hd]
     apply mul_le_mul_left'
     have := le_nfp (Mul.mul a) ((a^omega) * b + c)
-    rw [hd] at this
+    rw [hd] at this 
     have := (add_lt_add_left hc ((a^omega) * b)).trans_le this
-    rw [add_zero, mul_lt_mul_iff_left (opow_pos omega ha)] at this
+    rw [add_zero, mul_lt_mul_iff_left (opow_pos omega ha)] at this 
     rwa [succ_le_iff]
 #align ordinal.nfp_mul_opow_omega_add Ordinal.nfp_mul_opow_omega_add

0dd4319a

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -68,25 +68,33 @@ theorem nfpFamily_eq_sup (f : ι → Ordinal → Ordinal) (a) : nfpFamily f a =
 #align ordinal.nfp_family_eq_sup Ordinal.nfpFamily_eq_sup
 -/
 
+#print Ordinal.foldr_le_nfpFamily /-
 theorem foldr_le_nfpFamily (f : ι → Ordinal → Ordinal) (a l) : List.foldr f a l ≤ nfpFamily f a :=
   le_sup _ _
 #align ordinal.foldr_le_nfp_family Ordinal.foldr_le_nfpFamily
+-/
 
 theorem le_nfpFamily (f : ι → Ordinal → Ordinal) (a) : a ≤ nfpFamily f a :=
   le_sup _ []
 #align ordinal.le_nfp_family Ordinal.le_nfpFamily
 
+#print Ordinal.lt_nfpFamily /-
 theorem lt_nfpFamily {a b} : a < nfpFamily f b ↔ ∃ l, a < List.foldr f b l :=
   lt_sup
 #align ordinal.lt_nfp_family Ordinal.lt_nfpFamily
+-/
 
+#print Ordinal.nfpFamily_le_iff /-
 theorem nfpFamily_le_iff {a b} : nfpFamily f a ≤ b ↔ ∀ l, List.foldr f a l ≤ b :=
   sup_le_iff
 #align ordinal.nfp_family_le_iff Ordinal.nfpFamily_le_iff
+-/
 
+#print Ordinal.nfpFamily_le /-
 theorem nfpFamily_le {a b} : (∀ l, List.foldr f a l ≤ b) → nfpFamily f a ≤ b :=
   sup_le
 #align ordinal.nfp_family_le Ordinal.nfpFamily_le
+-/
 
 #print Ordinal.nfpFamily_monotone /-
 theorem nfpFamily_monotone (hf : ∀ i, Monotone (f i)) : Monotone (nfpFamily f) := fun a b h =>
@@ -95,12 +103,15 @@ theorem nfpFamily_monotone (hf : ∀ i, Monotone (f i)) : Monotone (nfpFamily f)
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Ordinal.apply_lt_nfpFamily /-
 theorem apply_lt_nfpFamily (H : ∀ i, IsNormal (f i)) {a b} (hb : b < nfpFamily f a) (i) :
     f i b < nfpFamily f a :=
   let ⟨l, hl⟩ := lt_nfpFamily.1 hb
   lt_sup.2 ⟨i::l, (H i).StrictMono hl⟩
 #align ordinal.apply_lt_nfp_family Ordinal.apply_lt_nfpFamily
+-/
 
+#print Ordinal.apply_lt_nfpFamily_iff /-
 theorem apply_lt_nfpFamily_iff [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
     (∀ i, f i b < nfpFamily f a) ↔ b < nfpFamily f a :=
   ⟨fun h =>
@@ -109,12 +120,16 @@ theorem apply_lt_nfpFamily_iff [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
       ⟨l, ((H _).self_le b).trans_lt hl⟩,
     apply_lt_nfpFamily H⟩
 #align ordinal.apply_lt_nfp_family_iff Ordinal.apply_lt_nfpFamily_iff
+-/
 
+#print Ordinal.nfpFamily_le_apply /-
 theorem nfpFamily_le_apply [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
     (∃ i, nfpFamily f a ≤ f i b) ↔ nfpFamily f a ≤ b := by rw [← not_iff_not]; push_neg;
   exact apply_lt_nfp_family_iff H
 #align ordinal.nfp_family_le_apply Ordinal.nfpFamily_le_apply
+-/
 
+#print Ordinal.nfpFamily_le_fp /-
 theorem nfpFamily_le_fp (H : ∀ i, Monotone (f i)) {a b} (ab : a ≤ b) (h : ∀ i, f i b ≤ b) :
     nfpFamily f a ≤ b :=
   sup_le fun l => by
@@ -124,6 +139,7 @@ theorem nfpFamily_le_fp (H : ∀ i, Monotone (f i)) {a b} (ab : a ≤ b) (h : 
       induction' l with i l IH generalizing a; · exact ab
       exact (H i (IH ab)).trans (h i)
 #align ordinal.nfp_family_le_fp Ordinal.nfpFamily_le_fp
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print Ordinal.nfpFamily_fp /-
@@ -137,6 +153,7 @@ theorem nfpFamily_fp {i} (H : IsNormal (f i)) (a) : f i (nfpFamily f a) = nfpFam
 #align ordinal.nfp_family_fp Ordinal.nfpFamily_fp
 -/
 
+#print Ordinal.apply_le_nfpFamily /-
 theorem apply_le_nfpFamily [hι : Nonempty ι] {f : ι → Ordinal → Ordinal} (H : ∀ i, IsNormal (f i))
     {a b} : (∀ i, f i b ≤ nfpFamily f a) ↔ b ≤ nfpFamily f a :=
   by
@@ -146,12 +163,14 @@ theorem apply_le_nfpFamily [hι : Nonempty ι] {f : ι → Ordinal → Ordinal}
   rw [← nfp_family_fp (H i)]
   exact (H i).Monotone h
 #align ordinal.apply_le_nfp_family Ordinal.apply_le_nfpFamily
+-/
 
 theorem nfpFamily_eq_self {f : ι → Ordinal → Ordinal} {a} (h : ∀ i, f i a = a) :
     nfpFamily f a = a :=
   le_antisymm (sup_le fun l => by rw [List.foldr_fixed' h l]) <| le_nfpFamily f a
 #align ordinal.nfp_family_eq_self Ordinal.nfpFamily_eq_self
 
+#print Ordinal.fp_family_unbounded /-
 -- Todo: This is actually a special case of the fact the intersection of club sets is a club set.
 /-- A generalization of the fixed point lemma for normal functions: any family of normal functions
     has an unbounded set of common fixed points. -/
@@ -161,6 +180,7 @@ theorem fp_family_unbounded (H : ∀ i, IsNormal (f i)) :
     rw [← hi]
     exact nfp_family_fp (H i) a, (le_nfpFamily f a).not_lt⟩
 #align ordinal.fp_family_unbounded Ordinal.fp_family_unbounded
+-/
 
 #print Ordinal.derivFamily /-
 /-- The derivative of a family of normal functions is the sequence of their common fixed points.
@@ -214,6 +234,7 @@ theorem derivFamily_fp {i} (H : IsNormal (f i)) (o : Ordinal.{max u v}) :
 #align ordinal.deriv_family_fp Ordinal.derivFamily_fp
 -/
 
+#print Ordinal.le_iff_derivFamily /-
 theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
     (∀ i, f i a ≤ a) ↔ ∃ o, derivFamily f o = a :=
   ⟨fun ha => by
@@ -234,6 +255,7 @@ theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
         IH o' h (le_of_not_le hl),
     fun ⟨o, e⟩ i => e ▸ (derivFamily_fp (H i) _).le⟩
 #align ordinal.le_iff_deriv_family Ordinal.le_iff_derivFamily
+-/
 
 #print Ordinal.fp_iff_derivFamily /-
 theorem fp_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
@@ -268,6 +290,7 @@ section
 
 variable {o : Ordinal.{u}} {f : ∀ b < o, Ordinal.{max u v} → Ordinal.{max u v}}
 
+#print Ordinal.nfpBFamily /-
 /-- The next common fixed point, at least `a`, for a family of normal functions indexed by ordinals.
 
 This is defined as `ordinal.nfp_family` of the type-indexed family associated to `f`.
@@ -275,40 +298,56 @@ This is defined as `ordinal.nfp_family` of the type-indexed family associated to
 def nfpBFamily (o : Ordinal) (f : ∀ b < o, Ordinal → Ordinal) : Ordinal → Ordinal :=
   nfpFamily (familyOfBFamily o f)
 #align ordinal.nfp_bfamily Ordinal.nfpBFamily
+-/
 
+#print Ordinal.nfpBFamily_eq_nfpFamily /-
 theorem nfpBFamily_eq_nfpFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) :
     nfpBFamily o f = nfpFamily (familyOfBFamily o f) :=
   rfl
 #align ordinal.nfp_bfamily_eq_nfp_family Ordinal.nfpBFamily_eq_nfpFamily
+-/
 
+#print Ordinal.foldr_le_nfpBFamily /-
 theorem foldr_le_nfpBFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) (a l) :
     List.foldr (familyOfBFamily o f) a l ≤ nfpBFamily o f a :=
   le_sup _ _
 #align ordinal.foldr_le_nfp_bfamily Ordinal.foldr_le_nfpBFamily
+-/
 
+#print Ordinal.le_nfpBFamily /-
 theorem le_nfpBFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) (a) : a ≤ nfpBFamily o f a :=
   le_sup _ []
 #align ordinal.le_nfp_bfamily Ordinal.le_nfpBFamily
+-/
 
+#print Ordinal.lt_nfpBFamily /-
 theorem lt_nfpBFamily {a b} :
     a < nfpBFamily o f b ↔ ∃ l, a < List.foldr (familyOfBFamily o f) b l :=
   lt_sup
 #align ordinal.lt_nfp_bfamily Ordinal.lt_nfpBFamily
+-/
 
+#print Ordinal.nfpBFamily_le_iff /-
 theorem nfpBFamily_le_iff {o : Ordinal} {f : ∀ b < o, Ordinal → Ordinal} {a b} :
     nfpBFamily o f a ≤ b ↔ ∀ l, List.foldr (familyOfBFamily o f) a l ≤ b :=
   sup_le_iff
 #align ordinal.nfp_bfamily_le_iff Ordinal.nfpBFamily_le_iff
+-/
 
+#print Ordinal.nfpBFamily_le /-
 theorem nfpBFamily_le {o : Ordinal} {f : ∀ b < o, Ordinal → Ordinal} {a b} :
     (∀ l, List.foldr (familyOfBFamily o f) a l ≤ b) → nfpBFamily o f a ≤ b :=
   sup_le
 #align ordinal.nfp_bfamily_le Ordinal.nfpBFamily_le
+-/
 
+#print Ordinal.nfpBFamily_monotone /-
 theorem nfpBFamily_monotone (hf : ∀ i hi, Monotone (f i hi)) : Monotone (nfpBFamily o f) :=
   nfpFamily_monotone fun i => hf _ _
 #align ordinal.nfp_bfamily_monotone Ordinal.nfpBFamily_monotone
+-/
 
+#print Ordinal.apply_lt_nfpBFamily /-
 theorem apply_lt_nfpBFamily (H : ∀ i hi, IsNormal (f i hi)) {a b} (hb : b < nfpBFamily o f a)
     (i hi) : f i hi b < nfpBFamily o f a :=
   by
@@ -316,7 +355,9 @@ theorem apply_lt_nfpBFamily (H : ∀ i hi, IsNormal (f i hi)) {a b} (hb : b < nf
   apply apply_lt_nfp_family _ hb
   exact fun _ => H _ _
 #align ordinal.apply_lt_nfp_bfamily Ordinal.apply_lt_nfpBFamily
+-/
 
+#print Ordinal.apply_lt_nfpBFamily_iff /-
 theorem apply_lt_nfpBFamily_iff (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
     (∀ i hi, f i hi b < nfpBFamily o f a) ↔ b < nfpBFamily o f a :=
   ⟨fun h => by
@@ -324,22 +365,30 @@ theorem apply_lt_nfpBFamily_iff (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi))
     refine' (apply_lt_nfp_family_iff _).1 fun _ => h _ _
     exact fun _ => H _ _, apply_lt_nfpBFamily H⟩
 #align ordinal.apply_lt_nfp_bfamily_iff Ordinal.apply_lt_nfpBFamily_iff
+-/
 
+#print Ordinal.nfpBFamily_le_apply /-
 theorem nfpBFamily_le_apply (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
     (∃ i hi, nfpBFamily o f a ≤ f i hi b) ↔ nfpBFamily o f a ≤ b := by rw [← not_iff_not]; push_neg;
   convert apply_lt_nfp_bfamily_iff ho H; simp only [not_le]
 #align ordinal.nfp_bfamily_le_apply Ordinal.nfpBFamily_le_apply
+-/
 
+#print Ordinal.nfpBFamily_le_fp /-
 theorem nfpBFamily_le_fp (H : ∀ i hi, Monotone (f i hi)) {a b} (ab : a ≤ b)
     (h : ∀ i hi, f i hi b ≤ b) : nfpBFamily o f a ≤ b :=
   nfpFamily_le_fp (fun _ => H _ _) ab fun i => h _ _
 #align ordinal.nfp_bfamily_le_fp Ordinal.nfpBFamily_le_fp
+-/
 
+#print Ordinal.nfpBFamily_fp /-
 theorem nfpBFamily_fp {i hi} (H : IsNormal (f i hi)) (a) :
     f i hi (nfpBFamily o f a) = nfpBFamily o f a := by rw [← family_of_bfamily_enum o f];
   apply nfp_family_fp; rw [family_of_bfamily_enum]; exact H
 #align ordinal.nfp_bfamily_fp Ordinal.nfpBFamily_fp
+-/
 
+#print Ordinal.apply_le_nfpBFamily /-
 theorem apply_le_nfpBFamily (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
     (∀ i hi, f i hi b ≤ nfpBFamily o f a) ↔ b ≤ nfpBFamily o f a :=
   by
@@ -349,12 +398,16 @@ theorem apply_le_nfpBFamily (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a
   · rw [← nfp_bfamily_fp (H i hi)]
     exact (H i hi).Monotone h
 #align ordinal.apply_le_nfp_bfamily Ordinal.apply_le_nfpBFamily
+-/
 
+#print Ordinal.nfpBFamily_eq_self /-
 theorem nfpBFamily_eq_self {a} (h : ∀ i hi, f i hi a = a) : nfpBFamily o f a = a :=
   nfpFamily_eq_self fun _ => h _ _
 #align ordinal.nfp_bfamily_eq_self Ordinal.nfpBFamily_eq_self
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
+#print Ordinal.fp_bfamily_unbounded /-
 /-- A generalization of the fixed point lemma for normal functions: any family of normal functions
     has an unbounded set of common fixed points. -/
 theorem fp_bfamily_unbounded (H : ∀ i hi, IsNormal (f i hi)) :
@@ -362,29 +415,37 @@ theorem fp_bfamily_unbounded (H : ∀ i hi, IsNormal (f i hi)) :
   ⟨_, by rw [Set.mem_iInter₂]; exact fun i hi => nfp_bfamily_fp (H i hi) _,
     (le_nfpBFamily f a).not_lt⟩
 #align ordinal.fp_bfamily_unbounded Ordinal.fp_bfamily_unbounded
+-/
 
+#print Ordinal.derivBFamily /-
 /-- The derivative of a family of normal functions is the sequence of their common fixed points.
 
 This is defined as `ordinal.deriv_family` of the type-indexed family associated to `f`. -/
 def derivBFamily (o : Ordinal) (f : ∀ b < o, Ordinal → Ordinal) : Ordinal → Ordinal :=
   derivFamily (familyOfBFamily o f)
 #align ordinal.deriv_bfamily Ordinal.derivBFamily
+-/
 
+#print Ordinal.derivBFamily_eq_derivFamily /-
 theorem derivBFamily_eq_derivFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) :
     derivBFamily o f = derivFamily (familyOfBFamily o f) :=
   rfl
 #align ordinal.deriv_bfamily_eq_deriv_family Ordinal.derivBFamily_eq_derivFamily
+-/
 
 theorem derivBFamily_isNormal {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) :
     IsNormal (derivBFamily o f) :=
   derivFamily_isNormal _
 #align ordinal.deriv_bfamily_is_normal Ordinal.derivBFamily_isNormal
 
+#print Ordinal.derivBFamily_fp /-
 theorem derivBFamily_fp {i hi} (H : IsNormal (f i hi)) (a : Ordinal) :
     f i hi (derivBFamily o f a) = derivBFamily o f a := by rw [← family_of_bfamily_enum o f];
   apply deriv_family_fp; rw [family_of_bfamily_enum]; exact H
 #align ordinal.deriv_bfamily_fp Ordinal.derivBFamily_fp
+-/
 
+#print Ordinal.le_iff_derivBFamily /-
 theorem le_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
     (∀ i hi, f i hi a ≤ a) ↔ ∃ b, derivBFamily o f b = a :=
   by
@@ -395,7 +456,9 @@ theorem le_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
     apply h
   · exact fun _ => H _ _
 #align ordinal.le_iff_deriv_bfamily Ordinal.le_iff_derivBFamily
+-/
 
+#print Ordinal.fp_iff_derivBFamily /-
 theorem fp_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
     (∀ i hi, f i hi a = a) ↔ ∃ b, derivBFamily o f b = a :=
   by
@@ -404,8 +467,10 @@ theorem fp_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
   rw [← (H i hi).le_iff_eq]
   exact h i hi
 #align ordinal.fp_iff_deriv_bfamily Ordinal.fp_iff_derivBFamily
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
+#print Ordinal.derivBFamily_eq_enumOrd /-
 /-- For a family of normal functions, `ordinal.deriv_bfamily` enumerates the common fixed points. -/
 theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
     derivBFamily o f = enumOrd (⋂ (i) (hi), Function.fixedPoints (f i hi)) :=
@@ -417,6 +482,7 @@ theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
   rw [Set.mem_iInter₂] at ha
   rwa [← fp_iff_deriv_bfamily H]
 #align ordinal.deriv_bfamily_eq_enum_ord Ordinal.derivBFamily_eq_enumOrd
+-/
 
 end
 
@@ -457,25 +523,35 @@ theorem sup_iterate_eq_nfp (f : Ordinal.{u} → Ordinal.{u}) :
 #align ordinal.sup_iterate_eq_nfp Ordinal.sup_iterate_eq_nfp
 -/
 
+#print Ordinal.iterate_le_nfp /-
 theorem iterate_le_nfp (f a n) : (f^[n]) a ≤ nfp f a := by rw [← sup_iterate_eq_nfp];
   exact le_sup _ n
 #align ordinal.iterate_le_nfp Ordinal.iterate_le_nfp
+-/
 
+#print Ordinal.le_nfp /-
 theorem le_nfp (f a) : a ≤ nfp f a :=
   iterate_le_nfp f a 0
 #align ordinal.le_nfp Ordinal.le_nfp
+-/
 
+#print Ordinal.lt_nfp /-
 theorem lt_nfp {a b} : a < nfp f b ↔ ∃ n, a < (f^[n]) b := by rw [← sup_iterate_eq_nfp];
   exact lt_sup
 #align ordinal.lt_nfp Ordinal.lt_nfp
+-/
 
+#print Ordinal.nfp_le_iff /-
 theorem nfp_le_iff {a b} : nfp f a ≤ b ↔ ∀ n, (f^[n]) a ≤ b := by rw [← sup_iterate_eq_nfp];
   exact sup_le_iff
 #align ordinal.nfp_le_iff Ordinal.nfp_le_iff
+-/
 
+#print Ordinal.nfp_le /-
 theorem nfp_le {a b} : (∀ n, (f^[n]) a ≤ b) → nfp f a ≤ b :=
   nfp_le_iff.2
 #align ordinal.nfp_le Ordinal.nfp_le
+-/
 
 #print Ordinal.nfp_id /-
 @[simp]
@@ -492,20 +568,26 @@ theorem nfp_monotone (hf : Monotone f) : Monotone (nfp f) :=
 #align ordinal.nfp_monotone Ordinal.nfp_monotone
 -/
 
+#print Ordinal.IsNormal.apply_lt_nfp /-
 theorem IsNormal.apply_lt_nfp {f} (H : IsNormal f) {a b} : f b < nfp f a ↔ b < nfp f a :=
   by
   unfold nfp
   rw [← @apply_lt_nfp_family_iff Unit (fun _ => f) _ (fun _ => H) a b]
   exact ⟨fun h _ => h, fun h => h Unit.unit⟩
 #align ordinal.is_normal.apply_lt_nfp Ordinal.IsNormal.apply_lt_nfp
+-/
 
+#print Ordinal.IsNormal.nfp_le_apply /-
 theorem IsNormal.nfp_le_apply {f} (H : IsNormal f) {a b} : nfp f a ≤ f b ↔ nfp f a ≤ b :=
   le_iff_le_iff_lt_iff_lt.2 H.apply_lt_nfp
 #align ordinal.is_normal.nfp_le_apply Ordinal.IsNormal.nfp_le_apply
+-/
 
+#print Ordinal.nfp_le_fp /-
 theorem nfp_le_fp {f} (H : Monotone f) {a b} (ab : a ≤ b) (h : f b ≤ b) : nfp f a ≤ b :=
   nfpFamily_le_fp (fun _ => H) ab fun _ => h
 #align ordinal.nfp_le_fp Ordinal.nfp_le_fp
+-/
 
 #print Ordinal.IsNormal.nfp_fp /-
 theorem IsNormal.nfp_fp {f} (H : IsNormal f) : ∀ a, f (nfp f a) = nfp f a :=
@@ -513,9 +595,11 @@ theorem IsNormal.nfp_fp {f} (H : IsNormal f) : ∀ a, f (nfp f a) = nfp f a :=
 #align ordinal.is_normal.nfp_fp Ordinal.IsNormal.nfp_fp
 -/
 
+#print Ordinal.IsNormal.apply_le_nfp /-
 theorem IsNormal.apply_le_nfp {f} (H : IsNormal f) {a b} : f b ≤ nfp f a ↔ b ≤ nfp f a :=
   ⟨le_trans (H.self_le _), fun h => by simpa only [H.nfp_fp] using H.le_iff.2 h⟩
 #align ordinal.is_normal.apply_le_nfp Ordinal.IsNormal.apply_le_nfp
+-/
 
 #print Ordinal.nfp_eq_self /-
 theorem nfp_eq_self {f : Ordinal → Ordinal} {a} (h : f a = a) : nfp f a = a :=
@@ -523,11 +607,13 @@ theorem nfp_eq_self {f : Ordinal → Ordinal} {a} (h : f a = a) : nfp f a = a :=
 #align ordinal.nfp_eq_self Ordinal.nfp_eq_self
 -/
 
+#print Ordinal.fp_unbounded /-
 /-- The fixed point lemma for normal functions: any normal function has an unbounded set of
 fixed points. -/
 theorem fp_unbounded (H : IsNormal f) : (Function.fixedPoints f).Unbounded (· < ·) := by
   convert fp_family_unbounded fun _ : Unit => H; exact (Set.iInter_const _).symm
 #align ordinal.fp_unbounded Ordinal.fp_unbounded
+-/
 
 #print Ordinal.deriv /-
 /-- The derivative of a normal function `f` is the sequence of fixed points of `f`.
@@ -582,12 +668,14 @@ theorem IsNormal.deriv_fp {f} (H : IsNormal f) : ∀ o, f (deriv f o) = deriv f
 #align ordinal.is_normal.deriv_fp Ordinal.IsNormal.deriv_fp
 -/
 
+#print Ordinal.IsNormal.le_iff_deriv /-
 theorem IsNormal.le_iff_deriv {f} (H : IsNormal f) {a} : f a ≤ a ↔ ∃ o, deriv f o = a :=
   by
   unfold deriv
   rw [← le_iff_deriv_family fun _ : Unit => H]
   exact ⟨fun h _ => h, fun h => h Unit.unit⟩
 #align ordinal.is_normal.le_iff_deriv Ordinal.IsNormal.le_iff_deriv
+-/
 
 #print Ordinal.IsNormal.fp_iff_deriv /-
 theorem IsNormal.fp_iff_deriv {f} (H : IsNormal f) {a} : f a = a ↔ ∃ o, deriv f o = a := by

0dd4319a

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -68,52 +68,22 @@ theorem nfpFamily_eq_sup (f : ι → Ordinal → Ordinal) (a) : nfpFamily f a =
 #align ordinal.nfp_family_eq_sup Ordinal.nfpFamily_eq_sup
 -/
 
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-Case conversion may be inaccurate. Consider using '#align ordinal.foldr_le_nfp_family Ordinal.foldr_le_nfpFamilyₓ'. -/
 theorem foldr_le_nfpFamily (f : ι → Ordinal → Ordinal) (a l) : List.foldr f a l ≤ nfpFamily f a :=
   le_sup _ _
 #align ordinal.foldr_le_nfp_family Ordinal.foldr_le_nfpFamily
 
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 theorem le_nfpFamily (f : ι → Ordinal → Ordinal) (a) : a ≤ nfpFamily f a :=
   le_sup _ []
 #align ordinal.le_nfp_family Ordinal.le_nfpFamily
 
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 theorem lt_nfpFamily {a b} : a < nfpFamily f b ↔ ∃ l, a < List.foldr f b l :=
   lt_sup
 #align ordinal.lt_nfp_family Ordinal.lt_nfpFamily
 
