set_theory.cardinal.continuum | 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

e08a42b2

(last sync)

chore(set_theory/cardinal/basic): missing lemmas about lift c < ℵ₀ and ℵ₀ < lift c (#18746)

We already had the le versions lift_le_aleph0 and aleph0_le_lift, this adds the lt ones lift_lt_aleph0 and aleph0_lt_lift.

This turns out to be useful for proving some results about finrank, as well as golfing some existing proofs.

Since they're trivial, this adds the same lemmas about continuum too.

Diff

@@ -39,6 +39,18 @@ by rw [←two_power_aleph_0, lift_two_power, lift_aleph_0, two_power_aleph_0]
 ### Inequalities
 -/
 
+@[simp] lemma continuum_le_lift {c : cardinal.{u}} : 𝔠 ≤ lift.{v} c ↔ 𝔠 ≤ c :=
+by rw [←lift_continuum, lift_le]
+
+@[simp] lemma lift_le_continuum {c : cardinal.{u}} : lift.{v} c ≤ 𝔠 ↔ c ≤ 𝔠 :=
+by rw [←lift_continuum, lift_le]
+
+@[simp] lemma continuum_lt_lift {c : cardinal.{u}} : 𝔠 < lift.{v} c ↔ 𝔠 < c :=
+by rw [←lift_continuum, lift_lt]
+
+@[simp] lemma lift_lt_continuum {c : cardinal.{u}} : lift.{v} c < 𝔠 ↔ c < 𝔠 :=
+by rw [←lift_continuum, lift_lt]
+
 lemma aleph_0_lt_continuum : ℵ₀ < 𝔠 := cantor ℵ₀
 
 lemma aleph_0_le_continuum : ℵ₀ ≤ 𝔠 := aleph_0_lt_continuum.le

3d7987cd

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

e08a42b2

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.SetTheory.Cardinal.Ordinal
+import SetTheory.Cardinal.Ordinal
 
 #align_import set_theory.cardinal.continuum from "leanprover-community/mathlib"@"e08a42b2dd544cf11eba72e5fc7bf199d4349925"

e08a42b2

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module set_theory.cardinal.continuum
-! leanprover-community/mathlib commit e08a42b2dd544cf11eba72e5fc7bf199d4349925
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.SetTheory.Cardinal.Ordinal
 
+#align_import set_theory.cardinal.continuum from "leanprover-community/mathlib"@"e08a42b2dd544cf11eba72e5fc7bf199d4349925"
+
 /-!
 # Cardinality of continuum

e08a42b2

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -38,18 +38,21 @@ def continuum : Cardinal.{u} :=
 #align cardinal.continuum Cardinal.continuum
 -/
 
--- mathport name: cardinal.continuum
 scoped notation "𝔠" => Cardinal.continuum
 
+#print Cardinal.two_power_aleph0 /-
 @[simp]
 theorem two_power_aleph0 : 2 ^ aleph0.{u} = continuum.{u} :=
   rfl
 #align cardinal.two_power_aleph_0 Cardinal.two_power_aleph0
+-/
 
+#print Cardinal.lift_continuum /-
 @[simp]
 theorem lift_continuum : lift.{v} 𝔠 = 𝔠 := by
   rw [← two_power_aleph_0, lift_two_power, lift_aleph_0, two_power_aleph_0]
 #align cardinal.lift_continuum Cardinal.lift_continuum
+-/
 
 /-!
 ### Inequalities
@@ -96,13 +99,17 @@ theorem aleph0_le_continuum : ℵ₀ ≤ 𝔠 :=
 #align cardinal.aleph_0_le_continuum Cardinal.aleph0_le_continuum
 -/
 
+#print Cardinal.beth_one /-
 @[simp]
 theorem beth_one : beth 1 = 𝔠 := by simpa using beth_succ 0
 #align cardinal.beth_one Cardinal.beth_one
+-/
 
+#print Cardinal.nat_lt_continuum /-
 theorem nat_lt_continuum (n : ℕ) : ↑n < 𝔠 :=
   (nat_lt_aleph0 n).trans aleph0_lt_continuum
 #align cardinal.nat_lt_continuum Cardinal.nat_lt_continuum
+-/
 
 #print Cardinal.mk_set_nat /-
 theorem mk_set_nat : (#Set ℕ) = 𝔠 := by simp
@@ -121,9 +128,11 @@ theorem continuum_ne_zero : 𝔠 ≠ 0 :=
 #align cardinal.continuum_ne_zero Cardinal.continuum_ne_zero
 -/
 
+#print Cardinal.aleph_one_le_continuum /-
 theorem aleph_one_le_continuum : aleph 1 ≤ 𝔠 := by rw [← succ_aleph_0];
   exact Order.succ_le_of_lt aleph_0_lt_continuum
 #align cardinal.aleph_one_le_continuum Cardinal.aleph_one_le_continuum
+-/
 
 #print Cardinal.continuum_toNat /-
 @[simp]
@@ -132,70 +141,92 @@ theorem continuum_toNat : continuum.toNat = 0 :=
 #align cardinal.continuum_to_nat Cardinal.continuum_toNat
 -/
 
+#print Cardinal.continuum_toPartENat /-
 @[simp]
 theorem continuum_toPartENat : continuum.toPartENat = ⊤ :=
   toPartENat_apply_of_aleph0_le aleph0_le_continuum
 #align cardinal.continuum_to_part_enat Cardinal.continuum_toPartENat
+-/
 
 /-!
 ### Addition
 -/
 
 
+#print Cardinal.aleph0_add_continuum /-
 @[simp]
 theorem aleph0_add_continuum : ℵ₀ + 𝔠 = 𝔠 :=
   add_eq_right aleph0_le_continuum aleph0_le_continuum
 #align cardinal.aleph_0_add_continuum Cardinal.aleph0_add_continuum
+-/
 
+#print Cardinal.continuum_add_aleph0 /-
 @[simp]
 theorem continuum_add_aleph0 : 𝔠 + ℵ₀ = 𝔠 :=
   (add_comm _ _).trans aleph0_add_continuum
 #align cardinal.continuum_add_aleph_0 Cardinal.continuum_add_aleph0
+-/
 
+#print Cardinal.continuum_add_self /-
 @[simp]
 theorem continuum_add_self : 𝔠 + 𝔠 = 𝔠 :=
   add_eq_right aleph0_le_continuum le_rfl
 #align cardinal.continuum_add_self Cardinal.continuum_add_self
+-/
 
+#print Cardinal.nat_add_continuum /-
 @[simp]
 theorem nat_add_continuum (n : ℕ) : ↑n + 𝔠 = 𝔠 :=
   add_eq_right aleph0_le_continuum (nat_lt_continuum n).le
 #align cardinal.nat_add_continuum Cardinal.nat_add_continuum
+-/
 
+#print Cardinal.continuum_add_nat /-
 @[simp]
 theorem continuum_add_nat (n : ℕ) : 𝔠 + n = 𝔠 :=
   (add_comm _ _).trans (nat_add_continuum n)
 #align cardinal.continuum_add_nat Cardinal.continuum_add_nat
+-/
 
 /-!
 ### Multiplication
 -/
 
 
+#print Cardinal.continuum_mul_self /-
 @[simp]
 theorem continuum_mul_self : 𝔠 * 𝔠 = 𝔠 :=
   mul_eq_left aleph0_le_continuum le_rfl continuum_ne_zero
 #align cardinal.continuum_mul_self Cardinal.continuum_mul_self
+-/
 
+#print Cardinal.continuum_mul_aleph0 /-
 @[simp]
 theorem continuum_mul_aleph0 : 𝔠 * ℵ₀ = 𝔠 :=
   mul_eq_left aleph0_le_continuum aleph0_le_continuum aleph0_ne_zero
 #align cardinal.continuum_mul_aleph_0 Cardinal.continuum_mul_aleph0
+-/
 
+#print Cardinal.aleph0_mul_continuum /-
 @[simp]
 theorem aleph0_mul_continuum : ℵ₀ * 𝔠 = 𝔠 :=
   (mul_comm _ _).trans continuum_mul_aleph0
 #align cardinal.aleph_0_mul_continuum Cardinal.aleph0_mul_continuum
+-/
 
+#print Cardinal.nat_mul_continuum /-
 @[simp]
 theorem nat_mul_continuum {n : ℕ} (hn : n ≠ 0) : ↑n * 𝔠 = 𝔠 :=
   mul_eq_right aleph0_le_continuum (nat_lt_continuum n).le (Nat.cast_ne_zero.2 hn)
 #align cardinal.nat_mul_continuum Cardinal.nat_mul_continuum
+-/
 
+#print Cardinal.continuum_mul_nat /-
 @[simp]
 theorem continuum_mul_nat {n : ℕ} (hn : n ≠ 0) : 𝔠 * n = 𝔠 :=
   (mul_comm _ _).trans (nat_mul_continuum hn)
 #align cardinal.continuum_mul_nat Cardinal.continuum_mul_nat
+-/
 
 /-!
 ### Power
@@ -209,10 +240,12 @@ theorem aleph0_power_aleph0 : aleph0.{u} ^ aleph0.{u} = 𝔠 :=
 #align cardinal.aleph_0_power_aleph_0 Cardinal.aleph0_power_aleph0
 -/
 
