data.set.pointwise.finite | 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

c941bb94

(last sync)

feat(data/set/finite): When s ×ˢ t is finite (#18674)

The one non-trivial result is infinite_image2, because it requires only injectivity of the f a and λ a, f a b rather than of the uncurrying of f.

Diff

@@ -6,10 +6,12 @@ Authors: Johan Commelin, Floris van Doorn
 import data.set.finite
 import data.set.pointwise.smul
 
-/-! # Finiteness lemmas for pointwise operations on sets 
+/-!
+# Finiteness lemmas for pointwise operations on sets
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
-> Any changes to this file require a corresponding PR to mathlib4.-/
+> Any changes to this file require a corresponding PR to mathlib4.
+-/
 
 open_locale pointwise
 
@@ -74,6 +76,7 @@ section has_smul_set
 variables [has_smul α β] {s : set β} {a : α}
 
 @[to_additive] lemma finite.smul_set : s.finite → (a • s).finite := finite.image _
+@[to_additive] lemma infinite.of_smul_set : (a • s).infinite → s.infinite := infinite.of_image _
 
 end has_smul_set
 
@@ -85,6 +88,30 @@ lemma finite.vsub (hs : s.finite) (ht : t.finite) : set.finite (s -ᵥ t) := hs.
 
 end vsub
 
+section cancel
+variables [has_mul α] [is_left_cancel_mul α] [is_right_cancel_mul α] {s t : set α}
+
+@[to_additive] lemma infinite_mul :
+  (s * t).infinite ↔ s.infinite ∧ t.nonempty ∨ t.infinite ∧ s.nonempty :=
+infinite_image2 (λ _ _, (mul_left_injective _).inj_on _) (λ _ _, (mul_right_injective _).inj_on _)
+
+end cancel
+
+section group
+variables [group α] [mul_action α β] {a : α} {s : set β}
+
+@[simp, to_additive] lemma finite_smul_set : (a • s).finite ↔ s.finite :=
+finite_image_iff $ (mul_action.injective _).inj_on _
+
+@[simp, to_additive] lemma infinite_smul_set : (a • s).infinite ↔ s.infinite :=
+infinite_image_iff $ (mul_action.injective _).inj_on _
+
+alias finite_smul_set ↔ finite.of_smul_set _
+alias infinite_smul_set ↔ _ infinite.smul_set
+
+attribute [to_additive] finite.of_smul_set infinite.smul_set
+
+end group
 end set
 
 open set

517cc149

feat(data/finset/pointwise): s ∩ t * s ∪ t ⊆ s * t (#17961)

and distributivity of set.to_finset/set.finite.to_finset over algebraic operations.

Diff

@@ -16,6 +16,12 @@ open_locale pointwise
 variables {F α β γ : Type*}
 
 namespace set
+section has_one
+variables [has_one α]
+
+@[simp, to_additive] lemma finite_one : (1 : set α).finite := finite_singleton _
+
+end has_one
 
 section has_involutive_inv
 variables [has_involutive_inv α] {s : set α}

0a0ec350

(no changes)

f93c1193

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

c941bb94

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Floris van Doorn
 -/
 import Data.Set.Finite
-import Data.Set.Pointwise.Smul
+import Data.Set.Pointwise.SMul
 
 #align_import data.set.pointwise.finite from "leanprover-community/mathlib"@"c941bb9426d62e266612b6d99e6c9fc93e7a1d07"
 
@@ -91,7 +91,7 @@ instance decidableMemPow [Fintype α] [DecidableEq α] [DecidablePred (· ∈ s)
     DecidablePred (· ∈ s ^ n) := by
   induction' n with n ih
   · simp_rw [pow_zero, mem_one]; infer_instance
-  · letI := ih; rw [pow_succ]; infer_instance
+  · letI := ih; rw [pow_succ']; infer_instance
 #align set.decidable_mem_pow Set.decidableMemPow
 #align set.decidable_mem_nsmul Set.decidableMemNSMul
 -/
@@ -225,7 +225,7 @@ theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k
   · refine' Set.eq_of_subset_of_card_le _ (le_trans (ge_of_eq h) _)
     · exact mul_subset_mul (set.singleton_subset_iff.mpr ha) Set.Subset.rfl
     · convert key a (S ^ n) ({a} * S ^ n) fun b hb => Set.mul_mem_mul (Set.mem_singleton a) hb
-  rw [pow_succ', ← h, mul_assoc, ← pow_succ', h]
+  rw [pow_succ, ← h, mul_assoc, ← pow_succ, h]
   rintro _ ⟨b, c, hb, hc, rfl⟩
   rwa [set.mem_singleton_iff.mp hb, inv_mul_cancel_left]
 #align group.card_pow_eq_card_pow_card_univ Group.card_pow_eq_card_pow_card_univ

c941bb94

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Floris van Doorn
 -/
-import Mathbin.Data.Set.Finite
-import Mathbin.Data.Set.Pointwise.Smul
+import Data.Set.Finite
+import Data.Set.Pointwise.Smul
 