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 theorem nfpFamily_le_iff {a b} : nfpFamily f a ≤ b ↔ ∀ l, List.foldr f a l ≤ b :=
   sup_le_iff
 #align ordinal.nfp_family_le_iff Ordinal.nfpFamily_le_iff
 
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 theorem nfpFamily_le {a b} : (∀ l, List.foldr f a l ≤ b) → nfpFamily f a ≤ b :=
   sup_le
 #align ordinal.nfp_family_le Ordinal.nfpFamily_le
@@ -124,12 +94,6 @@ theorem nfpFamily_monotone (hf : ∀ i, Monotone (f i)) : Monotone (nfpFamily f)
 #align ordinal.nfp_family_monotone Ordinal.nfpFamily_monotone
 -/
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem apply_lt_nfpFamily (H : ∀ i, IsNormal (f i)) {a b} (hb : b < nfpFamily f a) (i) :
     f i b < nfpFamily f a :=
@@ -137,12 +101,6 @@ theorem apply_lt_nfpFamily (H : ∀ i, IsNormal (f i)) {a b} (hb : b < nfpFamily
   lt_sup.2 ⟨i::l, (H i).StrictMono hl⟩
 #align ordinal.apply_lt_nfp_family Ordinal.apply_lt_nfpFamily
 
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 theorem apply_lt_nfpFamily_iff [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
     (∀ i, f i b < nfpFamily f a) ↔ b < nfpFamily f a :=
   ⟨fun h =>
@@ -152,23 +110,11 @@ theorem apply_lt_nfpFamily_iff [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
     apply_lt_nfpFamily H⟩
 #align ordinal.apply_lt_nfp_family_iff Ordinal.apply_lt_nfpFamily_iff
 
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 theorem nfpFamily_le_apply [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
     (∃ i, nfpFamily f a ≤ f i b) ↔ nfpFamily f a ≤ b := by rw [← not_iff_not]; push_neg;
   exact apply_lt_nfp_family_iff H
 #align ordinal.nfp_family_le_apply Ordinal.nfpFamily_le_apply
 
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 theorem nfpFamily_le_fp (H : ∀ i, Monotone (f i)) {a b} (ab : a ≤ b) (h : ∀ i, f i b ≤ b) :
     nfpFamily f a ≤ b :=
   sup_le fun l => by
@@ -191,12 +137,6 @@ theorem nfpFamily_fp {i} (H : IsNormal (f i)) (a) : f i (nfpFamily f a) = nfpFam
 #align ordinal.nfp_family_fp Ordinal.nfpFamily_fp
 -/
 
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 theorem apply_le_nfpFamily [hι : Nonempty ι] {f : ι → Ordinal → Ordinal} (H : ∀ i, IsNormal (f i))
     {a b} : (∀ i, f i b ≤ nfpFamily f a) ↔ b ≤ nfpFamily f a :=
   by
@@ -207,23 +147,11 @@ theorem apply_le_nfpFamily [hι : Nonempty ι] {f : ι → Ordinal → Ordinal}
   exact (H i).Monotone h
 #align ordinal.apply_le_nfp_family Ordinal.apply_le_nfpFamily
 
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 theorem nfpFamily_eq_self {f : ι → Ordinal → Ordinal} {a} (h : ∀ i, f i a = a) :
     nfpFamily f a = a :=
   le_antisymm (sup_le fun l => by rw [List.foldr_fixed' h l]) <| le_nfpFamily f a
 #align ordinal.nfp_family_eq_self Ordinal.nfpFamily_eq_self
 
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 -- Todo: This is actually a special case of the fact the intersection of club sets is a club set.
 /-- A generalization of the fixed point lemma for normal functions: any family of normal functions
     has an unbounded set of common fixed points. -/
@@ -266,12 +194,6 @@ theorem derivFamily_limit (f : ι → Ordinal → Ordinal) {o} :
 #align ordinal.deriv_family_limit Ordinal.derivFamily_limit
 -/
 
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 theorem derivFamily_isNormal (f : ι → Ordinal → Ordinal) : IsNormal (derivFamily f) :=
   ⟨fun o => by rw [deriv_family_succ, ← succ_le_iff] <;> apply le_nfp_family, fun o l a => by
     rw [deriv_family_limit _ l, bsup_le_iff]⟩
@@ -292,12 +214,6 @@ theorem derivFamily_fp {i} (H : IsNormal (f i)) (o : Ordinal.{max u v}) :
 #align ordinal.deriv_family_fp Ordinal.derivFamily_fp
 -/
 
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 theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
     (∀ i, f i a ≤ a) ↔ ∃ o, derivFamily f o = a :=
   ⟨fun ha => by
@@ -352,12 +268,6 @@ section
 
 variable {o : Ordinal.{u}} {f : ∀ b < o, Ordinal.{max u v} → Ordinal.{max u v}}
 
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 /-- The next common fixed point, at least `a`, for a family of normal functions indexed by ordinals.
 
 This is defined as `ordinal.nfp_family` of the type-indexed family associated to `f`.
@@ -366,87 +276,39 @@ def nfpBFamily (o : Ordinal) (f : ∀ b < o, Ordinal → Ordinal) : Ordinal →
   nfpFamily (familyOfBFamily o f)
 #align ordinal.nfp_bfamily Ordinal.nfpBFamily
 
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 theorem nfpBFamily_eq_nfpFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) :
     nfpBFamily o f = nfpFamily (familyOfBFamily o f) :=
   rfl
 #align ordinal.nfp_bfamily_eq_nfp_family Ordinal.nfpBFamily_eq_nfpFamily
 
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 theorem foldr_le_nfpBFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) (a l) :
     List.foldr (familyOfBFamily o f) a l ≤ nfpBFamily o f a :=
   le_sup _ _
 #align ordinal.foldr_le_nfp_bfamily Ordinal.foldr_le_nfpBFamily
 
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 theorem le_nfpBFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) (a) : a ≤ nfpBFamily o f a :=
   le_sup _ []
 #align ordinal.le_nfp_bfamily Ordinal.le_nfpBFamily
 
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 theorem lt_nfpBFamily {a b} :
     a < nfpBFamily o f b ↔ ∃ l, a < List.foldr (familyOfBFamily o f) b l :=
   lt_sup
 #align ordinal.lt_nfp_bfamily Ordinal.lt_nfpBFamily
 
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 theorem nfpBFamily_le_iff {o : Ordinal} {f : ∀ b < o, Ordinal → Ordinal} {a b} :
     nfpBFamily o f a ≤ b ↔ ∀ l, List.foldr (familyOfBFamily o f) a l ≤ b :=
   sup_le_iff
 #align ordinal.nfp_bfamily_le_iff Ordinal.nfpBFamily_le_iff
 
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 theorem nfpBFamily_le {o : Ordinal} {f : ∀ b < o, Ordinal → Ordinal} {a b} :
     (∀ l, List.foldr (familyOfBFamily o f) a l ≤ b) → nfpBFamily o f a ≤ b :=
   sup_le
 #align ordinal.nfp_bfamily_le Ordinal.nfpBFamily_le
 
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 theorem nfpBFamily_monotone (hf : ∀ i hi, Monotone (f i hi)) : Monotone (nfpBFamily o f) :=
   nfpFamily_monotone fun i => hf _ _
 #align ordinal.nfp_bfamily_monotone Ordinal.nfpBFamily_monotone
 
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 theorem apply_lt_nfpBFamily (H : ∀ i hi, IsNormal (f i hi)) {a b} (hb : b < nfpBFamily o f a)
     (i hi) : f i hi b < nfpBFamily o f a :=
   by
@@ -455,12 +317,6 @@ theorem apply_lt_nfpBFamily (H : ∀ i hi, IsNormal (f i hi)) {a b} (hb : b < nf
   exact fun _ => H _ _
 #align ordinal.apply_lt_nfp_bfamily Ordinal.apply_lt_nfpBFamily
 
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 theorem apply_lt_nfpBFamily_iff (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
     (∀ i hi, f i hi b < nfpBFamily o f a) ↔ b < nfpBFamily o f a :=
   ⟨fun h => by
@@ -469,45 +325,21 @@ theorem apply_lt_nfpBFamily_iff (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi))
     exact fun _ => H _ _, apply_lt_nfpBFamily H⟩
 #align ordinal.apply_lt_nfp_bfamily_iff Ordinal.apply_lt_nfpBFamily_iff
 
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 theorem nfpBFamily_le_apply (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
     (∃ i hi, nfpBFamily o f a ≤ f i hi b) ↔ nfpBFamily o f a ≤ b := by rw [← not_iff_not]; push_neg;
   convert apply_lt_nfp_bfamily_iff ho H; simp only [not_le]
 #align ordinal.nfp_bfamily_le_apply Ordinal.nfpBFamily_le_apply
 
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 theorem nfpBFamily_le_fp (H : ∀ i hi, Monotone (f i hi)) {a b} (ab : a ≤ b)
     (h : ∀ i hi, f i hi b ≤ b) : nfpBFamily o f a ≤ b :=
   nfpFamily_le_fp (fun _ => H _ _) ab fun i => h _ _
 #align ordinal.nfp_bfamily_le_fp Ordinal.nfpBFamily_le_fp
 
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 theorem nfpBFamily_fp {i hi} (H : IsNormal (f i hi)) (a) :
     f i hi (nfpBFamily o f a) = nfpBFamily o f a := by rw [← family_of_bfamily_enum o f];
   apply nfp_family_fp; rw [family_of_bfamily_enum]; exact H
 #align ordinal.nfp_bfamily_fp Ordinal.nfpBFamily_fp
 
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 theorem apply_le_nfpBFamily (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
     (∀ i hi, f i hi b ≤ nfpBFamily o f a) ↔ b ≤ nfpBFamily o f a :=
   by
@@ -518,22 +350,10 @@ theorem apply_le_nfpBFamily (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a
     exact (H i hi).Monotone h
 #align ordinal.apply_le_nfp_bfamily Ordinal.apply_le_nfpBFamily
 
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 theorem nfpBFamily_eq_self {a} (h : ∀ i hi, f i hi a = a) : nfpBFamily o f a = a :=
   nfpFamily_eq_self fun _ => h _ _
 #align ordinal.nfp_bfamily_eq_self Ordinal.nfpBFamily_eq_self
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 /-- A generalization of the fixed point lemma for normal functions: any family of normal functions
     has an unbounded set of common fixed points. -/
@@ -543,12 +363,6 @@ theorem fp_bfamily_unbounded (H : ∀ i hi, IsNormal (f i hi)) :
     (le_nfpBFamily f a).not_lt⟩
 #align ordinal.fp_bfamily_unbounded Ordinal.fp_bfamily_unbounded
 
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 /-- The derivative of a family of normal functions is the sequence of their common fixed points.
 
 This is defined as `ordinal.deriv_family` of the type-indexed family associated to `f`. -/
@@ -556,45 +370,21 @@ def derivBFamily (o : Ordinal) (f : ∀ b < o, Ordinal → Ordinal) : Ordinal 
   derivFamily (familyOfBFamily o f)
 #align ordinal.deriv_bfamily Ordinal.derivBFamily
 
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 theorem derivBFamily_eq_derivFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) :
     derivBFamily o f = derivFamily (familyOfBFamily o f) :=
   rfl
 #align ordinal.deriv_bfamily_eq_deriv_family Ordinal.derivBFamily_eq_derivFamily
 
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 theorem derivBFamily_isNormal {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) :
     IsNormal (derivBFamily o f) :=
   derivFamily_isNormal _
 #align ordinal.deriv_bfamily_is_normal Ordinal.derivBFamily_isNormal
 
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 theorem derivBFamily_fp {i hi} (H : IsNormal (f i hi)) (a : Ordinal) :
     f i hi (derivBFamily o f a) = derivBFamily o f a := by rw [← family_of_bfamily_enum o f];
   apply deriv_family_fp; rw [family_of_bfamily_enum]; exact H
 #align ordinal.deriv_bfamily_fp Ordinal.derivBFamily_fp
 
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 theorem le_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
     (∀ i hi, f i hi a ≤ a) ↔ ∃ b, derivBFamily o f b = a :=
   by
@@ -606,12 +396,6 @@ theorem le_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
   · exact fun _ => H _ _
 #align ordinal.le_iff_deriv_bfamily Ordinal.le_iff_derivBFamily
 
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 theorem fp_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
     (∀ i hi, f i hi a = a) ↔ ∃ b, derivBFamily o f b = a :=
   by
@@ -621,12 +405,6 @@ theorem fp_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
   exact h i hi
 #align ordinal.fp_iff_deriv_bfamily Ordinal.fp_iff_derivBFamily
 
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 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 /-- For a family of normal functions, `ordinal.deriv_bfamily` enumerates the common fixed points. -/
 theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
@@ -679,52 +457,22 @@ theorem sup_iterate_eq_nfp (f : Ordinal.{u} → Ordinal.{u}) :
 #align ordinal.sup_iterate_eq_nfp Ordinal.sup_iterate_eq_nfp
 -/
 
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 theorem iterate_le_nfp (f a n) : (f^[n]) a ≤ nfp f a := by rw [← sup_iterate_eq_nfp];
   exact le_sup _ n
 #align ordinal.iterate_le_nfp Ordinal.iterate_le_nfp
 
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 theorem le_nfp (f a) : a ≤ nfp f a :=
   iterate_le_nfp f a 0
 #align ordinal.le_nfp Ordinal.le_nfp
 
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 theorem lt_nfp {a b} : a < nfp f b ↔ ∃ n, a < (f^[n]) b := by rw [← sup_iterate_eq_nfp];
   exact lt_sup
 #align ordinal.lt_nfp Ordinal.lt_nfp
 
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 theorem nfp_le_iff {a b} : nfp f a ≤ b ↔ ∀ n, (f^[n]) a ≤ b := by rw [← sup_iterate_eq_nfp];
   exact sup_le_iff
 #align ordinal.nfp_le_iff Ordinal.nfp_le_iff
 
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 theorem nfp_le {a b} : (∀ n, (f^[n]) a ≤ b) → nfp f a ≤ b :=
   nfp_le_iff.2
 #align ordinal.nfp_le Ordinal.nfp_le
@@ -744,12 +492,6 @@ theorem nfp_monotone (hf : Monotone f) : Monotone (nfp f) :=
 #align ordinal.nfp_monotone Ordinal.nfp_monotone
 -/
 
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 theorem IsNormal.apply_lt_nfp {f} (H : IsNormal f) {a b} : f b < nfp f a ↔ b < nfp f a :=
   by
   unfold nfp
@@ -757,22 +499,10 @@ theorem IsNormal.apply_lt_nfp {f} (H : IsNormal f) {a b} : f b < nfp f a ↔ b <
   exact ⟨fun h _ => h, fun h => h Unit.unit⟩
 #align ordinal.is_normal.apply_lt_nfp Ordinal.IsNormal.apply_lt_nfp
 
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 theorem IsNormal.nfp_le_apply {f} (H : IsNormal f) {a b} : nfp f a ≤ f b ↔ nfp f a ≤ b :=
   le_iff_le_iff_lt_iff_lt.2 H.apply_lt_nfp
 #align ordinal.is_normal.nfp_le_apply Ordinal.IsNormal.nfp_le_apply
 
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 theorem nfp_le_fp {f} (H : Monotone f) {a b} (ab : a ≤ b) (h : f b ≤ b) : nfp f a ≤ b :=
   nfpFamily_le_fp (fun _ => H) ab fun _ => h
 #align ordinal.nfp_le_fp Ordinal.nfp_le_fp
@@ -783,12 +513,6 @@ theorem IsNormal.nfp_fp {f} (H : IsNormal f) : ∀ a, f (nfp f a) = nfp f a :=
 #align ordinal.is_normal.nfp_fp Ordinal.IsNormal.nfp_fp
 -/
 
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 theorem IsNormal.apply_le_nfp {f} (H : IsNormal f) {a b} : f b ≤ nfp f a ↔ b ≤ nfp f a :=
   ⟨le_trans (H.self_le _), fun h => by simpa only [H.nfp_fp] using H.le_iff.2 h⟩
 #align ordinal.is_normal.apply_le_nfp Ordinal.IsNormal.apply_le_nfp
@@ -799,12 +523,6 @@ theorem nfp_eq_self {f : Ordinal → Ordinal} {a} (h : f a = a) : nfp f a = a :=
 #align ordinal.nfp_eq_self Ordinal.nfp_eq_self
 -/
 
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 /-- The fixed point lemma for normal functions: any normal function has an unbounded set of
 fixed points. -/
 theorem fp_unbounded (H : IsNormal f) : (Function.fixedPoints f).Unbounded (· < ·) := by
@@ -864,12 +582,6 @@ theorem IsNormal.deriv_fp {f} (H : IsNormal f) : ∀ o, f (deriv f o) = deriv f
 #align ordinal.is_normal.deriv_fp Ordinal.IsNormal.deriv_fp
 -/
 
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 theorem IsNormal.le_iff_deriv {f} (H : IsNormal f) {a} : f a ≤ a ↔ ∃ o, deriv f o = a :=
   by
   unfold deriv
@@ -901,12 +613,6 @@ end
 /-! ### Fixed points of addition -/
 
 
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 @[simp]
 theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
   by
@@ -918,12 +624,6 @@ theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
     rw [Nat.cast_add, Nat.cast_one, mul_one_add, iterate_succ_apply', hn]
 #align ordinal.nfp_add_zero Ordinal.nfp_add_zero
 
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 theorem nfp_add_eq_mul_omega {a b} (hba : b ≤ a * omega) : nfp ((· + ·) a) b = a * omega :=
   by
   apply le_antisymm (nfp_le_fp (add_is_normal a).Monotone hba _)
@@ -932,12 +632,6 @@ theorem nfp_add_eq_mul_omega {a b} (hba : b ≤ a * omega) : nfp ((· + ·) a) b
   · rw [← mul_one_add, one_add_omega]
 #align ordinal.nfp_add_eq_mul_omega Ordinal.nfp_add_eq_mul_omega
 
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 theorem add_eq_right_iff_mul_omega_le {a b : Ordinal} : a + b = b ↔ a * omega ≤ b :=
   by
   refine' ⟨fun h => _, fun h => _⟩
@@ -950,22 +644,10 @@ theorem add_eq_right_iff_mul_omega_le {a b : Ordinal} : a + b = b ↔ a * omega
     rwa [← add_assoc, ← mul_one_add, one_add_omega]
 #align ordinal.add_eq_right_iff_mul_omega_le Ordinal.add_eq_right_iff_mul_omega_le
 
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 theorem add_le_right_iff_mul_omega_le {a b : Ordinal} : a + b ≤ b ↔ a * omega ≤ b := by
   rw [← add_eq_right_iff_mul_omega_le]; exact (add_is_normal a).le_iff_eq
 #align ordinal.add_le_right_iff_mul_omega_le Ordinal.add_le_right_iff_mul_omega_le
 
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 theorem deriv_add_eq_mul_omega_add (a b : Ordinal.{u}) : deriv ((· + ·) a) b = a * omega + b :=
   by
   revert b
@@ -983,12 +665,6 @@ theorem deriv_add_eq_mul_omega_add (a b : Ordinal.{u}) : deriv ((· + ·) a) b =
 -- mathport name: ordinal.pow
 local infixr:0 "^" => @pow Ordinal Ordinal Ordinal.hasPow
 
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 @[simp]
 theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega) :=
   by
@@ -1001,12 +677,6 @@ theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega)
   · exact ha
 #align ordinal.nfp_mul_one Ordinal.nfp_mul_one
 
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 @[simp]
 theorem nfp_mul_zero (a : Ordinal) : nfp ((· * ·) a) 0 = 0 :=
   by
@@ -1016,12 +686,6 @@ theorem nfp_mul_zero (a : Ordinal) : nfp ((· * ·) a) 0 = 0 :=
   rwa [iterate_succ_apply, MulZeroClass.mul_zero]
 #align ordinal.nfp_mul_zero Ordinal.nfp_mul_zero
 
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 @[simp]
 theorem nfp_zero_mul : nfp ((· * ·) 0) = id :=
   by
@@ -1034,23 +698,11 @@ theorem nfp_zero_mul : nfp ((· * ·) 0) = id :=
   exact Ordinal.zero_le a
 #align ordinal.nfp_zero_mul Ordinal.nfp_zero_mul
 
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 @[simp]
 theorem deriv_mul_zero : deriv ((· * ·) 0) = id :=
   deriv_eq_id_of_nfp_eq_id nfp_zero_mul
 #align ordinal.deriv_mul_zero Ordinal.deriv_mul_zero
 
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 theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega)) :
     nfp ((· * ·) a) b = (a^omega.{u}) :=
   by
@@ -1065,12 +717,6 @@ theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega
   exact nfp_monotone (mul_is_normal ha).Monotone (one_le_iff_pos.2 hb)
 #align ordinal.nfp_mul_eq_opow_omega Ordinal.nfp_mul_eq_opow_omega
 
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 theorem eq_zero_or_opow_omega_le_of_mul_eq_right {a b : Ordinal} (hab : a * b = b) :
     b = 0 ∨ (a^omega.{u}) ≤ b :=
   by
@@ -1085,12 +731,6 @@ theorem eq_zero_or_opow_omega_le_of_mul_eq_right {a b : Ordinal} (hab : a * b =
   exact nfp_le_fp (mul_is_normal ha).Monotone hb (le_of_eq hab)
 #align ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right Ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right
 
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 theorem mul_eq_right_iff_opow_omega_dvd {a b : Ordinal} : a * b = b ↔ (a^omega) ∣ b :=
   by
   cases' eq_zero_or_pos a with ha ha
@@ -1108,22 +748,10 @@ theorem mul_eq_right_iff_opow_omega_dvd {a b : Ordinal} : a * b = b ↔ (a^omega
   rw [hc, ← mul_assoc, ← opow_one_add, one_add_omega]
 #align ordinal.mul_eq_right_iff_opow_omega_dvd Ordinal.mul_eq_right_iff_opow_omega_dvd
 
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 theorem mul_le_right_iff_opow_omega_dvd {a b : Ordinal} (ha : 0 < a) : a * b ≤ b ↔ (a^omega) ∣ b :=
   by rw [← mul_eq_right_iff_opow_omega_dvd]; exact (mul_is_normal ha).le_iff_eq
 #align ordinal.mul_le_right_iff_opow_omega_dvd Ordinal.mul_le_right_iff_opow_omega_dvd
 
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-Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_opow_omega_add Ordinal.nfp_mul_opow_omega_addₓ'. -/
 theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hca : c ≤ (a^omega)) :
     nfp ((· * ·) a) ((a^omega) * b + c) = (a^omega.{u}) * succ b :=
   by
@@ -1143,12 +771,6 @@ theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hc
     rwa [succ_le_iff]
 #align ordinal.nfp_mul_opow_omega_add Ordinal.nfp_mul_opow_omega_add
 
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-Case conversion may be inaccurate. Consider using '#align ordinal.deriv_mul_eq_opow_omega_mul Ordinal.deriv_mul_eq_opow_omega_mulₓ'. -/
 theorem deriv_mul_eq_opow_omega_mul {a : Ordinal.{u}} (ha : 0 < a) (b) :
     deriv ((· * ·) a) b = (a^omega) * b := by
   revert b

0dd4319a

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -159,10 +159,7 @@ but is expected to have type
   forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} [_inst_1 : Nonempty.{succ u1} ι], (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (forall {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u1 u2}}, Iff (Exists.{succ u1} ι (fun (i : ι) => 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.nfpFamily.{u1, u2} ι f a) (f i b))) (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.nfpFamily.{u1, u2} ι f a) b))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_family_le_apply Ordinal.nfpFamily_le_applyₓ'. -/
 theorem nfpFamily_le_apply [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
-    (∃ i, nfpFamily f a ≤ f i b) ↔ nfpFamily f a ≤ b :=
-  by
-  rw [← not_iff_not]
-  push_neg
+    (∃ i, nfpFamily f a ≤ f i b) ↔ nfpFamily f a ≤ b := by rw [← not_iff_not]; push_neg;
   exact apply_lt_nfp_family_iff H
 #align ordinal.nfp_family_le_apply Ordinal.nfpFamily_le_apply
 
@@ -176,11 +173,9 @@ theorem nfpFamily_le_fp (H : ∀ i, Monotone (f i)) {a b} (ab : a ≤ b) (h : 
     nfpFamily f a ≤ b :=
   sup_le fun l => by
     by_cases hι : IsEmpty ι
-    · skip
-      rwa [Unique.eq_default l]
+    · skip; rwa [Unique.eq_default l]
     · haveI := not_isEmpty_iff.1 hι
-      induction' l with i l IH generalizing a
-      · exact ab
+      induction' l with i l IH generalizing a; · exact ab
       exact (H i (IH ab)).trans (h i)
 #align ordinal.nfp_family_le_fp Ordinal.nfpFamily_le_fp
 