+#print Cardinal.nat_power_aleph0 /-
 @[simp]
 theorem nat_power_aleph0 {n : ℕ} (hn : 2 ≤ n) : (n ^ aleph0.{u} : Cardinal.{u}) = 𝔠 :=
   nat_power_eq le_rfl hn
 #align cardinal.nat_power_aleph_0 Cardinal.nat_power_aleph0
+-/
 
 #print Cardinal.continuum_power_aleph0 /-
 @[simp]

e08a42b2

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -29,7 +29,7 @@ namespace Cardinal
 
 universe u v
 
-open Cardinal
+open scoped Cardinal
 
 #print Cardinal.continuum /-
 /-- Cardinality of continuum. -/
@@ -70,19 +70,25 @@ theorem lift_le_continuum {c : Cardinal.{u}} : lift.{v} c ≤ 𝔠 ↔ c ≤ 
 #align cardinal.lift_le_continuum Cardinal.lift_le_continuum
 -/
 
+#print Cardinal.continuum_lt_lift /-
 @[simp]
 theorem continuum_lt_lift {c : Cardinal.{u}} : 𝔠 < lift.{v} c ↔ 𝔠 < c := by
   rw [← lift_continuum, lift_lt]
 #align cardinal.continuum_lt_lift Cardinal.continuum_lt_lift
+-/
 
+#print Cardinal.lift_lt_continuum /-
 @[simp]
 theorem lift_lt_continuum {c : Cardinal.{u}} : lift.{v} c < 𝔠 ↔ c < 𝔠 := by
   rw [← lift_continuum, lift_lt]
 #align cardinal.lift_lt_continuum Cardinal.lift_lt_continuum
+-/
 
+#print Cardinal.aleph0_lt_continuum /-
 theorem aleph0_lt_continuum : ℵ₀ < 𝔠 :=
   cantor ℵ₀
 #align cardinal.aleph_0_lt_continuum Cardinal.aleph0_lt_continuum
+-/
 
 #print Cardinal.aleph0_le_continuum /-
 theorem aleph0_le_continuum : ℵ₀ ≤ 𝔠 :=
@@ -103,9 +109,11 @@ theorem mk_set_nat : (#Set ℕ) = 𝔠 := by simp
 #align cardinal.mk_set_nat Cardinal.mk_set_nat
 -/
 
+#print Cardinal.continuum_pos /-
 theorem continuum_pos : 0 < 𝔠 :=
   nat_lt_continuum 0
 #align cardinal.continuum_pos Cardinal.continuum_pos
+-/
 
 #print Cardinal.continuum_ne_zero /-
 theorem continuum_ne_zero : 𝔠 ≠ 0 :=

e08a42b2

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -41,23 +41,11 @@ def continuum : Cardinal.{u} :=
 -- mathport name: cardinal.continuum
 scoped notation "𝔠" => Cardinal.continuum
 
-/- warning: cardinal.two_power_aleph_0 -> Cardinal.two_power_aleph0 is a dubious translation:
-lean 3 declaration is
-  Eq.{succ (succ u1)} Cardinal.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) Cardinal.aleph0.{u1}) Cardinal.continuum.{u1}
-but is expected to have type
-  Eq.{succ (succ u1)} Cardinal.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Cardinal.aleph0.{u1}) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.two_power_aleph_0 Cardinal.two_power_aleph0ₓ'. -/
 @[simp]
 theorem two_power_aleph0 : 2 ^ aleph0.{u} = continuum.{u} :=
   rfl
 #align cardinal.two_power_aleph_0 Cardinal.two_power_aleph0
 
-/- warning: cardinal.lift_continuum -> Cardinal.lift_continuum is a dubious translation:
-lean 3 declaration is
-  Eq.{succ (succ (max u2 u1))} Cardinal.{max u2 u1} (Cardinal.lift.{u1, u2} Cardinal.continuum.{u2}) Cardinal.continuum.{max u2 u1}
-but is expected to have type
-  Eq.{max (succ (succ u2)) (succ (succ u1))} Cardinal.{max u1 u2} (Cardinal.lift.{u2, u1} Cardinal.continuum.{u1}) Cardinal.continuum.{max u2 u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.lift_continuum Cardinal.lift_continuumₓ'. -/
 @[simp]
 theorem lift_continuum : lift.{v} 𝔠 = 𝔠 := by
   rw [← two_power_aleph_0, lift_two_power, lift_aleph_0, two_power_aleph_0]
@@ -82,34 +70,16 @@ theorem lift_le_continuum {c : Cardinal.{u}} : lift.{v} c ≤ 𝔠 ↔ c ≤ 
 #align cardinal.lift_le_continuum Cardinal.lift_le_continuum
 -/
 
-/- warning: cardinal.continuum_lt_lift -> Cardinal.continuum_lt_lift is a dubious translation:
-lean 3 declaration is
-  forall {c : Cardinal.{u1}}, Iff (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) Cardinal.continuum.{max u1 u2} (Cardinal.lift.{u2, u1} c)) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.continuum.{u1} c)
-but is expected to have type
-  forall {c : Cardinal.{u1}}, Iff (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) Cardinal.continuum.{max u1 u2} (Cardinal.lift.{u2, u1} c)) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.continuum.{u1} c)
-Case conversion may be inaccurate. Consider using '#align cardinal.continuum_lt_lift Cardinal.continuum_lt_liftₓ'. -/
 @[simp]
 theorem continuum_lt_lift {c : Cardinal.{u}} : 𝔠 < lift.{v} c ↔ 𝔠 < c := by
   rw [← lift_continuum, lift_lt]
 #align cardinal.continuum_lt_lift Cardinal.continuum_lt_lift
 
-/- warning: cardinal.lift_lt_continuum -> Cardinal.lift_lt_continuum is a dubious translation:
-lean 3 declaration is
-  forall {c : Cardinal.{u1}}, Iff (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} c) Cardinal.continuum.{max u1 u2}) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c Cardinal.continuum.{u1})
-but is expected to have type
-  forall {c : Cardinal.{u1}}, Iff (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} c) Cardinal.continuum.{max u1 u2}) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c Cardinal.continuum.{u1})
-Case conversion may be inaccurate. Consider using '#align cardinal.lift_lt_continuum Cardinal.lift_lt_continuumₓ'. -/
 @[simp]
 theorem lift_lt_continuum {c : Cardinal.{u}} : lift.{v} c < 𝔠 ↔ c < 𝔠 := by
   rw [← lift_continuum, lift_lt]
 #align cardinal.lift_lt_continuum Cardinal.lift_lt_continuum
 
-/- warning: cardinal.aleph_0_lt_continuum -> Cardinal.aleph0_lt_continuum is a dubious translation:
-lean 3 declaration is
-  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}
-but is expected to have type
-  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.aleph_0_lt_continuum Cardinal.aleph0_lt_continuumₓ'. -/
 theorem aleph0_lt_continuum : ℵ₀ < 𝔠 :=
   cantor ℵ₀
 #align cardinal.aleph_0_lt_continuum Cardinal.aleph0_lt_continuum
@@ -120,22 +90,10 @@ theorem aleph0_le_continuum : ℵ₀ ≤ 𝔠 :=
 #align cardinal.aleph_0_le_continuum Cardinal.aleph0_le_continuum
 -/
 
-/- warning: cardinal.beth_one -> Cardinal.beth_one is a dubious translation:
-lean 3 declaration is
-  Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.beth.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) Cardinal.continuum.{u1}
-but is expected to have type
-  Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.beth.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.beth_one Cardinal.beth_oneₓ'. -/
 @[simp]
 theorem beth_one : beth 1 = 𝔠 := by simpa using beth_succ 0
 #align cardinal.beth_one Cardinal.beth_one
 
-/- warning: cardinal.nat_lt_continuum -> Cardinal.nat_lt_continuum is a dubious translation:
-lean 3 declaration is
-  forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n) Cardinal.continuum.{u1}
-but is expected to have type
-  forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.nat_lt_continuum Cardinal.nat_lt_continuumₓ'. -/
 theorem nat_lt_continuum (n : ℕ) : ↑n < 𝔠 :=
   (nat_lt_aleph0 n).trans aleph0_lt_continuum
 #align cardinal.nat_lt_continuum Cardinal.nat_lt_continuum
@@ -145,12 +103,6 @@ theorem mk_set_nat : (#Set ℕ) = 𝔠 := by simp
 #align cardinal.mk_set_nat Cardinal.mk_set_nat
 -/
 
-/- warning: cardinal.continuum_pos -> Cardinal.continuum_pos is a dubious translation:
-lean 3 declaration is
-  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1}))) Cardinal.continuum.{u1}
-but is expected to have type
-  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1})) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.continuum_pos Cardinal.continuum_posₓ'. -/
 theorem continuum_pos : 0 < 𝔠 :=
   nat_lt_continuum 0
 #align cardinal.continuum_pos Cardinal.continuum_pos
@@ -161,12 +113,6 @@ theorem continuum_ne_zero : 𝔠 ≠ 0 :=
 #align cardinal.continuum_ne_zero Cardinal.continuum_ne_zero
 -/
 
