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

@@ -88,7 +88,7 @@ theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
   cases' eq_or_ne (b * c) 0 with hz hz
   · rcases mul_eq_zero.mp hz with (rfl | rfl) <;> simp
   wlog h : c ≤ b
-  · cases le_total c b <;> [skip; rw [or_comm']] <;> apply_assumption; assumption'
+  · cases le_total c b <;> [skip; rw [or_comm]] <;> apply_assumption; assumption'
     all_goals rwa [mul_comm]
   left
   have habc := le_of_dvd hz hbc

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

@@ -48,13 +48,13 @@ theorem isUnit_iff : IsUnit a ↔ a = 1 :=
   refine' ⟨fun h => _, by rintro rfl; exact isUnit_one⟩
   rcases eq_or_ne a 0 with (rfl | ha)
   · exact (not_isUnit_zero h).elim
-  rw [isUnit_iff_forall_dvd] at h 
+  rw [isUnit_iff_forall_dvd] at h
   cases' h 1 with t ht
-  rw [eq_comm, mul_eq_one_iff'] at ht 
+  rw [eq_comm, mul_eq_one_iff'] at ht
   · exact ht.1
   all_goals rwa [one_le_iff_ne_zero]
   · rintro rfl
-    rw [MulZeroClass.mul_zero] at ht 
+    rw [MulZeroClass.mul_zero] at ht
     exact zero_ne_one ht
 #align cardinal.is_unit_iff Cardinal.isUnit_iff
 -/
@@ -92,7 +92,7 @@ theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
     all_goals rwa [mul_comm]
   left
   have habc := le_of_dvd hz hbc
-  rwa [mul_eq_max' <| ha.trans <| habc, max_def', if_pos h] at hbc 
+  rwa [mul_eq_max' <| ha.trans <| habc, max_def', if_pos h] at hbc
 #align cardinal.prime_of_aleph_0_le Cardinal.prime_of_aleph0_le
 -/
 
@@ -113,9 +113,9 @@ theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
   refine' ⟨_, fun ⟨h, ht⟩ => ⟨h, by exact_mod_cast ht⟩⟩
   rintro ⟨k, hk⟩
   have : ↑m < ℵ₀ := nat_lt_aleph_0 m
-  rw [hk, mul_lt_aleph_0_iff] at this 
+  rw [hk, mul_lt_aleph_0_iff] at this
   rcases this with (h | h | ⟨-, hk'⟩)
-  iterate 2 simp only [h, MulZeroClass.mul_zero, MulZeroClass.zero_mul, Nat.cast_eq_zero] at hk ;
+  iterate 2 simp only [h, MulZeroClass.mul_zero, MulZeroClass.zero_mul, Nat.cast_eq_zero] at hk;
     simp [hk]
   lift k to ℕ using hk'
   exact ⟨k, by exact_mod_cast hk⟩
@@ -141,7 +141,7 @@ theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
   rcases aleph_0_le_mul_iff.mp h' with ⟨hb, hc, hℵ₀⟩
   have hn : (n : Cardinal) ≠ 0 := by
     intro h
-    rw [h, zero_dvd_iff, mul_eq_zero] at hbc 
+    rw [h, zero_dvd_iff, mul_eq_zero] at hbc
     cases hbc <;> contradiction
   wlog hℵ₀b : ℵ₀ ≤ b
   · refine' (this h c b _ _ hc hb hℵ₀.symm hn (hℵ₀.resolve_left hℵ₀b)).symm <;> rwa [mul_comm]
@@ -172,7 +172,7 @@ theorem isPrimePow_iff {a : Cardinal} : IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n
   rintro ⟨p, k, hp, hk, hpk⟩
   have key : _ ≤ p ^ k :=
     power_le_power_left hp.ne_zero (show (1 : Cardinal) ≤ k by exact_mod_cast hk)
-  rw [power_one, hpk] at key 
+  rw [power_one, hpk] at key
   lift p to ℕ using key.trans_lt (nat_lt_aleph_0 a)
   exact ⟨p, k, nat_is_prime_iff.mp hp, hk, by exact_mod_cast hpk⟩
 #align cardinal.is_prime_pow_iff Cardinal.isPrimePow_iff

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Eric Rodriguez. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
 -/
-import Mathbin.Algebra.IsPrimePow
-import Mathbin.SetTheory.Cardinal.Ordinal
+import Algebra.IsPrimePow
+import SetTheory.Cardinal.Ordinal
 
 #align_import set_theory.cardinal.divisibility from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Eric Rodriguez. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
-
-! This file was ported from Lean 3 source module set_theory.cardinal.divisibility
-! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.IsPrimePow
 import Mathbin.SetTheory.Cardinal.Ordinal
 
+#align_import set_theory.cardinal.divisibility from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
+
 /-!
 # Cardinal Divisibility
 

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

@@ -81,6 +81,7 @@ theorem dvd_of_le_of_aleph0_le (ha : a ≠ 0) (h : a ≤ b) (hb : ℵ₀ ≤ b)
 #align cardinal.dvd_of_le_of_aleph_0_le Cardinal.dvd_of_le_of_aleph0_le
 -/
 
+#print Cardinal.prime_of_aleph0_le /-
 @[simp]
 theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
   by
@@ -96,6 +97,7 @@ theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
   have habc := le_of_dvd hz hbc
   rwa [mul_eq_max' <| ha.trans <| habc, max_def', if_pos h] at hbc 
 #align cardinal.prime_of_aleph_0_le Cardinal.prime_of_aleph0_le
+-/
 
 #print Cardinal.not_irreducible_of_aleph0_le /-
 theorem not_irreducible_of_aleph0_le (ha : ℵ₀ ≤ a) : ¬Irreducible a :=
@@ -107,6 +109,7 @@ theorem not_irreducible_of_aleph0_le (ha : ℵ₀ ≤ a) : ¬Irreducible a :=
 #align cardinal.not_irreducible_of_aleph_0_le Cardinal.not_irreducible_of_aleph0_le
 -/
 
+#print Cardinal.nat_coe_dvd_iff /-
 @[simp, norm_cast]
 theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
   by
@@ -120,7 +123,9 @@ theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
   lift k to ℕ using hk'
   exact ⟨k, by exact_mod_cast hk⟩
 #align cardinal.nat_coe_dvd_iff Cardinal.nat_coe_dvd_iff
+-/
 
