refactor(data/fintype/basic): split file (#17578)

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

archive/100-theorems-list/73_ascending_descending_sequences.lean

@@ -3,7 +3,7 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 -/
-import data.fintype.basic
+import data.fintype.powerset
 
 /-!
 # Erdős–Szekeres theorem

archive/imo/imo1987_q1.lean

@@ -3,7 +3,9 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import data.fintype.card
+import data.fintype.big_operators
+import data.fintype.perm
+import data.fintype.prod
 import dynamics.fixed_points.basic
 
 /-!

archive/imo/imo1994_q1.lean

@@ -5,7 +5,7 @@ Authors: Antoine Labelle
 -/
 import algebra.big_operators.basic
 import algebra.big_operators.order
-import data.fintype.card
+import data.fintype.big_operators
 import data.finset.sort
 import data.fin.interval
 import tactic.linarith

src/algebra/big_operators/basic.lean

@@ -7,9 +7,11 @@ Authors: Johannes Hölzl
 import algebra.group.pi
 import algebra.hom.equiv.basic
 import algebra.ring.opposite
-import data.finset.fold
-import data.fintype.basic
 import data.set.pairwise
+import data.finset.sum
+import data.fintype.basic
+import data.finset.sigma
+import algebra.group_power.lemmas
 
 /-!
 # Big operators
@@ -1414,7 +1416,13 @@ end
 @[simp]
 lemma sum_boole {s : finset α} {p : α → Prop} [non_assoc_semiring β] {hp : decidable_pred p} :
   (∑ x in s, if p x then (1 : β) else (0 : β)) = (s.filter p).card :=
-by simp [sum_ite]
+by simp only [add_zero,
+ mul_one,
+ finset.sum_const,
+ nsmul_eq_mul,
+ eq_self_iff_true,
+ finset.sum_const_zero,
+ finset.sum_ite]
 
 lemma _root_.commute.sum_right [non_unital_non_assoc_semiring β] (s : finset α)
   (f : α → β) (b : β) (h : ∀ i ∈ s, commute b (f i)) :

src/algebra/big_operators/fin.lean

@@ -3,7 +3,7 @@ Copyright (c) 2020 Yury Kudryashov, Anne Baanen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov, Anne Baanen
 -/
-import data.fintype.card
+import data.fintype.big_operators
 import data.fintype.fin
 import logic.equiv.fin
 

src/algebra/big_operators/pi.lean

@@ -3,6 +3,8 @@ Copyright (c) 2018 Simon Hudon. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Simon Hudon, Patrick Massot
 -/
+import data.fintype.card
+import algebra.group.prod
 import algebra.big_operators.basic
 import algebra.ring.pi
 

src/algebra/char_zero.lean

@@ -5,7 +5,8 @@ Authors: Mario Carneiro
 -/
 
 import data.nat.cast.field
-import data.fintype.basic
+import data.fintype.lattice
+import algebra.group_power.lemmas
 
 /-!
 # Characteristic zero (additional theorems)

src/algebra/group/conj.lean

@@ -8,6 +8,7 @@ import algebra.group_with_zero.basic
 import algebra.hom.aut
 import algebra.hom.group
 import data.finite.basic
+import data.fintype.units
 
 /-!
 # Conjugacy of group elements

src/algebra/order/field/pi.lean

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
 -/
 import algebra.order.field.basic
-import data.fintype.basic
+import data.fintype.lattice
 
 /-!
 # Lemmas about (finite domain) functions into fields.

src/algebra/order/field/power.lean

@@ -3,6 +3,7 @@ Copyright (c) 2014 Robert Lewis. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Robert Lewis, Leonardo de Moura, Mario Carneiro, Floris van Doorn
 -/
+import algebra.parity
 import algebra.char_zero
 import algebra.group_with_zero.power
 import algebra.order.field.basic

src/algebra/order/nonneg/ring.lean

@@ -3,6 +3,7 @@ Copyright (c) 2021 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
 -/
+import data.nat.cast.basic
 import algebra.order.ring.defs
 import algebra.order.ring.inj_surj
 import order.complete_lattice_intervals

src/algebra/ring/fin.lean

@@ -5,6 +5,7 @@ Authors: Anne Baanen
 -/
 import logic.equiv.fin
 import algebra.ring.equiv
+import algebra.group.prod
 