-/- warning: cardinal.aleph_one_le_continuum -> Cardinal.aleph_one_le_continuum is a dubious translation:
-lean 3 declaration is
-  LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.aleph.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) Cardinal.continuum.{u1}
-but is expected to have type
-  LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.aleph.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.aleph_one_le_continuum Cardinal.aleph_one_le_continuumₓ'. -/
 theorem aleph_one_le_continuum : aleph 1 ≤ 𝔠 := by rw [← succ_aleph_0];
   exact Order.succ_le_of_lt aleph_0_lt_continuum
 #align cardinal.aleph_one_le_continuum Cardinal.aleph_one_le_continuum
@@ -178,12 +124,6 @@ theorem continuum_toNat : continuum.toNat = 0 :=
 #align cardinal.continuum_to_nat Cardinal.continuum_toNat
 -/
 
-/- warning: cardinal.continuum_to_part_enat -> Cardinal.continuum_toPartENat is a dubious translation:
-lean 3 declaration is
-  Eq.{1} PartENat (coeFn.{succ (succ u1), succ (succ u1)} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) (fun (_x : AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) => Cardinal.{u1} -> PartENat) (AddMonoidHom.hasCoeToFun.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) Cardinal.toPartENat.{u1} Cardinal.continuum.{u1}) (Top.top.{0} PartENat PartENat.hasTop)
-but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) Cardinal.continuum.{u1}) (FunLike.coe.{succ (succ u1), succ (succ u1), 1} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) _x) (AddHomClass.toFunLike.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddZeroClass.toAdd.{succ u1} Cardinal.{u1} (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1}))))))))) (AddZeroClass.toAdd.{0} PartENat (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) (AddMonoidHomClass.toAddHomClass.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat))) (AddMonoidHom.addMonoidHomClass.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))))) Cardinal.toPartENat.{u1} Cardinal.continuum.{u1}) (Top.top.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) Cardinal.continuum.{u1}) PartENat.instTopPartENat)
-Case conversion may be inaccurate. Consider using '#align cardinal.continuum_to_part_enat Cardinal.continuum_toPartENatₓ'. -/
 @[simp]
 theorem continuum_toPartENat : continuum.toPartENat = ⊤ :=
   toPartENat_apply_of_aleph0_le aleph0_le_continuum
@@ -194,56 +134,26 @@ theorem continuum_toPartENat : continuum.toPartENat = ⊤ :=
 -/
 
 
-/- warning: cardinal.aleph_0_add_continuum -> Cardinal.aleph0_add_continuum is a dubious translation:
-lean 3 declaration is
-  Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
-but is expected to have type
-  Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.aleph_0_add_continuum Cardinal.aleph0_add_continuumₓ'. -/
 @[simp]
 theorem aleph0_add_continuum : ℵ₀ + 𝔠 = 𝔠 :=
   add_eq_right aleph0_le_continuum aleph0_le_continuum
 #align cardinal.aleph_0_add_continuum Cardinal.aleph0_add_continuum
 
-/- warning: cardinal.continuum_add_aleph_0 -> Cardinal.continuum_add_aleph0 is a dubious translation:
-lean 3 declaration is
-  Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) Cardinal.continuum.{u1} Cardinal.aleph0.{u1}) Cardinal.continuum.{u1}
-but is expected to have type
-  Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) Cardinal.continuum.{u1} Cardinal.aleph0.{u1}) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.continuum_add_aleph_0 Cardinal.continuum_add_aleph0ₓ'. -/
 @[simp]
 theorem continuum_add_aleph0 : 𝔠 + ℵ₀ = 𝔠 :=
   (add_comm _ _).trans aleph0_add_continuum
 #align cardinal.continuum_add_aleph_0 Cardinal.continuum_add_aleph0
 
-/- warning: cardinal.continuum_add_self -> Cardinal.continuum_add_self is a dubious translation:
-lean 3 declaration is
-  Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) Cardinal.continuum.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
-but is expected to have type
-  Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) Cardinal.continuum.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.continuum_add_self Cardinal.continuum_add_selfₓ'. -/
 @[simp]
 theorem continuum_add_self : 𝔠 + 𝔠 = 𝔠 :=
   add_eq_right aleph0_le_continuum le_rfl
 #align cardinal.continuum_add_self Cardinal.continuum_add_self
 
-/- warning: cardinal.nat_add_continuum -> Cardinal.nat_add_continuum is a dubious translation:
-lean 3 declaration is
-  forall (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) ((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) Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
-but is expected to have type
-  forall (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.nat_add_continuum Cardinal.nat_add_continuumₓ'. -/
 @[simp]
 theorem nat_add_continuum (n : ℕ) : ↑n + 𝔠 = 𝔠 :=
   add_eq_right aleph0_le_continuum (nat_lt_continuum n).le
 #align cardinal.nat_add_continuum Cardinal.nat_add_continuum
 
-/- warning: cardinal.continuum_add_nat -> Cardinal.continuum_add_nat is a dubious translation:
-lean 3 declaration is
-  forall (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) Cardinal.continuum.{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)) Cardinal.continuum.{u1}
-but is expected to have type
-  forall (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) Cardinal.continuum.{u1} (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.continuum_add_nat Cardinal.continuum_add_natₓ'. -/
 @[simp]
 theorem continuum_add_nat (n : ℕ) : 𝔠 + n = 𝔠 :=
   (add_comm _ _).trans (nat_add_continuum n)
@@ -254,56 +164,26 @@ theorem continuum_add_nat (n : ℕ) : 𝔠 + n = 𝔠 :=
 -/
 
 
-/- warning: cardinal.continuum_mul_self -> Cardinal.continuum_mul_self is a dubious translation:
-lean 3 declaration is
-  Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) Cardinal.continuum.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
-but is expected to have type
-  Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) Cardinal.continuum.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.continuum_mul_self Cardinal.continuum_mul_selfₓ'. -/
 @[simp]
 theorem continuum_mul_self : 𝔠 * 𝔠 = 𝔠 :=
   mul_eq_left aleph0_le_continuum le_rfl continuum_ne_zero
 #align cardinal.continuum_mul_self Cardinal.continuum_mul_self
 
-/- warning: cardinal.continuum_mul_aleph_0 -> Cardinal.continuum_mul_aleph0 is a dubious translation:
-lean 3 declaration is
-  Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) Cardinal.continuum.{u1} Cardinal.aleph0.{u1}) Cardinal.continuum.{u1}
-but is expected to have type
-  Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) Cardinal.continuum.{u1} Cardinal.aleph0.{u1}) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.continuum_mul_aleph_0 Cardinal.continuum_mul_aleph0ₓ'. -/
 @[simp]
 theorem continuum_mul_aleph0 : 𝔠 * ℵ₀ = 𝔠 :=
   mul_eq_left aleph0_le_continuum aleph0_le_continuum aleph0_ne_zero
 #align cardinal.continuum_mul_aleph_0 Cardinal.continuum_mul_aleph0
 
-/- warning: cardinal.aleph_0_mul_continuum -> Cardinal.aleph0_mul_continuum is a dubious translation:
-lean 3 declaration is
-  Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
-but is expected to have type
-  Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.aleph_0_mul_continuum Cardinal.aleph0_mul_continuumₓ'. -/
 @[simp]
 theorem aleph0_mul_continuum : ℵ₀ * 𝔠 = 𝔠 :=
   (mul_comm _ _).trans continuum_mul_aleph0
 #align cardinal.aleph_0_mul_continuum Cardinal.aleph0_mul_continuum
 
-/- warning: cardinal.nat_mul_continuum -> Cardinal.nat_mul_continuum is a dubious translation:
-lean 3 declaration is
-  forall {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) ((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) Cardinal.continuum.{u1}) Cardinal.continuum.{u1})
-but is expected to have type
-  forall {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) Cardinal.continuum.{u1}) Cardinal.continuum.{u1})
-Case conversion may be inaccurate. Consider using '#align cardinal.nat_mul_continuum Cardinal.nat_mul_continuumₓ'. -/
 @[simp]
 theorem nat_mul_continuum {n : ℕ} (hn : n ≠ 0) : ↑n * 𝔠 = 𝔠 :=
   mul_eq_right aleph0_le_continuum (nat_lt_continuum n).le (Nat.cast_ne_zero.2 hn)
 #align cardinal.nat_mul_continuum Cardinal.nat_mul_continuum
 
-/- warning: cardinal.continuum_mul_nat -> Cardinal.continuum_mul_nat is a dubious translation:
-lean 3 declaration is
-  forall {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) Cardinal.continuum.{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)) Cardinal.continuum.{u1})
-but is expected to have type
-  forall {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) Cardinal.continuum.{u1} (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) Cardinal.continuum.{u1})
-Case conversion may be inaccurate. Consider using '#align cardinal.continuum_mul_nat Cardinal.continuum_mul_natₓ'. -/
 @[simp]
 theorem continuum_mul_nat {n : ℕ} (hn : n ≠ 0) : 𝔠 * n = 𝔠 :=
   (mul_comm _ _).trans (nat_mul_continuum hn)
@@ -321,12 +201,6 @@ theorem aleph0_power_aleph0 : aleph0.{u} ^ aleph0.{u} = 𝔠 :=
 #align cardinal.aleph_0_power_aleph_0 Cardinal.aleph0_power_aleph0
 -/
 