+#print Cardinal.nat_is_prime_iff /-
 @[simp]
 theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
   by
@@ -145,7 +150,9 @@ theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
   · refine' (this h c b _ _ hc hb hℵ₀.symm hn (hℵ₀.resolve_left hℵ₀b)).symm <;> rwa [mul_comm]
   exact Or.inl (dvd_of_le_of_aleph_0_le hn ((nat_lt_aleph_0 n).le.trans hℵ₀b) hℵ₀b)
 #align cardinal.nat_is_prime_iff Cardinal.nat_is_prime_iff
+-/
 
+#print Cardinal.is_prime_iff /-
 theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ, a = p ∧ p.Prime :=
   by
   cases' le_or_lt ℵ₀ a with h h
@@ -153,7 +160,9 @@ theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ,
   lift a to ℕ using id h
   simp [not_le.mpr h]
 #align cardinal.is_prime_iff Cardinal.is_prime_iff
+-/
 
+#print Cardinal.isPrimePow_iff /-
 theorem isPrimePow_iff {a : Cardinal} : IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n : ℕ, a = n ∧ IsPrimePow n :=
   by
   by_cases h : ℵ₀ ≤ a
@@ -170,6 +179,7 @@ theorem isPrimePow_iff {a : Cardinal} : IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n
   lift p to ℕ using key.trans_lt (nat_lt_aleph_0 a)
   exact ⟨p, k, nat_is_prime_iff.mp hp, hk, by exact_mod_cast hpk⟩
 #align cardinal.is_prime_pow_iff Cardinal.isPrimePow_iff
+-/
 
 end Cardinal
 

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

@@ -51,13 +51,13 @@ theorem isUnit_iff : IsUnit a ↔ a = 1 :=
   refine' ⟨fun h => _, by rintro rfl; exact isUnit_one⟩
   rcases eq_or_ne a 0 with (rfl | ha)
   · exact (not_isUnit_zero h).elim
-  rw [isUnit_iff_forall_dvd] at h
+  rw [isUnit_iff_forall_dvd] at h 
   cases' h 1 with t ht
-  rw [eq_comm, mul_eq_one_iff'] at ht
+  rw [eq_comm, mul_eq_one_iff'] at ht 
   · exact ht.1
   all_goals rwa [one_le_iff_ne_zero]
   · rintro rfl
-    rw [MulZeroClass.mul_zero] at ht
+    rw [MulZeroClass.mul_zero] at ht 
     exact zero_ne_one ht
 #align cardinal.is_unit_iff Cardinal.isUnit_iff
 -/
@@ -90,11 +90,11 @@ theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
   cases' eq_or_ne (b * c) 0 with hz hz
   · rcases mul_eq_zero.mp hz with (rfl | rfl) <;> simp
   wlog h : c ≤ b
-  · cases le_total c b <;> [skip;rw [or_comm']] <;> apply_assumption; assumption'
+  · cases le_total c b <;> [skip; rw [or_comm']] <;> apply_assumption; assumption'
     all_goals rwa [mul_comm]
   left
   have habc := le_of_dvd hz hbc
-  rwa [mul_eq_max' <| ha.trans <| habc, max_def', if_pos h] at hbc
+  rwa [mul_eq_max' <| ha.trans <| habc, max_def', if_pos h] at hbc 
 #align cardinal.prime_of_aleph_0_le Cardinal.prime_of_aleph0_le
 
 #print Cardinal.not_irreducible_of_aleph0_le /-
@@ -113,9 +113,9 @@ theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
   refine' ⟨_, fun ⟨h, ht⟩ => ⟨h, by exact_mod_cast ht⟩⟩
   rintro ⟨k, hk⟩
   have : ↑m < ℵ₀ := nat_lt_aleph_0 m
-  rw [hk, mul_lt_aleph_0_iff] at this
+  rw [hk, mul_lt_aleph_0_iff] at this 
   rcases this with (h | h | ⟨-, hk'⟩)
-  iterate 2 simp only [h, MulZeroClass.mul_zero, MulZeroClass.zero_mul, Nat.cast_eq_zero] at hk;
+  iterate 2 simp only [h, MulZeroClass.mul_zero, MulZeroClass.zero_mul, Nat.cast_eq_zero] at hk ;
     simp [hk]
   lift k to ℕ using hk'
   exact ⟨k, by exact_mod_cast hk⟩
@@ -139,7 +139,7 @@ theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
   rcases aleph_0_le_mul_iff.mp h' with ⟨hb, hc, hℵ₀⟩
   have hn : (n : Cardinal) ≠ 0 := by
     intro h
-    rw [h, zero_dvd_iff, mul_eq_zero] at hbc
+    rw [h, zero_dvd_iff, mul_eq_zero] at hbc 
     cases hbc <;> contradiction
   wlog hℵ₀b : ℵ₀ ≤ b
   · refine' (this h c b _ _ hc hb hℵ₀.symm hn (hℵ₀.resolve_left hℵ₀b)).symm <;> rwa [mul_comm]
@@ -166,7 +166,7 @@ theorem isPrimePow_iff {a : Cardinal} : IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n
   rintro ⟨p, k, hp, hk, hpk⟩
   have key : _ ≤ p ^ k :=
     power_le_power_left hp.ne_zero (show (1 : Cardinal) ≤ k by exact_mod_cast hk)
-  rw [power_one, hpk] at key
+  rw [power_one, hpk] at key 
   lift p to ℕ using key.trans_lt (nat_lt_aleph_0 a)
   exact ⟨p, k, nat_is_prime_iff.mp hp, hk, by exact_mod_cast hpk⟩
 #align cardinal.is_prime_pow_iff Cardinal.isPrimePow_iff

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

@@ -38,7 +38,7 @@ Note furthermore that no infinite cardinal is irreducible
 
 namespace Cardinal
 
-open Cardinal
+open scoped Cardinal
 
 universe u
 

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

@@ -81,12 +81,6 @@ theorem dvd_of_le_of_aleph0_le (ha : a ≠ 0) (h : a ≤ b) (hb : ℵ₀ ≤ b)
 #align cardinal.dvd_of_le_of_aleph_0_le Cardinal.dvd_of_le_of_aleph0_le
 -/
 
-/- warning: cardinal.prime_of_aleph_0_le -> Cardinal.prime_of_aleph0_le is a dubious translation:
-lean 3 declaration is
-  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} Cardinal.commMonoidWithZero.{u1} a)
-but is expected to have type
-  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} Cardinal.instCommMonoidWithZeroCardinal.{u1} a)
-Case conversion may be inaccurate. Consider using '#align cardinal.prime_of_aleph_0_le Cardinal.prime_of_aleph0_leₓ'. -/
 @[simp]
 theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
   by
@@ -113,12 +107,6 @@ theorem not_irreducible_of_aleph0_le (ha : ℵ₀ ≤ a) : ¬Irreducible a :=
 #align cardinal.not_irreducible_of_aleph_0_le Cardinal.not_irreducible_of_aleph0_le
 -/
 
