data.fintype.quotient
⟷
Mathlib.Data.Fintype.Quotient
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/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -71,7 +71,7 @@ def Quotient.finChoice {ι : Type _} [DecidableEq ι] [Fintype ι] {α : ι →
Finset.univ.1 (fun l => Quotient.finChoiceAux l fun i _ => f i) fun a b h =>
by
have := fun a => Quotient.finChoiceAux_eq a fun i h => Quotient.out (f i)
- simp [Quotient.out_eq] at this
+ simp [Quotient.out_eq] at this
simp [this]
let g := fun a : Multiset ι => ⟦fun (i : ι) (h : i ∈ a) => Quotient.out (f i)⟧
refine' eq_of_hEq ((eq_rec_hEq _ _).trans (_ : HEq (g a) (g b)))
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-/
-import Mathbin.Data.Fintype.Basic
+import Data.Fintype.Basic
#align_import data.fintype.quotient from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-
-! This file was ported from Lean 3 source module data.fintype.quotient
-! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.Data.Fintype.Basic
+#align_import data.fintype.quotient from "leanprover-community/mathlib"@"a87d22575d946e1e156fc1edd1e1269600a8a282"
+
/-!
# Quotients of families indexed by a finite type
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -49,6 +49,7 @@ def Quotient.finChoiceAux {ι : Type _} [DecidableEq ι] {α : ι → Type _} [S
#align quotient.fin_choice_aux Quotient.finChoiceAux
-/
+#print Quotient.finChoiceAux_eq /-
theorem Quotient.finChoiceAux_eq {ι : Type _} [DecidableEq ι] {α : ι → Type _}
[S : ∀ i, Setoid (α i)] :
∀ (l : List ι) (f : ∀ i ∈ l, α i), (Quotient.finChoiceAux l fun i h => ⟦f i h⟧) = ⟦f⟧
@@ -59,6 +60,7 @@ theorem Quotient.finChoiceAux_eq {ι : Type _} [DecidableEq ι] {α : ι → Typ
by_cases e : j = i <;> simp [e]
subst j; rfl
#align quotient.fin_choice_aux_eq Quotient.finChoiceAux_eq
+-/
#print Quotient.finChoice /-
/-- Given a collection of setoids indexed by a fintype `ι` and a
@@ -81,6 +83,7 @@ def Quotient.finChoice {ι : Type _} [DecidableEq ι] [Fintype ι] {α : ι →
#align quotient.fin_choice Quotient.finChoice
-/
+#print Quotient.finChoice_eq /-
theorem Quotient.finChoice_eq {ι : Type _} [DecidableEq ι] [Fintype ι] {α : ι → Type _}
[∀ i, Setoid (α i)] (f : ∀ i, α i) : (Quotient.finChoice fun i => ⟦f i⟧) = ⟦f⟧ :=
by
@@ -90,4 +93,5 @@ theorem Quotient.finChoice_eq {ι : Type _} [DecidableEq ι] [Fintype ι] {α :
exact Quotient.inductionOn (@Finset.univ ι _).1 fun l => Quotient.finChoiceAux_eq _ _
simp [this]; exact Setoid.refl _
#align quotient.fin_choice_eq Quotient.finChoice_eq
+-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -72,7 +72,7 @@ def Quotient.finChoice {ι : Type _} [DecidableEq ι] [Fintype ι] {α : ι →
Finset.univ.1 (fun l => Quotient.finChoiceAux l fun i _ => f i) fun a b h =>
by
have := fun a => Quotient.finChoiceAux_eq a fun i h => Quotient.out (f i)
- simp [Quotient.out_eq] at this
+ simp [Quotient.out_eq] at this
simp [this]
let g := fun a : Multiset ι => ⟦fun (i : ι) (h : i ∈ a) => Quotient.out (f i)⟧
refine' eq_of_hEq ((eq_rec_hEq _ _).trans (_ : HEq (g a) (g b)))
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -49,12 +49,6 @@ def Quotient.finChoiceAux {ι : Type _} [DecidableEq ι] {α : ι → Type _} [S