-/- warning: cardinal.nat_power_aleph_0 -> Cardinal.nat_power_aleph0 is a dubious translation:
-lean 3 declaration is
-  forall {n : Nat}, (LE.le.{0} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) ((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) Cardinal.aleph0.{u1}) Cardinal.continuum.{u1})
-but is expected to have type
-  forall {n : Nat}, (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) Cardinal.aleph0.{u1}) Cardinal.continuum.{u1})
-Case conversion may be inaccurate. Consider using '#align cardinal.nat_power_aleph_0 Cardinal.nat_power_aleph0ₓ'. -/
 @[simp]
 theorem nat_power_aleph0 {n : ℕ} (hn : 2 ≤ n) : (n ^ aleph0.{u} : Cardinal.{u}) = 𝔠 :=
   nat_power_eq le_rfl hn

e08a42b2

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -167,9 +167,7 @@ lean 3 declaration is
 but is expected to have type
   LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.aleph.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) Cardinal.continuum.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.aleph_one_le_continuum Cardinal.aleph_one_le_continuumₓ'. -/
-theorem aleph_one_le_continuum : aleph 1 ≤ 𝔠 :=
-  by
-  rw [← succ_aleph_0]
+theorem aleph_one_le_continuum : aleph 1 ≤ 𝔠 := by rw [← succ_aleph_0];
   exact Order.succ_le_of_lt aleph_0_lt_continuum
 #align cardinal.aleph_one_le_continuum Cardinal.aleph_one_le_continuum

e08a42b2

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -82,25 +82,37 @@ theorem lift_le_continuum {c : Cardinal.{u}} : lift.{v} c ≤ 𝔠 ↔ c ≤ 
 #align cardinal.lift_le_continuum Cardinal.lift_le_continuum
 -/
 
-#print Cardinal.continuum_lt_lift /-
+/- warning: cardinal.continuum_lt_lift -> Cardinal.continuum_lt_lift is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{u1}}, Iff (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) Cardinal.continuum.{max u1 u2} (Cardinal.lift.{u2, u1} c)) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.continuum.{u1} c)
+but is expected to have type
+  forall {c : Cardinal.{u1}}, Iff (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) Cardinal.continuum.{max u1 u2} (Cardinal.lift.{u2, u1} c)) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.continuum.{u1} c)
+Case conversion may be inaccurate. Consider using '#align cardinal.continuum_lt_lift Cardinal.continuum_lt_liftₓ'. -/
 @[simp]
 theorem continuum_lt_lift {c : Cardinal.{u}} : 𝔠 < lift.{v} c ↔ 𝔠 < c := by
   rw [← lift_continuum, lift_lt]
 #align cardinal.continuum_lt_lift Cardinal.continuum_lt_lift
--/
 
-#print Cardinal.lift_lt_continuum /-
+/- warning: cardinal.lift_lt_continuum -> Cardinal.lift_lt_continuum is a dubious translation:
+lean 3 declaration is
+  forall {c : Cardinal.{u1}}, Iff (LT.lt.{succ (max u1 u2)} Cardinal.{max u1 u2} (Preorder.toHasLt.{succ (max u1 u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{succ (max u1 u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} c) Cardinal.continuum.{max u1 u2}) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c Cardinal.continuum.{u1})
+but is expected to have type
+  forall {c : Cardinal.{u1}}, Iff (LT.lt.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (Preorder.toLT.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} (PartialOrder.toPreorder.{max (succ u1) (succ u2)} Cardinal.{max u1 u2} Cardinal.partialOrder.{max u1 u2})) (Cardinal.lift.{u2, u1} c) Cardinal.continuum.{max u1 u2}) (LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) c Cardinal.continuum.{u1})
+Case conversion may be inaccurate. Consider using '#align cardinal.lift_lt_continuum Cardinal.lift_lt_continuumₓ'. -/
 @[simp]
 theorem lift_lt_continuum {c : Cardinal.{u}} : lift.{v} c < 𝔠 ↔ c < 𝔠 := by
   rw [← lift_continuum, lift_lt]
 #align cardinal.lift_lt_continuum Cardinal.lift_lt_continuum
--/
 
-#print Cardinal.aleph0_lt_continuum /-
+/- warning: cardinal.aleph_0_lt_continuum -> Cardinal.aleph0_lt_continuum is a dubious translation:
+lean 3 declaration is
+  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}
+but is expected to have type
+  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_0_lt_continuum Cardinal.aleph0_lt_continuumₓ'. -/
 theorem aleph0_lt_continuum : ℵ₀ < 𝔠 :=
   cantor ℵ₀
 #align cardinal.aleph_0_lt_continuum Cardinal.aleph0_lt_continuum
--/
 
 #print Cardinal.aleph0_le_continuum /-
 theorem aleph0_le_continuum : ℵ₀ ≤ 𝔠 :=
@@ -120,7 +132,7 @@ theorem beth_one : beth 1 = 𝔠 := by simpa using beth_succ 0
 
 /- warning: cardinal.nat_lt_continuum -> Cardinal.nat_lt_continuum is a dubious translation:
 lean 3 declaration is
-  forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n) Cardinal.continuum.{u1}
+  forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n) Cardinal.continuum.{u1}
 but is expected to have type
   forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) Cardinal.continuum.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.nat_lt_continuum Cardinal.nat_lt_continuumₓ'. -/
@@ -133,11 +145,15 @@ theorem mk_set_nat : (#Set ℕ) = 𝔠 := by simp
 #align cardinal.mk_set_nat Cardinal.mk_set_nat
 -/
 
-#print Cardinal.continuum_pos /-
+/- warning: cardinal.continuum_pos -> Cardinal.continuum_pos is a dubious translation:
+lean 3 declaration is
+  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toHasLt.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1}))) Cardinal.continuum.{u1}
+but is expected to have type
+  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1})) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.continuum_pos Cardinal.continuum_posₓ'. -/
 theorem continuum_pos : 0 < 𝔠 :=
   nat_lt_continuum 0
 #align cardinal.continuum_pos Cardinal.continuum_pos
--/
 
 #print Cardinal.continuum_ne_zero /-
 theorem continuum_ne_zero : 𝔠 ≠ 0 :=

e08a42b2

bump to nightly-2023-04-13-02

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

bd75793a

Diff

@@ -120,7 +120,7 @@ theorem beth_one : beth 1 = 𝔠 := by simpa using beth_succ 0
 
 /- warning: cardinal.nat_lt_continuum -> Cardinal.nat_lt_continuum is a dubious translation:
 lean 3 declaration is
-  forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) ((fun (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) Cardinal.continuum.{u1}
+  forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n) Cardinal.continuum.{u1}
 but is expected to have type
   forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) Cardinal.continuum.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.nat_lt_continuum Cardinal.nat_lt_continuumₓ'. -/

e08a42b2

bump to nightly-2023-04-10-00

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

542f5cb1

Diff

@@ -68,35 +68,39 @@ theorem lift_continuum : lift.{v} 𝔠 = 𝔠 := by
 -/
 
 
+#print Cardinal.continuum_le_lift /-
 @[simp]
 theorem continuum_le_lift {c : Cardinal.{u}} : 𝔠 ≤ lift.{v} c ↔ 𝔠 ≤ c := by
   rw [← lift_continuum, lift_le]
 #align cardinal.continuum_le_lift Cardinal.continuum_le_lift
+-/
 
+#print Cardinal.lift_le_continuum /-
 @[simp]
 theorem lift_le_continuum {c : Cardinal.{u}} : lift.{v} c ≤ 𝔠 ↔ c ≤ 𝔠 := by
   rw [← lift_continuum, lift_le]
 #align cardinal.lift_le_continuum Cardinal.lift_le_continuum
+-/
 
+#print Cardinal.continuum_lt_lift /-
 @[simp]
 theorem continuum_lt_lift {c : Cardinal.{u}} : 𝔠 < lift.{v} c ↔ 𝔠 < c := by
   rw [← lift_continuum, lift_lt]
 #align cardinal.continuum_lt_lift Cardinal.continuum_lt_lift
+-/
 
+#print Cardinal.lift_lt_continuum /-
 @[simp]
 theorem lift_lt_continuum {c : Cardinal.{u}} : lift.{v} c < 𝔠 ↔ c < 𝔠 := by
   rw [← lift_continuum, lift_lt]
 #align cardinal.lift_lt_continuum Cardinal.lift_lt_continuum
+-/
 
-/- warning: cardinal.aleph_0_lt_continuum -> Cardinal.aleph0_lt_continuum is a dubious translation:
-lean 3 declaration is
-  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}
-but is expected to have type
-  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.aleph_0_lt_continuum Cardinal.aleph0_lt_continuumₓ'. -/
+#print Cardinal.aleph0_lt_continuum /-
 theorem aleph0_lt_continuum : ℵ₀ < 𝔠 :=
   cantor ℵ₀
 #align cardinal.aleph_0_lt_continuum Cardinal.aleph0_lt_continuum
+-/
 
 #print Cardinal.aleph0_le_continuum /-
 theorem aleph0_le_continuum : ℵ₀ ≤ 𝔠 :=
@@ -129,15 +133,11 @@ theorem mk_set_nat : (#Set ℕ) = 𝔠 := by simp
 #align cardinal.mk_set_nat Cardinal.mk_set_nat
 -/
 
-/- warning: cardinal.continuum_pos -> Cardinal.continuum_pos is a dubious translation:
-lean 3 declaration is
-  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1}))) Cardinal.continuum.{u1}
-but is expected to have type
-  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1})) Cardinal.continuum.{u1}
-Case conversion may be inaccurate. Consider using '#align cardinal.continuum_pos Cardinal.continuum_posₓ'. -/
+#print Cardinal.continuum_pos /-
 theorem continuum_pos : 0 < 𝔠 :=
   nat_lt_continuum 0
 #align cardinal.continuum_pos Cardinal.continuum_pos
+-/
 