-/- warning: cardinal.nat_coe_dvd_iff -> Cardinal.nat_coe_dvd_iff is a dubious translation:
-lean 3 declaration is
-  forall {n : Nat} {m : Nat}, Iff (Dvd.Dvd.{succ u1} Cardinal.{u1} (semigroupDvd.{succ u1} Cardinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Cardinal.{u1} (NonUnitalSemiring.toSemigroupWithZero.{succ u1} Cardinal.{u1} (NonUnitalCommSemiring.toNonUnitalSemiring.{succ u1} Cardinal.{u1} (CommSemiring.toNonUnitalCommSemiring.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}))))) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) m)) (Dvd.Dvd.{0} Nat Nat.hasDvd n m)
-but is expected to have type
-  forall {n : Nat} {m : Nat}, Iff (Dvd.dvd.{succ u1} Cardinal.{u1} (semigroupDvd.{succ u1} Cardinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Cardinal.{u1} (NonUnitalSemiring.toSemigroupWithZero.{succ u1} Cardinal.{u1} (NonUnitalCommSemiring.toNonUnitalSemiring.{succ u1} Cardinal.{u1} (CommSemiring.toNonUnitalCommSemiring.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}))))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} m)) (Dvd.dvd.{0} Nat Nat.instDvdNat n m)
-Case conversion may be inaccurate. Consider using '#align cardinal.nat_coe_dvd_iff Cardinal.nat_coe_dvd_iffₓ'. -/
 @[simp, norm_cast]
 theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
   by
@@ -133,12 +121,6 @@ theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
   exact ⟨k, by exact_mod_cast hk⟩
 #align cardinal.nat_coe_dvd_iff Cardinal.nat_coe_dvd_iff
 
-/- warning: cardinal.nat_is_prime_iff -> Cardinal.nat_is_prime_iff is a dubious translation:
-lean 3 declaration is
-  forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} Cardinal.commMonoidWithZero.{u1} ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (Nat.Prime n)
-but is expected to have type
-  forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} Cardinal.instCommMonoidWithZeroCardinal.{u1} (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (Nat.Prime n)
-Case conversion may be inaccurate. Consider using '#align cardinal.nat_is_prime_iff Cardinal.nat_is_prime_iffₓ'. -/
 @[simp]
 theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
   by
@@ -164,12 +146,6 @@ theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
   exact Or.inl (dvd_of_le_of_aleph_0_le hn ((nat_lt_aleph_0 n).le.trans hℵ₀b) hℵ₀b)
 #align cardinal.nat_is_prime_iff Cardinal.nat_is_prime_iff
 
-/- warning: cardinal.is_prime_iff -> Cardinal.is_prime_iff is a dubious translation:
-lean 3 declaration is
-  forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} Cardinal.commMonoidWithZero.{u1} a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) p)) (Nat.Prime p))))
-but is expected to have type
-  forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} Cardinal.instCommMonoidWithZeroCardinal.{u1} a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} p)) (Nat.Prime p))))
-Case conversion may be inaccurate. Consider using '#align cardinal.is_prime_iff Cardinal.is_prime_iffₓ'. -/
 theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ, a = p ∧ p.Prime :=
   by
   cases' le_or_lt ℵ₀ a with h h
@@ -178,12 +154,6 @@ theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ,
   simp [not_le.mpr h]
 #align cardinal.is_prime_iff Cardinal.is_prime_iff
 
-/- warning: cardinal.is_prime_pow_iff -> Cardinal.isPrimePow_iff is a dubious translation:
-lean 3 declaration is
-  forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} Cardinal.commMonoidWithZero.{u1} a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
-but is expected to have type
-  forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} Cardinal.instCommMonoidWithZeroCardinal.{u1} a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
-Case conversion may be inaccurate. Consider using '#align cardinal.is_prime_pow_iff Cardinal.isPrimePow_iffₓ'. -/
 theorem isPrimePow_iff {a : Cardinal} : IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n : ℕ, a = n ∧ IsPrimePow n :=
   by
   by_cases h : ℵ₀ ≤ a

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

@@ -48,10 +48,7 @@ variable {a b : Cardinal.{u}} {n m : ℕ}
 @[simp]
 theorem isUnit_iff : IsUnit a ↔ a = 1 :=
   by
-  refine'
-    ⟨fun h => _, by
-      rintro rfl
-      exact isUnit_one⟩
+  refine' ⟨fun h => _, by rintro rfl; exact isUnit_one⟩
   rcases eq_or_ne a 0 with (rfl | ha)
   · exact (not_isUnit_zero h).elim
   rw [isUnit_iff_forall_dvd] at h
@@ -99,8 +96,7 @@ theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
   cases' eq_or_ne (b * c) 0 with hz hz
   · rcases mul_eq_zero.mp hz with (rfl | rfl) <;> simp
   wlog h : c ≤ b
-  · cases le_total c b <;> [skip;rw [or_comm']] <;> apply_assumption
-    assumption'
+  · cases le_total c b <;> [skip;rw [or_comm']] <;> apply_assumption; assumption'
     all_goals rwa [mul_comm]
   left
   have habc := le_of_dvd hz hbc

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

@@ -99,7 +99,7 @@ theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
   cases' eq_or_ne (b * c) 0 with hz hz
   · rcases mul_eq_zero.mp hz with (rfl | rfl) <;> simp
   wlog h : c ≤ b
-  · cases le_total c b <;> [skip, rw [or_comm']] <;> apply_assumption
+  · cases le_total c b <;> [skip;rw [or_comm']] <;> apply_assumption
     assumption'
     all_goals rwa [mul_comm]
   left