 /-!
 # Rings and `fin`

src/analysis/complex/upper_half_plane/basic.lean

@@ -3,7 +3,7 @@ Copyright (c) 2021 Alex Kontorovich and Heather Macbeth and Marc Masdeu. All rig
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Alex Kontorovich, Heather Macbeth, Marc Masdeu
 -/
-
+import data.fintype.parity
 import linear_algebra.special_linear_group
 import analysis.complex.basic
 import group_theory.group_action.defs

src/category_theory/Fintype.lean

@@ -8,7 +8,7 @@ import category_theory.concrete_category.basic
 import category_theory.full_subcategory
 import category_theory.skeletal
 import category_theory.elementwise
-import data.fintype.basic
+import data.fintype.card
 
 /-!
 # The category of finite types.

src/category_theory/enriched/basic.lean

@@ -5,6 +5,7 @@ Authors: Scott Morrison
 -/
 import category_theory.monoidal.types
 import category_theory.monoidal.center
+import tactic.apply_fun
 
 /-!
 # Enriched categories

src/category_theory/fin_category.lean

@@ -3,7 +3,7 @@ Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import data.fintype.basic
+import data.fintype.card
 import category_theory.discrete_category
 import category_theory.opposites
 import category_theory.category.ulift

src/category_theory/limits/concrete_category.lean

@@ -9,6 +9,7 @@ import category_theory.limits.shapes.wide_pullbacks
 import category_theory.limits.shapes.multiequalizer
 import category_theory.concrete_category.basic
 import category_theory.limits.shapes.kernels
+import tactic.apply_fun
 
 /-!
 # Facts about (co)limits of functors into concrete categories

src/category_theory/limits/constructions/limits_of_products_and_equalizers.lean

@@ -3,6 +3,8 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta, Scott Morrison
 -/
+import data.fintype.prod
+import data.fintype.sigma
 import category_theory.limits.shapes.equalizers
 import category_theory.limits.shapes.finite_products
 import category_theory.limits.preserves.shapes.products

src/category_theory/limits/lattice.lean

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Justus Springer
 -/
 import order.complete_lattice
+import data.fintype.lattice
 import category_theory.limits.shapes.pullbacks
 import category_theory.category.preorder
 import category_theory.limits.shapes.products

src/category_theory/limits/shapes/finite_limits.lean

@@ -8,7 +8,7 @@ import category_theory.limits.shapes.binary_products
 import category_theory.limits.shapes.equalizers
 import category_theory.limits.shapes.wide_pullbacks
 import category_theory.limits.shapes.pullbacks
-import data.fintype.basic
+import data.fintype.option
 
 /-!
 # Categories with finite limits.

src/combinatorics/configuration.lean

@@ -5,7 +5,7 @@ Authors: Thomas Browning
 -/
 import algebra.big_operators.order
 import combinatorics.hall.basic
-import data.fintype.card
+import data.fintype.big_operators
 import set_theory.cardinal.finite
 
 /-!

src/combinatorics/derangements/finite.lean

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Henry Swanson
 -/
 import combinatorics.derangements.basic
-import data.fintype.card
+import data.fintype.big_operators
 import tactic.delta_instance
 import tactic.ring
 

src/combinatorics/hales_jewett.lean

@@ -3,7 +3,9 @@ Copyright (c) 2021 David Wärn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: David Wärn
 -/
-import data.fintype.basic
+import data.fintype.option
+import data.fintype.pi
+import data.fintype.sum
 import algebra.big_operators.basic
 