@@ -287,10 +282,8 @@ theorem derivFamily_fp {i} (H : IsNormal (f i)) (o : Ordinal.{max u v}) :
     f i (derivFamily f o) = derivFamily f o :=
   by
   refine' limit_rec_on o _ (fun o IH => _) _
-  · rw [deriv_family_zero]
-    exact nfp_family_fp H 0
-  · rw [deriv_family_succ]
-    exact nfp_family_fp H _
+  · rw [deriv_family_zero]; exact nfp_family_fp H 0
+  · rw [deriv_family_succ]; exact nfp_family_fp H _
   · intro o l IH
     rw [deriv_family_limit _ l,
       IsNormal.bsup.{max u v, u, max u v} H (fun a _ => deriv_family f a) l.1]
@@ -314,13 +307,11 @@ theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
       limit_rec_on o (fun h₁ => ⟨0, le_antisymm _ h₁⟩) (fun o IH h₁ => _) fun o l IH h₁ => _
     · rw [deriv_family_zero]
       exact nfp_family_le_fp (fun i => (H i).Monotone) (Ordinal.zero_le _) ha
-    · cases le_or_lt a (deriv_family f o)
-      · exact IH h
+    · cases le_or_lt a (deriv_family f o); · exact IH h
       refine' ⟨succ o, le_antisymm _ h₁⟩
       rw [deriv_family_succ]
       exact nfp_family_le_fp (fun i => (H i).Monotone) (succ_le_of_lt h) ha
-    · cases eq_or_lt_of_le h₁
-      · exact ⟨_, h.symm⟩
+    · cases eq_or_lt_of_le h₁; · exact ⟨_, h.symm⟩
       rw [deriv_family_limit _ l, ← not_le, bsup_le_iff, not_ball] at h
       exact
         let ⟨o', h, hl⟩ := h
@@ -485,12 +476,8 @@ but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_le_apply Ordinal.nfpBFamily_le_applyₓ'. -/
 theorem nfpBFamily_le_apply (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
-    (∃ i hi, nfpBFamily o f a ≤ f i hi b) ↔ nfpBFamily o f a ≤ b :=
-  by
-  rw [← not_iff_not]
-  push_neg
-  convert apply_lt_nfp_bfamily_iff ho H
-  simp only [not_le]
+    (∃ i hi, nfpBFamily o f a ≤ f i hi b) ↔ nfpBFamily o f a ≤ b := by rw [← not_iff_not]; push_neg;
+  convert apply_lt_nfp_bfamily_iff ho H; simp only [not_le]
 #align ordinal.nfp_bfamily_le_apply Ordinal.nfpBFamily_le_apply
 
 /- warning: ordinal.nfp_bfamily_le_fp -> Ordinal.nfpBFamily_le_fp is a dubious translation:
@@ -511,12 +498,8 @@ but is expected to have type
   forall {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {i : Ordinal.{u1}} {hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o}, (Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i hi)) -> (forall (a : Ordinal.{max u2 u1}), Eq.{max (succ (succ u1)) (succ (succ u2))} Ordinal.{max u1 u2} (f i hi (Ordinal.nfpBFamily.{u1, u2} o f a)) (Ordinal.nfpBFamily.{u1, u2} o f a))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_fp Ordinal.nfpBFamily_fpₓ'. -/
 theorem nfpBFamily_fp {i hi} (H : IsNormal (f i hi)) (a) :
-    f i hi (nfpBFamily o f a) = nfpBFamily o f a :=
-  by
-  rw [← family_of_bfamily_enum o f]
-  apply nfp_family_fp
-  rw [family_of_bfamily_enum]
-  exact H
+    f i hi (nfpBFamily o f a) = nfpBFamily o f a := by rw [← family_of_bfamily_enum o f];
+  apply nfp_family_fp; rw [family_of_bfamily_enum]; exact H
 #align ordinal.nfp_bfamily_fp Ordinal.nfpBFamily_fp
 
 /- warning: ordinal.apply_le_nfp_bfamily -> Ordinal.apply_le_nfpBFamily is a dubious translation:
@@ -556,9 +539,8 @@ Case conversion may be inaccurate. Consider using '#align ordinal.fp_bfamily_unb
     has an unbounded set of common fixed points. -/
 theorem fp_bfamily_unbounded (H : ∀ i hi, IsNormal (f i hi)) :
     (⋂ (i) (hi), Function.fixedPoints (f i hi)).Unbounded (· < ·) := fun a =>
-  ⟨_, by
-    rw [Set.mem_iInter₂]
-    exact fun i hi => nfp_bfamily_fp (H i hi) _, (le_nfpBFamily f a).not_lt⟩
+  ⟨_, by rw [Set.mem_iInter₂]; exact fun i hi => nfp_bfamily_fp (H i hi) _,
+    (le_nfpBFamily f a).not_lt⟩
 #align ordinal.fp_bfamily_unbounded Ordinal.fp_bfamily_unbounded
 
 /- warning: ordinal.deriv_bfamily -> Ordinal.derivBFamily is a dubious translation:
@@ -603,12 +585,8 @@ but is expected to have type
   forall {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {i : Ordinal.{u1}} {hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o}, (Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i hi)) -> (forall (a : Ordinal.{max u1 u2}), Eq.{max (succ (succ u1)) (succ (succ u2))} Ordinal.{max u1 u2} (f i hi (Ordinal.derivBFamily.{u1, u2} o f a)) (Ordinal.derivBFamily.{u1, u2} o f a))
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_bfamily_fp Ordinal.derivBFamily_fpₓ'. -/
 theorem derivBFamily_fp {i hi} (H : IsNormal (f i hi)) (a : Ordinal) :
-    f i hi (derivBFamily o f a) = derivBFamily o f a :=
-  by
-  rw [← family_of_bfamily_enum o f]
-  apply deriv_family_fp
-  rw [family_of_bfamily_enum]
-  exact H
+    f i hi (derivBFamily o f a) = derivBFamily o f a := by rw [← family_of_bfamily_enum o f];
+  apply deriv_family_fp; rw [family_of_bfamily_enum]; exact H
 #align ordinal.deriv_bfamily_fp Ordinal.derivBFamily_fp
 
 /- warning: ordinal.le_iff_deriv_bfamily -> Ordinal.le_iff_derivBFamily is a dubious translation:
@@ -707,9 +685,7 @@ lean 3 declaration is
 but is expected to have type
   forall (f : Ordinal.{u1} -> Ordinal.{u1}) (a : Ordinal.{u1}) (n : Nat), LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Nat.iterate.{succ (succ u1)} Ordinal.{u1} f n a) (Ordinal.nfp.{u1} f a)
 Case conversion may be inaccurate. Consider using '#align ordinal.iterate_le_nfp Ordinal.iterate_le_nfpₓ'. -/
-theorem iterate_le_nfp (f a n) : (f^[n]) a ≤ nfp f a :=
-  by
-  rw [← sup_iterate_eq_nfp]
+theorem iterate_le_nfp (f a n) : (f^[n]) a ≤ nfp f a := by rw [← sup_iterate_eq_nfp];
   exact le_sup _ n
 #align ordinal.iterate_le_nfp Ordinal.iterate_le_nfp
 
@@ -729,9 +705,7 @@ lean 3 declaration is
 but is expected to have type
   forall {f : Ordinal.{u1} -> Ordinal.{u1}} {a : Ordinal.{u1}} {b : 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 (Ordinal.nfp.{u1} f b)) (Exists.{1} Nat (fun (n : Nat) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (Nat.iterate.{succ (succ u1)} Ordinal.{u1} f n b)))
 Case conversion may be inaccurate. Consider using '#align ordinal.lt_nfp Ordinal.lt_nfpₓ'. -/
-theorem lt_nfp {a b} : a < nfp f b ↔ ∃ n, a < (f^[n]) b :=
-  by
-  rw [← sup_iterate_eq_nfp]
+theorem lt_nfp {a b} : a < nfp f b ↔ ∃ n, a < (f^[n]) b := by rw [← sup_iterate_eq_nfp];
   exact lt_sup
 #align ordinal.lt_nfp Ordinal.lt_nfp
 
@@ -741,9 +715,7 @@ lean 3 declaration is
 but is expected to have type
   forall {f : Ordinal.{u1} -> Ordinal.{u1}} {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfp.{u1} f a) b) (forall (n : Nat), LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Nat.iterate.{succ (succ u1)} Ordinal.{u1} f n a) b)
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_le_iff Ordinal.nfp_le_iffₓ'. -/
-theorem nfp_le_iff {a b} : nfp f a ≤ b ↔ ∀ n, (f^[n]) a ≤ b :=
-  by
-  rw [← sup_iterate_eq_nfp]
+theorem nfp_le_iff {a b} : nfp f a ≤ b ↔ ∀ n, (f^[n]) a ≤ b := by rw [← sup_iterate_eq_nfp];
   exact sup_le_iff
 #align ordinal.nfp_le_iff Ordinal.nfp_le_iff
 
@@ -835,10 +807,8 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align ordinal.fp_unbounded Ordinal.fp_unboundedₓ'. -/
 /-- The fixed point lemma for normal functions: any normal function has an unbounded set of
 fixed points. -/
-theorem fp_unbounded (H : IsNormal f) : (Function.fixedPoints f).Unbounded (· < ·) :=
-  by
-  convert fp_family_unbounded fun _ : Unit => H
-  exact (Set.iInter_const _).symm
+theorem fp_unbounded (H : IsNormal f) : (Function.fixedPoints f).Unbounded (· < ·) := by
+  convert fp_family_unbounded fun _ : Unit => H; exact (Set.iInter_const _).symm
 #align ordinal.fp_unbounded Ordinal.fp_unbounded
 
 #print Ordinal.deriv /-
@@ -915,10 +885,8 @@ theorem IsNormal.fp_iff_deriv {f} (H : IsNormal f) {a} : f a = a ↔ ∃ o, deri
 
 #print Ordinal.deriv_eq_enumOrd /-
 /-- `ordinal.deriv` enumerates the fixed points of a normal function. -/
-theorem deriv_eq_enumOrd (H : IsNormal f) : deriv f = enumOrd (Function.fixedPoints f) :=
-  by
-  convert deriv_family_eq_enum_ord fun _ : Unit => H
-  exact (Set.iInter_const _).symm
+theorem deriv_eq_enumOrd (H : IsNormal f) : deriv f = enumOrd (Function.fixedPoints f) := by
+  convert deriv_family_eq_enum_ord fun _ : Unit => H; exact (Set.iInter_const _).symm
 #align ordinal.deriv_eq_enum_ord Ordinal.deriv_eq_enumOrd
 -/
 
@@ -988,10 +956,8 @@ lean 3 declaration is
 but is expected to have type
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 Case conversion may be inaccurate. Consider using '#align ordinal.add_le_right_iff_mul_omega_le Ordinal.add_le_right_iff_mul_omega_leₓ'. -/
-theorem add_le_right_iff_mul_omega_le {a b : Ordinal} : a + b ≤ b ↔ a * omega ≤ b :=
-  by
-  rw [← add_eq_right_iff_mul_omega_le]
-  exact (add_is_normal a).le_iff_eq
+theorem add_le_right_iff_mul_omega_le {a b : Ordinal} : a + b ≤ b ↔ a * omega ≤ b := by
+  rw [← add_eq_right_iff_mul_omega_le]; exact (add_is_normal a).le_iff_eq
 #align ordinal.add_le_right_iff_mul_omega_le Ordinal.add_le_right_iff_mul_omega_le
 
 /- warning: ordinal.deriv_add_eq_mul_omega_add -> Ordinal.deriv_add_eq_mul_omega_add is a dubious translation:
@@ -1027,9 +993,7 @@ Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_one Or
 theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega) :=
   by
   rw [← sup_iterate_eq_nfp, ← sup_opow_nat]
-  · dsimp
-    congr
-    funext
+  · dsimp; congr ; funext
     induction' n with n hn
     · rw [Nat.cast_zero, opow_zero, iterate_zero_apply]
     nth_rw 2 [Nat.succ_eq_one_add]
@@ -1151,9 +1115,7 @@ but is expected to have type
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) (Dvd.dvd.{succ u1} Ordinal.{u1} (semigroupDvd.{succ u1} Ordinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Ordinal.{u1} (MonoidWithZero.toSemigroupWithZero.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
 Case conversion may be inaccurate. Consider using '#align ordinal.mul_le_right_iff_opow_omega_dvd Ordinal.mul_le_right_iff_opow_omega_dvdₓ'. -/
 theorem mul_le_right_iff_opow_omega_dvd {a b : Ordinal} (ha : 0 < a) : a * b ≤ b ↔ (a^omega) ∣ b :=
-  by
-  rw [← mul_eq_right_iff_opow_omega_dvd]
-  exact (mul_is_normal ha).le_iff_eq
+  by rw [← mul_eq_right_iff_opow_omega_dvd]; exact (mul_is_normal ha).le_iff_eq
 #align ordinal.mul_le_right_iff_opow_omega_dvd Ordinal.mul_le_right_iff_opow_omega_dvd
 
 /- warning: ordinal.nfp_mul_opow_omega_add -> Ordinal.nfp_mul_opow_omega_add is a dubious translation:

0dd4319a

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -68,15 +68,19 @@ theorem nfpFamily_eq_sup (f : ι → Ordinal → Ordinal) (a) : nfpFamily f a =
 #align ordinal.nfp_family_eq_sup Ordinal.nfpFamily_eq_sup
 -/
 
-#print Ordinal.foldr_le_nfpFamily /-
+/- warning: ordinal.foldr_le_nfp_family -> Ordinal.foldr_le_nfpFamily is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}) (a : Ordinal.{max u1 u2}) (l : List.{u1} ι), 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})) (List.foldr.{u1, succ (max u1 u2)} ι Ordinal.{max u1 u2} f a l) (Ordinal.nfpFamily.{u1, u2} ι f a)
+but is expected to have type
+  forall {ι : Type.{u1}} (f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}) (a : Ordinal.{max u1 u2}) (l : List.{u1} ι), 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})) (List.foldr.{u1, succ (max u1 u2)} ι Ordinal.{max u1 u2} f a l) (Ordinal.nfpFamily.{u1, u2} ι f a)
+Case conversion may be inaccurate. Consider using '#align ordinal.foldr_le_nfp_family Ordinal.foldr_le_nfpFamilyₓ'. -/
 theorem foldr_le_nfpFamily (f : ι → Ordinal → Ordinal) (a l) : List.foldr f a l ≤ nfpFamily f a :=
   le_sup _ _
 #align ordinal.foldr_le_nfp_family Ordinal.foldr_le_nfpFamily
--/
 
 /- warning: ordinal.le_nfp_family -> Ordinal.le_nfpFamily is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} (f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}) (a : Ordinal.{max u1 u2}), LE.le.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLE.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) a (Ordinal.nfpFamily.{u1, u2} ι f a)
+  forall {ι : Type.{u1}} (f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}) (a : 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})) a (Ordinal.nfpFamily.{u1, u2} ι f a)
 but is expected to have type
   forall {ι : Type.{u2}} (f : ι -> Ordinal.{max u2 u1} -> Ordinal.{max u2 u1}) (a : Ordinal.{max u2 u1}), LE.le.{max (succ u2) (succ u1)} Ordinal.{max u2 u1} (Preorder.toLE.{max (succ u2) (succ u1)} Ordinal.{max u2 u1} (PartialOrder.toPreorder.{max (succ u2) (succ u1)} Ordinal.{max u2 u1} Ordinal.partialOrder.{max u2 u1})) a (Ordinal.nfpFamily.{u2, u1} ι f a)
 Case conversion may be inaccurate. Consider using '#align ordinal.le_nfp_family Ordinal.le_nfpFamilyₓ'. -/
@@ -84,23 +88,35 @@ theorem le_nfpFamily (f : ι → Ordinal → Ordinal) (a) : a ≤ nfpFamily f a
   le_sup _ []
 #align ordinal.le_nfp_family Ordinal.le_nfpFamily
 
-#print Ordinal.lt_nfpFamily /-
+/- warning: ordinal.lt_nfp_family -> Ordinal.lt_nfpFamily is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {a : Ordinal.{max u1 u2}} {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})) a (Ordinal.nfpFamily.{u1, u2} ι f b)) (Exists.{succ u1} (List.{u1} ι) (fun (l : List.{u1} ι) => LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) a (List.foldr.{u1, succ (max u1 u2)} ι Ordinal.{max u1 u2} f b l)))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {a : Ordinal.{max u2 u1}} {b : Ordinal.{max u1 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})) a (Ordinal.nfpFamily.{u1, u2} ι f b)) (Exists.{succ u1} (List.{u1} ι) (fun (l : List.{u1} ι) => 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})) a (List.foldr.{u1, max (succ u1) (succ u2)} ι Ordinal.{max u1 u2} f b l)))
+Case conversion may be inaccurate. Consider using '#align ordinal.lt_nfp_family Ordinal.lt_nfpFamilyₓ'. -/
 theorem lt_nfpFamily {a b} : a < nfpFamily f b ↔ ∃ l, a < List.foldr f b l :=
   lt_sup
 #align ordinal.lt_nfp_family Ordinal.lt_nfpFamily
--/
 
-#print Ordinal.nfpFamily_le_iff /-
+/- warning: ordinal.nfp_family_le_iff -> Ordinal.nfpFamily_le_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {a : Ordinal.{max u1 u2}} {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})) (Ordinal.nfpFamily.{u1, u2} ι f a) b) (forall (l : List.{u1} ι), 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})) (List.foldr.{u1, succ (max u1 u2)} ι Ordinal.{max u1 u2} f a l) b)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u2 u1}}, 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.nfpFamily.{u1, u2} ι f a) b) (forall (l : List.{u1} ι), 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})) (List.foldr.{u1, max (succ u1) (succ u2)} ι Ordinal.{max u1 u2} f a l) b)
+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_family_le_iff Ordinal.nfpFamily_le_iffₓ'. -/
 theorem nfpFamily_le_iff {a b} : nfpFamily f a ≤ b ↔ ∀ l, List.foldr f a l ≤ b :=
   sup_le_iff
 #align ordinal.nfp_family_le_iff Ordinal.nfpFamily_le_iff
--/
 
-#print Ordinal.nfpFamily_le /-
+/- warning: ordinal.nfp_family_le -> Ordinal.nfpFamily_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u1 u2}}, (forall (l : List.{u1} ι), 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})) (List.foldr.{u1, succ (max u1 u2)} ι Ordinal.{max u1 u2} f a l) b) -> (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})) (Ordinal.nfpFamily.{u1, u2} ι f a) b)
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u1 u2}}, (forall (l : List.{u1} ι), 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})) (List.foldr.{u1, max (succ u1) (succ u2)} ι Ordinal.{max u1 u2} f a l) b) -> (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.nfpFamily.{u1, u2} ι f a) b)
+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_family_le Ordinal.nfpFamily_leₓ'. -/
 theorem nfpFamily_le {a b} : (∀ l, List.foldr f a l ≤ b) → nfpFamily f a ≤ b :=
   sup_le
 #align ordinal.nfp_family_le Ordinal.nfpFamily_le
--/
 
 #print Ordinal.nfpFamily_monotone /-
 theorem nfpFamily_monotone (hf : ∀ i, Monotone (f i)) : Monotone (nfpFamily f) := fun a b h =>
@@ -108,16 +124,25 @@ theorem nfpFamily_monotone (hf : ∀ i, Monotone (f i)) : Monotone (nfpFamily f)
 #align ordinal.nfp_family_monotone Ordinal.nfpFamily_monotone
 -/
 
+/- warning: ordinal.apply_lt_nfp_family -> Ordinal.apply_lt_nfpFamily is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (forall {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b (Ordinal.nfpFamily.{u1, u2} ι f a)) -> (forall (i : ι), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i b) (Ordinal.nfpFamily.{u1, u2} ι f a)))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (forall {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u2 u1}}, (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})) b (Ordinal.nfpFamily.{u1, u2} ι f a)) -> (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i b) (Ordinal.nfpFamily.{u1, u2} ι f a)))
+Case conversion may be inaccurate. Consider using '#align ordinal.apply_lt_nfp_family Ordinal.apply_lt_nfpFamilyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-#print Ordinal.apply_lt_nfpFamily /-
 theorem apply_lt_nfpFamily (H : ∀ i, IsNormal (f i)) {a b} (hb : b < nfpFamily f a) (i) :
     f i b < nfpFamily f a :=
   let ⟨l, hl⟩ := lt_nfpFamily.1 hb
   lt_sup.2 ⟨i::l, (H i).StrictMono hl⟩
 #align ordinal.apply_lt_nfp_family Ordinal.apply_lt_nfpFamily
--/
 
-#print Ordinal.apply_lt_nfpFamily_iff /-
+/- warning: ordinal.apply_lt_nfp_family_iff -> Ordinal.apply_lt_nfpFamily_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} [_inst_1 : Nonempty.{succ u1} ι], (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (forall {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u1 u2}}, Iff (forall (i : ι), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i b) (Ordinal.nfpFamily.{u1, u2} ι f a)) (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.nfpFamily.{u1, u2} ι f a)))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} [_inst_1 : Nonempty.{succ u1} ι], (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (forall {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u1 u2}}, Iff (forall (i : ι), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i b) (Ordinal.nfpFamily.{u1, u2} ι f a)) (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.nfpFamily.{u1, u2} ι f a)))
+Case conversion may be inaccurate. Consider using '#align ordinal.apply_lt_nfp_family_iff Ordinal.apply_lt_nfpFamily_iffₓ'. -/
 theorem apply_lt_nfpFamily_iff [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
     (∀ i, f i b < nfpFamily f a) ↔ b < nfpFamily f a :=
   ⟨fun h =>
@@ -126,9 +151,13 @@ theorem apply_lt_nfpFamily_iff [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
       ⟨l, ((H _).self_le b).trans_lt hl⟩,
     apply_lt_nfpFamily H⟩
 #align ordinal.apply_lt_nfp_family_iff Ordinal.apply_lt_nfpFamily_iff
--/
 
-#print Ordinal.nfpFamily_le_apply /-
+/- warning: ordinal.nfp_family_le_apply -> Ordinal.nfpFamily_le_apply is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} [_inst_1 : Nonempty.{succ u1} ι], (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (forall {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u1 u2}}, Iff (Exists.{succ u1} ι (fun (i : ι) => 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})) (Ordinal.nfpFamily.{u1, u2} ι f a) (f i b))) (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})) (Ordinal.nfpFamily.{u1, u2} ι f a) b))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} [_inst_1 : Nonempty.{succ u1} ι], (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (forall {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u1 u2}}, Iff (Exists.{succ u1} ι (fun (i : ι) => 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.nfpFamily.{u1, u2} ι f a) (f i b))) (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.nfpFamily.{u1, u2} ι f a) b))
+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_family_le_apply Ordinal.nfpFamily_le_applyₓ'. -/
 theorem nfpFamily_le_apply [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
     (∃ i, nfpFamily f a ≤ f i b) ↔ nfpFamily f a ≤ b :=
   by
@@ -136,9 +165,13 @@ theorem nfpFamily_le_apply [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
   push_neg
   exact apply_lt_nfp_family_iff H
 #align ordinal.nfp_family_le_apply Ordinal.nfpFamily_le_apply
--/
 
-#print Ordinal.nfpFamily_le_fp /-
+/- warning: ordinal.nfp_family_le_fp -> Ordinal.nfpFamily_le_fp is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : ι), Monotone.{succ (max u1 u2), succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2}) (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2}) (f i)) -> (forall {a : Ordinal.{max u1 u2}} {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})) a b) -> (forall (i : ι), 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})) (f i b) b) -> (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})) (Ordinal.nfpFamily.{u1, u2} ι f a) b))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : ι), Monotone.{max (succ u1) (succ u2), max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2}) (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2}) (f i)) -> (forall {a : Ordinal.{max u1 u2}} {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})) a b) -> (forall (i : ι), 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})) (f i b) b) -> (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.nfpFamily.{u1, u2} ι f a) b))
+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_family_le_fp Ordinal.nfpFamily_le_fpₓ'. -/
 theorem nfpFamily_le_fp (H : ∀ i, Monotone (f i)) {a b} (ab : a ≤ b) (h : ∀ i, f i b ≤ b) :
     nfpFamily f a ≤ b :=
   sup_le fun l => by
@@ -150,7 +183,6 @@ theorem nfpFamily_le_fp (H : ∀ i, Monotone (f i)) {a b} (ab : a ≤ b) (h : 
       · exact ab
       exact (H i (IH ab)).trans (h i)
 #align ordinal.nfp_family_le_fp Ordinal.nfpFamily_le_fp
--/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print Ordinal.nfpFamily_fp /-
@@ -164,7 +196,12 @@ theorem nfpFamily_fp {i} (H : IsNormal (f i)) (a) : f i (nfpFamily f a) = nfpFam
 #align ordinal.nfp_family_fp Ordinal.nfpFamily_fp
 -/
 
-#print Ordinal.apply_le_nfpFamily /-
+/- warning: ordinal.apply_le_nfp_family -> Ordinal.apply_le_nfpFamily is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [hι : Nonempty.{succ u1} ι] {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (forall {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u1 u2}}, Iff (forall (i : ι), 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})) (f i b) (Ordinal.nfpFamily.{u1, u2} ι f a)) (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.nfpFamily.{u1, u2} ι f a)))
+but is expected to have type
+  forall {ι : Type.{u1}} [hι : Nonempty.{succ u1} ι] {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (forall {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u1 u2}}, Iff (forall (i : ι), 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})) (f i b) (Ordinal.nfpFamily.{u1, u2} ι f a)) (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.nfpFamily.{u1, u2} ι f a)))
+Case conversion may be inaccurate. Consider using '#align ordinal.apply_le_nfp_family Ordinal.apply_le_nfpFamilyₓ'. -/
 theorem apply_le_nfpFamily [hι : Nonempty ι] {f : ι → Ordinal → Ordinal} (H : ∀ i, IsNormal (f i))
     {a b} : (∀ i, f i b ≤ nfpFamily f a) ↔ b ≤ nfpFamily f a :=
   by
@@ -174,7 +211,6 @@ theorem apply_le_nfpFamily [hι : Nonempty ι] {f : ι → Ordinal → Ordinal}
   rw [← nfp_family_fp (H i)]
   exact (H i).Monotone h
 #align ordinal.apply_le_nfp_family Ordinal.apply_le_nfpFamily
--/
 
