data.rat.denumerable
⟷
Mathlib.Data.Rat.Denumerable
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
-import Mathbin.SetTheory.Cardinal.Basic
+import SetTheory.Cardinal.Basic
#align_import data.rat.denumerable from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -24,7 +24,7 @@ open Denumerable
instance : Infinite ℚ :=
Infinite.of_injective (coe : ℕ → ℚ) Nat.cast_injective
-private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.coprime x.2 }
+private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.Coprime x.2 }
where
toFun x := ⟨⟨x.1, x.2⟩, x.3, x.4⟩
invFun x := ⟨x.1.1, x.1.2, x.2.1, x.2.2⟩
@@ -34,7 +34,7 @@ private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs
/-- **Denumerability of the Rational Numbers** -/
instance : Denumerable ℚ :=
by
- let T := { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.coprime x.2 }
+ let T := { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.Coprime x.2 }
letI : Infinite T := Infinite.of_injective _ denumerable_aux.injective
letI : Encodable T := Subtype.encodable
letI : Denumerable T := of_encodable_of_infinite T
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module data.rat.denumerable
-! leanprover-community/mathlib commit 34ee86e6a59d911a8e4f89b68793ee7577ae79c7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.SetTheory.Cardinal.Basic
+#align_import data.rat.denumerable from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"
+
/-!
# Denumerability of ℚ
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -45,7 +45,7 @@ instance : Denumerable ℚ :=
end Rat
-open Cardinal
+open scoped Cardinal
#print Cardinal.mkRat /-
theorem Cardinal.mkRat : (#ℚ) = ℵ₀ := by simp
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -33,7 +33,6 @@ private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs
invFun x := ⟨x.1.1, x.1.2, x.2.1, x.2.2⟩
left_inv := fun ⟨_, _, _, _⟩ => rfl
right_inv := fun ⟨⟨_, _⟩, _, _⟩ => rfl
-#align rat.denumerable_aux rat.denumerable_aux
/-- **Denumerability of the Rational Numbers** -/
instance : Denumerable ℚ :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c
@@ -40,7 +40,7 @@ instance : Denumerable ℚ :=
by
let T := { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.coprime x.2 }
letI : Infinite T := Infinite.of_injective _ denumerable_aux.injective
- letI : Encodable T := Encodable.Subtype.encodable
+ letI : Encodable T := Subtype.encodable
letI : Denumerable T := of_encodable_of_infinite T
exact Denumerable.ofEquiv T denumerable_aux
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -22,7 +22,7 @@ open Denumerable
instance : Infinite ℚ :=
Infinite.of_injective ((↑) : ℕ → ℚ) Nat.cast_injective
-private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.coprime x.2 }
+private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.Coprime x.2 }
where
toFun x := ⟨⟨x.1, x.2⟩, Nat.pos_of_ne_zero x.3, x.4⟩
invFun x := ⟨x.1.1, x.1.2, ne_zero_of_lt x.2.1, x.2.2⟩
@@ -31,7 +31,7 @@ private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs
/-- **Denumerability of the Rational Numbers** -/
instance : Denumerable ℚ := by
- let T := { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.coprime x.2 }
+ let T := { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.Coprime x.2 }
letI : Infinite T := Infinite.of_injective _ denumerable_aux.injective
letI : Encodable T := Subtype.encodable
letI : Denumerable T := ofEncodableOfInfinite T
@@ -22,7 +22,7 @@ open Denumerable
instance : Infinite ℚ :=
Infinite.of_injective ((↑) : ℕ → ℚ) Nat.cast_injective
-private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.Coprime x.2 }
+private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.coprime x.2 }
where
toFun x := ⟨⟨x.1, x.2⟩, Nat.pos_of_ne_zero x.3, x.4⟩
invFun x := ⟨x.1.1, x.1.2, ne_zero_of_lt x.2.1, x.2.2⟩
@@ -31,7 +31,7 @@ private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs
/-- **Denumerability of the Rational Numbers** -/
instance : Denumerable ℚ := by
- let T := { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.Coprime x.2 }
+ let T := { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.coprime x.2 }
letI : Infinite T := Infinite.of_injective _ denumerable_aux.injective
letI : Encodable T := Subtype.encodable
letI : Denumerable T := ofEncodableOfInfinite T
Some changes have already been review and delegated in #6910 and #7148.
The diff that needs looking at is https://github.com/leanprover-community/mathlib4/pull/7174/commits/64d6d07ee18163627c8f517eb31455411921c5ac
The std bump PR was insta-merged already!
Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -22,7 +22,7 @@ open Denumerable
instance : Infinite ℚ :=
Infinite.of_injective ((↑) : ℕ → ℚ) Nat.cast_injective
-private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.coprime x.2 }
+private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.Coprime x.2 }
where
toFun x := ⟨⟨x.1, x.2⟩, Nat.pos_of_ne_zero x.3, x.4⟩
invFun x := ⟨x.1.1, x.1.2, ne_zero_of_lt x.2.1, x.2.2⟩
@@ -31,7 +31,7 @@ private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs
/-- **Denumerability of the Rational Numbers** -/
instance : Denumerable ℚ := by
- let T := { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.coprime x.2 }
+ let T := { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.Coprime x.2 }
letI : Infinite T := Infinite.of_injective _ denumerable_aux.injective
letI : Encodable T := Subtype.encodable
letI : Denumerable T := ofEncodableOfInfinite T
@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-/
import Mathlib.SetTheory.Cardinal.Basic
+import Mathlib.Data.Rat.Order
#align_import data.rat.denumerable from "leanprover-community/mathlib"@"dde670c9a3f503647fd5bfdf1037bad526d3397a"
@@ -2,14 +2,11 @@
Copyright (c) 2019 Chris Hughes. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Hughes
-
-! This file was ported from Lean 3 source module data.rat.denumerable
-! leanprover-community/mathlib commit dde670c9a3f503647fd5bfdf1037bad526d3397a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.SetTheory.Cardinal.Basic
+#align_import data.rat.denumerable from "leanprover-community/mathlib"@"dde670c9a3f503647fd5bfdf1037bad526d3397a"
+
/-!
# Denumerability of ℚ
@@ -43,6 +43,5 @@ end Rat
open Cardinal
-theorem Cardinal.mkRat : (#ℚ) = ℵ₀ := by simp only [mk_eq_aleph0]
+theorem Cardinal.mkRat : #ℚ = ℵ₀ := by simp only [mk_eq_aleph0]
#align cardinal.mk_rat Cardinal.mkRat
-
_root_
(#3630)
Mathport doesn't understand this, and apparently nor do many of the humans fixing the errors it creates.
If your #align
statement complains the def doesn't exist, don't change the #align; work out why it doesn't exist instead.
Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>
@@ -35,7 +35,7 @@ private def denumerable_aux : ℚ ≃ { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs
instance : Denumerable ℚ := by
let T := { x : ℤ × ℕ // 0 < x.2 ∧ x.1.natAbs.coprime x.2 }
letI : Infinite T := Infinite.of_injective _ denumerable_aux.injective
- letI : Encodable T := Encodable.Subtype.encodable
+ letI : Encodable T := Subtype.encodable
letI : Denumerable T := ofEncodableOfInfinite T
exact Denumerable.ofEquiv T denumerable_aux
The unported dependencies are