 #align_import data.set.pointwise.finite from "leanprover-community/mathlib"@"c941bb9426d62e266612b6d99e6c9fc93e7a1d07"

c941bb94

bump to nightly-2023-08-23-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

f612b9e0

Diff

@@ -181,10 +181,10 @@ theorem infinite_smul_set : (a • s).Infinite ↔ s.Infinite :=
 #align set.infinite_vadd_set Set.infinite_vadd_set
 -/
 
-alias finite_smul_set ↔ finite.of_smul_set _
+alias ⟨finite.of_smul_set, _⟩ := finite_smul_set
 #align set.finite.of_smul_set Set.Finite.of_smul_set
 
-alias infinite_smul_set ↔ _ infinite.smul_set
+alias ⟨_, infinite.smul_set⟩ := infinite_smul_set
 #align set.infinite.smul_set Set.Infinite.smul_set
 
 attribute [to_additive] finite.of_smul_set infinite.smul_set

c941bb94

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Floris van Doorn
-
-! This file was ported from Lean 3 source module data.set.pointwise.finite
-! leanprover-community/mathlib commit c941bb9426d62e266612b6d99e6c9fc93e7a1d07
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.Finite
 import Mathbin.Data.Set.Pointwise.Smul
 
+#align_import data.set.pointwise.finite from "leanprover-community/mathlib"@"c941bb9426d62e266612b6d99e6c9fc93e7a1d07"
+
 /-!
 # Finiteness lemmas for pointwise operations on sets

c941bb94

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -43,11 +43,13 @@ section InvolutiveInv
 
 variable [InvolutiveInv α] {s : Set α}
 
+#print Set.Finite.inv /-
 @[to_additive]
 theorem Finite.inv (hs : s.Finite) : s⁻¹.Finite :=
   hs.Preimage <| inv_injective.InjOn _
 #align set.finite.inv Set.Finite.inv
 #align set.finite.neg Set.Finite.neg
+-/
 
 end InvolutiveInv
 
@@ -78,12 +80,15 @@ section Monoid
 
 variable [Monoid α] {s t : Set α}
 
+#print Set.decidableMemMul /-
 @[to_additive]
 instance decidableMemMul [Fintype α] [DecidableEq α] [DecidablePred (· ∈ s)]
     [DecidablePred (· ∈ t)] : DecidablePred (· ∈ s * t) := fun _ => decidable_of_iff _ mem_mul.symm
 #align set.decidable_mem_mul Set.decidableMemMul
 #align set.decidable_mem_add Set.decidableMemAdd
+-/
 
+#print Set.decidableMemPow /-
 @[to_additive]
 instance decidableMemPow [Fintype α] [DecidableEq α] [DecidablePred (· ∈ s)] (n : ℕ) :
     DecidablePred (· ∈ s ^ n) := by
@@ -92,6 +97,7 @@ instance decidableMemPow [Fintype α] [DecidableEq α] [DecidablePred (· ∈ s)
   · letI := ih; rw [pow_succ]; infer_instance
 #align set.decidable_mem_pow Set.decidableMemPow
 #align set.decidable_mem_nsmul Set.decidableMemNSMul
+-/
 
 end Monoid
 
@@ -99,11 +105,13 @@ section SMul
 
 variable [SMul α β] {s : Set α} {t : Set β}
 
+#print Set.Finite.smul /-
 @[to_additive]
 theorem Finite.smul : s.Finite → t.Finite → (s • t).Finite :=
   Finite.image2 _
 #align set.finite.smul Set.Finite.smul
 #align set.finite.vadd Set.Finite.vadd
+-/
 
 end SMul
 
@@ -133,8 +141,6 @@ section Vsub
 
 variable [VSub α β] {s t : Set β}
 
-include α
-
 #print Set.Finite.vsub /-
 theorem Finite.vsub (hs : s.Finite) (ht : t.Finite) : Set.Finite (s -ᵥ t) :=
   hs.image2 _ ht
@@ -196,6 +202,7 @@ namespace Group
 
 variable {G : Type _} [Group G] [Fintype G] (S : Set G)
 