 /- warning: ordinal.nfp_family_eq_self -> Ordinal.nfpFamily_eq_self is a dubious translation:
 lean 3 declaration is
@@ -187,7 +223,12 @@ theorem nfpFamily_eq_self {f : ι → Ordinal → Ordinal} {a} (h : ∀ i, f i a
   le_antisymm (sup_le fun l => by rw [List.foldr_fixed' h l]) <| le_nfpFamily f a
 #align ordinal.nfp_family_eq_self Ordinal.nfpFamily_eq_self
 
-#print Ordinal.fp_family_unbounded /-
+/- warning: ordinal.fp_family_unbounded -> Ordinal.fp_family_unbounded is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (Set.Unbounded.{succ (max u1 u2)} Ordinal.{max u1 u2} (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2}))) (Set.iInter.{succ (max u1 u2), succ u1} Ordinal.{max u1 u2} ι (fun (i : ι) => Function.fixedPoints.{succ (max u1 u2)} Ordinal.{max u1 u2} (f i))))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (Set.Unbounded.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.1018 : Ordinal.{max u1 u2}) (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.1020 : 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.FixedPoint._hyg.1018 x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.1020) (Set.iInter.{max (succ u1) (succ u2), succ u1} Ordinal.{max u1 u2} ι (fun (i : ι) => Function.fixedPoints.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (f i))))
+Case conversion may be inaccurate. Consider using '#align ordinal.fp_family_unbounded Ordinal.fp_family_unboundedₓ'. -/
 -- Todo: This is actually a special case of the fact the intersection of club sets is a club set.
 /-- A generalization of the fixed point lemma for normal functions: any family of normal functions
     has an unbounded set of common fixed points. -/
@@ -197,7 +238,6 @@ theorem fp_family_unbounded (H : ∀ i, IsNormal (f i)) :
     rw [← hi]
     exact nfp_family_fp (H i) a, (le_nfpFamily f a).not_lt⟩
 #align ordinal.fp_family_unbounded Ordinal.fp_family_unbounded
--/
 
 #print Ordinal.derivFamily /-
 /-- The derivative of a family of normal functions is the sequence of their common fixed points.
@@ -259,7 +299,12 @@ theorem derivFamily_fp {i} (H : IsNormal (f i)) (o : Ordinal.{max u v}) :
 #align ordinal.deriv_family_fp Ordinal.derivFamily_fp
 -/
 
-#print Ordinal.le_iff_derivFamily /-
+/- warning: ordinal.le_iff_deriv_family -> Ordinal.le_iff_derivFamily is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (forall {a : Ordinal.{max u1 u2}}, Iff (forall (i : ι), 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})) (f i a) a) (Exists.{succ (succ (max u1 u2))} Ordinal.{max u1 u2} (fun (o : Ordinal.{max u1 u2}) => Eq.{succ (succ (max u1 u2))} Ordinal.{max u1 u2} (Ordinal.derivFamily.{u1, u2} ι f o) a)))
+but is expected to have type
+  forall {ι : Type.{u1}} {f : ι -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : ι), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i)) -> (forall {a : Ordinal.{max u1 u2}}, Iff (forall (i : ι), 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})) (f i a) a) (Exists.{max (succ (succ u1)) (succ (succ u2))} Ordinal.{max u1 u2} (fun (o : Ordinal.{max u1 u2}) => Eq.{max (succ (succ u1)) (succ (succ u2))} Ordinal.{max u1 u2} (Ordinal.derivFamily.{u1, u2} ι f o) a)))
+Case conversion may be inaccurate. Consider using '#align ordinal.le_iff_deriv_family Ordinal.le_iff_derivFamilyₓ'. -/
 theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
     (∀ i, f i a ≤ a) ↔ ∃ o, derivFamily f o = a :=
   ⟨fun ha => by
@@ -282,7 +327,6 @@ theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
         IH o' h (le_of_not_le hl),
     fun ⟨o, e⟩ i => e ▸ (derivFamily_fp (H i) _).le⟩
 #align ordinal.le_iff_deriv_family Ordinal.le_iff_derivFamily
--/
 
 #print Ordinal.fp_iff_derivFamily /-
 theorem fp_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
@@ -317,7 +361,12 @@ section
 
 variable {o : Ordinal.{u}} {f : ∀ b < o, Ordinal.{max u v} → Ordinal.{max u v}}
 
-#print Ordinal.nfpBFamily /-
+/- warning: ordinal.nfp_bfamily -> Ordinal.nfpBFamily is a dubious translation:
+lean 3 declaration is
+  forall (o : Ordinal.{u1}), (forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}
+but is expected to have type
+  forall (o : Ordinal.{u1}), (forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}) -> Ordinal.{max u2 u1} -> Ordinal.{max u2 u1}
+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily Ordinal.nfpBFamilyₓ'. -/
 /-- The next common fixed point, at least `a`, for a family of normal functions indexed by ordinals.
 
 This is defined as `ordinal.nfp_family` of the type-indexed family associated to `f`.
@@ -325,56 +374,88 @@ This is defined as `ordinal.nfp_family` of the type-indexed family associated to
 def nfpBFamily (o : Ordinal) (f : ∀ b < o, Ordinal → Ordinal) : Ordinal → Ordinal :=
   nfpFamily (familyOfBFamily o f)
 #align ordinal.nfp_bfamily Ordinal.nfpBFamily
--/
 
-#print Ordinal.nfpBFamily_eq_nfpFamily /-
+/- warning: ordinal.nfp_bfamily_eq_nfp_family -> Ordinal.nfpBFamily_eq_nfpFamily is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_eq_nfp_family Ordinal.nfpBFamily_eq_nfpFamilyₓ'. -/
 theorem nfpBFamily_eq_nfpFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) :
     nfpBFamily o f = nfpFamily (familyOfBFamily o f) :=
   rfl
 #align ordinal.nfp_bfamily_eq_nfp_family Ordinal.nfpBFamily_eq_nfpFamily
--/
 
-#print Ordinal.foldr_le_nfpBFamily /-
+/- warning: ordinal.foldr_le_nfp_bfamily -> Ordinal.foldr_le_nfpBFamily is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.foldr_le_nfp_bfamily Ordinal.foldr_le_nfpBFamilyₓ'. -/
 theorem foldr_le_nfpBFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) (a l) :
     List.foldr (familyOfBFamily o f) a l ≤ nfpBFamily o f a :=
   le_sup _ _
 #align ordinal.foldr_le_nfp_bfamily Ordinal.foldr_le_nfpBFamily
--/
 
-#print Ordinal.le_nfpBFamily /-
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+Case conversion may be inaccurate. Consider using '#align ordinal.le_nfp_bfamily Ordinal.le_nfpBFamilyₓ'. -/
 theorem le_nfpBFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) (a) : a ≤ nfpBFamily o f a :=
   le_sup _ []
 #align ordinal.le_nfp_bfamily Ordinal.le_nfpBFamily
--/
 
-#print Ordinal.lt_nfpBFamily /-
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+Case conversion may be inaccurate. Consider using '#align ordinal.lt_nfp_bfamily Ordinal.lt_nfpBFamilyₓ'. -/
 theorem lt_nfpBFamily {a b} :
     a < nfpBFamily o f b ↔ ∃ l, a < List.foldr (familyOfBFamily o f) b l :=
   lt_sup
 #align ordinal.lt_nfp_bfamily Ordinal.lt_nfpBFamily
--/
 
-#print Ordinal.nfpBFamily_le_iff /-
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_le_iff Ordinal.nfpBFamily_le_iffₓ'. -/
 theorem nfpBFamily_le_iff {o : Ordinal} {f : ∀ b < o, Ordinal → Ordinal} {a b} :
     nfpBFamily o f a ≤ b ↔ ∀ l, List.foldr (familyOfBFamily o f) a l ≤ b :=
   sup_le_iff
 #align ordinal.nfp_bfamily_le_iff Ordinal.nfpBFamily_le_iff
--/
 
-#print Ordinal.nfpBFamily_le /-
+/- warning: ordinal.nfp_bfamily_le -> Ordinal.nfpBFamily_le is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_le Ordinal.nfpBFamily_leₓ'. -/
 theorem nfpBFamily_le {o : Ordinal} {f : ∀ b < o, Ordinal → Ordinal} {a b} :
     (∀ l, List.foldr (familyOfBFamily o f) a l ≤ b) → nfpBFamily o f a ≤ b :=
   sup_le
 #align ordinal.nfp_bfamily_le Ordinal.nfpBFamily_le
--/
 
-#print Ordinal.nfpBFamily_monotone /-
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_monotone Ordinal.nfpBFamily_monotoneₓ'. -/
 theorem nfpBFamily_monotone (hf : ∀ i hi, Monotone (f i hi)) : Monotone (nfpBFamily o f) :=
   nfpFamily_monotone fun i => hf _ _
 #align ordinal.nfp_bfamily_monotone Ordinal.nfpBFamily_monotone
--/
 
-#print Ordinal.apply_lt_nfpBFamily /-
+/- warning: ordinal.apply_lt_nfp_bfamily -> Ordinal.apply_lt_nfpBFamily is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.apply_lt_nfp_bfamily Ordinal.apply_lt_nfpBFamilyₓ'. -/
 theorem apply_lt_nfpBFamily (H : ∀ i hi, IsNormal (f i hi)) {a b} (hb : b < nfpBFamily o f a)
     (i hi) : f i hi b < nfpBFamily o f a :=
   by
@@ -382,9 +463,13 @@ theorem apply_lt_nfpBFamily (H : ∀ i hi, IsNormal (f i hi)) {a b} (hb : b < nf
   apply apply_lt_nfp_family _ hb
   exact fun _ => H _ _
 #align ordinal.apply_lt_nfp_bfamily Ordinal.apply_lt_nfpBFamily
--/
 
-#print Ordinal.apply_lt_nfpBFamily_iff /-
+/- warning: ordinal.apply_lt_nfp_bfamily_iff -> Ordinal.apply_lt_nfpBFamily_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.apply_lt_nfp_bfamily_iff Ordinal.apply_lt_nfpBFamily_iffₓ'. -/
 theorem apply_lt_nfpBFamily_iff (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
     (∀ i hi, f i hi b < nfpBFamily o f a) ↔ b < nfpBFamily o f a :=
   ⟨fun h => by
@@ -392,9 +477,13 @@ theorem apply_lt_nfpBFamily_iff (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi))
     refine' (apply_lt_nfp_family_iff _).1 fun _ => h _ _
     exact fun _ => H _ _, apply_lt_nfpBFamily H⟩
 #align ordinal.apply_lt_nfp_bfamily_iff Ordinal.apply_lt_nfpBFamily_iff
--/
 
-#print Ordinal.nfpBFamily_le_apply /-
+/- warning: ordinal.nfp_bfamily_le_apply -> Ordinal.nfpBFamily_le_apply is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_le_apply Ordinal.nfpBFamily_le_applyₓ'. -/
 theorem nfpBFamily_le_apply (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
     (∃ i hi, nfpBFamily o f a ≤ f i hi b) ↔ nfpBFamily o f a ≤ b :=
   by
@@ -403,16 +492,24 @@ theorem nfpBFamily_le_apply (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a
   convert apply_lt_nfp_bfamily_iff ho H
   simp only [not_le]
 #align ordinal.nfp_bfamily_le_apply Ordinal.nfpBFamily_le_apply
--/
 
-#print Ordinal.nfpBFamily_le_fp /-
+/- warning: ordinal.nfp_bfamily_le_fp -> Ordinal.nfpBFamily_le_fp is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_le_fp Ordinal.nfpBFamily_le_fpₓ'. -/
 theorem nfpBFamily_le_fp (H : ∀ i hi, Monotone (f i hi)) {a b} (ab : a ≤ b)
     (h : ∀ i hi, f i hi b ≤ b) : nfpBFamily o f a ≤ b :=
   nfpFamily_le_fp (fun _ => H _ _) ab fun i => h _ _
 #align ordinal.nfp_bfamily_le_fp Ordinal.nfpBFamily_le_fp
--/
 
-#print Ordinal.nfpBFamily_fp /-
+/- warning: ordinal.nfp_bfamily_fp -> Ordinal.nfpBFamily_fp is a dubious translation:
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+  forall {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {i : Ordinal.{u1}} {hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o}, (Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i hi)) -> (forall (a : Ordinal.{max u1 u2}), Eq.{succ (succ (max u1 u2))} Ordinal.{max u1 u2} (f i hi (Ordinal.nfpBFamily.{u1, u2} o f a)) (Ordinal.nfpBFamily.{u1, u2} o f a))
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_fp Ordinal.nfpBFamily_fpₓ'. -/
 theorem nfpBFamily_fp {i hi} (H : IsNormal (f i hi)) (a) :
     f i hi (nfpBFamily o f a) = nfpBFamily o f a :=
   by
@@ -421,9 +518,13 @@ theorem nfpBFamily_fp {i hi} (H : IsNormal (f i hi)) (a) :
   rw [family_of_bfamily_enum]
   exact H
 #align ordinal.nfp_bfamily_fp Ordinal.nfpBFamily_fp
--/
 
-#print Ordinal.apply_le_nfpBFamily /-
+/- warning: ordinal.apply_le_nfp_bfamily -> Ordinal.apply_le_nfpBFamily is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.apply_le_nfp_bfamily Ordinal.apply_le_nfpBFamilyₓ'. -/
 theorem apply_le_nfpBFamily (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
     (∀ i hi, f i hi b ≤ nfpBFamily o f a) ↔ b ≤ nfpBFamily o f a :=
   by
@@ -433,16 +534,24 @@ theorem apply_le_nfpBFamily (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a
   · rw [← nfp_bfamily_fp (H i hi)]
     exact (H i hi).Monotone h
 #align ordinal.apply_le_nfp_bfamily Ordinal.apply_le_nfpBFamily
--/
 
-#print Ordinal.nfpBFamily_eq_self /-
+/- warning: ordinal.nfp_bfamily_eq_self -> Ordinal.nfpBFamily_eq_self is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_bfamily_eq_self Ordinal.nfpBFamily_eq_selfₓ'. -/
 theorem nfpBFamily_eq_self {a} (h : ∀ i hi, f i hi a = a) : nfpBFamily o f a = a :=
   nfpFamily_eq_self fun _ => h _ _
 #align ordinal.nfp_bfamily_eq_self Ordinal.nfpBFamily_eq_self
--/
 
+/- warning: ordinal.fp_bfamily_unbounded -> Ordinal.fp_bfamily_unbounded is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align ordinal.fp_bfamily_unbounded Ordinal.fp_bfamily_unboundedₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-#print Ordinal.fp_bfamily_unbounded /-
 /-- A generalization of the fixed point lemma for normal functions: any family of normal functions
     has an unbounded set of common fixed points. -/
 theorem fp_bfamily_unbounded (H : ∀ i hi, IsNormal (f i hi)) :
@@ -451,27 +560,34 @@ theorem fp_bfamily_unbounded (H : ∀ i hi, IsNormal (f i hi)) :
     rw [Set.mem_iInter₂]
     exact fun i hi => nfp_bfamily_fp (H i hi) _, (le_nfpBFamily f a).not_lt⟩
 #align ordinal.fp_bfamily_unbounded Ordinal.fp_bfamily_unbounded
--/
 
-#print Ordinal.derivBFamily /-
+/- warning: ordinal.deriv_bfamily -> Ordinal.derivBFamily is a dubious translation:
+lean 3 declaration is
+  forall (o : Ordinal.{u1}), (forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}
+but is expected to have type
+  forall (o : Ordinal.{u1}), (forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}) -> Ordinal.{max u2 u1} -> Ordinal.{max u2 u1}
+Case conversion may be inaccurate. Consider using '#align ordinal.deriv_bfamily Ordinal.derivBFamilyₓ'. -/
 /-- The derivative of a family of normal functions is the sequence of their common fixed points.
 
 This is defined as `ordinal.deriv_family` of the type-indexed family associated to `f`. -/
 def derivBFamily (o : Ordinal) (f : ∀ b < o, Ordinal → Ordinal) : Ordinal → Ordinal :=
   derivFamily (familyOfBFamily o f)
 #align ordinal.deriv_bfamily Ordinal.derivBFamily
--/
 
-#print Ordinal.derivBFamily_eq_derivFamily /-
+/- warning: ordinal.deriv_bfamily_eq_deriv_family -> Ordinal.derivBFamily_eq_derivFamily is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}} (f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}), Eq.{succ (succ (max u1 u2))} (Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}) (Ordinal.derivBFamily.{u1, u2} o f) (Ordinal.derivFamily.{u1, u2} (WellOrder.α.{u1} (Quotient.out.{succ (succ u1)} WellOrder.{u1} Ordinal.isEquivalent.{u1} o)) (Ordinal.familyOfBFamily.{succ (max u1 u2), u1} (Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}) o f))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.deriv_bfamily_eq_deriv_family Ordinal.derivBFamily_eq_derivFamilyₓ'. -/
 theorem derivBFamily_eq_derivFamily {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal) :
     derivBFamily o f = derivFamily (familyOfBFamily o f) :=
   rfl
 #align ordinal.deriv_bfamily_eq_deriv_family Ordinal.derivBFamily_eq_derivFamily
--/
 
 /- warning: ordinal.deriv_bfamily_is_normal -> Ordinal.derivBFamily_isNormal is a dubious translation:
 lean 3 declaration is
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+  forall {o : Ordinal.{u1}} (f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}), Ordinal.IsNormal.{max u1 u2, max u1 u2} (Ordinal.derivBFamily.{u1, u2} o f)
 but is expected to have type
   forall {o : Ordinal.{u2}} (f : forall (b : Ordinal.{u2}), (LT.lt.{succ u2} Ordinal.{u2} (Preorder.toLT.{succ u2} Ordinal.{u2} (PartialOrder.toPreorder.{succ u2} Ordinal.{u2} Ordinal.partialOrder.{u2})) b o) -> Ordinal.{max u2 u1} -> Ordinal.{max u2 u1}), Ordinal.IsNormal.{max u1 u2, max u1 u2} (Ordinal.derivBFamily.{u2, u1} o f)
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_bfamily_is_normal Ordinal.derivBFamily_isNormalₓ'. -/
@@ -480,7 +596,12 @@ theorem derivBFamily_isNormal {o : Ordinal} (f : ∀ b < o, Ordinal → Ordinal)
   derivFamily_isNormal _
 #align ordinal.deriv_bfamily_is_normal Ordinal.derivBFamily_isNormal
 
-#print Ordinal.derivBFamily_fp /-
+/- warning: ordinal.deriv_bfamily_fp -> Ordinal.derivBFamily_fp is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {i : Ordinal.{u1}} {hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o}, (Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i hi)) -> (forall (a : Ordinal.{max u1 u2}), Eq.{succ (succ (max u1 u2))} Ordinal.{max u1 u2} (f i hi (Ordinal.derivBFamily.{u1, u2} o f a)) (Ordinal.derivBFamily.{u1, u2} o f a))
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+  forall {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}} {i : Ordinal.{u1}} {hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o}, (Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i hi)) -> (forall (a : Ordinal.{max u1 u2}), Eq.{max (succ (succ u1)) (succ (succ u2))} Ordinal.{max u1 u2} (f i hi (Ordinal.derivBFamily.{u1, u2} o f a)) (Ordinal.derivBFamily.{u1, u2} o f a))
+Case conversion may be inaccurate. Consider using '#align ordinal.deriv_bfamily_fp Ordinal.derivBFamily_fpₓ'. -/
 theorem derivBFamily_fp {i hi} (H : IsNormal (f i hi)) (a : Ordinal) :
     f i hi (derivBFamily o f a) = derivBFamily o f a :=
   by
@@ -489,9 +610,13 @@ theorem derivBFamily_fp {i hi} (H : IsNormal (f i hi)) (a : Ordinal) :
   rw [family_of_bfamily_enum]
   exact H
 #align ordinal.deriv_bfamily_fp Ordinal.derivBFamily_fp
--/
 
-#print Ordinal.le_iff_derivBFamily /-
+/- warning: ordinal.le_iff_deriv_bfamily -> Ordinal.le_iff_derivBFamily is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i hi)) -> (forall {a : Ordinal.{max u1 u2}}, Iff (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), 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})) (f i hi a) a) (Exists.{succ (succ (max u1 u2))} Ordinal.{max u1 u2} (fun (b : Ordinal.{max u1 u2}) => Eq.{succ (succ (max u1 u2))} Ordinal.{max u1 u2} (Ordinal.derivBFamily.{u1, u2} o f b) a)))
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+Case conversion may be inaccurate. Consider using '#align ordinal.le_iff_deriv_bfamily Ordinal.le_iff_derivBFamilyₓ'. -/
 theorem le_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
     (∀ i hi, f i hi a ≤ a) ↔ ∃ b, derivBFamily o f b = a :=
   by
@@ -502,9 +627,13 @@ theorem le_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
     apply h
   · exact fun _ => H _ _
 #align ordinal.le_iff_deriv_bfamily Ordinal.le_iff_derivBFamily
--/
 
-#print Ordinal.fp_iff_derivBFamily /-
+/- warning: ordinal.fp_iff_deriv_bfamily -> Ordinal.fp_iff_derivBFamily 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.fp_iff_deriv_bfamily Ordinal.fp_iff_derivBFamilyₓ'. -/
 theorem fp_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
     (∀ i hi, f i hi a = a) ↔ ∃ b, derivBFamily o f b = a :=
   by
@@ -513,10 +642,14 @@ theorem fp_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
   rw [← (H i hi).le_iff_eq]
   exact h i hi
 #align ordinal.fp_iff_deriv_bfamily Ordinal.fp_iff_derivBFamily
--/
 
+/- warning: ordinal.deriv_bfamily_eq_enum_ord -> Ordinal.derivBFamily_eq_enumOrd 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.deriv_bfamily_eq_enum_ord Ordinal.derivBFamily_eq_enumOrdₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
-#print Ordinal.derivBFamily_eq_enumOrd /-
 /-- For a family of normal functions, `ordinal.deriv_bfamily` enumerates the common fixed points. -/
 theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
     derivBFamily o f = enumOrd (⋂ (i) (hi), Function.fixedPoints (f i hi)) :=
@@ -528,7 +661,6 @@ theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
   rw [Set.mem_iInter₂] at ha
   rwa [← fp_iff_deriv_bfamily H]
 #align ordinal.deriv_bfamily_eq_enum_ord Ordinal.derivBFamily_eq_enumOrd
--/
 
 end
 
@@ -569,41 +701,61 @@ theorem sup_iterate_eq_nfp (f : Ordinal.{u} → Ordinal.{u}) :
 #align ordinal.sup_iterate_eq_nfp Ordinal.sup_iterate_eq_nfp
 -/
 
-#print Ordinal.iterate_le_nfp /-
+/- warning: ordinal.iterate_le_nfp -> Ordinal.iterate_le_nfp 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.iterate_le_nfp Ordinal.iterate_le_nfpₓ'. -/
 theorem iterate_le_nfp (f a n) : (f^[n]) a ≤ nfp f a :=
   by
   rw [← sup_iterate_eq_nfp]
   exact le_sup _ n
 #align ordinal.iterate_le_nfp Ordinal.iterate_le_nfp
--/
 
-#print Ordinal.le_nfp /-
+/- warning: ordinal.le_nfp -> Ordinal.le_nfp is a dubious translation:
+lean 3 declaration is
+  forall (f : Ordinal.{u1} -> Ordinal.{u1}) (a : Ordinal.{u1}), LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (Ordinal.nfp.{u1} f a)
+but is expected to have type
+  forall (f : Ordinal.{u1} -> Ordinal.{u1}) (a : Ordinal.{u1}), LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (Ordinal.nfp.{u1} f a)
+Case conversion may be inaccurate. Consider using '#align ordinal.le_nfp Ordinal.le_nfpₓ'. -/
 theorem le_nfp (f a) : a ≤ nfp f a :=
   iterate_le_nfp f a 0
 #align ordinal.le_nfp Ordinal.le_nfp
--/
 
-#print Ordinal.lt_nfp /-
+/- warning: ordinal.lt_nfp -> Ordinal.lt_nfp is a dubious translation:
+lean 3 declaration is
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}} {a : Ordinal.{u1}} {b : 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 (Ordinal.nfp.{u1} f b)) (Exists.{1} Nat (fun (n : Nat) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (Nat.iterate.{succ (succ u1)} Ordinal.{u1} f n b)))
+but is expected to have type
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}} {a : Ordinal.{u1}} {b : 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 (Ordinal.nfp.{u1} f b)) (Exists.{1} Nat (fun (n : Nat) => LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) a (Nat.iterate.{succ (succ u1)} Ordinal.{u1} f n b)))
+Case conversion may be inaccurate. Consider using '#align ordinal.lt_nfp Ordinal.lt_nfpₓ'. -/
 theorem lt_nfp {a b} : a < nfp f b ↔ ∃ n, a < (f^[n]) b :=
   by
   rw [← sup_iterate_eq_nfp]
   exact lt_sup
 #align ordinal.lt_nfp Ordinal.lt_nfp
--/
 