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

@@ -88,7 +88,7 @@ theorem dvd_of_le_of_aleph0_le (ha : a ≠ 0) (h : a ≤ b) (hb : ℵ₀ ≤ b)
 lean 3 declaration is
   forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} Cardinal.commMonoidWithZero.{u1} a)
 but is expected to have type
-  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.instLinearOrderedCommMonoidWithZeroCardinal.{u1}) a)
+  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} Cardinal.instCommMonoidWithZeroCardinal.{u1} a)
 Case conversion may be inaccurate. Consider using '#align cardinal.prime_of_aleph_0_le Cardinal.prime_of_aleph0_leₓ'. -/
 @[simp]
 theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
@@ -141,7 +141,7 @@ theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
 lean 3 declaration is
   forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} Cardinal.commMonoidWithZero.{u1} ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (Nat.Prime n)
 but is expected to have type
-  forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.instLinearOrderedCommMonoidWithZeroCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (Nat.Prime n)
+  forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} Cardinal.instCommMonoidWithZeroCardinal.{u1} (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (Nat.Prime n)
 Case conversion may be inaccurate. Consider using '#align cardinal.nat_is_prime_iff Cardinal.nat_is_prime_iffₓ'. -/
 @[simp]
 theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
@@ -172,7 +172,7 @@ theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
 lean 3 declaration is
   forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} Cardinal.commMonoidWithZero.{u1} a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) p)) (Nat.Prime p))))
 but is expected to have type
-  forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.instLinearOrderedCommMonoidWithZeroCardinal.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} p)) (Nat.Prime p))))
+  forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} Cardinal.instCommMonoidWithZeroCardinal.{u1} a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} p)) (Nat.Prime p))))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_prime_iff Cardinal.is_prime_iffₓ'. -/
 theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ, a = p ∧ p.Prime :=
   by
@@ -186,7 +186,7 @@ theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ,
 lean 3 declaration is
   forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} Cardinal.commMonoidWithZero.{u1} a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
 but is expected to have type
-  forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.instLinearOrderedCommMonoidWithZeroCardinal.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
+  forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} Cardinal.instCommMonoidWithZeroCardinal.{u1} a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_prime_pow_iff Cardinal.isPrimePow_iffₓ'. -/
 theorem isPrimePow_iff {a : Cardinal} : IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n : ℕ, a = n ∧ IsPrimePow n :=
   by

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

@@ -86,7 +86,7 @@ theorem dvd_of_le_of_aleph0_le (ha : a ≠ 0) (h : a ≤ b) (hb : ℵ₀ ≤ b)
 
 /- warning: cardinal.prime_of_aleph_0_le -> Cardinal.prime_of_aleph0_le is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.linearOrderedCommMonoidWithZero.{u1}) a)
+  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} Cardinal.commMonoidWithZero.{u1} a)
 but is expected to have type
   forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.instLinearOrderedCommMonoidWithZeroCardinal.{u1}) a)
 Case conversion may be inaccurate. Consider using '#align cardinal.prime_of_aleph_0_le Cardinal.prime_of_aleph0_leₓ'. -/
@@ -139,7 +139,7 @@ theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
 
 /- warning: cardinal.nat_is_prime_iff -> Cardinal.nat_is_prime_iff is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.linearOrderedCommMonoidWithZero.{u1}) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (Nat.Prime n)
+  forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} Cardinal.commMonoidWithZero.{u1} ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (Nat.Prime n)
 but is expected to have type
   forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.instLinearOrderedCommMonoidWithZeroCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (Nat.Prime n)
 Case conversion may be inaccurate. Consider using '#align cardinal.nat_is_prime_iff Cardinal.nat_is_prime_iffₓ'. -/
@@ -170,7 +170,7 @@ theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
 
 /- warning: cardinal.is_prime_iff -> Cardinal.is_prime_iff is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.linearOrderedCommMonoidWithZero.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) p)) (Nat.Prime p))))
+  forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} Cardinal.commMonoidWithZero.{u1} a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) p)) (Nat.Prime p))))
 but is expected to have type
   forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.instLinearOrderedCommMonoidWithZeroCardinal.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} p)) (Nat.Prime p))))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_prime_iff Cardinal.is_prime_iffₓ'. -/
@@ -184,7 +184,7 @@ theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ,
 
 /- warning: cardinal.is_prime_pow_iff -> Cardinal.isPrimePow_iff is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.linearOrderedCommMonoidWithZero.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
+  forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} Cardinal.commMonoidWithZero.{u1} a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
 but is expected to have type
   forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.instLinearOrderedCommMonoidWithZeroCardinal.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_prime_pow_iff Cardinal.isPrimePow_iffₓ'. -/

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

@@ -44,12 +44,7 @@ universe u
 
 variable {a b : Cardinal.{u}} {n m : ℕ}
 
-/- warning: cardinal.is_unit_iff -> Cardinal.isUnit_iff is a dubious translation:
-lean 3 declaration is
-  forall {a : Cardinal.{u1}}, Iff (IsUnit.{succ u1} Cardinal.{u1} (MonoidWithZero.toMonoid.{succ u1} Cardinal.{u1} (Semiring.toMonoidWithZero.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1}))))) a) (Eq.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (OfNat.mk.{succ u1} Cardinal.{u1} 1 (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1}))))
-but is expected to have type
-  forall {a : Cardinal.{u1}}, Iff (IsUnit.{succ u1} Cardinal.{u1} (MonoidWithZero.toMonoid.{succ u1} Cardinal.{u1} (Semiring.toMonoidWithZero.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1}))))) a) (Eq.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (One.toOfNat1.{succ u1} Cardinal.{u1} Cardinal.instOneCardinal.{u1})))
-Case conversion may be inaccurate. Consider using '#align cardinal.is_unit_iff Cardinal.isUnit_iffₓ'. -/
+#print Cardinal.isUnit_iff /-
 @[simp]
 theorem isUnit_iff : IsUnit a ↔ a = 1 :=
   by
@@ -68,6 +63,7 @@ theorem isUnit_iff : IsUnit a ↔ a = 1 :=
     rw [MulZeroClass.mul_zero] at ht
     exact zero_ne_one ht
 #align cardinal.is_unit_iff Cardinal.isUnit_iff
+-/
 
 instance : Unique Cardinal.{u}ˣ where
   default := 1
@@ -92,7 +88,7 @@ theorem dvd_of_le_of_aleph0_le (ha : a ≠ 0) (h : a ≤ b) (hb : ℵ₀ ≤ b)
 lean 3 declaration is
   forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.linearOrderedCommMonoidWithZero.{u1}) a)
 but is expected to have type
-  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) a)
+  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.instLinearOrderedCommMonoidWithZeroCardinal.{u1}) a)
 Case conversion may be inaccurate. Consider using '#align cardinal.prime_of_aleph_0_le Cardinal.prime_of_aleph0_leₓ'. -/
 @[simp]
 theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
@@ -111,12 +107,7 @@ theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
   rwa [mul_eq_max' <| ha.trans <| habc, max_def', if_pos h] at hbc
 #align cardinal.prime_of_aleph_0_le Cardinal.prime_of_aleph0_le
 