 #print Cardinal.continuum_ne_zero /-
 theorem continuum_ne_zero : 𝔠 ≠ 0 :=
@@ -168,7 +168,7 @@ theorem continuum_toNat : continuum.toNat = 0 :=
 lean 3 declaration is
   Eq.{1} PartENat (coeFn.{succ (succ u1), succ (succ u1)} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) (fun (_x : AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) => Cardinal.{u1} -> PartENat) (AddMonoidHom.hasCoeToFun.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) Cardinal.toPartENat.{u1} Cardinal.continuum.{u1}) (Top.top.{0} PartENat PartENat.hasTop)
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) Cardinal.continuum.{u1}) (FunLike.coe.{succ (succ u1), succ (succ u1), 1} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) _x) (AddHomClass.toFunLike.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddZeroClass.toAdd.{succ u1} Cardinal.{u1} (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1}))))))))) (AddZeroClass.toAdd.{0} PartENat (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) (AddMonoidHomClass.toAddHomClass.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat))) (AddMonoidHom.addMonoidHomClass.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))))) Cardinal.toPartENat.{u1} Cardinal.continuum.{u1}) (Top.top.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) Cardinal.continuum.{u1}) PartENat.instTopPartENat)
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) Cardinal.continuum.{u1}) (FunLike.coe.{succ (succ u1), succ (succ u1), 1} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) _x) (AddHomClass.toFunLike.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddZeroClass.toAdd.{succ u1} Cardinal.{u1} (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1}))))))))) (AddZeroClass.toAdd.{0} PartENat (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) (AddMonoidHomClass.toAddHomClass.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat))) (AddMonoidHom.addMonoidHomClass.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))))) Cardinal.toPartENat.{u1} Cardinal.continuum.{u1}) (Top.top.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) Cardinal.continuum.{u1}) PartENat.instTopPartENat)
 Case conversion may be inaccurate. Consider using '#align cardinal.continuum_to_part_enat Cardinal.continuum_toPartENatₓ'. -/
 @[simp]
 theorem continuum_toPartENat : continuum.toPartENat = ⊤ :=

e08a42b2

bump to nightly-2023-04-07-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

3f979973

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.continuum
-! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
+! leanprover-community/mathlib commit e08a42b2dd544cf11eba72e5fc7bf199d4349925
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -68,6 +68,26 @@ theorem lift_continuum : lift.{v} 𝔠 = 𝔠 := by
 -/
 
 
+@[simp]
+theorem continuum_le_lift {c : Cardinal.{u}} : 𝔠 ≤ lift.{v} c ↔ 𝔠 ≤ c := by
+  rw [← lift_continuum, lift_le]
+#align cardinal.continuum_le_lift Cardinal.continuum_le_lift
+
+@[simp]
+theorem lift_le_continuum {c : Cardinal.{u}} : lift.{v} c ≤ 𝔠 ↔ c ≤ 𝔠 := by
+  rw [← lift_continuum, lift_le]
+#align cardinal.lift_le_continuum Cardinal.lift_le_continuum
+
+@[simp]
+theorem continuum_lt_lift {c : Cardinal.{u}} : 𝔠 < lift.{v} c ↔ 𝔠 < c := by
+  rw [← lift_continuum, lift_lt]
+#align cardinal.continuum_lt_lift Cardinal.continuum_lt_lift
+
+@[simp]
+theorem lift_lt_continuum {c : Cardinal.{u}} : lift.{v} c < 𝔠 ↔ c < 𝔠 := by
+  rw [← lift_continuum, lift_lt]
+#align cardinal.lift_lt_continuum Cardinal.lift_lt_continuum
+
 /- warning: cardinal.aleph_0_lt_continuum -> Cardinal.aleph0_lt_continuum is a dubious translation:
 lean 3 declaration is
   LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}

ee05e9ce

bump to nightly-2023-04-03-02

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

8477bcac

Diff

@@ -68,11 +68,15 @@ theorem lift_continuum : lift.{v} 𝔠 = 𝔠 := by
 -/
 
 
-#print Cardinal.aleph0_lt_continuum /-
+/- warning: cardinal.aleph_0_lt_continuum -> Cardinal.aleph0_lt_continuum is a dubious translation:
+lean 3 declaration is
+  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}
+but is expected to have type
+  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_0_lt_continuum Cardinal.aleph0_lt_continuumₓ'. -/
 theorem aleph0_lt_continuum : ℵ₀ < 𝔠 :=
   cantor ℵ₀
 #align cardinal.aleph_0_lt_continuum Cardinal.aleph0_lt_continuum
--/
 
 #print Cardinal.aleph0_le_continuum /-
 theorem aleph0_le_continuum : ℵ₀ ≤ 𝔠 :=
@@ -92,7 +96,7 @@ theorem beth_one : beth 1 = 𝔠 := by simpa using beth_succ 0
 
 /- warning: cardinal.nat_lt_continuum -> Cardinal.nat_lt_continuum is a dubious translation:
 lean 3 declaration is
-  forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n) Cardinal.continuum.{u1}
+  forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) ((fun (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) Cardinal.continuum.{u1}
 but is expected to have type
   forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) Cardinal.continuum.{u1}
 Case conversion may be inaccurate. Consider using '#align cardinal.nat_lt_continuum Cardinal.nat_lt_continuumₓ'. -/
@@ -105,11 +109,15 @@ theorem mk_set_nat : (#Set ℕ) = 𝔠 := by simp
 #align cardinal.mk_set_nat Cardinal.mk_set_nat
 -/
 
-#print Cardinal.continuum_pos /-
+/- warning: cardinal.continuum_pos -> Cardinal.continuum_pos is a dubious translation:
+lean 3 declaration is
+  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} (OrderedAddCommMonoid.toPartialOrder.{succ u1} Cardinal.{u1} (OrderedSemiring.toOrderedAddCommMonoid.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (OfNat.mk.{succ u1} Cardinal.{u1} 0 (Zero.zero.{succ u1} Cardinal.{u1} Cardinal.hasZero.{u1}))) Cardinal.continuum.{u1}
+but is expected to have type
+  LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (OfNat.ofNat.{succ u1} Cardinal.{u1} 0 (Zero.toOfNat0.{succ u1} Cardinal.{u1} Cardinal.instZeroCardinal.{u1})) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.continuum_pos Cardinal.continuum_posₓ'. -/
 theorem continuum_pos : 0 < 𝔠 :=
   nat_lt_continuum 0
 #align cardinal.continuum_pos Cardinal.continuum_pos
--/
 
 #print Cardinal.continuum_ne_zero /-
 theorem continuum_ne_zero : 𝔠 ≠ 0 :=

ee05e9ce

bump to nightly-2023-03-11-22

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

a8ee822f

Diff

@@ -140,7 +140,7 @@ theorem continuum_toNat : continuum.toNat = 0 :=
 lean 3 declaration is
   Eq.{1} PartENat (coeFn.{succ (succ u1), succ (succ u1)} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) (fun (_x : AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) => Cardinal.{u1} -> PartENat) (AddMonoidHom.hasCoeToFun.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) Cardinal.toPartENat.{u1} Cardinal.continuum.{u1}) (Top.top.{0} PartENat PartENat.hasTop)
 but is expected to have type
-  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Cardinal.{u1}) => PartENat) Cardinal.continuum.{u1}) (FunLike.coe.{succ (succ u1), succ (succ u1), 1} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Cardinal.{u1}) => PartENat) _x) (AddHomClass.toFunLike.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddZeroClass.toAdd.{succ u1} Cardinal.{u1} (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1}))))))))) (AddZeroClass.toAdd.{0} PartENat (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) (AddMonoidHomClass.toAddHomClass.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat))) (AddMonoidHom.addMonoidHomClass.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))))) Cardinal.toPartENat.{u1} Cardinal.continuum.{u1}) (Top.top.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Cardinal.{u1}) => PartENat) Cardinal.continuum.{u1}) PartENat.instTopPartENat)
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) Cardinal.continuum.{u1}) (FunLike.coe.{succ (succ u1), succ (succ u1), 1} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) _x) (AddHomClass.toFunLike.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddZeroClass.toAdd.{succ u1} Cardinal.{u1} (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1}))))))))) (AddZeroClass.toAdd.{0} PartENat (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) (AddMonoidHomClass.toAddHomClass.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat))) (AddMonoidHom.addMonoidHomClass.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))))) Cardinal.toPartENat.{u1} Cardinal.continuum.{u1}) (Top.top.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.403 : Cardinal.{u1}) => PartENat) Cardinal.continuum.{u1}) PartENat.instTopPartENat)
 Case conversion may be inaccurate. Consider using '#align cardinal.continuum_to_part_enat Cardinal.continuum_toPartENatₓ'. -/
 @[simp]
 theorem continuum_toPartENat : continuum.toPartENat = ⊤ :=

ee05e9ce

bump to nightly-2023-03-02-03

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

db7421c3

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.continuum
-! leanprover-community/mathlib commit 3d7987cda72abc473c7cdbbb075170e9ac620042
+! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.SetTheory.Cardinal.Ordinal
 /-!
 # Cardinality of continuum
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define `cardinal.continuum` (notation: `𝔠`, localized in `cardinal`) to be `2 ^ ℵ₀`.
 We also prove some `simp` lemmas about cardinal arithmetic involving `𝔠`.