-#print Ordinal.nfp_le_iff /-
+/- warning: ordinal.nfp_le_iff -> Ordinal.nfp_le_iff is a dubious translation:
+lean 3 declaration is
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}} {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfp.{u1} f a) b) (forall (n : Nat), LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Nat.iterate.{succ (succ u1)} Ordinal.{u1} f n a) b)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_le_iff Ordinal.nfp_le_iffₓ'. -/
 theorem nfp_le_iff {a b} : nfp f a ≤ b ↔ ∀ n, (f^[n]) a ≤ b :=
   by
   rw [← sup_iterate_eq_nfp]
   exact sup_le_iff
 #align ordinal.nfp_le_iff Ordinal.nfp_le_iff
--/
 
-#print Ordinal.nfp_le /-
+/- warning: ordinal.nfp_le -> Ordinal.nfp_le is a dubious translation:
+lean 3 declaration is
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}} {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (forall (n : Nat), LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Nat.iterate.{succ (succ u1)} Ordinal.{u1} f n a) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfp.{u1} f a) b)
+but is expected to have type
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}} {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (forall (n : Nat), LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Nat.iterate.{succ (succ u1)} Ordinal.{u1} f n a) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfp.{u1} f a) b)
+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_le Ordinal.nfp_leₓ'. -/
 theorem nfp_le {a b} : (∀ n, (f^[n]) a ≤ b) → nfp f a ≤ b :=
   nfp_le_iff.2
 #align ordinal.nfp_le Ordinal.nfp_le
--/
 
 #print Ordinal.nfp_id /-
 @[simp]
@@ -620,26 +772,38 @@ theorem nfp_monotone (hf : Monotone f) : Monotone (nfp f) :=
 #align ordinal.nfp_monotone Ordinal.nfp_monotone
 -/
 
-#print Ordinal.IsNormal.apply_lt_nfp /-
+/- warning: ordinal.is_normal.apply_lt_nfp -> Ordinal.IsNormal.apply_lt_nfp is a dubious translation:
+lean 3 declaration is
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}}, (Ordinal.IsNormal.{u1, u1} f) -> (forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f b) (Ordinal.nfp.{u1} f a)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (Ordinal.nfp.{u1} f a)))
+but is expected to have type
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}}, (Ordinal.IsNormal.{u1, u1} f) -> (forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f b) (Ordinal.nfp.{u1} f a)) (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (Ordinal.nfp.{u1} f a)))
+Case conversion may be inaccurate. Consider using '#align ordinal.is_normal.apply_lt_nfp Ordinal.IsNormal.apply_lt_nfpₓ'. -/
 theorem IsNormal.apply_lt_nfp {f} (H : IsNormal f) {a b} : f b < nfp f a ↔ b < nfp f a :=
   by
   unfold nfp
   rw [← @apply_lt_nfp_family_iff Unit (fun _ => f) _ (fun _ => H) a b]
   exact ⟨fun h _ => h, fun h => h Unit.unit⟩
 #align ordinal.is_normal.apply_lt_nfp Ordinal.IsNormal.apply_lt_nfp
--/
 
-#print Ordinal.IsNormal.nfp_le_apply /-
+/- warning: ordinal.is_normal.nfp_le_apply -> Ordinal.IsNormal.nfp_le_apply is a dubious translation:
+lean 3 declaration is
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}}, (Ordinal.IsNormal.{u1, u1} f) -> (forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfp.{u1} f a) (f b)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfp.{u1} f a) b))
+but is expected to have type
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}}, (Ordinal.IsNormal.{u1, u1} f) -> (forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfp.{u1} f a) (f b)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfp.{u1} f a) b))
+Case conversion may be inaccurate. Consider using '#align ordinal.is_normal.nfp_le_apply Ordinal.IsNormal.nfp_le_applyₓ'. -/
 theorem IsNormal.nfp_le_apply {f} (H : IsNormal f) {a b} : nfp f a ≤ f b ↔ nfp f a ≤ b :=
   le_iff_le_iff_lt_iff_lt.2 H.apply_lt_nfp
 #align ordinal.is_normal.nfp_le_apply Ordinal.IsNormal.nfp_le_apply
--/
 
-#print Ordinal.nfp_le_fp /-
+/- warning: ordinal.nfp_le_fp -> Ordinal.nfp_le_fp is a dubious translation:
+lean 3 declaration is
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}}, (Monotone.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) f) -> (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 b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f b) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (Ordinal.nfp.{u1} f a) b))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ordinal.nfp_le_fp Ordinal.nfp_le_fpₓ'. -/
 theorem nfp_le_fp {f} (H : Monotone f) {a b} (ab : a ≤ b) (h : f b ≤ b) : nfp f a ≤ b :=
   nfpFamily_le_fp (fun _ => H) ab fun _ => h
 #align ordinal.nfp_le_fp Ordinal.nfp_le_fp
--/
 
 #print Ordinal.IsNormal.nfp_fp /-
 theorem IsNormal.nfp_fp {f} (H : IsNormal f) : ∀ a, f (nfp f a) = nfp f a :=
@@ -647,11 +811,15 @@ theorem IsNormal.nfp_fp {f} (H : IsNormal f) : ∀ a, f (nfp f a) = nfp f a :=
 #align ordinal.is_normal.nfp_fp Ordinal.IsNormal.nfp_fp
 -/
 
-#print Ordinal.IsNormal.apply_le_nfp /-
+/- warning: ordinal.is_normal.apply_le_nfp -> Ordinal.IsNormal.apply_le_nfp is a dubious translation:
+lean 3 declaration is
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}}, (Ordinal.IsNormal.{u1, u1} f) -> (forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f b) (Ordinal.nfp.{u1} f a)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (Ordinal.nfp.{u1} f a)))
+but is expected to have type
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}}, (Ordinal.IsNormal.{u1, u1} f) -> (forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f b) (Ordinal.nfp.{u1} f a)) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (Ordinal.nfp.{u1} f a)))
+Case conversion may be inaccurate. Consider using '#align ordinal.is_normal.apply_le_nfp Ordinal.IsNormal.apply_le_nfpₓ'. -/
 theorem IsNormal.apply_le_nfp {f} (H : IsNormal f) {a b} : f b ≤ nfp f a ↔ b ≤ nfp f a :=
   ⟨le_trans (H.self_le _), fun h => by simpa only [H.nfp_fp] using H.le_iff.2 h⟩
 #align ordinal.is_normal.apply_le_nfp Ordinal.IsNormal.apply_le_nfp
--/
 
 #print Ordinal.nfp_eq_self /-
 theorem nfp_eq_self {f : Ordinal → Ordinal} {a} (h : f a = a) : nfp f a = a :=
@@ -659,7 +827,12 @@ theorem nfp_eq_self {f : Ordinal → Ordinal} {a} (h : f a = a) : nfp f a = a :=
 #align ordinal.nfp_eq_self Ordinal.nfp_eq_self
 -/
 
-#print Ordinal.fp_unbounded /-
+/- warning: ordinal.fp_unbounded -> Ordinal.fp_unbounded is a dubious translation:
+lean 3 declaration is
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}}, (Ordinal.IsNormal.{u1, u1} f) -> (Set.Unbounded.{succ u1} Ordinal.{u1} (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}))) (Function.fixedPoints.{succ u1} Ordinal.{u1} f))
+but is expected to have type
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}}, (Ordinal.IsNormal.{u1, u1} f) -> (Set.Unbounded.{succ u1} Ordinal.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5212 : Ordinal.{u1}) (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5214 : 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.FixedPoint._hyg.5212 x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5214) (Function.fixedPoints.{succ u1} Ordinal.{u1} f))
+Case conversion may be inaccurate. Consider using '#align ordinal.fp_unbounded Ordinal.fp_unboundedₓ'. -/
 /-- The fixed point lemma for normal functions: any normal function has an unbounded set of
 fixed points. -/
 theorem fp_unbounded (H : IsNormal f) : (Function.fixedPoints f).Unbounded (· < ·) :=
@@ -667,7 +840,6 @@ theorem fp_unbounded (H : IsNormal f) : (Function.fixedPoints f).Unbounded (· <
   convert fp_family_unbounded fun _ : Unit => H
   exact (Set.iInter_const _).symm
 #align ordinal.fp_unbounded Ordinal.fp_unbounded
--/
 
 #print Ordinal.deriv /-
 /-- The derivative of a normal function `f` is the sequence of fixed points of `f`.
@@ -722,14 +894,18 @@ theorem IsNormal.deriv_fp {f} (H : IsNormal f) : ∀ o, f (deriv f o) = deriv f
 #align ordinal.is_normal.deriv_fp Ordinal.IsNormal.deriv_fp
 -/
 
-#print Ordinal.IsNormal.le_iff_deriv /-
+/- warning: ordinal.is_normal.le_iff_deriv -> Ordinal.IsNormal.le_iff_deriv is a dubious translation:
+lean 3 declaration is
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}}, (Ordinal.IsNormal.{u1, u1} f) -> (forall {a : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (f a) a) (Exists.{succ (succ u1)} Ordinal.{u1} (fun (o : Ordinal.{u1}) => Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} f o) a)))
+but is expected to have type
+  forall {f : Ordinal.{u1} -> Ordinal.{u1}}, (Ordinal.IsNormal.{u1, u1} f) -> (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})) (f a) a) (Exists.{succ (succ u1)} Ordinal.{u1} (fun (o : Ordinal.{u1}) => Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} f o) a)))
+Case conversion may be inaccurate. Consider using '#align ordinal.is_normal.le_iff_deriv Ordinal.IsNormal.le_iff_derivₓ'. -/
 theorem IsNormal.le_iff_deriv {f} (H : IsNormal f) {a} : f a ≤ a ↔ ∃ o, deriv f o = a :=
   by
   unfold deriv
   rw [← le_iff_deriv_family fun _ : Unit => H]
   exact ⟨fun h _ => h, fun h => h Unit.unit⟩
 #align ordinal.is_normal.le_iff_deriv Ordinal.IsNormal.le_iff_deriv
--/
 
 #print Ordinal.IsNormal.fp_iff_deriv /-
 theorem IsNormal.fp_iff_deriv {f} (H : IsNormal f) {a} : f a = a ↔ ∃ o, deriv f o = a := by
@@ -776,7 +952,7 @@ theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
 
 /- warning: ordinal.nfp_add_eq_mul_omega -> Ordinal.nfp_add_eq_mul_omega is a dubious translation:
 lean 3 declaration is
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+  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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
 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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5911 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5911) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_add_eq_mul_omega Ordinal.nfp_add_eq_mul_omegaₓ'. -/
@@ -790,7 +966,7 @@ theorem nfp_add_eq_mul_omega {a b} (hba : b ≤ a * omega) : nfp ((· + ·) a) b
 
 /- warning: ordinal.add_eq_right_iff_mul_omega_le -> Ordinal.add_eq_right_iff_mul_omega_le is a dubious translation:
 lean 3 declaration is
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (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}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (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}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 but is expected to have type
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (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}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 Case conversion may be inaccurate. Consider using '#align ordinal.add_eq_right_iff_mul_omega_le Ordinal.add_eq_right_iff_mul_omega_leₓ'. -/
@@ -808,7 +984,7 @@ theorem add_eq_right_iff_mul_omega_le {a b : Ordinal} : a + b = b ↔ a * omega
 
 /- warning: ordinal.add_le_right_iff_mul_omega_le -> Ordinal.add_le_right_iff_mul_omega_le is a dubious translation:
 lean 3 declaration is
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 but is expected to have type
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 Case conversion may be inaccurate. Consider using '#align ordinal.add_le_right_iff_mul_omega_le Ordinal.add_le_right_iff_mul_omega_leₓ'. -/
@@ -843,7 +1019,7 @@ local infixr:0 "^" => @pow Ordinal Ordinal Ordinal.hasPow
 
 /- warning: ordinal.nfp_mul_one -> Ordinal.nfp_mul_one is a dubious translation:
 lean 3 declaration is
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+  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{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})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
 but is expected to have type
   forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6456 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6456) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_one Ordinal.nfp_mul_oneₓ'. -/
@@ -907,7 +1083,7 @@ theorem deriv_mul_zero : deriv ((· * ·) 0) = id :=
 
 /- warning: ordinal.nfp_mul_eq_opow_omega -> Ordinal.nfp_mul_eq_opow_omega is a dubious translation:
 lean 3 declaration is
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
 but is expected to have type
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6933 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6933) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_eq_opow_omega Ordinal.nfp_mul_eq_opow_omegaₓ'. -/
@@ -927,7 +1103,7 @@ theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega
 
 /- warning: ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right -> Ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right is a dubious translation:
 lean 3 declaration is
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+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (Eq.{succ (succ u1)} Ordinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) -> (Or (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})))) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
 but is expected to have type
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (Eq.{succ (succ u1)} Ordinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) -> (Or (Eq.{succ (succ u1)} Ordinal.{u1} b (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
 Case conversion may be inaccurate. Consider using '#align ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right Ordinal.eq_zero_or_opow_omega_le_of_mul_eq_rightₓ'. -/
@@ -970,7 +1146,7 @@ theorem mul_eq_right_iff_opow_omega_dvd {a b : Ordinal} : a * b = b ↔ (a^omega
 
 /- warning: ordinal.mul_le_right_iff_opow_omega_dvd -> Ordinal.mul_le_right_iff_opow_omega_dvd is a dubious translation:
 lean 3 declaration is
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) (Dvd.Dvd.{succ u1} Ordinal.{u1} (semigroupDvd.{succ u1} Ordinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Ordinal.{u1} (MonoidWithZero.toSemigroupWithZero.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) (Dvd.Dvd.{succ u1} Ordinal.{u1} (semigroupDvd.{succ u1} Ordinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Ordinal.{u1} (MonoidWithZero.toSemigroupWithZero.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
 but is expected to have type
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) (Dvd.dvd.{succ u1} Ordinal.{u1} (semigroupDvd.{succ u1} Ordinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Ordinal.{u1} (MonoidWithZero.toSemigroupWithZero.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
 Case conversion may be inaccurate. Consider using '#align ordinal.mul_le_right_iff_opow_omega_dvd Ordinal.mul_le_right_iff_opow_omega_dvdₓ'. -/
@@ -982,7 +1158,7 @@ theorem mul_le_right_iff_opow_omega_dvd {a b : Ordinal} (ha : 0 < a) : a * b ≤
 
 /- warning: ordinal.nfp_mul_opow_omega_add -> Ordinal.nfp_mul_opow_omega_add is a dubious translation:
 lean 3 declaration is
-  forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (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}))) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
+  forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (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}))) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toHasLe.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
 but is expected to have type
   forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (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})) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7632 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7632) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_opow_omega_add Ordinal.nfp_mul_opow_omega_addₓ'. -/
@@ -1007,7 +1183,7 @@ theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hc
 
 /- warning: ordinal.deriv_mul_eq_opow_omega_mul -> Ordinal.deriv_mul_eq_opow_omega_mul is a dubious translation:
 lean 3 declaration is
-  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
+  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toHasLt.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
 but is expected to have type
   forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7992 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7992) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_mul_eq_opow_omega_mul Ordinal.deriv_mul_eq_opow_omega_mulₓ'. -/

0dd4319a

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -303,7 +303,7 @@ theorem derivFamily_eq_enumOrd (H : ∀ i, IsNormal (f i)) :
   · rintro a S ⟨i, hi⟩
     rw [← hi]
     exact deriv_family_fp (H i) a
-  rw [Set.mem_interᵢ] at ha
+  rw [Set.mem_iInter] at ha
   rwa [← fp_iff_deriv_family H]
 #align ordinal.deriv_family_eq_enum_ord Ordinal.derivFamily_eq_enumOrd
 -/
@@ -448,7 +448,7 @@ theorem nfpBFamily_eq_self {a} (h : ∀ i hi, f i hi a = a) : nfpBFamily o f a =
 theorem fp_bfamily_unbounded (H : ∀ i hi, IsNormal (f i hi)) :
     (⋂ (i) (hi), Function.fixedPoints (f i hi)).Unbounded (· < ·) := fun a =>
   ⟨_, by
-    rw [Set.mem_interᵢ₂]
+    rw [Set.mem_iInter₂]
     exact fun i hi => nfp_bfamily_fp (H i hi) _, (le_nfpBFamily f a).not_lt⟩
 #align ordinal.fp_bfamily_unbounded Ordinal.fp_bfamily_unbounded
 -/
@@ -524,8 +524,8 @@ theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
   rw [← eq_enum_ord _ (fp_bfamily_unbounded H)]
   use (deriv_bfamily_is_normal f).StrictMono
   rw [Set.range_eq_iff]
-  refine' ⟨fun a => Set.mem_interᵢ₂.2 fun i hi => deriv_bfamily_fp (H i hi) a, fun a ha => _⟩
-  rw [Set.mem_interᵢ₂] at ha
+  refine' ⟨fun a => Set.mem_iInter₂.2 fun i hi => deriv_bfamily_fp (H i hi) a, fun a ha => _⟩
+  rw [Set.mem_iInter₂] at ha
   rwa [← fp_iff_deriv_bfamily H]
 #align ordinal.deriv_bfamily_eq_enum_ord Ordinal.derivBFamily_eq_enumOrd
 -/
@@ -665,7 +665,7 @@ fixed points. -/
 theorem fp_unbounded (H : IsNormal f) : (Function.fixedPoints f).Unbounded (· < ·) :=
   by
   convert fp_family_unbounded fun _ : Unit => H
-  exact (Set.interᵢ_const _).symm
+  exact (Set.iInter_const _).symm
 #align ordinal.fp_unbounded Ordinal.fp_unbounded
 -/
 
@@ -742,7 +742,7 @@ theorem IsNormal.fp_iff_deriv {f} (H : IsNormal f) {a} : f a = a ↔ ∃ o, deri
 theorem deriv_eq_enumOrd (H : IsNormal f) : deriv f = enumOrd (Function.fixedPoints f) :=
   by
   convert deriv_family_eq_enum_ord fun _ : Unit => H
-  exact (Set.interᵢ_const _).symm
+  exact (Set.iInter_const _).symm
 #align ordinal.deriv_eq_enum_ord Ordinal.deriv_eq_enumOrd
 -/

0dd4319a

bump to nightly-2023-05-03-22

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

aa7b8e08

Diff

@@ -761,7 +761,7 @@ end
 lean 3 declaration is
   forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{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})))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
 but is expected to have type
-  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5776 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5776) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
+  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5774 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5774) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_add_zero Ordinal.nfp_add_zeroₓ'. -/
 @[simp]
 theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
@@ -778,7 +778,7 @@ theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
 lean 3 declaration is
   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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
 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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5915 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5915) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
+  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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5911 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5911) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_add_eq_mul_omega Ordinal.nfp_add_eq_mul_omegaₓ'. -/
 theorem nfp_add_eq_mul_omega {a b} (hba : b ≤ a * omega) : nfp ((· + ·) a) b = a * omega :=
   by
@@ -822,7 +822,7 @@ theorem add_le_right_iff_mul_omega_le {a b : Ordinal} : a + b ≤ b ↔ a * omeg
 lean 3 declaration is
   forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 but is expected to have type
-  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6291 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6291) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
+  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6287 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6287) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_add_eq_mul_omega_add Ordinal.deriv_add_eq_mul_omega_addₓ'. -/
 theorem deriv_add_eq_mul_omega_add (a b : Ordinal.{u}) : deriv ((· + ·) a) b = a * omega + b :=
   by
@@ -845,7 +845,7 @@ local infixr:0 "^" => @pow Ordinal Ordinal Ordinal.hasPow
 lean 3 declaration is
   forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{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})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
 but is expected to have type
-  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6460 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6460) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
+  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6456 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6456) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_one Ordinal.nfp_mul_oneₓ'. -/
 @[simp]
 theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega) :=
@@ -865,7 +865,7 @@ theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega)
 lean 3 declaration is
   forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{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})))) (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}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6621 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6621) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
+  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6617 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6617) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_zero Ordinal.nfp_mul_zeroₓ'. -/
 @[simp]
 theorem nfp_mul_zero (a : Ordinal) : nfp ((· * ·) a) 0 = 0 :=
@@ -909,7 +909,7 @@ theorem deriv_mul_zero : deriv ((· * ·) 0) = id :=
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
 but is expected to have type
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6937 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6937) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6933 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6933) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_eq_opow_omega Ordinal.nfp_mul_eq_opow_omegaₓ'. -/
 theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega)) :
     nfp ((· * ·) a) b = (a^omega.{u}) :=
@@ -984,7 +984,7 @@ theorem mul_le_right_iff_opow_omega_dvd {a b : Ordinal} (ha : 0 < a) : a * b ≤
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (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}))) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
 but is expected to have type
-  forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (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})) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7636 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7636) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
+  forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (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})) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7632 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7632) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_opow_omega_add Ordinal.nfp_mul_opow_omega_addₓ'. -/
 theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hca : c ≤ (a^omega)) :
     nfp ((· * ·) a) ((a^omega) * b + c) = (a^omega.{u}) * succ b :=
@@ -1009,7 +1009,7 @@ theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hc
 lean 3 declaration is
   forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
 but is expected to have type
-  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7996 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7996) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
+  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7992 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7992) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_mul_eq_opow_omega_mul Ordinal.deriv_mul_eq_opow_omega_mulₓ'. -/
 theorem deriv_mul_eq_opow_omega_mul {a : Ordinal.{u}} (ha : 0 < a) (b) :
     deriv ((· * ·) a) b = (a^omega) * b := by

0dd4319a

bump to nightly-2023-04-01-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

bfc4190c

Diff

@@ -761,7 +761,7 @@ end
 lean 3 declaration is
   forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{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})))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
 but is expected to have type
-  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5798 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5798) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
+  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5776 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5776) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_add_zero Ordinal.nfp_add_zeroₓ'. -/
 @[simp]
 theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
@@ -778,7 +778,7 @@ theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
 lean 3 declaration is
   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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
 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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5937 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5937) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
+  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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5915 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5915) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_add_eq_mul_omega Ordinal.nfp_add_eq_mul_omegaₓ'. -/
 theorem nfp_add_eq_mul_omega {a b} (hba : b ≤ a * omega) : nfp ((· + ·) a) b = a * omega :=
   by
@@ -822,7 +822,7 @@ theorem add_le_right_iff_mul_omega_le {a b : Ordinal} : a + b ≤ b ↔ a * omeg
 lean 3 declaration is
   forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 but is expected to have type
-  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6313 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6313) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
+  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6291 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6291) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_add_eq_mul_omega_add Ordinal.deriv_add_eq_mul_omega_addₓ'. -/
 theorem deriv_add_eq_mul_omega_add (a b : Ordinal.{u}) : deriv ((· + ·) a) b = a * omega + b :=
   by
@@ -845,7 +845,7 @@ local infixr:0 "^" => @pow Ordinal Ordinal Ordinal.hasPow
 lean 3 declaration is
   forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{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})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
 but is expected to have type
-  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6482 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6482) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
+  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6460 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6460) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_one Ordinal.nfp_mul_oneₓ'. -/
 @[simp]
 theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega) :=
@@ -865,7 +865,7 @@ theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega)
 lean 3 declaration is
   forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{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})))) (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}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6643 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6643) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
+  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6621 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6621) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_zero Ordinal.nfp_mul_zeroₓ'. -/
 @[simp]
 theorem nfp_mul_zero (a : Ordinal) : nfp ((· * ·) a) 0 = 0 :=
@@ -909,7 +909,7 @@ theorem deriv_mul_zero : deriv ((· * ·) 0) = id :=
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
 but is expected to have type
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6959 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6959) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6937 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6937) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_eq_opow_omega Ordinal.nfp_mul_eq_opow_omegaₓ'. -/
 theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega)) :
     nfp ((· * ·) a) b = (a^omega.{u}) :=
@@ -984,7 +984,7 @@ theorem mul_le_right_iff_opow_omega_dvd {a b : Ordinal} (ha : 0 < a) : a * b ≤
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (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}))) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
 but is expected to have type
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+  forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (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})) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7636 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7636) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_opow_omega_add Ordinal.nfp_mul_opow_omega_addₓ'. -/
 theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hca : c ≤ (a^omega)) :
     nfp ((· * ·) a) ((a^omega) * b + c) = (a^omega.{u}) * succ b :=
@@ -1009,7 +1009,7 @@ theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hc
 lean 3 declaration is
   forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
 but is expected to have type
-  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.8018 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.8018) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
+  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7996 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7996) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_mul_eq_opow_omega_mul Ordinal.deriv_mul_eq_opow_omega_mulₓ'. -/
 theorem deriv_mul_eq_opow_omega_mul {a : Ordinal.{u}} (ha : 0 < a) (b) :
     deriv ((· * ·) a) b = (a^omega) * b := by

0dd4319a

bump to nightly-2023-03-29-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/0148d455199ed64bf8eb2f493a1e7eb9211ce170

5cbaeba8

Diff

@@ -374,12 +374,7 @@ theorem nfpBFamily_monotone (hf : ∀ i hi, Monotone (f i hi)) : Monotone (nfpBF
 #align ordinal.nfp_bfamily_monotone Ordinal.nfpBFamily_monotone
 -/
 