-/- warning: cardinal.not_irreducible_of_aleph_0_le -> Cardinal.not_irreducible_of_aleph0_le is a dubious translation:
-lean 3 declaration is
-  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (Not (Irreducible.{succ u1} Cardinal.{u1} (MonoidWithZero.toMonoid.{succ u1} Cardinal.{u1} (Semiring.toMonoidWithZero.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1}))))) a))
-but is expected to have type
-  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) -> (Not (Irreducible.{succ u1} Cardinal.{u1} (MonoidWithZero.toMonoid.{succ u1} Cardinal.{u1} (Semiring.toMonoidWithZero.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1}))))) a))
-Case conversion may be inaccurate. Consider using '#align cardinal.not_irreducible_of_aleph_0_le Cardinal.not_irreducible_of_aleph0_leₓ'. -/
+#print Cardinal.not_irreducible_of_aleph0_le /-
 theorem not_irreducible_of_aleph0_le (ha : ℵ₀ ≤ a) : ¬Irreducible a :=
   by
   rw [irreducible_iff, not_and_or]
@@ -124,6 +115,7 @@ theorem not_irreducible_of_aleph0_le (ha : ℵ₀ ≤ a) : ¬Irreducible a :=
   simpa [mul_aleph_0_eq ha, is_unit_iff, (one_lt_aleph_0.trans_le ha).ne', one_lt_aleph_0.ne'] using
     h a ℵ₀
 #align cardinal.not_irreducible_of_aleph_0_le Cardinal.not_irreducible_of_aleph0_le
+-/
 
 /- warning: cardinal.nat_coe_dvd_iff -> Cardinal.nat_coe_dvd_iff is a dubious translation:
 lean 3 declaration is
@@ -149,7 +141,7 @@ theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
 lean 3 declaration is
   forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.linearOrderedCommMonoidWithZero.{u1}) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (Nat.Prime n)
 but is expected to have type
-  forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (Nat.Prime n)
+  forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.instLinearOrderedCommMonoidWithZeroCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (Nat.Prime n)
 Case conversion may be inaccurate. Consider using '#align cardinal.nat_is_prime_iff Cardinal.nat_is_prime_iffₓ'. -/
 @[simp]
 theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
@@ -180,7 +172,7 @@ theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
 lean 3 declaration is
   forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.linearOrderedCommMonoidWithZero.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) p)) (Nat.Prime p))))
 but is expected to have type
-  forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} p)) (Nat.Prime p))))
+  forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.instLinearOrderedCommMonoidWithZeroCardinal.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} p)) (Nat.Prime p))))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_prime_iff Cardinal.is_prime_iffₓ'. -/
 theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ, a = p ∧ p.Prime :=
   by
@@ -194,7 +186,7 @@ theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ,
 lean 3 declaration is
   forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.linearOrderedCommMonoidWithZero.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
 but is expected to have type
-  forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
+  forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.instLinearOrderedCommMonoidWithZeroCardinal.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_prime_pow_iff Cardinal.isPrimePow_iffₓ'. -/
 theorem isPrimePow_iff {a : Cardinal} : IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n : ℕ, a = n ∧ IsPrimePow n :=
   by

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

@@ -88,7 +88,12 @@ theorem dvd_of_le_of_aleph0_le (ha : a ≠ 0) (h : a ≤ b) (hb : ℵ₀ ≤ b)
 #align cardinal.dvd_of_le_of_aleph_0_le Cardinal.dvd_of_le_of_aleph0_le
 -/
 
-#print Cardinal.prime_of_aleph0_le /-
+/- warning: cardinal.prime_of_aleph_0_le -> Cardinal.prime_of_aleph0_le is a dubious translation:
+lean 3 declaration is
+  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.linearOrderedCommMonoidWithZero.{u1}) a)
+but is expected to have type
+  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) -> (Prime.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) a)
+Case conversion may be inaccurate. Consider using '#align cardinal.prime_of_aleph_0_le Cardinal.prime_of_aleph0_leₓ'. -/
 @[simp]
 theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
   by
@@ -105,7 +110,6 @@ theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
   have habc := le_of_dvd hz hbc
   rwa [mul_eq_max' <| ha.trans <| habc, max_def', if_pos h] at hbc
 #align cardinal.prime_of_aleph_0_le Cardinal.prime_of_aleph0_le
--/
 
 /- warning: cardinal.not_irreducible_of_aleph_0_le -> Cardinal.not_irreducible_of_aleph0_le is a dubious translation:
 lean 3 declaration is
@@ -143,7 +147,7 @@ theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
 
 /- warning: cardinal.nat_is_prime_iff -> Cardinal.nat_is_prime_iff is a dubious translation:
 lean 3 declaration is
-  forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (Nat.Prime n)
+  forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.linearOrderedCommMonoidWithZero.{u1}) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (Nat.Prime n)
 but is expected to have type
   forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (Nat.Prime n)
 Case conversion may be inaccurate. Consider using '#align cardinal.nat_is_prime_iff Cardinal.nat_is_prime_iffₓ'. -/
@@ -174,7 +178,7 @@ theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
 
 /- warning: cardinal.is_prime_iff -> Cardinal.is_prime_iff is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) p)) (Nat.Prime p))))
+  forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.linearOrderedCommMonoidWithZero.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) p)) (Nat.Prime p))))
 but is expected to have type
   forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} p)) (Nat.Prime p))))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_prime_iff Cardinal.is_prime_iffₓ'. -/
@@ -188,7 +192,7 @@ theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ,
 
 /- warning: cardinal.is_prime_pow_iff -> Cardinal.isPrimePow_iff is a dubious translation:
 lean 3 declaration is
-  forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
+  forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.linearOrderedCommMonoidWithZero.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
 but is expected to have type
   forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
 Case conversion may be inaccurate. Consider using '#align cardinal.is_prime_pow_iff Cardinal.isPrimePow_iffₓ'. -/

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

@@ -65,7 +65,7 @@ theorem isUnit_iff : IsUnit a ↔ a = 1 :=
   · exact ht.1
   all_goals rwa [one_le_iff_ne_zero]
   · rintro rfl
-    rw [mul_zero] at ht
+    rw [MulZeroClass.mul_zero] at ht
     exact zero_ne_one ht
 #align cardinal.is_unit_iff Cardinal.isUnit_iff
 
@@ -77,8 +77,8 @@ instance : Unique Cardinal.{u}ˣ where
 theorem le_of_dvd : ∀ {a b : Cardinal}, b ≠ 0 → a ∣ b → a ≤ b
   | a, _, b0, ⟨b, rfl⟩ => by
     simpa only [mul_one] using
-      mul_le_mul_left' (one_le_iff_ne_zero.2 fun h : b = 0 => by simpa only [h, mul_zero] using b0)
-        a
+      mul_le_mul_left'
+        (one_le_iff_ne_zero.2 fun h : b = 0 => by simpa only [h, MulZeroClass.mul_zero] using b0) a
 #align cardinal.le_of_dvd Cardinal.le_of_dvd
 -/
 