+#print Group.card_pow_eq_card_pow_card_univ /-
 @[to_additive]
 theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k)] :
     ∀ k, Fintype.card G ≤ k → Fintype.card ↥(S ^ k) = Fintype.card ↥(S ^ Fintype.card G) :=
@@ -226,6 +233,7 @@ theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k
   rwa [set.mem_singleton_iff.mp hb, inv_mul_cancel_left]
 #align group.card_pow_eq_card_pow_card_univ Group.card_pow_eq_card_pow_card_univ
 #align add_group.card_nsmul_eq_card_nsmul_card_univ AddGroup.card_nsmul_eq_card_nsmul_card_univ
+-/
 
 end Group

c941bb94

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -213,8 +213,9 @@ theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k
     exact Subtype.ext (mul_left_cancel (subtype.ext_iff.mp hbc))
   have mono : Monotone (fun n => Fintype.card ↥(S ^ n) : ℕ → ℕ) :=
     monotone_nat_of_le_succ fun n => key a _ _ fun b hb => Set.mul_mem_mul ha hb
-  convert card_pow_eq_card_pow_card_univ_aux mono (fun n => set_fintype_card_le_univ (S ^ n))
-      fun n h => le_antisymm (mono (n + 1).le_succ) (key a⁻¹ _ _ _)
+  convert
+    card_pow_eq_card_pow_card_univ_aux mono (fun n => set_fintype_card_le_univ (S ^ n)) fun n h =>
+      le_antisymm (mono (n + 1).le_succ) (key a⁻¹ _ _ _)
   · simp only [Finset.filter_congr_decidable, Fintype.card_ofFinset]
   replace h : {a} * S ^ n = S ^ (n + 1)
   · refine' Set.eq_of_subset_of_card_le _ (le_trans (ge_of_eq h) _)

c941bb94

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -215,7 +215,7 @@ theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k
     monotone_nat_of_le_succ fun n => key a _ _ fun b hb => Set.mul_mem_mul ha hb
   convert card_pow_eq_card_pow_card_univ_aux mono (fun n => set_fintype_card_le_univ (S ^ n))
       fun n h => le_antisymm (mono (n + 1).le_succ) (key a⁻¹ _ _ _)
-  · simp only [[anonymous], Fintype.card_ofFinset]
+  · simp only [Finset.filter_congr_decidable, Fintype.card_ofFinset]
   replace h : {a} * S ^ n = S ^ (n + 1)
   · refine' Set.eq_of_subset_of_card_le _ (le_trans (ge_of_eq h) _)
     · exact mul_subset_mul (set.singleton_subset_iff.mpr ha) Set.Subset.rfl

c941bb94

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -19,7 +19,7 @@ import Mathbin.Data.Set.Pointwise.Smul
 -/
 
 
-open Pointwise
+open scoped Pointwise
 
 variable {F α β γ : Type _}

c941bb94

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -43,12 +43,6 @@ section InvolutiveInv
 
 variable [InvolutiveInv α] {s : Set α}
 
-/- warning: set.finite.inv -> Set.Finite.inv is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : InvolutiveInv.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Set.Finite.{u1} α (Inv.inv.{u1} (Set.{u1} α) (Set.inv.{u1} α (InvolutiveInv.toHasInv.{u1} α _inst_1)) s))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : InvolutiveInv.{u1} α] {s : Set.{u1} α}, (Set.Finite.{u1} α s) -> (Set.Finite.{u1} α (Inv.inv.{u1} (Set.{u1} α) (Set.inv.{u1} α (InvolutiveInv.toInv.{u1} α _inst_1)) s))
-Case conversion may be inaccurate. Consider using '#align set.finite.inv Set.Finite.invₓ'. -/
 @[to_additive]
 theorem Finite.inv (hs : s.Finite) : s⁻¹.Finite :=
   hs.Preimage <| inv_injective.InjOn _
@@ -84,24 +78,12 @@ section Monoid
 