-/- warning: ordinal.apply_lt_nfp_bfamily -> Ordinal.apply_lt_nfpBFamily is a dubious translation:
-lean 3 declaration is
-  forall {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i hi)) -> (forall {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b (Ordinal.nfpBFamily.{u1, u2} o f a)) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i hi b) (Ordinal.nfpBFamily.{u1, u2} o f a)))
-but is expected to have type
-  forall {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (Ne.{succ (succ u1)} Ordinal.{u1} o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i hi)) -> (forall {b : Ordinal.{max u2 u1}} {hb : Ordinal.{max u1 u2}}, Iff (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i hi hb) (Ordinal.nfpBFamily.{u1, u2} o f b)) (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})) hb (Ordinal.nfpBFamily.{u1, u2} o f b)))
-Case conversion may be inaccurate. Consider using '#align ordinal.apply_lt_nfp_bfamily Ordinal.apply_lt_nfpBFamilyₓ'. -/
+#print Ordinal.apply_lt_nfpBFamily /-
 theorem apply_lt_nfpBFamily (H : ∀ i hi, IsNormal (f i hi)) {a b} (hb : b < nfpBFamily o f a)
     (i hi) : f i hi b < nfpBFamily o f a :=
   by
@@ -387,7 +382,9 @@ theorem apply_lt_nfpBFamily (H : ∀ i hi, IsNormal (f i hi)) {a b} (hb : b < nf
   apply apply_lt_nfp_family _ hb
   exact fun _ => H _ _
 #align ordinal.apply_lt_nfp_bfamily Ordinal.apply_lt_nfpBFamily
+-/
 
+#print Ordinal.apply_lt_nfpBFamily_iff /-
 theorem apply_lt_nfpBFamily_iff (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
     (∀ i hi, f i hi b < nfpBFamily o f a) ↔ b < nfpBFamily o f a :=
   ⟨fun h => by
@@ -395,6 +392,7 @@ theorem apply_lt_nfpBFamily_iff (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi))
     refine' (apply_lt_nfp_family_iff _).1 fun _ => h _ _
     exact fun _ => H _ _, apply_lt_nfpBFamily H⟩
 #align ordinal.apply_lt_nfp_bfamily_iff Ordinal.apply_lt_nfpBFamily_iff
+-/
 
 #print Ordinal.nfpBFamily_le_apply /-
 theorem nfpBFamily_le_apply (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
@@ -763,7 +761,7 @@ end
 lean 3 declaration is
   forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{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})))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
 but is expected to have type
-  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5742 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5742) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
+  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5798 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5798) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_add_zero Ordinal.nfp_add_zeroₓ'. -/
 @[simp]
 theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
@@ -780,7 +778,7 @@ theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
 lean 3 declaration is
   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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
 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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5881 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5881) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
+  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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5937 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5937) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_add_eq_mul_omega Ordinal.nfp_add_eq_mul_omegaₓ'. -/
 theorem nfp_add_eq_mul_omega {a b} (hba : b ≤ a * omega) : nfp ((· + ·) a) b = a * omega :=
   by
@@ -824,7 +822,7 @@ theorem add_le_right_iff_mul_omega_le {a b : Ordinal} : a + b ≤ b ↔ a * omeg
 lean 3 declaration is
   forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 but is expected to have type
-  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6257 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6257) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
+  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6313 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6313) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_add_eq_mul_omega_add Ordinal.deriv_add_eq_mul_omega_addₓ'. -/
 theorem deriv_add_eq_mul_omega_add (a b : Ordinal.{u}) : deriv ((· + ·) a) b = a * omega + b :=
   by
@@ -847,7 +845,7 @@ local infixr:0 "^" => @pow Ordinal Ordinal Ordinal.hasPow
 lean 3 declaration is
   forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{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})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
 but is expected to have type
-  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6426 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6426) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
+  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6482 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6482) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_one Ordinal.nfp_mul_oneₓ'. -/
 @[simp]
 theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega) :=
@@ -867,7 +865,7 @@ theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega)
 lean 3 declaration is
   forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{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})))) (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}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6587 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6587) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
+  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6643 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6643) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_zero Ordinal.nfp_mul_zeroₓ'. -/
 @[simp]
 theorem nfp_mul_zero (a : Ordinal) : nfp ((· * ·) a) 0 = 0 :=
@@ -911,7 +909,7 @@ theorem deriv_mul_zero : deriv ((· * ·) 0) = id :=
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
 but is expected to have type
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6903 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6903) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6959 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6959) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_eq_opow_omega Ordinal.nfp_mul_eq_opow_omegaₓ'. -/
 theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega)) :
     nfp ((· * ·) a) b = (a^omega.{u}) :=
@@ -986,7 +984,7 @@ theorem mul_le_right_iff_opow_omega_dvd {a b : Ordinal} (ha : 0 < a) : a * b ≤
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (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}))) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
 but is expected to have type
-  forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (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})) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7602 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7602) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
+  forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (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})) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7658 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7658) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_opow_omega_add Ordinal.nfp_mul_opow_omega_addₓ'. -/
 theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hca : c ≤ (a^omega)) :
     nfp ((· * ·) a) ((a^omega) * b + c) = (a^omega.{u}) * succ b :=
@@ -1011,7 +1009,7 @@ theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hc
 lean 3 declaration is
   forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
 but is expected to have type
-  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7962 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7962) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
+  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.8018 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.8018) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_mul_eq_opow_omega_mul Ordinal.deriv_mul_eq_opow_omega_mulₓ'. -/
 theorem deriv_mul_eq_opow_omega_mul {a : Ordinal.{u}} (ha : 0 < a) (b) :
     deriv ((· * ·) a) b = (a^omega) * b := by

0dd4319a

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -763,7 +763,7 @@ end
 lean 3 declaration is
   forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{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})))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
 but is expected to have type
-  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5664 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5664) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
+  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5742 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5742) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_add_zero Ordinal.nfp_add_zeroₓ'. -/
 @[simp]
 theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
@@ -780,7 +780,7 @@ theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
 lean 3 declaration is
   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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
 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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5803 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5803) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
+  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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5881 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5881) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_add_eq_mul_omega Ordinal.nfp_add_eq_mul_omegaₓ'. -/
 theorem nfp_add_eq_mul_omega {a b} (hba : b ≤ a * omega) : nfp ((· + ·) a) b = a * omega :=
   by
@@ -824,7 +824,7 @@ theorem add_le_right_iff_mul_omega_le {a b : Ordinal} : a + b ≤ b ↔ a * omeg
 lean 3 declaration is
   forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 but is expected to have type
-  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6179 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6179) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
+  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6257 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6257) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_add_eq_mul_omega_add Ordinal.deriv_add_eq_mul_omega_addₓ'. -/
 theorem deriv_add_eq_mul_omega_add (a b : Ordinal.{u}) : deriv ((· + ·) a) b = a * omega + b :=
   by
@@ -847,7 +847,7 @@ local infixr:0 "^" => @pow Ordinal Ordinal Ordinal.hasPow
 lean 3 declaration is
   forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{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})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
 but is expected to have type
-  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6348 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6348) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
+  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6426 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6426) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_one Ordinal.nfp_mul_oneₓ'. -/
 @[simp]
 theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega) :=
@@ -867,7 +867,7 @@ theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega)
 lean 3 declaration is
   forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{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})))) (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}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6509 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6509) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
+  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6587 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6587) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_zero Ordinal.nfp_mul_zeroₓ'. -/
 @[simp]
 theorem nfp_mul_zero (a : Ordinal) : nfp ((· * ·) a) 0 = 0 :=
@@ -911,7 +911,7 @@ theorem deriv_mul_zero : deriv ((· * ·) 0) = id :=
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
 but is expected to have type
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6825 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6825) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6903 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6903) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_eq_opow_omega Ordinal.nfp_mul_eq_opow_omegaₓ'. -/
 theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega)) :
     nfp ((· * ·) a) b = (a^omega.{u}) :=
@@ -986,7 +986,7 @@ theorem mul_le_right_iff_opow_omega_dvd {a b : Ordinal} (ha : 0 < a) : a * b ≤
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (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}))) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
 but is expected to have type
-  forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (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})) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7524 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7524) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
+  forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (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})) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7602 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7602) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_opow_omega_add Ordinal.nfp_mul_opow_omega_addₓ'. -/
 theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hca : c ≤ (a^omega)) :
     nfp ((· * ·) a) ((a^omega) * b + c) = (a^omega.{u}) * succ b :=
@@ -1011,7 +1011,7 @@ theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hc
 lean 3 declaration is
   forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
 but is expected to have type
-  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7884 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7884) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
+  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7962 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7962) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_mul_eq_opow_omega_mul Ordinal.deriv_mul_eq_opow_omega_mulₓ'. -/
 theorem deriv_mul_eq_opow_omega_mul {a : Ordinal.{u}} (ha : 0 < a) (b) :
     deriv ((· * ·) a) b = (a^omega) * b := by

0dd4319a

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -771,7 +771,7 @@ theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
   simp_rw [← sup_iterate_eq_nfp, ← sup_mul_nat]
   congr ; funext
   induction' n with n hn
-  · rw [Nat.cast_zero, mul_zero, iterate_zero_apply]
+  · rw [Nat.cast_zero, MulZeroClass.mul_zero, iterate_zero_apply]
   · nth_rw 2 [Nat.succ_eq_one_add]
     rw [Nat.cast_add, Nat.cast_one, mul_one_add, iterate_succ_apply', hn]
 #align ordinal.nfp_add_zero Ordinal.nfp_add_zero
@@ -875,7 +875,7 @@ theorem nfp_mul_zero (a : Ordinal) : nfp ((· * ·) a) 0 = 0 :=
   rw [← Ordinal.le_zero, nfp_le_iff]
   intro n
   induction' n with n hn; · rfl
-  rwa [iterate_succ_apply, mul_zero]
+  rwa [iterate_succ_apply, MulZeroClass.mul_zero]
 #align ordinal.nfp_mul_zero Ordinal.nfp_mul_zero
 
 /- warning: ordinal.nfp_zero_mul -> Ordinal.nfp_zero_mul is a dubious translation:
@@ -892,7 +892,7 @@ theorem nfp_zero_mul : nfp ((· * ·) 0) = id :=
   induction' n with n hn; · rfl
   rw [Function.iterate_succ']
   change 0 * _ ≤ a
-  rw [zero_mul]
+  rw [MulZeroClass.zero_mul]
   exact Ordinal.zero_le a
 #align ordinal.nfp_zero_mul Ordinal.nfp_zero_mul
 
@@ -956,7 +956,7 @@ Case conversion may be inaccurate. Consider using '#align ordinal.mul_eq_right_i
 theorem mul_eq_right_iff_opow_omega_dvd {a b : Ordinal} : a * b = b ↔ (a^omega) ∣ b :=
   by
   cases' eq_zero_or_pos a with ha ha
-  · rw [ha, zero_mul, zero_opow omega_ne_zero, zero_dvd_iff]
+  · rw [ha, MulZeroClass.zero_mul, zero_opow omega_ne_zero, zero_dvd_iff]
     exact eq_comm
   refine' ⟨fun hab => _, fun h => _⟩
   · rw [dvd_iff_mod_eq_zero]
@@ -1019,7 +1019,7 @@ theorem deriv_mul_eq_opow_omega_mul {a : Ordinal.{u}} (ha : 0 < a) (b) :
   rw [← funext_iff,
     is_normal.eq_iff_zero_and_succ (deriv_is_normal _) (mul_is_normal (opow_pos omega ha))]
   refine' ⟨_, fun c h => _⟩
-  · rw [deriv_zero, nfp_mul_zero, mul_zero]
+  · rw [deriv_zero, nfp_mul_zero, MulZeroClass.mul_zero]
   · rw [deriv_succ, h]
     exact nfp_mul_opow_omega_add c ha zero_lt_one (one_le_iff_pos.2 (opow_pos _ ha))
 #align ordinal.deriv_mul_eq_opow_omega_mul Ordinal.deriv_mul_eq_opow_omega_mul

0dd4319a

bump to nightly-2023-03-02-03

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

db7421c3

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios, Mario Carneiro
 
 ! This file was ported from Lean 3 source module set_theory.ordinal.fixed_point
-! leanprover-community/mathlib commit c6b53304a1c87e90e6c14e3b28ca8fdc39070217
+! leanprover-community/mathlib commit 0dd4319a17376eda5763cd0a7e0d35bbaaa50e83
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -52,6 +52,9 @@ variable {ι : Type u} {f : ι → Ordinal.{max u v} → Ordinal.{max u v}}
 #print Ordinal.nfpFamily /-
 /-- The next common fixed point, at least `a`, for a family of normal functions.
 
+This is defined for any family of functions, as the supremum of all values reachable by applying
+finitely many functions in the family to `a`.
+
 `ordinal.nfp_family_fp` shows this is a fixed point, `ordinal.le_nfp_family` shows it's at
 least `a`, and `ordinal.nfp_family_le_fp` shows this is the least ordinal with these properties. -/
 def nfpFamily (f : ι → Ordinal → Ordinal) (a) : Ordinal :=
@@ -119,7 +122,7 @@ theorem apply_lt_nfpFamily_iff [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
     (∀ i, f i b < nfpFamily f a) ↔ b < nfpFamily f a :=
   ⟨fun h =>
     lt_nfpFamily.2 <|
-      let ⟨l, hl⟩ := lt_sup.1 (h (Classical.arbitrary ι))
+      let ⟨l, hl⟩ := lt_sup.1 <| h <| Classical.arbitrary ι
       ⟨l, ((H _).self_le b).trans_lt hl⟩,
     apply_lt_nfpFamily H⟩
 #align ordinal.apply_lt_nfp_family_iff Ordinal.apply_lt_nfpFamily_iff
@@ -181,10 +184,11 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_family_eq_self Ordinal.nfpFamily_eq_selfₓ'. -/
 theorem nfpFamily_eq_self {f : ι → Ordinal → Ordinal} {a} (h : ∀ i, f i a = a) :
     nfpFamily f a = a :=
-  le_antisymm (sup_le fun l => by rw [List.foldr_fixed' h l]) (le_nfpFamily f a)
+  le_antisymm (sup_le fun l => by rw [List.foldr_fixed' h l]) <| le_nfpFamily f a
 #align ordinal.nfp_family_eq_self Ordinal.nfpFamily_eq_self
 
 #print Ordinal.fp_family_unbounded /-
+-- Todo: This is actually a special case of the fact the intersection of club sets is a club set.
 /-- A generalization of the fixed point lemma for normal functions: any family of normal functions
     has an unbounded set of common fixed points. -/
 theorem fp_family_unbounded (H : ∀ i, IsNormal (f i)) :
@@ -196,7 +200,10 @@ theorem fp_family_unbounded (H : ∀ i, IsNormal (f i)) :
 -/
 
 #print Ordinal.derivFamily /-
-/-- The derivative of a family of normal functions is the sequence of their common fixed points. -/
+/-- The derivative of a family of normal functions is the sequence of their common fixed points.
+
+This is defined for all functions such that `ordinal.deriv_family_zero`,
+`ordinal.deriv_family_succ`, and `ordinal.deriv_family_limit` are satisfied. -/
 def derivFamily (f : ι → Ordinal → Ordinal) (o : Ordinal) : Ordinal :=
   limitRecOn o (nfpFamily f 0) (fun a IH => nfpFamily f (succ IH)) fun a l => bsup.{max u v, u} a
 #align ordinal.deriv_family Ordinal.derivFamily
@@ -273,7 +280,7 @@ theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
       exact
         let ⟨o', h, hl⟩ := h
         IH o' h (le_of_not_le hl),
-    fun ⟨o, e⟩ i => e ▸ le_of_eq (derivFamily_fp (H i) _)⟩
+    fun ⟨o, e⟩ i => e ▸ (derivFamily_fp (H i) _).le⟩
 #align ordinal.le_iff_deriv_family Ordinal.le_iff_derivFamily
 -/
 
@@ -285,6 +292,7 @@ theorem fp_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
 -/
 
 #print Ordinal.derivFamily_eq_enumOrd /-
+/-- For a family of normal functions, `ordinal.deriv_family` enumerates the common fixed points. -/
 theorem derivFamily_eq_enumOrd (H : ∀ i, IsNormal (f i)) :
     derivFamily f = enumOrd (⋂ i, Function.fixedPoints (f i)) :=
   by
@@ -311,6 +319,8 @@ variable {o : Ordinal.{u}} {f : ∀ b < o, Ordinal.{max u v} → Ordinal.{max u
 
 #print Ordinal.nfpBFamily /-
 /-- The next common fixed point, at least `a`, for a family of normal functions indexed by ordinals.
+
+This is defined as `ordinal.nfp_family` of the type-indexed family associated to `f`.
 -/
 def nfpBFamily (o : Ordinal) (f : ∀ b < o, Ordinal → Ordinal) : Ordinal → Ordinal :=
   nfpFamily (familyOfBFamily o f)
@@ -422,8 +432,8 @@ theorem apply_le_nfpBFamily (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a
   refine' ⟨fun h => _, fun h i hi => _⟩
   · have ho' : 0 < o := Ordinal.pos_iff_ne_zero.2 ho
     exact ((H 0 ho').self_le b).trans (h 0 ho')
-  rw [← nfp_bfamily_fp (H i hi)]
-  exact (H i hi).Monotone h
+  · rw [← nfp_bfamily_fp (H i hi)]
+    exact (H i hi).Monotone h
 #align ordinal.apply_le_nfp_bfamily Ordinal.apply_le_nfpBFamily
 -/
 
@@ -446,7 +456,9 @@ theorem fp_bfamily_unbounded (H : ∀ i hi, IsNormal (f i hi)) :
 -/
 
 #print Ordinal.derivBFamily /-
-/-- The derivative of a family of normal functions is the sequence of their common fixed points. -/
+/-- The derivative of a family of normal functions is the sequence of their common fixed points.
+
+This is defined as `ordinal.deriv_family` of the type-indexed family associated to `f`. -/
 def derivBFamily (o : Ordinal) (f : ∀ b < o, Ordinal → Ordinal) : Ordinal → Ordinal :=
   derivFamily (familyOfBFamily o f)
 #align ordinal.deriv_bfamily Ordinal.derivBFamily
@@ -490,7 +502,7 @@ theorem le_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
   · refine' ⟨fun h i => h _ _, fun h i hi => _⟩
     rw [← family_of_bfamily_enum o f]
     apply h
-  exact fun _ => H _ _
+  · exact fun _ => H _ _
 #align ordinal.le_iff_deriv_bfamily Ordinal.le_iff_derivBFamily
 -/
 
@@ -507,6 +519,7 @@ theorem fp_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:107:6: warning: expanding binder group (i hi) -/
 #print Ordinal.derivBFamily_eq_enumOrd /-
+/-- For a family of normal functions, `ordinal.deriv_bfamily` enumerates the common fixed points. -/
 theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
     derivBFamily o f = enumOrd (⋂ (i) (hi), Function.fixedPoints (f i hi)) :=
   by
@@ -530,7 +543,8 @@ variable {f : Ordinal.{u} → Ordinal.{u}}
 
 #print Ordinal.nfp /-
 /-- The next fixed point function, the least fixed point of the normal function `f`, at least `a`.
--/
+
+This is defined as `ordinal.nfp_family` applied to a family consisting only of `f`. -/
 def nfp (f : Ordinal → Ordinal) : Ordinal → Ordinal :=
   nfpFamily fun _ : Unit => f
 #align ordinal.nfp Ordinal.nfp
@@ -658,7 +672,9 @@ theorem fp_unbounded (H : IsNormal f) : (Function.fixedPoints f).Unbounded (· <
 -/
 
 #print Ordinal.deriv /-
-/-- The derivative of a normal function `f` is the sequence of fixed points of `f`. -/
+/-- The derivative of a normal function `f` is the sequence of fixed points of `f`.
+
+This is defined as `ordinal.deriv_family` applied to a trivial family consisting only of `f`. -/
 def deriv (f : Ordinal → Ordinal) : Ordinal → Ordinal :=
   derivFamily fun _ : Unit => f
 #align ordinal.deriv Ordinal.deriv
@@ -724,6 +740,7 @@ theorem IsNormal.fp_iff_deriv {f} (H : IsNormal f) {a} : f a = a ↔ ∃ o, deri
 -/
 
 #print Ordinal.deriv_eq_enumOrd /-
+/-- `ordinal.deriv` enumerates the fixed points of a normal function. -/
 theorem deriv_eq_enumOrd (H : IsNormal f) : deriv f = enumOrd (Function.fixedPoints f) :=
   by
   convert deriv_family_eq_enum_ord fun _ : Unit => H
@@ -733,7 +750,7 @@ theorem deriv_eq_enumOrd (H : IsNormal f) : deriv f = enumOrd (Function.fixedPoi
 
 #print Ordinal.deriv_eq_id_of_nfp_eq_id /-
 theorem deriv_eq_id_of_nfp_eq_id {f : Ordinal → Ordinal} (h : nfp f = id) : deriv f = id :=
-  (IsNormal.eq_iff_zero_and_succ (deriv_isNormal _) IsNormal.refl).2 (by simp [h])
+  (IsNormal.eq_iff_zero_and_succ (deriv_isNormal _) IsNormal.refl).2 <| by simp [h]
 #align ordinal.deriv_eq_id_of_nfp_eq_id Ordinal.deriv_eq_id_of_nfp_eq_id
 -/

c6b53304

bump to nightly-2023-02-27-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

e1a04c87

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios, Mario Carneiro
 
 ! This file was ported from Lean 3 source module set_theory.ordinal.fixed_point
-! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
+! leanprover-community/mathlib commit c6b53304a1c87e90e6c14e3b28ca8fdc39070217
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -364,19 +364,27 @@ theorem nfpBFamily_monotone (hf : ∀ i hi, Monotone (f i hi)) : Monotone (nfpBF
 #align ordinal.nfp_bfamily_monotone Ordinal.nfpBFamily_monotone
 -/
 
-#print Ordinal.apply_lt_nfpBFamily /-
-theorem apply_lt_nfpBFamily (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
-    (∀ i hi, f i hi b < nfpBFamily o f a) ↔ b < nfpBFamily o f a :=
+/- warning: ordinal.apply_lt_nfp_bfamily -> Ordinal.apply_lt_nfpBFamily is a dubious translation:
+lean 3 declaration is
+  forall {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i hi)) -> (forall {a : Ordinal.{max u1 u2}} {b : Ordinal.{max u1 u2}}, (LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) b (Ordinal.nfpBFamily.{u1, u2} o f a)) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{succ (max u1 u2)} Ordinal.{max u1 u2} (Preorder.toLT.{succ (max u1 u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i hi b) (Ordinal.nfpBFamily.{u1, u2} o f a)))
+but is expected to have type
+  forall {o : Ordinal.{u1}} {f : forall (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b o) -> Ordinal.{max u1 u2} -> Ordinal.{max u1 u2}}, (Ne.{succ (succ u1)} Ordinal.{u1} o (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) -> (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), Ordinal.IsNormal.{max u1 u2, max u1 u2} (f i hi)) -> (forall {b : Ordinal.{max u2 u1}} {hb : Ordinal.{max u1 u2}}, Iff (forall (i : Ordinal.{u1}) (hi : LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) i o), LT.lt.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Ordinal.{max u1 u2} Ordinal.partialOrder.{max u1 u2})) (f i hi hb) (Ordinal.nfpBFamily.{u1, u2} o f b)) (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})) hb (Ordinal.nfpBFamily.{u1, u2} o f b)))
+Case conversion may be inaccurate. Consider using '#align ordinal.apply_lt_nfp_bfamily Ordinal.apply_lt_nfpBFamilyₓ'. -/
+theorem apply_lt_nfpBFamily (H : ∀ i hi, IsNormal (f i hi)) {a b} (hb : b < nfpBFamily o f a)
+    (i hi) : f i hi b < nfpBFamily o f a :=
   by
-  unfold nfp_bfamily
-  rw [←
-    @apply_lt_nfp_family_iff _ (family_of_bfamily o f) (out_nonempty_iff_ne_zero.2 ho) fun i =>
-      H _ _]
-  refine' ⟨fun h i => h _ (typein_lt_self i), fun h i hio => _⟩
   rw [← family_of_bfamily_enum o f]
-  apply h
+  apply apply_lt_nfp_family _ hb
+  exact fun _ => H _ _
 #align ordinal.apply_lt_nfp_bfamily Ordinal.apply_lt_nfpBFamily
--/
+
+theorem apply_lt_nfpBFamily_iff (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
+    (∀ i hi, f i hi b < nfpBFamily o f a) ↔ b < nfpBFamily o f a :=
+  ⟨fun h => by
+    haveI := out_nonempty_iff_ne_zero.2 ho
+    refine' (apply_lt_nfp_family_iff _).1 fun _ => h _ _
+    exact fun _ => H _ _, apply_lt_nfpBFamily H⟩
+#align ordinal.apply_lt_nfp_bfamily_iff Ordinal.apply_lt_nfpBFamily_iff
 
 #print Ordinal.nfpBFamily_le_apply /-
 theorem nfpBFamily_le_apply (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
@@ -384,7 +392,7 @@ theorem nfpBFamily_le_apply (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a
   by
   rw [← not_iff_not]
   push_neg
-  convert apply_lt_nfp_bfamily ho H
+  convert apply_lt_nfp_bfamily_iff ho H
   simp only [not_le]
 #align ordinal.nfp_bfamily_le_apply Ordinal.nfpBFamily_le_apply
 -/