@@ -135,7 +135,8 @@ theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
   have : ↑m < ℵ₀ := nat_lt_aleph_0 m
   rw [hk, mul_lt_aleph_0_iff] at this
   rcases this with (h | h | ⟨-, hk'⟩)
-  iterate 2 simp only [h, mul_zero, zero_mul, Nat.cast_eq_zero] at hk; simp [hk]
+  iterate 2 simp only [h, MulZeroClass.mul_zero, MulZeroClass.zero_mul, Nat.cast_eq_zero] at hk;
+    simp [hk]
   lift k to ℕ using hk'
   exact ⟨k, by exact_mod_cast hk⟩
 #align cardinal.nat_coe_dvd_iff Cardinal.nat_coe_dvd_iff

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.divisibility
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
+! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.SetTheory.Cardinal.Ordinal
 /-!
 # Cardinal Divisibility
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We show basic results about divisibility in the cardinal numbers. This relation can be characterised
 in the following simple way: if `a` and `b` are both less than `ℵ₀`, then `a ∣ b` iff they are
 divisible as natural numbers. If `b` is greater than `ℵ₀`, then `a ∣ b` iff `a ≤ b`. This

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

@@ -41,6 +41,12 @@ universe u
 
 variable {a b : Cardinal.{u}} {n m : ℕ}
 
+/- warning: cardinal.is_unit_iff -> Cardinal.isUnit_iff is a dubious translation:
+lean 3 declaration is
+  forall {a : Cardinal.{u1}}, Iff (IsUnit.{succ u1} Cardinal.{u1} (MonoidWithZero.toMonoid.{succ u1} Cardinal.{u1} (Semiring.toMonoidWithZero.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1}))))) a) (Eq.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (OfNat.mk.{succ u1} Cardinal.{u1} 1 (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1}))))
+but is expected to have type
+  forall {a : Cardinal.{u1}}, Iff (IsUnit.{succ u1} Cardinal.{u1} (MonoidWithZero.toMonoid.{succ u1} Cardinal.{u1} (Semiring.toMonoidWithZero.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1}))))) a) (Eq.{succ (succ u1)} Cardinal.{u1} a (OfNat.ofNat.{succ u1} Cardinal.{u1} 1 (One.toOfNat1.{succ u1} Cardinal.{u1} Cardinal.instOneCardinal.{u1})))
+Case conversion may be inaccurate. Consider using '#align cardinal.is_unit_iff Cardinal.isUnit_iffₓ'. -/
 @[simp]
 theorem isUnit_iff : IsUnit a ↔ a = 1 :=
   by
@@ -64,17 +70,22 @@ instance : Unique Cardinal.{u}ˣ where
   default := 1
   uniq a := Units.val_eq_one.mp <| isUnit_iff.mp a.IsUnit
 
+#print Cardinal.le_of_dvd /-
 theorem le_of_dvd : ∀ {a b : Cardinal}, b ≠ 0 → a ∣ b → a ≤ b
   | a, _, b0, ⟨b, rfl⟩ => by
     simpa only [mul_one] using
       mul_le_mul_left' (one_le_iff_ne_zero.2 fun h : b = 0 => by simpa only [h, mul_zero] using b0)
         a
 #align cardinal.le_of_dvd Cardinal.le_of_dvd
+-/
 
+#print Cardinal.dvd_of_le_of_aleph0_le /-
 theorem dvd_of_le_of_aleph0_le (ha : a ≠ 0) (h : a ≤ b) (hb : ℵ₀ ≤ b) : a ∣ b :=
   ⟨b, (mul_eq_right hb h ha).symm⟩
 #align cardinal.dvd_of_le_of_aleph_0_le Cardinal.dvd_of_le_of_aleph0_le
+-/
 
+#print Cardinal.prime_of_aleph0_le /-
 @[simp]
 theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
   by
@@ -91,7 +102,14 @@ theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a :=
   have habc := le_of_dvd hz hbc
   rwa [mul_eq_max' <| ha.trans <| habc, max_def', if_pos h] at hbc
 #align cardinal.prime_of_aleph_0_le Cardinal.prime_of_aleph0_le
+-/
 
+/- warning: cardinal.not_irreducible_of_aleph_0_le -> Cardinal.not_irreducible_of_aleph0_le is a dubious translation:
+lean 3 declaration is
+  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) -> (Not (Irreducible.{succ u1} Cardinal.{u1} (MonoidWithZero.toMonoid.{succ u1} Cardinal.{u1} (Semiring.toMonoidWithZero.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1}))))) a))
+but is expected to have type
+  forall {a : Cardinal.{u1}}, (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) -> (Not (Irreducible.{succ u1} Cardinal.{u1} (MonoidWithZero.toMonoid.{succ u1} Cardinal.{u1} (Semiring.toMonoidWithZero.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1}))))) a))
+Case conversion may be inaccurate. Consider using '#align cardinal.not_irreducible_of_aleph_0_le Cardinal.not_irreducible_of_aleph0_leₓ'. -/
 theorem not_irreducible_of_aleph0_le (ha : ℵ₀ ≤ a) : ¬Irreducible a :=
   by
   rw [irreducible_iff, not_and_or]
@@ -100,6 +118,12 @@ theorem not_irreducible_of_aleph0_le (ha : ℵ₀ ≤ a) : ¬Irreducible a :=
     h a ℵ₀
 #align cardinal.not_irreducible_of_aleph_0_le Cardinal.not_irreducible_of_aleph0_le
 
+/- warning: cardinal.nat_coe_dvd_iff -> Cardinal.nat_coe_dvd_iff is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat} {m : Nat}, Iff (Dvd.Dvd.{succ u1} Cardinal.{u1} (semigroupDvd.{succ u1} Cardinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Cardinal.{u1} (NonUnitalSemiring.toSemigroupWithZero.{succ u1} Cardinal.{u1} (NonUnitalCommSemiring.toNonUnitalSemiring.{succ u1} Cardinal.{u1} (CommSemiring.toNonUnitalCommSemiring.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}))))) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) m)) (Dvd.Dvd.{0} Nat Nat.hasDvd n m)
+but is expected to have type
+  forall {n : Nat} {m : Nat}, Iff (Dvd.dvd.{succ u1} Cardinal.{u1} (semigroupDvd.{succ u1} Cardinal.{u1} (SemigroupWithZero.toSemigroup.{succ u1} Cardinal.{u1} (NonUnitalSemiring.toSemigroupWithZero.{succ u1} Cardinal.{u1} (NonUnitalCommSemiring.toNonUnitalSemiring.{succ u1} Cardinal.{u1} (CommSemiring.toNonUnitalCommSemiring.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}))))) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} m)) (Dvd.dvd.{0} Nat Nat.instDvdNat n m)
+Case conversion may be inaccurate. Consider using '#align cardinal.nat_coe_dvd_iff Cardinal.nat_coe_dvd_iffₓ'. -/
 @[simp, norm_cast]
 theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
   by
@@ -113,6 +137,12 @@ theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m :=
   exact ⟨k, by exact_mod_cast hk⟩
 #align cardinal.nat_coe_dvd_iff Cardinal.nat_coe_dvd_iff
 