3d7987cd

bump to nightly-2023-02-25-00

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

aca219f8

Diff

@@ -28,19 +28,33 @@ universe u v
 
 open Cardinal
 
+#print Cardinal.continuum /-
 /-- Cardinality of continuum. -/
 def continuum : Cardinal.{u} :=
   2 ^ aleph0.{u}
 #align cardinal.continuum Cardinal.continuum
+-/
 
 -- mathport name: cardinal.continuum
 scoped notation "𝔠" => Cardinal.continuum
 
+/- warning: cardinal.two_power_aleph_0 -> Cardinal.two_power_aleph0 is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Cardinal.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (OfNat.mk.{succ u1} Cardinal.{u1} 2 (bit0.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1} (One.one.{succ u1} Cardinal.{u1} Cardinal.hasOne.{u1})))) Cardinal.aleph0.{u1}) Cardinal.continuum.{u1}
+but is expected to have type
+  Eq.{succ (succ u1)} Cardinal.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (OfNat.ofNat.{succ u1} Cardinal.{u1} 2 (instOfNat.{succ u1} Cardinal.{u1} 2 Cardinal.instNatCastCardinal.{u1} (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Cardinal.aleph0.{u1}) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.two_power_aleph_0 Cardinal.two_power_aleph0ₓ'. -/
 @[simp]
 theorem two_power_aleph0 : 2 ^ aleph0.{u} = continuum.{u} :=
   rfl
 #align cardinal.two_power_aleph_0 Cardinal.two_power_aleph0
 
+/- warning: cardinal.lift_continuum -> Cardinal.lift_continuum is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ (max u2 u1))} Cardinal.{max u2 u1} (Cardinal.lift.{u1, u2} Cardinal.continuum.{u2}) Cardinal.continuum.{max u2 u1}
+but is expected to have type
+  Eq.{max (succ (succ u2)) (succ (succ u1))} Cardinal.{max u1 u2} (Cardinal.lift.{u2, u1} Cardinal.continuum.{u1}) Cardinal.continuum.{max u2 u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.lift_continuum Cardinal.lift_continuumₓ'. -/
 @[simp]
 theorem lift_continuum : lift.{v} 𝔠 = 𝔠 := by
   rw [← two_power_aleph_0, lift_two_power, lift_aleph_0, two_power_aleph_0]
@@ -51,44 +65,80 @@ theorem lift_continuum : lift.{v} 𝔠 = 𝔠 := by
 -/
 
 
+#print Cardinal.aleph0_lt_continuum /-
 theorem aleph0_lt_continuum : ℵ₀ < 𝔠 :=
   cantor ℵ₀
 #align cardinal.aleph_0_lt_continuum Cardinal.aleph0_lt_continuum
+-/
 
+#print Cardinal.aleph0_le_continuum /-
 theorem aleph0_le_continuum : ℵ₀ ≤ 𝔠 :=
   aleph0_lt_continuum.le
 #align cardinal.aleph_0_le_continuum Cardinal.aleph0_le_continuum
+-/
 
+/- warning: cardinal.beth_one -> Cardinal.beth_one is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.beth.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) Cardinal.continuum.{u1}
+but is expected to have type
+  Eq.{succ (succ u1)} Cardinal.{u1} (Cardinal.beth.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.beth_one Cardinal.beth_oneₓ'. -/
 @[simp]
 theorem beth_one : beth 1 = 𝔠 := by simpa using beth_succ 0
 #align cardinal.beth_one Cardinal.beth_one
 
+/- warning: cardinal.nat_lt_continuum -> Cardinal.nat_lt_continuum is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) ((fun (a : Type) (b : Type.{succ u1}) [self : HasLiftT.{1, succ (succ u1)} a b] => self.0) Nat Cardinal.{u1} (HasLiftT.mk.{1, succ (succ u1)} Nat Cardinal.{u1} (CoeTCₓ.coe.{1, succ (succ u1)} Nat Cardinal.{u1} (Nat.castCoe.{succ u1} Cardinal.{u1} Cardinal.hasNatCast.{u1}))) n) Cardinal.continuum.{u1}
+but is expected to have type
+  forall (n : Nat), LT.lt.{succ u1} Cardinal.{u1} (Preorder.toLT.{succ u1} Cardinal.{u1} (PartialOrder.toPreorder.{succ u1} Cardinal.{u1} Cardinal.partialOrder.{u1})) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.nat_lt_continuum Cardinal.nat_lt_continuumₓ'. -/
 theorem nat_lt_continuum (n : ℕ) : ↑n < 𝔠 :=
   (nat_lt_aleph0 n).trans aleph0_lt_continuum
 #align cardinal.nat_lt_continuum Cardinal.nat_lt_continuum
 
+#print Cardinal.mk_set_nat /-
 theorem mk_set_nat : (#Set ℕ) = 𝔠 := by simp
 #align cardinal.mk_set_nat Cardinal.mk_set_nat
+-/
 
+#print Cardinal.continuum_pos /-
 theorem continuum_pos : 0 < 𝔠 :=
   nat_lt_continuum 0
 #align cardinal.continuum_pos Cardinal.continuum_pos
+-/
 
+#print Cardinal.continuum_ne_zero /-
 theorem continuum_ne_zero : 𝔠 ≠ 0 :=
   continuum_pos.ne'
 #align cardinal.continuum_ne_zero Cardinal.continuum_ne_zero
+-/
 
+/- warning: cardinal.aleph_one_le_continuum -> Cardinal.aleph_one_le_continuum is a dubious translation:
+lean 3 declaration is
+  LE.le.{succ u1} Cardinal.{u1} Cardinal.hasLe.{u1} (Cardinal.aleph.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (OfNat.mk.{succ u1} Ordinal.{u1} 1 (One.one.{succ u1} Ordinal.{u1} Ordinal.hasOne.{u1})))) Cardinal.continuum.{u1}
+but is expected to have type
+  LE.le.{succ u1} Cardinal.{u1} Cardinal.instLECardinal.{u1} (Cardinal.aleph.{u1} (OfNat.ofNat.{succ u1} Ordinal.{u1} 1 (One.toOfNat1.{succ u1} Ordinal.{u1} Ordinal.one.{u1}))) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_one_le_continuum Cardinal.aleph_one_le_continuumₓ'. -/
 theorem aleph_one_le_continuum : aleph 1 ≤ 𝔠 :=
   by
   rw [← succ_aleph_0]
   exact Order.succ_le_of_lt aleph_0_lt_continuum
 #align cardinal.aleph_one_le_continuum Cardinal.aleph_one_le_continuum
 
+#print Cardinal.continuum_toNat /-
 @[simp]
 theorem continuum_toNat : continuum.toNat = 0 :=
   toNat_apply_of_aleph0_le aleph0_le_continuum
 #align cardinal.continuum_to_nat Cardinal.continuum_toNat
+-/
 
+/- warning: cardinal.continuum_to_part_enat -> Cardinal.continuum_toPartENat is a dubious translation:
+lean 3 declaration is
+  Eq.{1} PartENat (coeFn.{succ (succ u1), succ (succ u1)} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) (fun (_x : AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) => Cardinal.{u1} -> PartENat) (AddMonoidHom.hasCoeToFun.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.canonicallyOrderedCommSemiring.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.addCommMonoidWithOne)))) Cardinal.toPartENat.{u1} Cardinal.continuum.{u1}) (Top.top.{0} PartENat PartENat.hasTop)
+but is expected to have type
+  Eq.{1} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Cardinal.{u1}) => PartENat) Cardinal.continuum.{u1}) (FunLike.coe.{succ (succ u1), succ (succ u1), 1} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} (fun (_x : Cardinal.{u1}) => (fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Cardinal.{u1}) => PartENat) _x) (AddHomClass.toFunLike.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddZeroClass.toAdd.{succ u1} Cardinal.{u1} (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1}))))))))) (AddZeroClass.toAdd.{0} PartENat (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) (AddMonoidHomClass.toAddHomClass.{succ u1, succ u1, 0} (AddMonoidHom.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))) Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat))) (AddMonoidHom.addMonoidHomClass.{succ u1, 0} Cardinal.{u1} PartENat (AddMonoid.toAddZeroClass.{succ u1} Cardinal.{u1} (AddMonoidWithOne.toAddMonoid.{succ u1} Cardinal.{u1} (AddCommMonoidWithOne.toAddMonoidWithOne.{succ u1} Cardinal.{u1} (NonAssocSemiring.toAddCommMonoidWithOne.{succ u1} Cardinal.{u1} (Semiring.toNonAssocSemiring.{succ u1} Cardinal.{u1} (OrderedSemiring.toSemiring.{succ u1} Cardinal.{u1} (OrderedCommSemiring.toOrderedSemiring.{succ u1} Cardinal.{u1} (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{succ u1} Cardinal.{u1} Cardinal.instCanonicallyOrderedCommSemiringCardinal.{u1})))))))) (AddMonoid.toAddZeroClass.{0} PartENat (AddMonoidWithOne.toAddMonoid.{0} PartENat (AddCommMonoidWithOne.toAddMonoidWithOne.{0} PartENat PartENat.instAddCommMonoidWithOnePartENat)))))) Cardinal.toPartENat.{u1} Cardinal.continuum.{u1}) (Top.top.{0} ((fun (x._@.Mathlib.Algebra.Hom.Group._hyg.398 : Cardinal.{u1}) => PartENat) Cardinal.continuum.{u1}) PartENat.instTopPartENat)
+Case conversion may be inaccurate. Consider using '#align cardinal.continuum_to_part_enat Cardinal.continuum_toPartENatₓ'. -/
 @[simp]
 theorem continuum_toPartENat : continuum.toPartENat = ⊤ :=
   toPartENat_apply_of_aleph0_le aleph0_le_continuum
@@ -99,26 +149,56 @@ theorem continuum_toPartENat : continuum.toPartENat = ⊤ :=
 -/
 