 variable [Monoid α] {s t : Set α}
 
-/- warning: set.decidable_mem_mul -> Set.decidableMemMul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Monoid.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α} [_inst_2 : Fintype.{u1} α] [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : DecidablePred.{succ u1} α (fun (_x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) _x s)] [_inst_5 : DecidablePred.{succ u1} α (fun (_x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) _x t)], DecidablePred.{succ u1} α (fun (_x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) _x (HMul.hMul.{u1, u1, u1} (Set.{u1} α) (Set.{u1} α) (Set.{u1} α) (instHMul.{u1} (Set.{u1} α) (Set.mul.{u1} α (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α _inst_1)))) s t))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Monoid.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α} [_inst_2 : Fintype.{u1} α] [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : DecidablePred.{succ u1} α (fun (_x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) _x s)] [_inst_5 : DecidablePred.{succ u1} α (fun (_x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) _x t)], DecidablePred.{succ u1} α (fun (_x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) _x (HMul.hMul.{u1, u1, u1} (Set.{u1} α) (Set.{u1} α) (Set.{u1} α) (instHMul.{u1} (Set.{u1} α) (Set.mul.{u1} α (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α _inst_1)))) s t))
-Case conversion may be inaccurate. Consider using '#align set.decidable_mem_mul Set.decidableMemMulₓ'. -/
 @[to_additive]
 instance decidableMemMul [Fintype α] [DecidableEq α] [DecidablePred (· ∈ s)]
     [DecidablePred (· ∈ t)] : DecidablePred (· ∈ s * t) := fun _ => decidable_of_iff _ mem_mul.symm
 #align set.decidable_mem_mul Set.decidableMemMul
 #align set.decidable_mem_add Set.decidableMemAdd
 
-/- warning: set.decidable_mem_pow -> Set.decidableMemPow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : Monoid.{u1} α] {s : Set.{u1} α} [_inst_2 : Fintype.{u1} α] [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : DecidablePred.{succ u1} α (fun (_x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) _x s)] (n : Nat), DecidablePred.{succ u1} α (fun (_x : α) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) _x (HPow.hPow.{u1, 0, u1} (Set.{u1} α) Nat (Set.{u1} α) (instHPow.{u1, 0} (Set.{u1} α) Nat (Set.NPow.{u1} α (MulOneClass.toHasOne.{u1} α (Monoid.toMulOneClass.{u1} α _inst_1)) (MulOneClass.toHasMul.{u1} α (Monoid.toMulOneClass.{u1} α _inst_1)))) s n))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : Monoid.{u1} α] {s : Set.{u1} α} [_inst_2 : Fintype.{u1} α] [_inst_3 : DecidableEq.{succ u1} α] [_inst_4 : DecidablePred.{succ u1} α (fun (_x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) _x s)] (n : Nat), DecidablePred.{succ u1} α (fun (_x : α) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) _x (HPow.hPow.{u1, 0, u1} (Set.{u1} α) Nat (Set.{u1} α) (instHPow.{u1, 0} (Set.{u1} α) Nat (Set.NPow.{u1} α (Monoid.toOne.{u1} α _inst_1) (MulOneClass.toMul.{u1} α (Monoid.toMulOneClass.{u1} α _inst_1)))) s n))
-Case conversion may be inaccurate. Consider using '#align set.decidable_mem_pow Set.decidableMemPowₓ'. -/
 @[to_additive]
 instance decidableMemPow [Fintype α] [DecidableEq α] [DecidablePred (· ∈ s)] (n : ℕ) :
     DecidablePred (· ∈ s ^ n) := by
@@ -117,12 +99,6 @@ section SMul
 
 variable [SMul α β] {s : Set α} {t : Set β}
 
-/- warning: set.finite.smul -> Set.Finite.smul is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : SMul.{u1, u2} α β] {s : Set.{u1} α} {t : Set.{u2} β}, (Set.Finite.{u1} α s) -> (Set.Finite.{u2} β t) -> (Set.Finite.{u2} β (SMul.smul.{u1, u2} (Set.{u1} α) (Set.{u2} β) (Set.smul.{u1, u2} α β _inst_1) s t))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : SMul.{u2, u1} α β] {s : Set.{u2} α} {t : Set.{u1} β}, (Set.Finite.{u2} α s) -> (Set.Finite.{u1} β t) -> (Set.Finite.{u1} β (HSMul.hSMul.{u2, u1, u1} (Set.{u2} α) (Set.{u1} β) (Set.{u1} β) (instHSMul.{u2, u1} (Set.{u2} α) (Set.{u1} β) (Set.smul.{u2, u1} α β _inst_1)) s t))
-Case conversion may be inaccurate. Consider using '#align set.finite.smul Set.Finite.smulₓ'. -/
 @[to_additive]
 theorem Finite.smul : s.Finite → t.Finite → (s • t).Finite :=
   Finite.image2 _
@@ -220,12 +196,6 @@ namespace Group
 
 variable {G : Type _} [Group G] [Fintype G] (S : Set G)
 