#align quotient.fin_choice_aux Quotient.finChoiceAux
-/
-/- warning: quotient.fin_choice_aux_eq -> Quotient.finChoiceAux_eq is a dubious translation:
-lean 3 declaration is
- forall {ι : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} ι] {α : ι -> Type.{u2}} [S : forall (i : ι), Setoid.{succ u2} (α i)] (l : List.{u1} ι) (f : forall (i : ι), (Membership.Mem.{u1, u1} ι (List.{u1} ι) (List.hasMem.{u1} ι) i l) -> (α i)), Eq.{max (succ u1) (succ u2)} (Quotient.{max (succ u1) (succ u2)} (forall (i : ι), (Membership.Mem.{u1, u1} ι (List.{u1} ι) (List.hasMem.{u1} ι) i l) -> (α i)) (piSetoid.{succ u1, succ u2} ι (fun (i : ι) => (Membership.Mem.{u1, u1} ι (List.{u1} ι) (List.hasMem.{u1} ι) i l) -> (α i)) (fun (i : ι) => piSetoid.{0, succ u2} (Membership.Mem.{u1, u1} ι (List.{u1} ι) (List.hasMem.{u1} ι) i l) (fun (H : Membership.Mem.{u1, u1} ι (List.{u1} ι) (List.hasMem.{u1} ι) i l) => α i) (fun (i_1 : Membership.Mem.{u1, u1} ι (List.{u1} ι) (List.hasMem.{u1} ι) i l) => S i)))) (Quotient.finChoiceAux.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) (fun (i : ι) => α i) (fun (i : ι) => S i) l (fun (i : ι) (h : Membership.Mem.{u1, u1} ι (List.{u1} ι) (List.hasMem.{u1} ι) i l) => Quotient.mk'.{succ u2} (α i) (S i) (f i h))) (Quotient.mk'.{max (succ u1) (succ u2)} (forall (i : ι), (Membership.Mem.{u1, u1} ι (List.{u1} ι) (List.hasMem.{u1} ι) i l) -> (α i)) (piSetoid.{succ u1, succ u2} ι (fun (i : ι) => (Membership.Mem.{u1, u1} ι (List.{u1} ι) (List.hasMem.{u1} ι) i l) -> (α i)) (fun (i : ι) => piSetoid.{0, succ u2} (Membership.Mem.{u1, u1} ι (List.{u1} ι) (List.hasMem.{u1} ι) i l) (fun (H : Membership.Mem.{u1, u1} ι (List.{u1} ι) (List.hasMem.{u1} ι) i l) => α i) (fun (i_1 : Membership.Mem.{u1, u1} ι (List.{u1} ι) (List.hasMem.{u1} ι) i l) => S i))) f)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align quotient.fin_choice_aux_eq Quotient.finChoiceAux_eqₓ'. -/
theorem Quotient.finChoiceAux_eq {ι : Type _} [DecidableEq ι] {α : ι → Type _}
[S : ∀ i, Setoid (α i)] :
∀ (l : List ι) (f : ∀ i ∈ l, α i), (Quotient.finChoiceAux l fun i h => ⟦f i h⟧) = ⟦f⟧
@@ -87,12 +81,6 @@ def Quotient.finChoice {ι : Type _} [DecidableEq ι] [Fintype ι] {α : ι →
#align quotient.fin_choice Quotient.finChoice
-/
-/- warning: quotient.fin_choice_eq -> Quotient.finChoice_eq is a dubious translation:
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theorem Quotient.finChoice_eq {ι : Type _} [DecidableEq ι] [Fintype ι] {α : ι → Type _}
[∀ i, Setoid (α i)] (f : ∀ i, α i) : (Quotient.finChoice fun i => ⟦f i⟧) = ⟦f⟧ :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -44,8 +44,7 @@ def Quotient.finChoiceAux {ι : Type _} [DecidableEq ι] {α : ι → Type _} [S
⟦fun j h => if e : j = i then by rw [e] <;> exact a else l _ (h.resolve_left e)⟧
refine' fun a₁ l₁ a₂ l₂ h₁ h₂ => Quotient.sound fun j h => _
by_cases e : j = i <;> simp [e]
- · subst j
- exact h₁
+ · subst j; exact h₁
· exact h₂ _ _
#align quotient.fin_choice_aux Quotient.finChoiceAux
-/
@@ -97,13 +96,10 @@ Case conversion may be inaccurate. Consider using '#align quotient.fin_choice_eq