23aa88e3

bump to nightly-2023-02-23-03

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

5c91f1b0

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios, Mario Carneiro
 
 ! This file was ported from Lean 3 source module set_theory.ordinal.fixed_point
-! leanprover-community/mathlib commit f1e061e3caef3022f0daa99d670ecf2c30e0b5c6
+! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.SetTheory.Ordinal.Exponential
 /-!
 # Fixed points of normal functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We prove various statements about the fixed points of normal ordinal functions. We state them in
 three forms: as statements about type-indexed families of normal functions, as statements about
 ordinal-indexed families of normal functions, and as statements about a single normal function. For

f1e061e3

bump to nightly-2023-02-22-22

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

294ba122

Diff

@@ -735,7 +735,7 @@ end
 lean 3 declaration is
   forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{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})))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
 but is expected to have type
-  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5664 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5664) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
+  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5664 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5664) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_add_zero Ordinal.nfp_add_zeroₓ'. -/
 @[simp]
 theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
@@ -752,7 +752,7 @@ theorem nfp_add_zero (a) : nfp ((· + ·) a) 0 = a * omega :=
 lean 3 declaration is
   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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
 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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5803 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5803) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
+  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})) b (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5803 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.5803) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_add_eq_mul_omega Ordinal.nfp_add_eq_mul_omegaₓ'. -/
 theorem nfp_add_eq_mul_omega {a b} (hba : b ≤ a * omega) : nfp ((· + ·) a) b = a * omega :=
   by
@@ -766,7 +766,7 @@ theorem nfp_add_eq_mul_omega {a b} (hba : b ≤ a * omega) : nfp ((· + ·) a) b
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (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}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 but is expected to have type
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (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}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (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}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 Case conversion may be inaccurate. Consider using '#align ordinal.add_eq_right_iff_mul_omega_le Ordinal.add_eq_right_iff_mul_omega_leₓ'. -/
 theorem add_eq_right_iff_mul_omega_le {a b : Ordinal} : a + b = b ↔ a * omega ≤ b :=
   by
@@ -784,7 +784,7 @@ theorem add_eq_right_iff_mul_omega_le {a b : Ordinal} : a + b = b ↔ a * omega
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 but is expected to have type
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a b) b) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 Case conversion may be inaccurate. Consider using '#align ordinal.add_le_right_iff_mul_omega_le Ordinal.add_le_right_iff_mul_omega_leₓ'. -/
 theorem add_le_right_iff_mul_omega_le {a b : Ordinal} : a + b ≤ b ↔ a * omega ≤ b :=
   by
@@ -796,7 +796,7 @@ theorem add_le_right_iff_mul_omega_le {a b : Ordinal} : a + b ≤ b ↔ a * omeg
 lean 3 declaration is
   forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 but is expected to have type
-  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6179 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6179) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
+  forall (a : Ordinal.{u1}) (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6179 : Ordinal.{u1}) => HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6179) b) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a Ordinal.omega.{u1}) b)
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_add_eq_mul_omega_add Ordinal.deriv_add_eq_mul_omega_addₓ'. -/
 theorem deriv_add_eq_mul_omega_add (a b : Ordinal.{u}) : deriv ((· + ·) a) b = a * omega + b :=
   by
@@ -819,7 +819,7 @@ local infixr:0 "^" => @pow Ordinal Ordinal Ordinal.hasPow
 lean 3 declaration is
   forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{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})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
 but is expected to have type
-  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6348 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6348) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
+  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6348 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6348) (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_one Ordinal.nfp_mul_oneₓ'. -/
 @[simp]
 theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega) :=
@@ -839,7 +839,7 @@ theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp ((· * ·) a) 1 = (a^omega)
 lean 3 declaration is
   forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{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})))) (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}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6509 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6509) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))
+  forall (a : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6509 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6509) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_zero Ordinal.nfp_mul_zeroₓ'. -/
 @[simp]
 theorem nfp_mul_zero (a : Ordinal) : nfp ((· * ·) a) 0 = 0 :=
@@ -854,7 +854,7 @@ theorem nfp_mul_zero (a : Ordinal) : nfp ((· * ·) a) 0 = 0 :=
 lean 3 declaration is
   Eq.{succ (succ u1)} (Ordinal.{u1} -> Ordinal.{u1}) (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))))) (id.{succ (succ u1)} Ordinal.{u1})
 but is expected to have type
-  Eq.{succ (succ u1)} (Ordinal.{u1} -> Ordinal.{u1}) (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))) (id.{succ (succ u1)} Ordinal.{u1})
+  Eq.{succ (succ u1)} (Ordinal.{u1} -> Ordinal.{u1}) (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})))) (id.{succ (succ u1)} Ordinal.{u1})
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_zero_mul Ordinal.nfp_zero_mulₓ'. -/
 @[simp]
 theorem nfp_zero_mul : nfp ((· * ·) 0) = id :=
@@ -872,7 +872,7 @@ theorem nfp_zero_mul : nfp ((· * ·) 0) = id :=
 lean 3 declaration is
   Eq.{succ (succ u1)} (Ordinal.{u1} -> Ordinal.{u1}) (Ordinal.deriv.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))))) (id.{succ (succ u1)} Ordinal.{u1})
 but is expected to have type
-  Eq.{succ (succ u1)} (Ordinal.{u1} -> Ordinal.{u1}) (Ordinal.deriv.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})))) (id.{succ (succ u1)} Ordinal.{u1})
+  Eq.{succ (succ u1)} (Ordinal.{u1} -> Ordinal.{u1}) (Ordinal.deriv.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})))) (id.{succ (succ u1)} Ordinal.{u1})
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_mul_zero Ordinal.deriv_mul_zeroₓ'. -/
 @[simp]
 theorem deriv_mul_zero : deriv ((· * ·) 0) = id :=
@@ -883,7 +883,7 @@ theorem deriv_mul_zero : deriv ((· * ·) 0) = id :=
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
 but is expected to have type
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6825 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6825) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}))
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) b) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) b (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6825 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.6825) b) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_eq_opow_omega Ordinal.nfp_mul_eq_opow_omegaₓ'. -/
 theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega)) :
     nfp ((· * ·) a) b = (a^omega.{u}) :=
@@ -903,7 +903,7 @@ theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (Eq.{succ (succ u1)} Ordinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) -> (Or (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})))) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
 but is expected to have type
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (Eq.{succ (succ u1)} Ordinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) -> (Or (Eq.{succ (succ u1)} Ordinal.{u1} b (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (Eq.{succ (succ u1)} Ordinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) -> (Or (Eq.{succ (succ u1)} Ordinal.{u1} b (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1}))) (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
 Case conversion may be inaccurate. Consider using '#align ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right Ordinal.eq_zero_or_opow_omega_le_of_mul_eq_rightₓ'. -/
 theorem eq_zero_or_opow_omega_le_of_mul_eq_right {a b : Ordinal} (hab : a * b = b) :
     b = 0 ∨ (a^omega.{u}) ≤ b :=
@@ -923,7 +923,7 @@ theorem eq_zero_or_opow_omega_le_of_mul_eq_right {a b : Ordinal} (hab : a * b =
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (Eq.{succ (succ u1)} Ordinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) (Dvd.Dvd.{succ u1} Ordinal.{u1} (semigroupDvd.{succ u1} Ordinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Ordinal.{u1} (MonoidWithZero.toSemigroupWithZero.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b)
 but is expected to have type
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (Eq.{succ (succ u1)} Ordinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) (Dvd.dvd.{succ u1} Ordinal.{u1} (semigroupDvd.{succ u1} Ordinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Ordinal.{u1} (MonoidWithZero.toSemigroupWithZero.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b)
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, Iff (Eq.{succ (succ u1)} Ordinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) (Dvd.dvd.{succ u1} Ordinal.{u1} (semigroupDvd.{succ u1} Ordinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Ordinal.{u1} (MonoidWithZero.toSemigroupWithZero.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b)
 Case conversion may be inaccurate. Consider using '#align ordinal.mul_eq_right_iff_opow_omega_dvd Ordinal.mul_eq_right_iff_opow_omega_dvdₓ'. -/
 theorem mul_eq_right_iff_opow_omega_dvd {a b : Ordinal} : a * b = b ↔ (a^omega) ∣ b :=
   by
@@ -946,7 +946,7 @@ theorem mul_eq_right_iff_opow_omega_dvd {a b : Ordinal} : a * b = b ↔ (a^omega
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) (Dvd.Dvd.{succ u1} Ordinal.{u1} (semigroupDvd.{succ u1} Ordinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Ordinal.{u1} (MonoidWithZero.toSemigroupWithZero.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
 but is expected to have type
-  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})) a) -> (Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) (Dvd.dvd.{succ u1} Ordinal.{u1} (semigroupDvd.{succ u1} Ordinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Ordinal.{u1} (MonoidWithZero.toSemigroupWithZero.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
+  forall {a : Ordinal.{u1}} {b : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (Iff (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a b) b) (Dvd.dvd.{succ u1} Ordinal.{u1} (semigroupDvd.{succ u1} Ordinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Ordinal.{u1} (MonoidWithZero.toSemigroupWithZero.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1}))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
 Case conversion may be inaccurate. Consider using '#align ordinal.mul_le_right_iff_opow_omega_dvd Ordinal.mul_le_right_iff_opow_omega_dvdₓ'. -/
 theorem mul_le_right_iff_opow_omega_dvd {a b : Ordinal} (ha : 0 < a) : a * b ≤ b ↔ (a^omega) ∣ b :=
   by
@@ -958,7 +958,7 @@ theorem mul_le_right_iff_opow_omega_dvd {a b : Ordinal} (ha : 0 < a) : a * b ≤
 lean 3 declaration is
   forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (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}))) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
 but is expected to have type
-  forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})) a) -> (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.hasZero.{u1})) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7524 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7524) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.hasAdd.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
+  forall {a : Ordinal.{u1}} {c : Ordinal.{u1}} (b : Ordinal.{u1}), (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (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})) c) -> (LE.le.{succ u1} Ordinal.{u1} (Preorder.toLE.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) c (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1})) -> (Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.nfp.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7524 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7524) (HAdd.hAdd.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHAdd.{succ u1} Ordinal.{u1} Ordinal.add.{u1}) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b) c)) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) (Order.succ.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1}) Ordinal.succOrder.{u1} b)))
 Case conversion may be inaccurate. Consider using '#align ordinal.nfp_mul_opow_omega_add Ordinal.nfp_mul_opow_omega_addₓ'. -/
 theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hca : c ≤ (a^omega)) :
     nfp ((· * ·) a) ((a^omega) * b + c) = (a^omega.{u}) * succ b :=
@@ -983,7 +983,7 @@ theorem nfp_mul_opow_omega_add {a c : Ordinal} (b) (ha : 0 < a) (hc : 0 < c) (hc
 lean 3 declaration is
   forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (OfNat.mk.{succ u1} Ordinal.{u1} 0 (Zero.zero.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1}))) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toHasMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
 but is expected to have type
-  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.hasZero.{u1})) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7884 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7884) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.hasPow.{u1}) a Ordinal.omega.{u1}) b))
+  forall {a : Ordinal.{u1}}, (LT.lt.{succ u1} Ordinal.{u1} (Preorder.toLT.{succ u1} Ordinal.{u1} (PartialOrder.toPreorder.{succ u1} Ordinal.{u1} Ordinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Ordinal.{u1} 0 (Zero.toOfNat0.{succ u1} Ordinal.{u1} Ordinal.zero.{u1})) a) -> (forall (b : Ordinal.{u1}), Eq.{succ (succ u1)} Ordinal.{u1} (Ordinal.deriv.{u1} (fun (x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7884 : Ordinal.{u1}) => HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) a x._@.Mathlib.SetTheory.Ordinal.FixedPoint._hyg.7884) b) (HMul.hMul.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHMul.{succ u1} Ordinal.{u1} (MulZeroClass.toMul.{succ u1} Ordinal.{u1} (MulZeroOneClass.toMulZeroClass.{succ u1} Ordinal.{u1} (MonoidWithZero.toMulZeroOneClass.{succ u1} Ordinal.{u1} Ordinal.monoidWithZero.{u1})))) (HPow.hPow.{succ u1, succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.{u1} (instHPow.{succ u1, succ u1} Ordinal.{u1} Ordinal.{u1} Ordinal.pow.{u1}) a Ordinal.omega.{u1}) b))
 Case conversion may be inaccurate. Consider using '#align ordinal.deriv_mul_eq_opow_omega_mul Ordinal.deriv_mul_eq_opow_omega_mulₓ'. -/
 theorem deriv_mul_eq_opow_omega_mul {a : Ordinal.{u}} (ha : 0 < a) (b) :
     deriv ((· * ·) a) b = (a^omega) * b := by

f1e061e3

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

0dd4319a

chore: backports from #11997, adaptations for nightly-2024-04-07 (#12176)

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

02293f49

Diff

@@ -668,7 +668,7 @@ theorem eq_zero_or_opow_omega_le_of_mul_eq_right {a b : Ordinal} (hab : a * b =
   rw [or_iff_not_imp_left]
   intro hb
   rw [← nfp_mul_one ha]
-  rw [← Ne.def, ← one_le_iff_ne_zero] at hb
+  rw [← Ne, ← one_le_iff_ne_zero] at hb
   exact nfp_le_fp (mul_isNormal ha).monotone hb (le_of_eq hab)
 #align ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right Ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right

0dd4319a

chore: remove more bex and ball from lemma names (#11615)

Follow-up to #10816.

Remaining places containing such lemmas are

Option.bex_ne_none and Option.ball_ne_none: defined in Lean core
Nat.decidableBallLT and Nat.decidableBallLE: defined in Lean core
bef_def is still used in a number of places and could be renamed
BAll.imp_{left,right}, BEx.imp_{left,right}, BEx.intro and BEx.elim

I only audited the first ~150 lemmas mentioning "ball"; too many lemmas named after Metric.ball/openBall/closedBall.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

7b7bbd73

Diff

@@ -213,7 +213,7 @@ theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
     · intro h₁
       cases' eq_or_lt_of_le h₁ with h h
       · exact ⟨_, h.symm⟩
-      rw [derivFamily_limit _ l, ← not_le, bsup_le_iff, not_ball] at h
+      rw [derivFamily_limit _ l, ← not_le, bsup_le_iff, not_forall₂] at h
       exact
         let ⟨o', h, hl⟩ := h
         IH o' h (le_of_not_le hl),

0dd4319a

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -606,7 +606,7 @@ theorem deriv_add_eq_mul_omega_add (a b : Ordinal.{u}) : deriv (a + ·) b = a *
 
 /-! ### Fixed points of multiplication -/
 
---Porting note: commented out, doesn't seem necessary
+-- Porting note: commented out, doesn't seem necessary
 -- local infixr:0 "^" => @Pow.pow Ordinal Ordinal Ordinal.hasPow
 
 @[simp]

0dd4319a

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

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

This follows on from #6964.

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

a13e8040

Diff

@@ -196,8 +196,8 @@ theorem derivFamily_fp {i} (H : IsNormal (f i)) (o : Ordinal.{max u v}) :
 theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
     (∀ i, f i a ≤ a) ↔ ∃ o, derivFamily.{u, v} f o = a :=
   ⟨fun ha => by
-    suffices : ∀ (o) (_ : a ≤ derivFamily.{u, v} f o), ∃ o, derivFamily.{u, v} f o = a
-    exact this a ((derivFamily_isNormal _).self_le _)
+    suffices ∀ (o) (_ : a ≤ derivFamily.{u, v} f o), ∃ o, derivFamily.{u, v} f o = a from
+      this a ((derivFamily_isNormal _).self_le _)
     intro o
     induction' o using limitRecOn with o IH o l IH
     · intro h₁

0dd4319a

chore: remove uses of cases' (#9171)

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

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

3fca282c

Diff

@@ -205,7 +205,7 @@ theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
       rw [derivFamily_zero]
       exact nfpFamily_le_fp (fun i => (H i).monotone) (Ordinal.zero_le _) ha
     · intro h₁
-      cases' le_or_lt a (derivFamily.{u, v} f o) with h h
+      rcases le_or_lt a (derivFamily.{u, v} f o) with h | h
       · exact IH h
       refine' ⟨succ o, le_antisymm _ h₁⟩
       rw [derivFamily_succ]
@@ -649,7 +649,7 @@ theorem deriv_mul_zero : deriv (HMul.hMul 0) = id :=
 
 theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega)) :
     nfp (a * ·) b = (a^omega.{u}) := by
-  cases' eq_zero_or_pos a with ha ha
+  rcases eq_zero_or_pos a with ha | ha
   · rw [ha, zero_opow omega_ne_zero] at hba ⊢
     rw [Ordinal.le_zero.1 hba, nfp_zero_mul]
     rfl
@@ -662,7 +662,7 @@ theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega
 
 theorem eq_zero_or_opow_omega_le_of_mul_eq_right {a b : Ordinal} (hab : a * b = b) :
     b = 0 ∨ (a^omega.{u}) ≤ b := by
-  cases' eq_zero_or_pos a with ha ha
+  rcases eq_zero_or_pos a with ha | ha
   · rw [ha, zero_opow omega_ne_zero]
     exact Or.inr (Ordinal.zero_le b)
   rw [or_iff_not_imp_left]
@@ -673,7 +673,7 @@ theorem eq_zero_or_opow_omega_le_of_mul_eq_right {a b : Ordinal} (hab : a * b =
 #align ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right Ordinal.eq_zero_or_opow_omega_le_of_mul_eq_right
 
 theorem mul_eq_right_iff_opow_omega_dvd {a b : Ordinal} : a * b = b ↔ (a^omega) ∣ b := by
-  cases' eq_zero_or_pos a with ha ha
+  rcases eq_zero_or_pos a with ha | ha
   · rw [ha, zero_mul, zero_opow omega_ne_zero, zero_dvd_iff]
     exact eq_comm
   refine' ⟨fun hab => _, fun h => _⟩

0dd4319a

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

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

d14658b4

Diff

@@ -598,9 +598,9 @@ theorem deriv_add_eq_mul_omega_add (a b : Ordinal.{u}) : deriv (a + ·) b = a *
   revert b
   rw [← funext_iff, IsNormal.eq_iff_zero_and_succ (deriv_isNormal _) (add_isNormal _)]
   refine' ⟨_, fun a h => _⟩
-  · dsimp; rw [deriv_zero, add_zero]
+  · rw [deriv_zero, add_zero]
     exact nfp_add_zero a
-  · dsimp; rw [deriv_succ, h, add_succ]
+  · rw [deriv_succ, h, add_succ]
     exact nfp_eq_self (add_eq_right_iff_mul_omega_le.2 ((le_add_right _ _).trans (le_succ _)))
 #align ordinal.deriv_add_eq_mul_omega_add Ordinal.deriv_add_eq_mul_omega_add
 
@@ -655,7 +655,7 @@ theorem nfp_mul_eq_opow_omega {a b : Ordinal} (hb : 0 < b) (hba : b ≤ (a^omega
     rfl
   apply le_antisymm
   · apply nfp_le_fp (mul_isNormal ha).monotone hba
-    dsimp only; rw [← opow_one_add, one_add_omega]
+    rw [← opow_one_add, one_add_omega]
   rw [← nfp_mul_one ha]
   exact nfp_monotone (mul_isNormal ha).monotone (one_le_iff_pos.2 hb)
 #align ordinal.nfp_mul_eq_opow_omega Ordinal.nfp_mul_eq_opow_omega

0dd4319a

chore: space after ← (#8178)

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

5fb9beab

Diff

@@ -292,7 +292,7 @@ theorem nfpBFamily_monotone (hf : ∀ i hi, Monotone (f i hi)) : Monotone (nfpBF
 
 theorem apply_lt_nfpBFamily (H : ∀ i hi, IsNormal (f i hi)) {a b} (hb : b < nfpBFamily.{u, v} o f a)
     (i hi) : f i hi b < nfpBFamily.{u, v} o f a := by
-  rw [←familyOfBFamily_enum o f]
+  rw [← familyOfBFamily_enum o f]
   apply apply_lt_nfpFamily (fun _ => H _ _) hb
 #align ordinal.apply_lt_nfp_bfamily Ordinal.apply_lt_nfpBFamily

0dd4319a

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -154,7 +154,7 @@ theorem fp_family_unbounded (H : ∀ i, IsNormal (f i)) :
 This is defined for all functions such that `Ordinal.derivFamily_zero`,
 `Ordinal.derivFamily_succ`, and `Ordinal.derivFamily_limit` are satisfied. -/
 def derivFamily (f : ι → Ordinal → Ordinal) (o : Ordinal) : Ordinal :=
-  limitRecOn.{max u v} o (nfpFamily.{u, v} f 0) (fun _ IH => nfpFamily.{u, v} f (succ IH))
+  limitRecOn o (nfpFamily.{u, v} f 0) (fun _ IH => nfpFamily.{u, v} f (succ IH))
     fun a _ => bsup.{max u v, u} a
 #align ordinal.deriv_family Ordinal.derivFamily

0dd4319a

chore: use · instead of . (#6085)

898a8e78

Diff

@@ -610,7 +610,7 @@ theorem deriv_add_eq_mul_omega_add (a b : Ordinal.{u}) : deriv (a + ·) b = a *
 -- local infixr:0 "^" => @Pow.pow Ordinal Ordinal Ordinal.hasPow
 
 @[simp]
-theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp (a * .) 1 = (a^omega) := by
+theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp (a * ·) 1 = (a^omega) := by
   rw [← sup_iterate_eq_nfp, ← sup_opow_nat]
   · dsimp
     congr
@@ -623,7 +623,7 @@ theorem nfp_mul_one {a : Ordinal} (ha : 0 < a) : nfp (a * .) 1 = (a^omega) := by
 #align ordinal.nfp_mul_one Ordinal.nfp_mul_one
 
 @[simp]
-theorem nfp_mul_zero (a : Ordinal) : nfp (a * .) 0 = 0 := by
+theorem nfp_mul_zero (a : Ordinal) : nfp (a * ·) 0 = 0 := by
   rw [← Ordinal.le_zero, nfp_le_iff]
   intro n
   induction' n with n hn; · rfl

0dd4319a

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2018 Violeta Hernández Palacios, Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios, Mario Carneiro
-
-! This file was ported from Lean 3 source module set_theory.ordinal.fixed_point
-! leanprover-community/mathlib commit 0dd4319a17376eda5763cd0a7e0d35bbaaa50e83
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.SetTheory.Ordinal.Arithmetic
 import Mathlib.SetTheory.Ordinal.Exponential
 
+#align_import set_theory.ordinal.fixed_point from "leanprover-community/mathlib"@"0dd4319a17376eda5763cd0a7e0d35bbaaa50e83"
+
 /-!
 # Fixed points of normal functions

0dd4319a

chore: cleanup whitespace (#5988)

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

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

12343aa5

Diff

@@ -185,7 +185,7 @@ theorem derivFamily_isNormal (f : ι → Ordinal → Ordinal) : IsNormal (derivF
 
 theorem derivFamily_fp {i} (H : IsNormal (f i)) (o : Ordinal.{max u v}) :
     f i (derivFamily.{u, v} f o) = derivFamily.{u, v} f o := by
-  induction' o using limitRecOn with o _  o l IH
+  induction' o using limitRecOn with o _ o l IH
   · rw [derivFamily_zero]
     exact nfpFamily_fp H 0
   · rw [derivFamily_succ]

0dd4319a

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

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

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

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

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

c795bd35

Diff

@@ -567,7 +567,7 @@ end
 @[simp]
 theorem nfp_add_zero (a) : nfp (a + ·) 0 = a * omega := by
   simp_rw [← sup_iterate_eq_nfp, ← sup_mul_nat]
-  congr ; funext n
+  congr; funext n
   induction' n with n hn
   · rw [Nat.cast_zero, mul_zero, iterate_zero_apply]
   · nth_rw 2 [Nat.succ_eq_one_add]

0dd4319a

fix precedence of Nat.iterate (#5589)

bd2fff86

Diff

@@ -425,7 +425,7 @@ theorem nfp_eq_nfpFamily (f : Ordinal → Ordinal) : nfp f = nfpFamily fun _ : U
 
 @[simp]
 theorem sup_iterate_eq_nfp (f : Ordinal.{u} → Ordinal.{u}) :
-    (fun a => sup fun n : ℕ => (f^[n]) a) = nfp f := by
+    (fun a => sup fun n : ℕ => f^[n] a) = nfp f := by
   refine' funext fun a => le_antisymm _ (sup_le fun l => _)
   · rw [sup_le_iff]
     intro n
@@ -435,7 +435,7 @@ theorem sup_iterate_eq_nfp (f : Ordinal.{u} → Ordinal.{u}) :
     exact le_sup _ _
 #align ordinal.sup_iterate_eq_nfp Ordinal.sup_iterate_eq_nfp
 
-theorem iterate_le_nfp (f a n) : (f^[n]) a ≤ nfp f a := by
+theorem iterate_le_nfp (f a n) : f^[n] a ≤ nfp f a := by
   rw [← sup_iterate_eq_nfp]
   exact le_sup _ n
 #align ordinal.iterate_le_nfp Ordinal.iterate_le_nfp
@@ -444,17 +444,17 @@ theorem le_nfp (f a) : a ≤ nfp f a :=
   iterate_le_nfp f a 0
 #align ordinal.le_nfp Ordinal.le_nfp
 
-theorem lt_nfp {a b} : a < nfp f b ↔ ∃ n, a < (f^[n]) b := by
+theorem lt_nfp {a b} : a < nfp f b ↔ ∃ n, a < f^[n] b := by
   rw [← sup_iterate_eq_nfp]
   exact lt_sup
 #align ordinal.lt_nfp Ordinal.lt_nfp
 
-theorem nfp_le_iff {a b} : nfp f a ≤ b ↔ ∀ n, (f^[n]) a ≤ b := by
+theorem nfp_le_iff {a b} : nfp f a ≤ b ↔ ∀ n, f^[n] a ≤ b := by
   rw [← sup_iterate_eq_nfp]
   exact sup_le_iff
 #align ordinal.nfp_le_iff Ordinal.nfp_le_iff
 
-theorem nfp_le {a b} : (∀ n, (f^[n]) a ≤ b) → nfp f a ≤ b :=
+theorem nfp_le {a b} : (∀ n, f^[n] a ≤ b) → nfp f a ≤ b :=
   nfp_le_iff.2
 #align ordinal.nfp_le Ordinal.nfp_le
 
@@ -636,7 +636,7 @@ theorem nfp_mul_zero (a : Ordinal) : nfp (a * .) 0 = 0 := by
 @[simp]
 theorem nfp_zero_mul : nfp (HMul.hMul 0) = id := by
   rw [← sup_iterate_eq_nfp]
-  refine' funext fun a => (sup_le fun n => _).antisymm (le_sup (fun n => ((· * ·) 0^[n]) a) 0)
+  refine' funext fun a => (sup_le fun n => _).antisymm (le_sup (fun n => (0 * ·)^[n] a) 0)
   induction' n with n _
   · rfl
   rw [Function.iterate_succ']

0dd4319a

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

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

27d257fc

Diff

@@ -253,7 +253,7 @@ variable {o : Ordinal.{u}} {f : ∀ b < o, Ordinal.{max u v} → Ordinal.{max u
 
 /-- The next common fixed point, at least `a`, for a family of normal functions indexed by ordinals.
 