-/- warning: group.card_pow_eq_card_pow_card_univ -> Group.card_pow_eq_card_pow_card_univ is a dubious translation:
-lean 3 declaration is
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] [_inst_2 : Fintype.{u1} G] (S : Set.{u1} G) [_inst_3 : forall (k : Nat), DecidablePred.{succ u1} G (fun (_x : G) => Membership.Mem.{u1, u1} G (Set.{u1} G) (Set.hasMem.{u1} G) _x (HPow.hPow.{u1, 0, u1} (Set.{u1} G) Nat (Set.{u1} G) (instHPow.{u1, 0} (Set.{u1} G) Nat (Set.NPow.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S k))] (k : Nat), (LE.le.{0} Nat Nat.hasLe (Fintype.card.{u1} G _inst_2) k) -> (Eq.{1} Nat (Fintype.card.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} G) Type.{u1} (Set.hasCoeToSort.{u1} G) (HPow.hPow.{u1, 0, u1} (Set.{u1} G) Nat (Set.{u1} G) (instHPow.{u1, 0} (Set.{u1} G) Nat (Set.NPow.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S k)) (Subtype.fintype.{u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Set.{u1} G) (Set.hasMem.{u1} G) x (HPow.hPow.{u1, 0, u1} (Set.{u1} G) Nat (Set.{u1} G) (instHPow.{u1, 0} (Set.{u1} G) Nat (Set.NPow.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S k)) (fun (a : G) => _inst_3 k a) _inst_2)) (Fintype.card.{u1} (coeSort.{succ u1, succ (succ u1)} (Set.{u1} G) Type.{u1} (Set.hasCoeToSort.{u1} G) (HPow.hPow.{u1, 0, u1} (Set.{u1} G) Nat (Set.{u1} G) (instHPow.{u1, 0} (Set.{u1} G) Nat (Set.NPow.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S (Fintype.card.{u1} G _inst_2))) (Subtype.fintype.{u1} G (fun (x : G) => Membership.Mem.{u1, u1} G (Set.{u1} G) (Set.hasMem.{u1} G) x (HPow.hPow.{u1, 0, u1} (Set.{u1} G) Nat (Set.{u1} G) (instHPow.{u1, 0} (Set.{u1} G) Nat (Set.NPow.{u1} G (MulOneClass.toHasOne.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))) (MulOneClass.toHasMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S (Fintype.card.{u1} G _inst_2))) (fun (a : G) => _inst_3 (Fintype.card.{u1} G _inst_2) a) _inst_2)))
-but is expected to have type
-  forall {G : Type.{u1}} [_inst_1 : Group.{u1} G] [_inst_2 : Fintype.{u1} G] (S : Set.{u1} G) [_inst_3 : forall (k : Nat), DecidablePred.{succ u1} G (fun (_x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) _x (HPow.hPow.{u1, 0, u1} (Set.{u1} G) Nat (Set.{u1} G) (instHPow.{u1, 0} (Set.{u1} G) Nat (Set.NPow.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S k))] (k : Nat), (LE.le.{0} Nat instLENat (Fintype.card.{u1} G _inst_2) k) -> (Eq.{1} Nat (Fintype.card.{u1} (Set.Elem.{u1} G (HPow.hPow.{u1, 0, u1} (Set.{u1} G) Nat (Set.{u1} G) (instHPow.{u1, 0} (Set.{u1} G) Nat (Set.NPow.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S k)) (Subtype.fintype.{u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (HPow.hPow.{u1, 0, u1} (Set.{u1} G) Nat (Set.{u1} G) (instHPow.{u1, 0} (Set.{u1} G) Nat (Set.NPow.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S k)) (fun (a : G) => _inst_3 k a) _inst_2)) (Fintype.card.{u1} (Set.Elem.{u1} G (HPow.hPow.{u1, 0, u1} (Set.{u1} G) Nat (Set.{u1} G) (instHPow.{u1, 0} (Set.{u1} G) Nat (Set.NPow.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S (Fintype.card.{u1} G _inst_2))) (Subtype.fintype.{u1} G (fun (x : G) => Membership.mem.{u1, u1} G (Set.{u1} G) (Set.instMembershipSet.{u1} G) x (HPow.hPow.{u1, 0, u1} (Set.{u1} G) Nat (Set.{u1} G) (instHPow.{u1, 0} (Set.{u1} G) Nat (Set.NPow.{u1} G (InvOneClass.toOne.{u1} G (DivInvOneMonoid.toInvOneClass.{u1} G (DivisionMonoid.toDivInvOneMonoid.{u1} G (Group.toDivisionMonoid.{u1} G _inst_1)))) (MulOneClass.toMul.{u1} G (Monoid.toMulOneClass.{u1} G (DivInvMonoid.toMonoid.{u1} G (Group.toDivInvMonoid.{u1} G _inst_1)))))) S (Fintype.card.{u1} G _inst_2))) (fun (a : G) => _inst_3 (Fintype.card.{u1} G _inst_2) a) _inst_2)))
-Case conversion may be inaccurate. Consider using '#align group.card_pow_eq_card_pow_card_univ Group.card_pow_eq_card_pow_card_univₓ'. -/
 @[to_additive]
 theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k)] :
     ∀ k, Fintype.card G ≤ k → Fintype.card ↥(S ^ k) = Fintype.card ↥(S ^ Fintype.card G) :=