theorem Quotient.finChoice_eq {ι : Type _} [DecidableEq ι] [Fintype ι] {α : ι → Type _}
[∀ i, Setoid (α i)] (f : ∀ i, α i) : (Quotient.finChoice fun i => ⟦f i⟧) = ⟦f⟧ :=
by
- let q
- swap
- change Quotient.liftOn q _ _ = _
+ let q; swap; change Quotient.liftOn q _ _ = _
have : q = ⟦fun i h => f i⟧ := by
dsimp only [q]
exact Quotient.inductionOn (@Finset.univ ι _).1 fun l => Quotient.finChoiceAux_eq _ _
- simp [this]
- exact Setoid.refl _
+ simp [this]; exact Setoid.refl _
#align quotient.fin_choice_eq Quotient.finChoice_eq
mathlib commit https://github.com/leanprover-community/mathlib/commit/e1a18cad9cd462973d760af7de36b05776b8811c
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
! This file was ported from Lean 3 source module data.fintype.quotient
-! leanprover-community/mathlib commit d78597269638367c3863d40d45108f52207e03cf
+! leanprover-community/mathlib commit a87d22575d946e1e156fc1edd1e1269600a8a282
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.Data.Fintype.Basic
/-!
# Quotients of families indexed by a finite type
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file provides `quotient.fin_choice`, a mechanism to go from a finite family of quotients
to a quotient of finite families.
mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b
@@ -23,6 +23,7 @@ to a quotient of finite families.
-/
+#print Quotient.finChoiceAux /-
/-- An auxiliary function for `quotient.fin_choice`. Given a
collection of setoids indexed by a type `ι`, a (finite) list `l` of
indices, and a function that for each `i ∈ l` gives a term of the
@@ -44,7 +45,14 @@ def Quotient.finChoiceAux {ι : Type _} [DecidableEq ι] {α : ι → Type _} [S
exact h₁
· exact h₂ _ _
#align quotient.fin_choice_aux Quotient.finChoiceAux
+-/
+/- warning: quotient.fin_choice_aux_eq -> Quotient.finChoiceAux_eq is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align quotient.fin_choice_aux_eq Quotient.finChoiceAux_eqₓ'. -/
theorem Quotient.finChoiceAux_eq {ι : Type _} [DecidableEq ι] {α : ι → Type _}
[S : ∀ i, Setoid (α i)] :
∀ (l : List ι) (f : ∀ i ∈ l, α i), (Quotient.finChoiceAux l fun i h => ⟦f i h⟧) = ⟦f⟧
@@ -56,6 +64,7 @@ theorem Quotient.finChoiceAux_eq {ι : Type _} [DecidableEq ι] {α : ι → Typ
subst j; rfl
#align quotient.fin_choice_aux_eq Quotient.finChoiceAux_eq
+#print Quotient.finChoice /-
/-- Given a collection of setoids indexed by a fintype `ι` and a
function that for each `i : ι` gives a term of the corresponding
quotient type, then there is corresponding term in the quotient of the
@@ -74,7 +83,14 @@ def Quotient.finChoice {ι : Type _} [DecidableEq ι] [Fintype ι] {α : ι →
congr 1; exact Quotient.sound h)
(fun f => ⟦fun i => f i (Finset.mem_univ _)⟧) fun a b h => Quotient.sound fun i => h _ _
#align quotient.fin_choice Quotient.finChoice
+-/
+/- warning: quotient.fin_choice_eq -> Quotient.finChoice_eq is a dubious translation:
+lean 3 declaration is