+/- warning: cardinal.nat_is_prime_iff -> Cardinal.nat_is_prime_iff is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (Nat.Prime n)
+but is expected to have type
+  forall {n : Nat}, Iff (Prime.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (Nat.Prime n)
+Case conversion may be inaccurate. Consider using '#align cardinal.nat_is_prime_iff Cardinal.nat_is_prime_iffₓ'. -/
 @[simp]
 theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
   by
@@ -138,6 +168,12 @@ theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime :=
   exact Or.inl (dvd_of_le_of_aleph_0_le hn ((nat_lt_aleph_0 n).le.trans hℵ₀b) hℵ₀b)
 #align cardinal.nat_is_prime_iff Cardinal.nat_is_prime_iff
 
+/- warning: cardinal.is_prime_iff -> Cardinal.is_prime_iff is a dubious translation:
+lean 3 declaration is
+  forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) p)) (Nat.Prime p))))
+but is expected to have type
+  forall {a : Cardinal.{u1}}, Iff (Prime.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (p : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} p)) (Nat.Prime p))))
+Case conversion may be inaccurate. Consider using '#align cardinal.is_prime_iff Cardinal.is_prime_iffₓ'. -/
 theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ, a = p ∧ p.Prime :=
   by
   cases' le_or_lt ℵ₀ a with h h
@@ -146,6 +182,12 @@ theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ,
   simp [not_le.mpr h]
 #align cardinal.is_prime_iff Cardinal.is_prime_iff
 
+/- warning: cardinal.is_prime_pow_iff -> Cardinal.isPrimePow_iff is a dubious translation:
+lean 3 declaration is
+  forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
+but is expected to have type
+  forall {a : Cardinal.{u1}}, Iff (IsPrimePow.{succ u1} Cardinal.{u1} (CommSemiring.toCommMonoidWithZero.{succ u1} Cardinal.{u1} Cardinal.commSemiring.{u1}) a) (Or (LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} Cardinal.aleph0.{u1} a) (Exists.{1} Nat (fun (n : Nat) => And (Eq.{succ (succ u1)} Cardinal.{u1} a (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) (IsPrimePow.{0} Nat (LinearOrderedCommMonoidWithZero.toCommMonoidWithZero.{0} Nat Nat.linearOrderedCommMonoidWithZero) n))))
+Case conversion may be inaccurate. Consider using '#align cardinal.is_prime_pow_iff Cardinal.isPrimePow_iffₓ'. -/
 theorem isPrimePow_iff {a : Cardinal} : IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n : ℕ, a = n ∧ IsPrimePow n :=
   by
   by_cases h : ℵ₀ ≤ a

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

The removal of some pointless tactics flagged by #11308.

@@ -80,7 +80,8 @@ theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a := by
   rcases eq_or_ne (b * c) 0 with hz | hz
   · rcases mul_eq_zero.mp hz with (rfl | rfl) <;> simp
   wlog h : c ≤ b
-  · cases le_total c b <;> [skip; rw [or_comm]] <;> apply_assumption
+  · cases le_total c b <;> [solve_by_elim; rw [or_comm]]
+    apply_assumption
     assumption'
     all_goals rwa [mul_comm]
   left

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.

@@ -77,7 +77,7 @@ theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a := by
   refine' ⟨(aleph0_pos.trans_le ha).ne', _, fun b c hbc => _⟩
   · rw [isUnit_iff]
     exact (one_lt_aleph0.trans_le ha).ne'
-  cases' eq_or_ne (b * c) 0 with hz hz
+  rcases eq_or_ne (b * c) 0 with hz | hz
   · rcases mul_eq_zero.mp hz with (rfl | rfl) <;> simp
   wlog h : c ≤ b
   · cases le_total c b <;> [skip; rw [or_comm]] <;> apply_assumption
@@ -134,7 +134,7 @@ theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime := by
 #align cardinal.nat_is_prime_iff Cardinal.nat_is_prime_iff
 
 theorem is_prime_iff {a : Cardinal} : Prime a ↔ ℵ₀ ≤ a ∨ ∃ p : ℕ, a = p ∧ p.Prime := by
-  cases' le_or_lt ℵ₀ a with h h
+  rcases le_or_lt ℵ₀ a with h | h
   · simp [h]
   lift a to ℕ using id h
   simp [not_le.mpr h]

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

@@ -151,7 +151,7 @@ theorem isPrimePow_iff {a : Cardinal} : IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n
           ⟨p, k, nat_is_prime_iff.2 hp, hk, by rw [han]; exact mod_cast h⟩⟩
   rintro ⟨p, k, hp, hk, hpk⟩
   have key : p ^ (1 : Cardinal) ≤ ↑a := by
-    rw [←hpk]; apply power_le_power_left hp.ne_zero; exact mod_cast hk
+    rw [← hpk]; apply power_le_power_left hp.ne_zero; exact mod_cast hk
   rw [power_one] at key
   lift p to ℕ using key.trans_lt (nat_lt_aleph0 a)
   exact ⟨a, rfl, p, k, nat_is_prime_iff.mp hp, hk, mod_cast hpk⟩

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

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

@@ -97,14 +97,14 @@ theorem not_irreducible_of_aleph0_le (ha : ℵ₀ ≤ a) : ¬Irreducible a := by
 
 @[simp, norm_cast]
 theorem nat_coe_dvd_iff : (n : Cardinal) ∣ m ↔ n ∣ m := by
-  refine' ⟨_, fun ⟨h, ht⟩ => ⟨h, by exact_mod_cast ht⟩⟩
+  refine' ⟨_, fun ⟨h, ht⟩ => ⟨h, mod_cast ht⟩⟩
   rintro ⟨k, hk⟩
   have : ↑m < ℵ₀ := nat_lt_aleph0 m
   rw [hk, mul_lt_aleph0_iff] at this
   rcases this with (h | h | ⟨-, hk'⟩)
   iterate 2 simp only [h, mul_zero, zero_mul, Nat.cast_eq_zero] at hk; simp [hk]
   lift k to ℕ using hk'
-  exact ⟨k, by exact_mod_cast hk⟩
+  exact ⟨k, mod_cast hk⟩
 #align cardinal.nat_coe_dvd_iff Cardinal.nat_coe_dvd_iff
 