c941bb94

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -106,11 +106,8 @@ Case conversion may be inaccurate. Consider using '#align set.decidable_mem_pow
 instance decidableMemPow [Fintype α] [DecidableEq α] [DecidablePred (· ∈ s)] (n : ℕ) :
     DecidablePred (· ∈ s ^ n) := by
   induction' n with n ih
-  · simp_rw [pow_zero, mem_one]
-    infer_instance
-  · letI := ih
-    rw [pow_succ]
-    infer_instance
+  · simp_rw [pow_zero, mem_one]; infer_instance
+  · letI := ih; rw [pow_succ]; infer_instance
 #align set.decidable_mem_pow Set.decidableMemPow
 #align set.decidable_mem_nsmul Set.decidableMemNSMul

c941bb94

bump to nightly-2023-04-01-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/172bf2812857f5e56938cc148b7a539f52f84ca9

b22e1dc9

Diff

@@ -146,11 +146,13 @@ theorem Finite.smul_set : s.Finite → (a • s).Finite :=
 #align set.finite.vadd_set Set.Finite.vadd_set
 -/
 
+#print Set.Infinite.of_smul_set /-
 @[to_additive]
 theorem Infinite.of_smul_set : (a • s).Infinite → s.Infinite :=
   Infinite.of_image _
 #align set.infinite.of_smul_set Set.Infinite.of_smul_set
 #align set.infinite.of_vadd_set Set.Infinite.of_vadd_set
+-/
 
 end HasSmulSet
 
@@ -172,12 +174,14 @@ section Cancel
 
 variable [Mul α] [IsLeftCancelMul α] [IsRightCancelMul α] {s t : Set α}
 
+#print Set.infinite_mul /-
 @[to_additive]
 theorem infinite_mul : (s * t).Infinite ↔ s.Infinite ∧ t.Nonempty ∨ t.Infinite ∧ s.Nonempty :=
   infinite_image2 (fun _ _ => (mul_left_injective _).InjOn _) fun _ _ =>
     (mul_right_injective _).InjOn _
 #align set.infinite_mul Set.infinite_mul
 #align set.infinite_add Set.infinite_add
+-/
 
 end Cancel
 
@@ -185,17 +189,21 @@ section Group
 
 variable [Group α] [MulAction α β] {a : α} {s : Set β}
 
+#print Set.finite_smul_set /-
 @[simp, to_additive]
 theorem finite_smul_set : (a • s).Finite ↔ s.Finite :=
   finite_image_iff <| (MulAction.injective _).InjOn _
 #align set.finite_smul_set Set.finite_smul_set
 #align set.finite_vadd_set Set.finite_vadd_set
+-/
 
+#print Set.infinite_smul_set /-
 @[simp, to_additive]
 theorem infinite_smul_set : (a • s).Infinite ↔ s.Infinite :=
   infinite_image_iff <| (MulAction.injective _).InjOn _
 #align set.infinite_smul_set Set.infinite_smul_set
 #align set.infinite_vadd_set Set.infinite_vadd_set
+-/
 
 alias finite_smul_set ↔ finite.of_smul_set _
 #align set.finite.of_smul_set Set.Finite.of_smul_set

c941bb94

bump to nightly-2023-03-31-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a

c3ffa91f

Diff

@@ -4,17 +4,19 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Floris van Doorn
 
 ! This file was ported from Lean 3 source module data.set.pointwise.finite
-! leanprover-community/mathlib commit 517cc149e0b515d2893baa376226ed10feb319c7
+! leanprover-community/mathlib commit c941bb9426d62e266612b6d99e6c9fc93e7a1d07
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Data.Set.Finite
 import Mathbin.Data.Set.Pointwise.Smul
 
-/-! # Finiteness lemmas for pointwise operations on sets 
+/-!
+# Finiteness lemmas for pointwise operations on sets
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
-> Any changes to this file require a corresponding PR to mathlib4.-/
+> Any changes to this file require a corresponding PR to mathlib4.
+-/
 
 
 open Pointwise
@@ -144,6 +146,12 @@ theorem Finite.smul_set : s.Finite → (a • s).Finite :=
 #align set.finite.vadd_set Set.Finite.vadd_set
 -/
 