 /-!

src/combinatorics/set_family/harris_kleitman.lean

@@ -5,7 +5,7 @@ Authors: Yaël Dillies
 -/
 import combinatorics.set_family.compression.down
 import order.upper_lower
-import data.fintype.card
+import data.fintype.big_operators
 
 /-!
 # Harris-Kleitman inequality

src/combinatorics/set_family/intersecting.lean

@@ -3,7 +3,7 @@ Copyright (c) 2022 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
 -/
-import data.fintype.basic
+import data.fintype.card
 import order.upper_lower
 
 /-!

src/computability/DFA.lean

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Fox Thomson
 -/
 
-import data.fintype.basic
+import data.fintype.card
 import computability.language
 import tactic.norm_num
 

src/computability/NFA.lean

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Fox Thomson
 -/
 import computability.DFA
+import data.fintype.powerset
 
 /-!
 # Nondeterministic Finite Automata

src/computability/turing_machine.lean

@@ -3,7 +3,10 @@ Copyright (c) 2018 Mario Carneiro. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
 -/
-import data.fintype.basic
+import data.fintype.option
+import data.fintype.prod
+import data.fintype.pi
+import data.vector.basic
 import data.pfun
 import logic.function.iterate
 import order.basic

src/data/dfinsupp/interval.lean

@@ -5,7 +5,7 @@ Authors: Yaël Dillies
 -/
 import data.finset.locally_finite
 import data.finset.pointwise
-import data.fintype.card
+import data.fintype.big_operators
 import data.dfinsupp.order
 
 /-!

src/data/fin/tuple/bubble_sort_induction.lean

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Michael Stoll
 -/
 import data.fin.tuple.sort
+import data.fintype.perm
 import order.well_founded
 
 /-!

src/data/fin/tuple/sort.lean

@@ -7,6 +7,7 @@ Authors: Kyle Miller
 import data.fin.basic
 import data.finset.sort
 import data.prod.lex
+import group_theory.perm.basic
 
 /-!
 

src/data/finite/basic.lean

@@ -3,7 +3,11 @@ Copyright (c) 2022 Kyle Miller. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kyle Miller
 -/
-import data.fintype.basic
+import data.fintype.powerset
+import data.fintype.prod
+import data.fintype.sigma
+import data.fintype.sum
+import data.fintype.vector
 
 /-!
 # Finite types

src/data/finite/set.lean

@@ -3,7 +3,7 @@ Copyright (c) 2022 Kyle Miller. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kyle Miller
 -/
-import data.fintype.basic
+import data.fintype.card
 
 /-!
 # Lemmas about `finite` and `set`s

src/data/finset/finsupp.lean

@@ -6,7 +6,7 @@ Authors: Yaël Dillies
 import algebra.big_operators.finsupp
 import data.finset.pointwise
 import data.finsupp.indicator
-import data.fintype.card
+import data.fintype.big_operators
 
 /-!
 # Finitely supported product of finsets

src/data/finset/noncomm_prod.lean

@@ -3,6 +3,7 @@ Copyright (c) 2021 Yakov Pechersky. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yakov Pechersky
 -/
+import data.fintype.card
 import algebra.hom.commute
 import algebra.big_operators.basic
 

src/data/finset/pi_induction.lean

@@ -3,7 +3,8 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import data.fintype.basic
+import data.fintype.lattice
+import data.finset.sigma
 
 /-!
 # Induction principles for `Π i, finset (α i)`

src/data/finset/sort.lean

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Mario Carneiro
 -/
 import order.rel_iso.set
-import data.fintype.basic
+import data.fintype.lattice
 import data.multiset.sort
 import data.list.nodup_equiv_fin
 

src/data/finset/sym.lean

@@ -3,7 +3,8 @@ Copyright (c) 2021 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
 -/
-import data.finset.prod
+import data.fintype.prod
+import data.fintype.vector
 import data.sym.sym2
 
 /-!