 
+/- warning: cardinal.aleph_0_add_continuum -> Cardinal.aleph0_add_continuum is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
+but is expected to have type
+  Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_0_add_continuum Cardinal.aleph0_add_continuumₓ'. -/
 @[simp]
 theorem aleph0_add_continuum : ℵ₀ + 𝔠 = 𝔠 :=
   add_eq_right aleph0_le_continuum aleph0_le_continuum
 #align cardinal.aleph_0_add_continuum Cardinal.aleph0_add_continuum
 
+/- warning: cardinal.continuum_add_aleph_0 -> Cardinal.continuum_add_aleph0 is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) Cardinal.continuum.{u1} Cardinal.aleph0.{u1}) Cardinal.continuum.{u1}
+but is expected to have type
+  Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) Cardinal.continuum.{u1} Cardinal.aleph0.{u1}) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.continuum_add_aleph_0 Cardinal.continuum_add_aleph0ₓ'. -/
 @[simp]
 theorem continuum_add_aleph0 : 𝔠 + ℵ₀ = 𝔠 :=
   (add_comm _ _).trans aleph0_add_continuum
 #align cardinal.continuum_add_aleph_0 Cardinal.continuum_add_aleph0
 
+/- warning: cardinal.continuum_add_self -> Cardinal.continuum_add_self is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) Cardinal.continuum.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
+but is expected to have type
+  Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) Cardinal.continuum.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.continuum_add_self Cardinal.continuum_add_selfₓ'. -/
 @[simp]
 theorem continuum_add_self : 𝔠 + 𝔠 = 𝔠 :=
   add_eq_right aleph0_le_continuum le_rfl
 #align cardinal.continuum_add_self Cardinal.continuum_add_self
 
+/- warning: cardinal.nat_add_continuum -> Cardinal.nat_add_continuum is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) ((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) Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
+but is expected to have type
+  forall (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.nat_add_continuum Cardinal.nat_add_continuumₓ'. -/
 @[simp]
 theorem nat_add_continuum (n : ℕ) : ↑n + 𝔠 = 𝔠 :=
   add_eq_right aleph0_le_continuum (nat_lt_continuum n).le
 #align cardinal.nat_add_continuum Cardinal.nat_add_continuum
 
+/- warning: cardinal.continuum_add_nat -> Cardinal.continuum_add_nat is a dubious translation:
+lean 3 declaration is
+  forall (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.hasAdd.{u1}) Cardinal.continuum.{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)) Cardinal.continuum.{u1}
+but is expected to have type
+  forall (n : Nat), Eq.{succ (succ u1)} Cardinal.{u1} (HAdd.hAdd.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHAdd.{succ u1} Cardinal.{u1} Cardinal.instAddCardinal.{u1}) Cardinal.continuum.{u1} (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.continuum_add_nat Cardinal.continuum_add_natₓ'. -/
 @[simp]
 theorem continuum_add_nat (n : ℕ) : 𝔠 + n = 𝔠 :=
   (add_comm _ _).trans (nat_add_continuum n)
@@ -129,26 +209,56 @@ theorem continuum_add_nat (n : ℕ) : 𝔠 + n = 𝔠 :=
 -/
 
 
+/- warning: cardinal.continuum_mul_self -> Cardinal.continuum_mul_self is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) Cardinal.continuum.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
+but is expected to have type
+  Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) Cardinal.continuum.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.continuum_mul_self Cardinal.continuum_mul_selfₓ'. -/
 @[simp]
 theorem continuum_mul_self : 𝔠 * 𝔠 = 𝔠 :=
   mul_eq_left aleph0_le_continuum le_rfl continuum_ne_zero
 #align cardinal.continuum_mul_self Cardinal.continuum_mul_self
 
+/- warning: cardinal.continuum_mul_aleph_0 -> Cardinal.continuum_mul_aleph0 is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) Cardinal.continuum.{u1} Cardinal.aleph0.{u1}) Cardinal.continuum.{u1}
+but is expected to have type
+  Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) Cardinal.continuum.{u1} Cardinal.aleph0.{u1}) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.continuum_mul_aleph_0 Cardinal.continuum_mul_aleph0ₓ'. -/
 @[simp]
 theorem continuum_mul_aleph0 : 𝔠 * ℵ₀ = 𝔠 :=
   mul_eq_left aleph0_le_continuum aleph0_le_continuum aleph0_ne_zero
 #align cardinal.continuum_mul_aleph_0 Cardinal.continuum_mul_aleph0
 
+/- warning: cardinal.aleph_0_mul_continuum -> Cardinal.aleph0_mul_continuum is a dubious translation:
+lean 3 declaration is
+  Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
+but is expected to have type
+  Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) Cardinal.aleph0.{u1} Cardinal.continuum.{u1}) Cardinal.continuum.{u1}
+Case conversion may be inaccurate. Consider using '#align cardinal.aleph_0_mul_continuum Cardinal.aleph0_mul_continuumₓ'. -/
 @[simp]
 theorem aleph0_mul_continuum : ℵ₀ * 𝔠 = 𝔠 :=
   (mul_comm _ _).trans continuum_mul_aleph0
 #align cardinal.aleph_0_mul_continuum Cardinal.aleph0_mul_continuum
 
+/- warning: cardinal.nat_mul_continuum -> Cardinal.nat_mul_continuum is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) ((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) Cardinal.continuum.{u1}) Cardinal.continuum.{u1})
+but is expected to have type
+  forall {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) Cardinal.continuum.{u1}) Cardinal.continuum.{u1})
+Case conversion may be inaccurate. Consider using '#align cardinal.nat_mul_continuum Cardinal.nat_mul_continuumₓ'. -/
 @[simp]
 theorem nat_mul_continuum {n : ℕ} (hn : n ≠ 0) : ↑n * 𝔠 = 𝔠 :=
   mul_eq_right aleph0_le_continuum (nat_lt_continuum n).le (Nat.cast_ne_zero.2 hn)
 #align cardinal.nat_mul_continuum Cardinal.nat_mul_continuum
 
+/- warning: cardinal.continuum_mul_nat -> Cardinal.continuum_mul_nat is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.hasMul.{u1}) Cardinal.continuum.{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)) Cardinal.continuum.{u1})
+but is expected to have type
+  forall {n : Nat}, (Ne.{1} Nat n (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HMul.hMul.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHMul.{succ u1} Cardinal.{u1} Cardinal.instMulCardinal.{u1}) Cardinal.continuum.{u1} (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n)) Cardinal.continuum.{u1})
+Case conversion may be inaccurate. Consider using '#align cardinal.continuum_mul_nat Cardinal.continuum_mul_natₓ'. -/
 @[simp]
 theorem continuum_mul_nat {n : ℕ} (hn : n ≠ 0) : 𝔠 * n = 𝔠 :=
   (mul_comm _ _).trans (nat_mul_continuum hn)
@@ -159,20 +269,30 @@ theorem continuum_mul_nat {n : ℕ} (hn : n ≠ 0) : 𝔠 * n = 𝔠 :=
 -/
 
 
+#print Cardinal.aleph0_power_aleph0 /-
 @[simp]
 theorem aleph0_power_aleph0 : aleph0.{u} ^ aleph0.{u} = 𝔠 :=
   power_self_eq le_rfl
 #align cardinal.aleph_0_power_aleph_0 Cardinal.aleph0_power_aleph0
+-/
 
+/- warning: cardinal.nat_power_aleph_0 -> Cardinal.nat_power_aleph0 is a dubious translation:
+lean 3 declaration is
+  forall {n : Nat}, (LE.le.{0} Nat Nat.hasLe (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) n) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.hasPow.{u1}) ((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) Cardinal.aleph0.{u1}) Cardinal.continuum.{u1})
+but is expected to have type
+  forall {n : Nat}, (LE.le.{0} Nat instLENat (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) n) -> (Eq.{succ (succ u1)} Cardinal.{u1} (HPow.hPow.{succ u1, succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.{u1} (instHPow.{succ u1, succ u1} Cardinal.{u1} Cardinal.{u1} Cardinal.instPowCardinal.{u1}) (Nat.cast.{succ u1} Cardinal.{u1} Cardinal.instNatCastCardinal.{u1} n) Cardinal.aleph0.{u1}) Cardinal.continuum.{u1})
+Case conversion may be inaccurate. Consider using '#align cardinal.nat_power_aleph_0 Cardinal.nat_power_aleph0ₓ'. -/
 @[simp]
 theorem nat_power_aleph0 {n : ℕ} (hn : 2 ≤ n) : (n ^ aleph0.{u} : Cardinal.{u}) = 𝔠 :=
   nat_power_eq le_rfl hn
 #align cardinal.nat_power_aleph_0 Cardinal.nat_power_aleph0
 