+ forall {ι : Type.{u1}} [_inst_1 : DecidableEq.{succ u1} ι] [_inst_2 : Fintype.{u1} ι] {α : ι -> Type.{u2}} [_inst_3 : forall (i : ι), Setoid.{succ u2} (α i)] (f : forall (i : ι), α i), Eq.{max (succ u1) (succ u2)} (Quotient.{max (succ u1) (succ u2)} (forall (i : ι), α i) (piSetoid.{succ u1, succ u2} ι (fun (i : ι) => α i) (fun (i : ι) => _inst_3 i))) (Quotient.finChoice.{u1, u2} ι (fun (a : ι) (b : ι) => _inst_1 a b) _inst_2 (fun (i : ι) => α i) (fun (i : ι) => _inst_3 i) (fun (i : ι) => Quotient.mk'.{succ u2} (α i) (_inst_3 i) (f i))) (Quotient.mk'.{max (succ u1) (succ u2)} (forall (i : ι), α i) (piSetoid.{succ u1, succ u2} ι (fun (i : ι) => α i) (fun (i : ι) => _inst_3 i)) f)
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+Case conversion may be inaccurate. Consider using '#align quotient.fin_choice_eq Quotient.finChoice_eqₓ'. -/
theorem Quotient.finChoice_eq {ι : Type _} [DecidableEq ι] [Fintype ι] {α : ι → Type _}
[∀ i, Setoid (α i)] (f : ∀ i, α i) : (Quotient.finChoice fun i => ⟦f i⟧) = ⟦f⟧ :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -32,8 +32,8 @@ def Quotient.finChoiceAux {ι : Type*} [DecidableEq ι] {α : ι → Type*} [S :
refine'
Quotient.liftOn₂ (f i (List.mem_cons_self _ _))
(Quotient.finChoiceAux l fun j h => f j (List.mem_cons_of_mem _ h)) _ _
- exact fun a l => ⟦fun j h =>
- if e : j = i then by rw [e]; exact a else l _ ((List.mem_cons.1 h).resolve_left e)⟧
+ · exact fun a l => ⟦fun j h =>
+ if e : j = i then by rw [e]; exact a else l _ ((List.mem_cons.1 h).resolve_left e)⟧
refine' fun a₁ l₁ a₂ l₂ h₁ h₂ => Quotient.sound fun j h => _
by_cases e : j = i <;> simp [e]
· subst j
@@ -62,7 +62,7 @@ def Quotient.finChoice {ι : Type*} [DecidableEq ι] [Fintype ι] {α : ι → T
(@Quotient.recOn _ _ (fun l : Multiset ι => @Quotient (∀ i ∈ l, α i) (by infer_instance))
Finset.univ.1 (fun l => Quotient.finChoiceAux l fun i _ => f i) (fun a b h => by
have := fun a => Quotient.finChoiceAux_eq a fun i _ => Quotient.out (f i)
- simp [Quotient.out_eq] at this
+ simp? [Quotient.out_eq] at this says simp only [out_eq] at this
simp only [Multiset.quot_mk_to_coe, this]
let g := fun a : Multiset ι =>
(⟦fun (i : ι) (_ : i ∈ a) => Quotient.out (f i)⟧ : Quotient (by infer_instance))
Removes nonterminal simps on lines looking like simp [...]
@@ -46,7 +46,7 @@ theorem Quotient.finChoiceAux_eq {ι : Type*} [DecidableEq ι] {α : ι → Type
∀ (l : List ι) (f : ∀ i ∈ l, α i), (Quotient.finChoiceAux l fun i h => ⟦f i h⟧) = ⟦f⟧
| [], f => Quotient.sound fun i h => nomatch List.not_mem_nil _ h
| i :: l, f => by
- simp [Quotient.finChoiceAux, Quotient.finChoiceAux_eq l, -Quotient.eq]
+ simp only [finChoiceAux, Quotient.finChoiceAux_eq l, eq_mpr_eq_cast, lift_mk]
refine' Quotient.sound fun j h => _
by_cases e : j = i <;> simp [e] <;> try exact Setoid.refl _
subst j; exact Setoid.refl _
@@ -63,7 +63,7 @@ def Quotient.finChoice {ι : Type*} [DecidableEq ι] [Fintype ι] {α : ι → T
Finset.univ.1 (fun l => Quotient.finChoiceAux l fun i _ => f i) (fun a b h => by
have := fun a => Quotient.finChoiceAux_eq a fun i _ => Quotient.out (f i)
simp [Quotient.out_eq] at this
- simp [this]
+ simp only [Multiset.quot_mk_to_coe, this]
let g := fun a : Multiset ι =>
(⟦fun (i : ι) (_ : i ∈ a) => Quotient.out (f i)⟧ : Quotient (by infer_instance))
apply eq_of_heq
Type _
and Sort _
(#6499)
We remove all possible occurences of Type _
and Sort _
in favor of Type*
and Sort*
.