-This is defined as `ordinal.nfp_family` of the type-indexed family associated to `f`. -/
+This is defined as `Ordinal.nfpFamily` of the type-indexed family associated to `f`. -/
 def nfpBFamily (o : Ordinal) (f : ∀ b < o, Ordinal → Ordinal) : Ordinal → Ordinal :=
   nfpFamily (familyOfBFamily o f)
 #align ordinal.nfp_bfamily Ordinal.nfpBFamily
@@ -392,7 +392,7 @@ theorem fp_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
   exact h i hi
 #align ordinal.fp_iff_deriv_bfamily Ordinal.fp_iff_derivBFamily
 
-/-- For a family of normal functions, `ordinal.deriv_bfamily` enumerates the common fixed points. -/
+/-- For a family of normal functions, `Ordinal.derivBFamily` enumerates the common fixed points. -/
 theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
     derivBFamily.{u, v} o f = enumOrd (⋂ (i) (hi), Function.fixedPoints (f i hi)) := by
   rw [← eq_enumOrd _ (fp_bfamily_unbounded.{u, v} H)]
@@ -549,7 +549,7 @@ theorem IsNormal.fp_iff_deriv {f} (H : IsNormal f) {a} : f a = a ↔ ∃ o, deri
   rw [← H.le_iff_eq, H.le_iff_deriv]
 #align ordinal.is_normal.fp_iff_deriv Ordinal.IsNormal.fp_iff_deriv
 
-/-- `ordinal.deriv` enumerates the fixed points of a normal function. -/
+/-- `Ordinal.deriv` enumerates the fixed points of a normal function. -/
 theorem deriv_eq_enumOrd (H : IsNormal f) : deriv f = enumOrd (Function.fixedPoints f) := by
   convert derivFamily_eq_enumOrd fun _ : Unit => H
   exact (Set.iInter_const _).symm

0dd4319a

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

supₛ → sSup
infₛ → sInf
supᵢ → iSup
infᵢ → iInf
bsupₛ → bsSup
binfₛ → bsInf
bsupᵢ → biSup
binfᵢ → biInf
csupₛ → csSup
cinfₛ → csInf
csupᵢ → ciSup
cinfᵢ → ciInf
unionₛ → sUnion
interₛ → sInter
unionᵢ → iUnion
interᵢ → iInter
bunionₛ → bsUnion
binterₛ → bsInter
bunionᵢ → biUnion
binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

d1eb6264

Diff

@@ -238,7 +238,7 @@ theorem derivFamily_eq_enumOrd (H : ∀ i, IsNormal (f i)) :
   · rintro a S ⟨i, hi⟩
     rw [← hi]
     exact derivFamily_fp (H i) a
-  rw [Set.mem_interᵢ] at ha
+  rw [Set.mem_iInter] at ha
   rwa [← fp_iff_derivFamily H]
 #align ordinal.deriv_family_eq_enum_ord Ordinal.derivFamily_eq_enumOrd
 
@@ -345,7 +345,7 @@ theorem nfpBFamily_eq_self {a} (h : ∀ i hi, f i hi a = a) : nfpBFamily.{u, v}
 theorem fp_bfamily_unbounded (H : ∀ i hi, IsNormal (f i hi)) :
     (⋂ (i) (hi), Function.fixedPoints (f i hi)).Unbounded (· < ·) := fun a =>
   ⟨nfpBFamily.{u, v} _ f a, by
-    rw [Set.mem_interᵢ₂]
+    rw [Set.mem_iInter₂]
     exact fun i hi => nfpBFamily_fp (H i hi) _, (le_nfpBFamily f a).not_lt⟩
 #align ordinal.fp_bfamily_unbounded Ordinal.fp_bfamily_unbounded
 
@@ -398,8 +398,8 @@ theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
   rw [← eq_enumOrd _ (fp_bfamily_unbounded.{u, v} H)]
   use (derivBFamily_isNormal f).strictMono
   rw [Set.range_eq_iff]
-  refine' ⟨fun a => Set.mem_interᵢ₂.2 fun i hi => derivBFamily_fp (H i hi) a, fun a ha => _⟩
-  rw [Set.mem_interᵢ₂] at ha
+  refine' ⟨fun a => Set.mem_iInter₂.2 fun i hi => derivBFamily_fp (H i hi) a, fun a ha => _⟩
+  rw [Set.mem_iInter₂] at ha
   rwa [← fp_iff_derivBFamily H]
 #align ordinal.deriv_bfamily_eq_enum_ord Ordinal.derivBFamily_eq_enumOrd
 
@@ -499,7 +499,7 @@ theorem nfp_eq_self {f : Ordinal → Ordinal} {a} (h : f a = a) : nfp f a = a :=
 fixed points. -/
 theorem fp_unbounded (H : IsNormal f) : (Function.fixedPoints f).Unbounded (· < ·) := by
   convert fp_family_unbounded fun _ : Unit => H
-  exact (Set.interᵢ_const _).symm
+  exact (Set.iInter_const _).symm
 #align ordinal.fp_unbounded Ordinal.fp_unbounded
 
 /-- The derivative of a normal function `f` is the sequence of fixed points of `f`.
@@ -552,7 +552,7 @@ theorem IsNormal.fp_iff_deriv {f} (H : IsNormal f) {a} : f a = a ↔ ∃ o, deri
 /-- `ordinal.deriv` enumerates the fixed points of a normal function. -/
 theorem deriv_eq_enumOrd (H : IsNormal f) : deriv f = enumOrd (Function.fixedPoints f) := by
   convert derivFamily_eq_enumOrd fun _ : Unit => H
-  exact (Set.interᵢ_const _).symm
+  exact (Set.iInter_const _).symm
 #align ordinal.deriv_eq_enum_ord Ordinal.deriv_eq_enumOrd
 
 theorem deriv_eq_id_of_nfp_eq_id {f : Ordinal → Ordinal} (h : nfp f = id) : deriv f = id :=

0dd4319a

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -691,8 +691,8 @@ theorem mul_eq_right_iff_opow_omega_dvd {a b : Ordinal} : a * b = b ↔ (a^omega
   rw [hc, ← mul_assoc, ← opow_one_add, one_add_omega]
 #align ordinal.mul_eq_right_iff_opow_omega_dvd Ordinal.mul_eq_right_iff_opow_omega_dvd
 
-theorem mul_le_right_iff_opow_omega_dvd {a b : Ordinal} (ha : 0 < a) : a * b ≤ b ↔ (a^omega) ∣ b :=
-  by
+theorem mul_le_right_iff_opow_omega_dvd {a b : Ordinal} (ha : 0 < a) :
+    a * b ≤ b ↔ (a^omega) ∣ b := by
   rw [← mul_eq_right_iff_opow_omega_dvd]
   exact (mul_isNormal ha).le_iff_eq
 #align ordinal.mul_le_right_iff_opow_omega_dvd Ordinal.mul_le_right_iff_opow_omega_dvd

0dd4319a

chore: tidy various files (#3124)

55209140

Diff

@@ -87,7 +87,6 @@ theorem nfpFamily_monotone (hf : ∀ i, Monotone (f i)) : Monotone (nfpFamily.{u
   fun _ _ h => sup_le.{u, v} fun l => (List.foldr_monotone hf l h).trans (le_sup.{u, v} _ l)
 #align ordinal.nfp_family_monotone Ordinal.nfpFamily_monotone
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem apply_lt_nfpFamily (H : ∀ i, IsNormal (f i)) {a b} (hb : b < nfpFamily.{u, v} f a) (i) :
     f i b < nfpFamily.{u, v} f a :=
   let ⟨l, hl⟩ := lt_nfpFamily.1 hb
@@ -114,15 +113,12 @@ theorem nfpFamily_le_fp (H : ∀ i, Monotone (f i)) {a b} (ab : a ≤ b) (h : 
     nfpFamily.{u, v} f a ≤ b :=
   sup_le fun l => by
     by_cases hι : IsEmpty ι
-    · skip
-      rwa [Unique.eq_default l]
-    · haveI := not_isEmpty_iff.1 hι
-      induction' l with i l IH generalizing a
+    · rwa [Unique.eq_default l]
+    · induction' l with i l IH generalizing a
       · exact ab
       exact (H i (IH ab)).trans (h i)
 #align ordinal.nfp_family_le_fp Ordinal.nfpFamily_le_fp
 
-/- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem nfpFamily_fp {i} (H : IsNormal (f i)) (a) :
     f i (nfpFamily.{u, v} f a) = nfpFamily.{u, v} f a := by
   unfold nfpFamily
@@ -641,7 +637,8 @@ theorem nfp_mul_zero (a : Ordinal) : nfp (a * .) 0 = 0 := by
 theorem nfp_zero_mul : nfp (HMul.hMul 0) = id := by
   rw [← sup_iterate_eq_nfp]
   refine' funext fun a => (sup_le fun n => _).antisymm (le_sup (fun n => ((· * ·) 0^[n]) a) 0)
-  induction' n with n _; · rfl
+  induction' n with n _
+  · rfl
   rw [Function.iterate_succ']
   change 0 * _ ≤ a
   rw [zero_mul]

0dd4319a

feat: port ordinal fixed point changes (#3155)

Ports https://github.com/leanprover-community/mathlib/pull/18322 and https://github.com/leanprover-community/mathlib/pull/18323.

956b01d8

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Violeta Hernández Palacios, Mario Carneiro
 
 ! This file was ported from Lean 3 source module set_theory.ordinal.fixed_point
-! leanprover-community/mathlib commit bd9851ca476957ea4549eb19b40e7b5ade9428cc
+! leanprover-community/mathlib commit 0dd4319a17376eda5763cd0a7e0d35bbaaa50e83
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -48,6 +48,9 @@ variable {ι : Type u} {f : ι → Ordinal.{max u v} → Ordinal.{max u v}}
 
 /-- The next common fixed point, at least `a`, for a family of normal functions.
 
+This is defined for any family of functions, as the supremum of all values reachable by applying
+finitely many functions in the family to `a`.
+
 `Ordinal.nfpFamily_fp` shows this is a fixed point, `Ordinal.le_nfpFamily` shows it's at
 least `a`, and `Ordinal.nfpFamily_le_fp` shows this is the least ordinal with these properties. -/
 def nfpFamily (f : ι → Ordinal → Ordinal) (a : Ordinal) : Ordinal :=
@@ -95,7 +98,7 @@ theorem apply_lt_nfpFamily_iff [Nonempty ι] (H : ∀ i, IsNormal (f i)) {a b} :
     (∀ i, f i b < nfpFamily.{u, v} f a) ↔ b < nfpFamily.{u, v} f a :=
   ⟨fun h =>
     lt_nfpFamily.2 <|
-      let ⟨l, hl⟩ := lt_sup.1 (h (Classical.arbitrary ι))
+      let ⟨l, hl⟩ := lt_sup.1 <| h <| Classical.arbitrary ι
       ⟨l, ((H _).self_le b).trans_lt hl⟩,
     apply_lt_nfpFamily H⟩
 #align ordinal.apply_lt_nfp_family_iff Ordinal.apply_lt_nfpFamily_iff
@@ -140,9 +143,10 @@ theorem apply_le_nfpFamily [hι : Nonempty ι] {f : ι → Ordinal → Ordinal}
 
 theorem nfpFamily_eq_self {f : ι → Ordinal → Ordinal} {a} (h : ∀ i, f i a = a) :
     nfpFamily f a = a :=
-  le_antisymm (sup_le fun l => by rw [List.foldr_fixed' h l]) (le_nfpFamily f a)
+  le_antisymm (sup_le fun l => by rw [List.foldr_fixed' h l]) <| le_nfpFamily f a
 #align ordinal.nfp_family_eq_self Ordinal.nfpFamily_eq_self
 
+-- Todo: This is actually a special case of the fact the intersection of club sets is a club set.
 /-- A generalization of the fixed point lemma for normal functions: any family of normal functions
     has an unbounded set of common fixed points. -/
 theorem fp_family_unbounded (H : ∀ i, IsNormal (f i)) :
@@ -152,7 +156,10 @@ theorem fp_family_unbounded (H : ∀ i, IsNormal (f i)) :
     exact nfpFamily_fp.{u, v} (H i) a, (le_nfpFamily f a).not_lt⟩
 #align ordinal.fp_family_unbounded Ordinal.fp_family_unbounded
 
-/-- The derivative of a family of normal functions is the sequence of their common fixed points. -/
+/-- The derivative of a family of normal functions is the sequence of their common fixed points.
+
+This is defined for all functions such that `Ordinal.derivFamily_zero`,
+`Ordinal.derivFamily_succ`, and `Ordinal.derivFamily_limit` are satisfied. -/
 def derivFamily (f : ι → Ordinal → Ordinal) (o : Ordinal) : Ordinal :=
   limitRecOn.{max u v} o (nfpFamily.{u, v} f 0) (fun _ IH => nfpFamily.{u, v} f (succ IH))
     fun a _ => bsup.{max u v, u} a
@@ -217,7 +224,7 @@ theorem le_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
       exact
         let ⟨o', h, hl⟩ := h
         IH o' h (le_of_not_le hl),
-    fun ⟨o, e⟩ i => e ▸ le_of_eq (derivFamily_fp (H i) _)⟩
+    fun ⟨o, e⟩ i => e ▸ (derivFamily_fp (H i) _).le⟩
 #align ordinal.le_iff_deriv_family Ordinal.le_iff_derivFamily
 
 theorem fp_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
@@ -225,6 +232,7 @@ theorem fp_iff_derivFamily (H : ∀ i, IsNormal (f i)) {a} :
   Iff.trans ⟨fun h i => le_of_eq (h i), fun h i => (H i).le_iff_eq.1 (h i)⟩ (le_iff_derivFamily H)
 #align ordinal.fp_iff_deriv_family Ordinal.fp_iff_derivFamily
 
+/-- For a family of normal functions, `Ordinal.derivFamily` enumerates the common fixed points. -/
 theorem derivFamily_eq_enumOrd (H : ∀ i, IsNormal (f i)) :
     derivFamily.{u, v} f = enumOrd (⋂ i, Function.fixedPoints (f i)) := by
   rw [← eq_enumOrd _ (fp_family_unbounded.{u, v} H)]
@@ -248,7 +256,8 @@ section
 variable {o : Ordinal.{u}} {f : ∀ b < o, Ordinal.{max u v} → Ordinal.{max u v}}
 
 /-- The next common fixed point, at least `a`, for a family of normal functions indexed by ordinals.
--/
+
+This is defined as `ordinal.nfp_family` of the type-indexed family associated to `f`. -/
 def nfpBFamily (o : Ordinal) (f : ∀ b < o, Ordinal → Ordinal) : Ordinal → Ordinal :=
   nfpFamily (familyOfBFamily o f)
 #align ordinal.nfp_bfamily Ordinal.nfpBFamily
@@ -288,22 +297,25 @@ theorem nfpBFamily_monotone (hf : ∀ i hi, Monotone (f i hi)) : Monotone (nfpBF
   nfpFamily_monotone fun _ => hf _ _
 #align ordinal.nfp_bfamily_monotone Ordinal.nfpBFamily_monotone
 
-theorem apply_lt_nfpBFamily (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
-    (∀ i hi, f i hi b < nfpBFamily.{u, v} o f a) ↔ b < nfpBFamily.{u, v} o f a := by
-  unfold nfpBFamily
-  rw [←
-    @apply_lt_nfpFamily_iff _ (familyOfBFamily o f) (out_nonempty_iff_ne_zero.2 ho) fun i =>
-      H _ _]
-  refine' ⟨fun h i => h _ (typein_lt_self i), fun h i hio => _⟩
-  rw [← familyOfBFamily_enum o f]
-  apply h
+theorem apply_lt_nfpBFamily (H : ∀ i hi, IsNormal (f i hi)) {a b} (hb : b < nfpBFamily.{u, v} o f a)
+    (i hi) : f i hi b < nfpBFamily.{u, v} o f a := by
+  rw [←familyOfBFamily_enum o f]
+  apply apply_lt_nfpFamily (fun _ => H _ _) hb
 #align ordinal.apply_lt_nfp_bfamily Ordinal.apply_lt_nfpBFamily
 
+theorem apply_lt_nfpBFamily_iff (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
+    (∀ i hi, f i hi b < nfpBFamily.{u, v} o f a) ↔ b < nfpBFamily.{u, v} o f a :=
+  ⟨fun h => by
+    haveI := out_nonempty_iff_ne_zero.2 ho
+    refine' (apply_lt_nfpFamily_iff.{u, v} _).1 fun _ => h _ _
+    exact fun _ => H _ _, apply_lt_nfpBFamily H⟩
+#align ordinal.apply_lt_nfp_bfamily_iff Ordinal.apply_lt_nfpBFamily_iff
+
 theorem nfpBFamily_le_apply (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a b} :
     (∃ i hi, nfpBFamily.{u, v} o f a ≤ f i hi b) ↔ nfpBFamily.{u, v} o f a ≤ b := by
   rw [← not_iff_not]
   push_neg
-  exact apply_lt_nfpBFamily.{u, v} ho H
+  exact apply_lt_nfpBFamily_iff.{u, v} ho H
 #align ordinal.nfp_bfamily_le_apply Ordinal.nfpBFamily_le_apply
 
 theorem nfpBFamily_le_fp (H : ∀ i hi, Monotone (f i hi)) {a b} (ab : a ≤ b)
@@ -324,8 +336,8 @@ theorem apply_le_nfpBFamily (ho : o ≠ 0) (H : ∀ i hi, IsNormal (f i hi)) {a
   refine' ⟨fun h => _, fun h i hi => _⟩
   · have ho' : 0 < o := Ordinal.pos_iff_ne_zero.2 ho
     exact ((H 0 ho').self_le b).trans (h 0 ho')
-  rw [← nfpBFamily_fp (H i hi)]
-  exact (H i hi).monotone h
+  · rw [← nfpBFamily_fp (H i hi)]
+    exact (H i hi).monotone h
 #align ordinal.apply_le_nfp_bfamily Ordinal.apply_le_nfpBFamily
 
 theorem nfpBFamily_eq_self {a} (h : ∀ i hi, f i hi a = a) : nfpBFamily.{u, v} o f a = a :=
@@ -341,7 +353,9 @@ theorem fp_bfamily_unbounded (H : ∀ i hi, IsNormal (f i hi)) :
     exact fun i hi => nfpBFamily_fp (H i hi) _, (le_nfpBFamily f a).not_lt⟩
 #align ordinal.fp_bfamily_unbounded Ordinal.fp_bfamily_unbounded
 
-/-- The derivative of a family of normal functions is the sequence of their common fixed points. -/
+/-- The derivative of a family of normal functions is the sequence of their common fixed points.
+
+This is defined as `Ordinal.derivFamily` of the type-indexed family associated to `f`. -/
 def derivBFamily (o : Ordinal) (f : ∀ b < o, Ordinal → Ordinal) : Ordinal → Ordinal :=
   derivFamily (familyOfBFamily o f)
 #align ordinal.deriv_bfamily Ordinal.derivBFamily
@@ -371,7 +385,7 @@ theorem le_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
   · refine' ⟨fun h i => h _ _, fun h i hi => _⟩
     rw [← familyOfBFamily_enum o f]
     apply h
-  exact fun _ => H _ _
+  · exact fun _ => H _ _
 #align ordinal.le_iff_deriv_bfamily Ordinal.le_iff_derivBFamily
 
 theorem fp_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
@@ -382,6 +396,7 @@ theorem fp_iff_derivBFamily (H : ∀ i hi, IsNormal (f i hi)) {a} :
   exact h i hi
 #align ordinal.fp_iff_deriv_bfamily Ordinal.fp_iff_derivBFamily
 
+/-- For a family of normal functions, `ordinal.deriv_bfamily` enumerates the common fixed points. -/
 theorem derivBFamily_eq_enumOrd (H : ∀ i hi, IsNormal (f i hi)) :
     derivBFamily.{u, v} o f = enumOrd (⋂ (i) (hi), Function.fixedPoints (f i hi)) := by
   rw [← eq_enumOrd _ (fp_bfamily_unbounded.{u, v} H)]
@@ -402,7 +417,8 @@ section
 variable {f : Ordinal.{u} → Ordinal.{u}}
 
 /-- The next fixed point function, the least fixed point of the normal function `f`, at least `a`.
--/
+
+This is defined as `ordinal.nfpFamily` applied to a family consisting only of `f`. -/
 def nfp (f : Ordinal → Ordinal) : Ordinal → Ordinal :=
   nfpFamily fun _ : Unit => f
 #align ordinal.nfp Ordinal.nfp
@@ -490,7 +506,9 @@ theorem fp_unbounded (H : IsNormal f) : (Function.fixedPoints f).Unbounded (· <
   exact (Set.interᵢ_const _).symm
 #align ordinal.fp_unbounded Ordinal.fp_unbounded
 
-/-- The derivative of a normal function `f` is the sequence of fixed points of `f`. -/
+/-- The derivative of a normal function `f` is the sequence of fixed points of `f`.
+
+This is defined as `Ordinal.derivFamily` applied to a trivial family consisting only of `f`. -/
 def deriv (f : Ordinal → Ordinal) : Ordinal → Ordinal :=
   derivFamily fun _ : Unit => f
 #align ordinal.deriv Ordinal.deriv
@@ -535,13 +553,14 @@ theorem IsNormal.fp_iff_deriv {f} (H : IsNormal f) {a} : f a = a ↔ ∃ o, deri
   rw [← H.le_iff_eq, H.le_iff_deriv]
 #align ordinal.is_normal.fp_iff_deriv Ordinal.IsNormal.fp_iff_deriv
 
+/-- `ordinal.deriv` enumerates the fixed points of a normal function. -/
 theorem deriv_eq_enumOrd (H : IsNormal f) : deriv f = enumOrd (Function.fixedPoints f) := by
   convert derivFamily_eq_enumOrd fun _ : Unit => H
   exact (Set.interᵢ_const _).symm
 #align ordinal.deriv_eq_enum_ord Ordinal.deriv_eq_enumOrd
 
 theorem deriv_eq_id_of_nfp_eq_id {f : Ordinal → Ordinal} (h : nfp f = id) : deriv f = id :=
-  (IsNormal.eq_iff_zero_and_succ (deriv_isNormal _) IsNormal.refl).2 (by simp [h])
+  (IsNormal.eq_iff_zero_and_succ (deriv_isNormal _) IsNormal.refl).2 <| by simp [h]
 #align ordinal.deriv_eq_id_of_nfp_eq_id Ordinal.deriv_eq_id_of_nfp_eq_id
 
 end

bd9851ca

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

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

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

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

61ca0ea8

Diff

@@ -537,7 +537,6 @@ theorem IsNormal.fp_iff_deriv {f} (H : IsNormal f) {a} : f a = a ↔ ∃ o, deri
 
 theorem deriv_eq_enumOrd (H : IsNormal f) : deriv f = enumOrd (Function.fixedPoints f) := by
   convert derivFamily_eq_enumOrd fun _ : Unit => H
-  refine congr_arg enumOrd ?_
   exact (Set.interᵢ_const _).symm
 #align ordinal.deriv_eq_enum_ord Ordinal.deriv_eq_enumOrd

bd9851ca

feat: port SetTheory.Ordinal.FixedPoint (#2416)

628f140f

`set_theory.ordinal.fixed_point` ⟷ `Mathlib.SetTheory.Ordinal.FixedPoint`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 7 + 307

set_theory.ordinal.fixed_point ⟷ Mathlib.SetTheory.Ordinal.FixedPoint

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 7 + 307

`set_theory.ordinal.fixed_point` ⟷ `Mathlib.SetTheory.Ordinal.FixedPoint`