+@[to_additive]
+theorem Infinite.of_smul_set : (a • s).Infinite → s.Infinite :=
+  Infinite.of_image _
+#align set.infinite.of_smul_set Set.Infinite.of_smul_set
+#align set.infinite.of_vadd_set Set.Infinite.of_vadd_set
+
 end HasSmulSet
 
 section Vsub
@@ -160,6 +168,45 @@ theorem Finite.vsub (hs : s.Finite) (ht : t.Finite) : Set.Finite (s -ᵥ t) :=
 
 end Vsub
 
+section Cancel
+
+variable [Mul α] [IsLeftCancelMul α] [IsRightCancelMul α] {s t : Set α}
+
+@[to_additive]
+theorem infinite_mul : (s * t).Infinite ↔ s.Infinite ∧ t.Nonempty ∨ t.Infinite ∧ s.Nonempty :=
+  infinite_image2 (fun _ _ => (mul_left_injective _).InjOn _) fun _ _ =>
+    (mul_right_injective _).InjOn _
+#align set.infinite_mul Set.infinite_mul
+#align set.infinite_add Set.infinite_add
+
+end Cancel
+
+section Group
+
+variable [Group α] [MulAction α β] {a : α} {s : Set β}
+
+@[simp, to_additive]
+theorem finite_smul_set : (a • s).Finite ↔ s.Finite :=
+  finite_image_iff <| (MulAction.injective _).InjOn _
+#align set.finite_smul_set Set.finite_smul_set
+#align set.finite_vadd_set Set.finite_vadd_set
+
+@[simp, to_additive]
+theorem infinite_smul_set : (a • s).Infinite ↔ s.Infinite :=
+  infinite_image_iff <| (MulAction.injective _).InjOn _
+#align set.infinite_smul_set Set.infinite_smul_set
+#align set.infinite_vadd_set Set.infinite_vadd_set
+
+alias finite_smul_set ↔ finite.of_smul_set _
+#align set.finite.of_smul_set Set.Finite.of_smul_set
+
+alias infinite_smul_set ↔ _ infinite.smul_set
+#align set.infinite.smul_set Set.Infinite.smul_set
+
+attribute [to_additive] finite.of_smul_set infinite.smul_set
+
+end Group
+
 end Set
 
 open Set

517cc149

bump to nightly-2023-03-27-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce86f4e05e9a9b8da5e316b22c76ce76440c56a1

a9497265

Diff

@@ -27,11 +27,13 @@ section One
 
 variable [One α]
 
+#print Set.finite_one /-
 @[simp, to_additive]
 theorem finite_one : (1 : Set α).Finite :=
   finite_singleton _
 #align set.finite_one Set.finite_one
 #align set.finite_zero Set.finite_zero
+-/
 
 end One

517cc149

bump to nightly-2023-03-26-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

ca5de00c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Floris van Doorn
 
 ! This file was ported from Lean 3 source module data.set.pointwise.finite
-! leanprover-community/mathlib commit 68d1483e8a718ec63219f0e227ca3f0140361086
+! leanprover-community/mathlib commit 517cc149e0b515d2893baa376226ed10feb319c7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -23,6 +23,18 @@ variable {F α β γ : Type _}
 
 namespace Set
 
+section One
+
+variable [One α]
+
+@[simp, to_additive]
+theorem finite_one : (1 : Set α).Finite :=
+  finite_singleton _
+#align set.finite_one Set.finite_one
+#align set.finite_zero Set.finite_zero
+
+end One
+
 section InvolutiveInv
 
 variable [InvolutiveInv α] {s : Set α}

68d1483e

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -177,9 +177,8 @@ theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k
     exact Subtype.ext (mul_left_cancel (subtype.ext_iff.mp hbc))
   have mono : Monotone (fun n => Fintype.card ↥(S ^ n) : ℕ → ℕ) :=
     monotone_nat_of_le_succ fun n => key a _ _ fun b hb => Set.mul_mem_mul ha hb
-  convert
-    card_pow_eq_card_pow_card_univ_aux mono (fun n => set_fintype_card_le_univ (S ^ n)) fun n h =>
-      le_antisymm (mono (n + 1).le_succ) (key a⁻¹ _ _ _)
+  convert card_pow_eq_card_pow_card_univ_aux mono (fun n => set_fintype_card_le_univ (S ^ n))
+      fun n h => le_antisymm (mono (n + 1).le_succ) (key a⁻¹ _ _ _)
   · simp only [[anonymous], Fintype.card_ofFinset]
   replace h : {a} * S ^ n = S ^ (n + 1)
   · refine' Set.eq_of_subset_of_card_le _ (le_trans (ge_of_eq h) _)

68d1483e

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

c941bb94

chore: remove unnecessary classical! (#12255)

classical! appears to never actually be necessary, and is just being used out of habit, and we can get rid of it to reduce the number of ways to say the same thing.