This has nice performance benefits.
@@ -25,7 +25,7 @@ collection of setoids indexed by a type `ι`, a (finite) list `l` of
indices, and a function that for each `i ∈ l` gives a term of the
corresponding quotient type, then there is a corresponding term in the
quotient of the product of the setoids indexed by `l`. -/
-def Quotient.finChoiceAux {ι : Type _} [DecidableEq ι] {α : ι → Type _} [S : ∀ i, Setoid (α i)] :
+def Quotient.finChoiceAux {ι : Type*} [DecidableEq ι] {α : ι → Type*} [S : ∀ i, Setoid (α i)] :
∀ l : List ι, (∀ i ∈ l, Quotient (S i)) → @Quotient (∀ i ∈ l, α i) (by infer_instance)
| [], _ => ⟦fun i h => nomatch List.not_mem_nil _ h⟧
| i :: l, f => by
@@ -41,7 +41,7 @@ def Quotient.finChoiceAux {ι : Type _} [DecidableEq ι] {α : ι → Type _} [S
· exact h₂ _ _
#align quotient.fin_choice_aux Quotient.finChoiceAux
-theorem Quotient.finChoiceAux_eq {ι : Type _} [DecidableEq ι] {α : ι → Type _}
+theorem Quotient.finChoiceAux_eq {ι : Type*} [DecidableEq ι] {α : ι → Type*}
[S : ∀ i, Setoid (α i)] :
∀ (l : List ι) (f : ∀ i ∈ l, α i), (Quotient.finChoiceAux l fun i h => ⟦f i h⟧) = ⟦f⟧
| [], f => Quotient.sound fun i h => nomatch List.not_mem_nil _ h
@@ -56,7 +56,7 @@ theorem Quotient.finChoiceAux_eq {ι : Type _} [DecidableEq ι] {α : ι → Typ
function that for each `i : ι` gives a term of the corresponding
quotient type, then there is corresponding term in the quotient of the
product of the setoids. -/
-def Quotient.finChoice {ι : Type _} [DecidableEq ι] [Fintype ι] {α : ι → Type _}
+def Quotient.finChoice {ι : Type*} [DecidableEq ι] [Fintype ι] {α : ι → Type*}
[S : ∀ i, Setoid (α i)] (f : ∀ i, Quotient (S i)) : @Quotient (∀ i, α i) (by infer_instance) :=
Quotient.liftOn
(@Quotient.recOn _ _ (fun l : Multiset ι => @Quotient (∀ i ∈ l, α i) (by infer_instance))
@@ -74,7 +74,7 @@ def Quotient.finChoice {ι : Type _} [DecidableEq ι] [Fintype ι] {α : ι →
(fun f => ⟦fun i => f i (Finset.mem_univ _)⟧) (fun a b h => Quotient.sound fun i => by apply h)
#align quotient.fin_choice Quotient.finChoice
-theorem Quotient.finChoice_eq {ι : Type _} [DecidableEq ι] [Fintype ι] {α : ι → Type _}
+theorem Quotient.finChoice_eq {ι : Type*} [DecidableEq ι] [Fintype ι] {α : ι → Type*}
[∀ i, Setoid (α i)] (f : ∀ i, α i) : (Quotient.finChoice fun i => ⟦f i⟧) = ⟦f⟧ := by
dsimp only [Quotient.finChoice]
conv_lhs =>
@@ -2,14 +2,11 @@
Copyright (c) 2018 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro
-
-! This file was ported from Lean 3 source module data.fintype.quotient
-! leanprover-community/mathlib commit d78597269638367c3863d40d45108f52207e03cf
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.Data.Fintype.Basic
+#align_import data.fintype.quotient from "leanprover-community/mathlib"@"d78597269638367c3863d40d45108f52207e03cf"
+
/-!
# Quotients of families indexed by a finite type
The unported dependencies are