 @[simp]
@@ -112,15 +112,15 @@ theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime := by
   simp only [Prime, Nat.prime_iff]
   refine' and_congr (by simp) (and_congr _ ⟨fun h b c hbc => _, fun h b c hbc => _⟩)
   · simp only [isUnit_iff, Nat.isUnit_iff]
-    exact_mod_cast Iff.rfl
-  · exact_mod_cast h b c (by exact_mod_cast hbc)
+    exact mod_cast Iff.rfl
+  · exact mod_cast h b c (mod_cast hbc)
   cases' lt_or_le (b * c) ℵ₀ with h' h'
   · rcases mul_lt_aleph0_iff.mp h' with (rfl | rfl | ⟨hb, hc⟩)
     · simp
     · simp
     lift b to ℕ using hb
     lift c to ℕ using hc
-    exact_mod_cast h b c (by exact_mod_cast hbc)
+    exact mod_cast h b c (mod_cast hbc)
   rcases aleph0_le_mul_iff.mp h' with ⟨hb, hc, hℵ₀⟩
   have hn : (n : Cardinal) ≠ 0 := by
     intro h
@@ -148,13 +148,13 @@ theorem isPrimePow_iff {a : Cardinal} : IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n
   rw [isPrimePow_def]
   refine'
     ⟨_, fun ⟨n, han, p, k, hp, hk, h⟩ =>
-          ⟨p, k, nat_is_prime_iff.2 hp, hk, by rw [han]; exact_mod_cast h⟩⟩
+          ⟨p, k, nat_is_prime_iff.2 hp, hk, by rw [han]; exact mod_cast h⟩⟩
   rintro ⟨p, k, hp, hk, hpk⟩
   have key : p ^ (1 : Cardinal) ≤ ↑a := by
-    rw [←hpk]; apply power_le_power_left hp.ne_zero; exact_mod_cast hk
+    rw [←hpk]; apply power_le_power_left hp.ne_zero; exact mod_cast hk
   rw [power_one] at key
   lift p to ℕ using key.trans_lt (nat_lt_aleph0 a)
-  exact ⟨a, rfl, p, k, nat_is_prime_iff.mp hp, hk, by exact_mod_cast hpk⟩
+  exact ⟨a, rfl, p, k, nat_is_prime_iff.mp hp, hk, mod_cast hpk⟩
 #align cardinal.is_prime_pow_iff Cardinal.isPrimePow_iff
 
 end Cardinal

PR contents

This is the supremum of

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

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

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

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

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

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

leanprover/lean4#2778

We can get rid of all the

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

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

leanprover/lean4#2722

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

leanprover/lean4#2783

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

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

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

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

@@ -150,7 +150,8 @@ theorem isPrimePow_iff {a : Cardinal} : IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n
     ⟨_, fun ⟨n, han, p, k, hp, hk, h⟩ =>
           ⟨p, k, nat_is_prime_iff.2 hp, hk, by rw [han]; exact_mod_cast h⟩⟩
   rintro ⟨p, k, hp, hk, hpk⟩
-  have key : p ^ 1 ≤ ↑a := by rw [←hpk]; apply power_le_power_left hp.ne_zero; exact_mod_cast hk
+  have key : p ^ (1 : Cardinal) ≤ ↑a := by
+    rw [←hpk]; apply power_le_power_left hp.ne_zero; exact_mod_cast hk
   rw [power_one] at key
   lift p to ℕ using key.trans_lt (nat_lt_aleph0 a)
   exact ⟨a, rfl, p, k, nat_is_prime_iff.mp hp, hk, by exact_mod_cast hpk⟩

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Eric Rodriguez. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
-
-! This file was ported from Lean 3 source module set_theory.cardinal.divisibility
-! leanprover-community/mathlib commit ea050b44c0f9aba9d16a948c7cc7d2e7c8493567
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.IsPrimePow
 import Mathlib.SetTheory.Cardinal.Ordinal
 import Mathlib.Tactic.WLOG
 
+#align_import set_theory.cardinal.divisibility from "leanprover-community/mathlib"@"ea050b44c0f9aba9d16a948c7cc7d2e7c8493567"
+
 /-!
 # Cardinal Divisibility
 

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

@@ -83,7 +83,7 @@ theorem prime_of_aleph0_le (ha : ℵ₀ ≤ a) : Prime a := by
   cases' eq_or_ne (b * c) 0 with hz hz
   · rcases mul_eq_zero.mp hz with (rfl | rfl) <;> simp
   wlog h : c ≤ b
-  · cases le_total c b <;> [skip, rw [or_comm]] <;> apply_assumption
+  · cases le_total c b <;> [skip; rw [or_comm]] <;> apply_assumption
     assumption'
     all_goals rwa [mul_comm]
   left

Mathlib 3: https://github.com/leanprover-community/mathlib/pull/18714

Co-authored-by: Scott Morrison <scott@tqft.net>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Eric Rodriguez
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.divisibility
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
+! leanprover-community/mathlib commit ea050b44c0f9aba9d16a948c7cc7d2e7c8493567
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

vscode is already configured by .vscode/settings.json to trim these on save. It's not clear how they've managed to stick around.

By doing this all in one PR now, it avoids getting random whitespace diffs in PRs later.

This was done with a regex search in vscode,

@@ -132,7 +132,7 @@ theorem nat_is_prime_iff : Prime (n : Cardinal) ↔ n.Prime := by
   wlog hℵ₀b : ℵ₀ ≤ b
   refine' (this h c b _ _ hc hb hℵ₀.symm hn (hℵ₀.resolve_left hℵ₀b)).symm <;> try assumption
   rwa [mul_comm] at hbc
-  rwa [mul_comm] at h' 
+  rwa [mul_comm] at h'
   exact Or.inl (dvd_of_le_of_aleph0_le hn ((nat_lt_aleph0 n).le.trans hℵ₀b) hℵ₀b)
 #align cardinal.nat_is_prime_iff Cardinal.nat_is_prime_iff
 
@@ -160,4 +160,3 @@ theorem isPrimePow_iff {a : Cardinal} : IsPrimePow a ↔ ℵ₀ ≤ a ∨ ∃ n
 #align cardinal.is_prime_pow_iff Cardinal.isPrimePow_iff
 
 end Cardinal
-

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