+#print Cardinal.continuum_power_aleph0 /-
 @[simp]
 theorem continuum_power_aleph0 : continuum.{u} ^ aleph0.{u} = 𝔠 := by
   rw [← two_power_aleph_0, ← power_mul, mul_eq_left le_rfl le_rfl aleph_0_ne_zero]
 #align cardinal.continuum_power_aleph_0 Cardinal.continuum_power_aleph0
+-/
 
 end Cardinal

3d7987cd

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

e08a42b2

chore: remove mathport name: <expression> lines (#11928)

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

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

11431c65

Diff

@@ -30,7 +30,6 @@ def continuum : Cardinal.{u} :=
   2 ^ ℵ₀
 #align cardinal.continuum Cardinal.continuum
 
--- mathport name: Cardinal.continuum
 scoped notation "𝔠" => Cardinal.continuum
 
 @[simp]

e08a42b2

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

@@ -45,25 +45,25 @@ theorem lift_continuum : lift.{v} 𝔠 = 𝔠 := by
 
 @[simp]
 theorem continuum_le_lift {c : Cardinal.{u}} : 𝔠 ≤ lift.{v} c ↔ 𝔠 ≤ c := by
-  -- porting note: added explicit universes
+  -- Porting note: added explicit universes
   rw [← lift_continuum.{u,v}, lift_le]
 #align cardinal.continuum_le_lift Cardinal.continuum_le_lift
 
 @[simp]
 theorem lift_le_continuum {c : Cardinal.{u}} : lift.{v} c ≤ 𝔠 ↔ c ≤ 𝔠 := by
-  -- porting note: added explicit universes
+  -- Porting note: added explicit universes
   rw [← lift_continuum.{u,v}, lift_le]
 #align cardinal.lift_le_continuum Cardinal.lift_le_continuum
 
 @[simp]
 theorem continuum_lt_lift {c : Cardinal.{u}} : 𝔠 < lift.{v} c ↔ 𝔠 < c := by
-  -- porting note: added explicit universes
+  -- Porting note: added explicit universes
   rw [← lift_continuum.{u,v}, lift_lt]
 #align cardinal.continuum_lt_lift Cardinal.continuum_lt_lift
 
 @[simp]
 theorem lift_lt_continuum {c : Cardinal.{u}} : lift.{v} c < 𝔠 ↔ c < 𝔠 := by
-  -- porting note: added explicit universes
+  -- Porting note: added explicit universes
   rw [← lift_continuum.{u,v}, lift_lt]
 #align cardinal.lift_lt_continuum Cardinal.lift_lt_continuum

e08a42b2

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

a577026a

Diff

@@ -27,7 +27,7 @@ open Cardinal
 
 /-- Cardinality of continuum. -/
 def continuum : Cardinal.{u} :=
-  2 ^ aleph0.{u}
+  2 ^ ℵ₀
 #align cardinal.continuum Cardinal.continuum
 
 -- mathport name: Cardinal.continuum
@@ -131,12 +131,12 @@ theorem continuum_add_aleph0 : 𝔠 + ℵ₀ = 𝔠 :=
 
 @[simp]
 theorem continuum_add_self : 𝔠 + 𝔠 = 𝔠 :=
-  add_eq_right aleph0_le_continuum le_rfl
+  add_eq_self aleph0_le_continuum
 #align cardinal.continuum_add_self Cardinal.continuum_add_self
 
 @[simp]
 theorem nat_add_continuum (n : ℕ) : ↑n + 𝔠 = 𝔠 :=
-  add_eq_right aleph0_le_continuum (nat_lt_continuum n).le
+  nat_add_eq n aleph0_le_continuum
 #align cardinal.nat_add_continuum Cardinal.nat_add_continuum
 
 @[simp]
@@ -144,6 +144,16 @@ theorem continuum_add_nat (n : ℕ) : 𝔠 + n = 𝔠 :=
   (add_comm _ _).trans (nat_add_continuum n)
 #align cardinal.continuum_add_nat Cardinal.continuum_add_nat
 
+-- See note [no_index around OfNat.ofNat]
+@[simp]
+theorem ofNat_add_continuum {n : ℕ} [Nat.AtLeastTwo n] : no_index (OfNat.ofNat n) + 𝔠 = 𝔠 :=
+  nat_add_continuum n
+
+-- See note [no_index around OfNat.ofNat]
+@[simp]
+theorem continuum_add_ofNat {n : ℕ} [Nat.AtLeastTwo n] : 𝔠 + no_index (OfNat.ofNat n) = 𝔠 :=
+  continuum_add_nat n
+
 /-!
 ### Multiplication
 -/
@@ -174,6 +184,16 @@ theorem continuum_mul_nat {n : ℕ} (hn : n ≠ 0) : 𝔠 * n = 𝔠 :=
   (mul_comm _ _).trans (nat_mul_continuum hn)
 #align cardinal.continuum_mul_nat Cardinal.continuum_mul_nat
 
+-- See note [no_index around OfNat.ofNat]
+@[simp]
+theorem ofNat_mul_continuum {n : ℕ} [Nat.AtLeastTwo n] : no_index (OfNat.ofNat n) * 𝔠 = 𝔠 :=
+  nat_mul_continuum (OfNat.ofNat_ne_zero n)
+
+-- See note [no_index around OfNat.ofNat]
+@[simp]
+theorem continuum_mul_ofNat {n : ℕ} [Nat.AtLeastTwo n] : 𝔠 * no_index (OfNat.ofNat n) = 𝔠 :=
+  continuum_mul_nat (OfNat.ofNat_ne_zero n)
+
 /-!
 ### Power
 -/

e08a42b2

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module set_theory.cardinal.continuum
-! leanprover-community/mathlib commit e08a42b2dd544cf11eba72e5fc7bf199d4349925
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.SetTheory.Cardinal.Ordinal
 
+#align_import set_theory.cardinal.continuum from "leanprover-community/mathlib"@"e08a42b2dd544cf11eba72e5fc7bf199d4349925"
+
 /-!
 # Cardinality of continuum

e08a42b2

fix: precedence of # (#5623)

d450fcd7

Diff

@@ -91,7 +91,7 @@ theorem nat_lt_continuum (n : ℕ) : ↑n < 𝔠 :=
   (nat_lt_aleph0 n).trans aleph0_lt_continuum
 #align cardinal.nat_lt_continuum Cardinal.nat_lt_continuum
 
-theorem mk_set_nat : (#Set ℕ) = 𝔠 := by simp
+theorem mk_set_nat : #(Set ℕ) = 𝔠 := by simp
 #align cardinal.mk_set_nat Cardinal.mk_set_nat
 
 theorem continuum_pos : 0 < 𝔠 :=

e08a42b2

feat: port changes to Cardinal files (#3343)

My bad for letting these pile up.

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

f13648cc

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module set_theory.cardinal.continuum
-! leanprover-community/mathlib commit 3d7987cda72abc473c7cdbbb075170e9ac620042
+! leanprover-community/mathlib commit e08a42b2dd544cf11eba72e5fc7bf199d4349925
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -46,6 +46,30 @@ theorem lift_continuum : lift.{v} 𝔠 = 𝔠 := by
   rw [← two_power_aleph0, lift_two_power, lift_aleph0, two_power_aleph0]
 #align cardinal.lift_continuum Cardinal.lift_continuum
 
+@[simp]
+theorem continuum_le_lift {c : Cardinal.{u}} : 𝔠 ≤ lift.{v} c ↔ 𝔠 ≤ c := by
+  -- porting note: added explicit universes
+  rw [← lift_continuum.{u,v}, lift_le]
+#align cardinal.continuum_le_lift Cardinal.continuum_le_lift
+
+@[simp]
+theorem lift_le_continuum {c : Cardinal.{u}} : lift.{v} c ≤ 𝔠 ↔ c ≤ 𝔠 := by
+  -- porting note: added explicit universes
+  rw [← lift_continuum.{u,v}, lift_le]
+#align cardinal.lift_le_continuum Cardinal.lift_le_continuum
+
+@[simp]
+theorem continuum_lt_lift {c : Cardinal.{u}} : 𝔠 < lift.{v} c ↔ 𝔠 < c := by
+  -- porting note: added explicit universes
+  rw [← lift_continuum.{u,v}, lift_lt]
+#align cardinal.continuum_lt_lift Cardinal.continuum_lt_lift
+
+@[simp]
+theorem lift_lt_continuum {c : Cardinal.{u}} : lift.{v} c < 𝔠 ↔ c < 𝔠 := by
+  -- porting note: added explicit universes
+  rw [← lift_continuum.{u,v}, lift_lt]
+#align cardinal.lift_lt_continuum Cardinal.lift_lt_continuum
+
 /-!
 ### Inequalities
 -/

3d7987cd

feat: Port SetTheory.Cardinal.Continuum (#2474)

43fabded

`set_theory.cardinal.continuum` ⟷ `Mathlib.SetTheory.Cardinal.Continuum`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 348

set_theory.cardinal.continuum ⟷ Mathlib.SetTheory.Cardinal.Continuum

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 348

`set_theory.cardinal.continuum` ⟷ `Mathlib.SetTheory.Cardinal.Continuum`