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

1d4a7225

Diff

@@ -194,7 +194,7 @@ theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k
     fun n h ↦ le_antisymm (mono (n + 1).le_succ) (key a⁻¹ (S ^ (n + 2)) (S ^ (n + 1)) _)
   replace h₂ : S ^ n * {a} = S ^ (n + 1) := by
     have : Fintype (S ^ n * Set.singleton a) := by
-      classical!
+      classical
       apply fintypeMul
     refine' Set.eq_of_subset_of_card_le _ (le_trans (ge_of_eq h) _)
     · exact mul_subset_mul Set.Subset.rfl (Set.singleton_subset_iff.mpr ha)

c941bb94

change the order of operation in zsmulRec and nsmulRec (#11451)

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

pow_succ and pow_succ' have switched their meanings.
Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

9a3feeae

Diff

@@ -184,24 +184,24 @@ theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k
   · refine' fun k hk ↦ Fintype.card_congr _
     rw [empty_pow (hG.trans_le hk).ne', empty_pow (ne_of_gt hG)]
   have key : ∀ (a) (s t : Set G) [Fintype s] [Fintype t],
-      (∀ b : G, b ∈ s → a * b ∈ t) → Fintype.card s ≤ Fintype.card t := by
-    refine' fun a s t _ _ h ↦ Fintype.card_le_of_injective (fun ⟨b, hb⟩ ↦ ⟨a * b, h b hb⟩) _
+      (∀ b : G, b ∈ s → b * a ∈ t) → Fintype.card s ≤ Fintype.card t := by
+    refine' fun a s t _ _ h ↦ Fintype.card_le_of_injective (fun ⟨b, hb⟩ ↦ ⟨b * a, h b hb⟩) _
     rintro ⟨b, hb⟩ ⟨c, hc⟩ hbc
-    exact Subtype.ext (mul_left_cancel (Subtype.ext_iff.mp hbc))
+    exact Subtype.ext (mul_right_cancel (Subtype.ext_iff.mp hbc))
   have mono : Monotone (fun n ↦ Fintype.card (↥(S ^ n)) : ℕ → ℕ) :=
-    monotone_nat_of_le_succ fun n ↦ key a _ _ fun b hb ↦ Set.mul_mem_mul ha hb
+    monotone_nat_of_le_succ fun n ↦ key a _ _ fun b hb ↦ Set.mul_mem_mul hb ha
   refine' card_pow_eq_card_pow_card_univ_aux mono (fun n ↦ set_fintype_card_le_univ (S ^ n))
     fun n h ↦ le_antisymm (mono (n + 1).le_succ) (key a⁻¹ (S ^ (n + 2)) (S ^ (n + 1)) _)
-  replace h₂ : {a} * S ^ n = S ^ (n + 1) := by
-    have : Fintype (Set.singleton a * S ^ n) := by
-      classical
+  replace h₂ : S ^ n * {a} = S ^ (n + 1) := by
+    have : Fintype (S ^ n * Set.singleton a) := by
+      classical!
       apply fintypeMul
     refine' Set.eq_of_subset_of_card_le _ (le_trans (ge_of_eq h) _)
-    · exact mul_subset_mul (Set.singleton_subset_iff.mpr ha) Set.Subset.rfl
-    · convert key a (S ^ n) ({a} * S ^ n) fun b hb ↦ Set.mul_mem_mul (Set.mem_singleton a) hb
-  rw [pow_succ', ← h₂, mul_assoc, ← pow_succ', h₂, singleton_mul, forall_mem_image]
+    · exact mul_subset_mul Set.Subset.rfl (Set.singleton_subset_iff.mpr ha)
+    · convert key a (S ^ n) (S ^ n * {a}) fun b hb ↦ Set.mul_mem_mul hb (Set.mem_singleton a)
+  rw [pow_succ', ← h₂, ← mul_assoc, ← pow_succ', h₂, mul_singleton, forall_mem_image]
   intro x hx
-  rwa [inv_mul_cancel_left]
+  rwa [mul_inv_cancel_right]
 #align group.card_pow_eq_card_pow_card_univ Group.card_pow_eq_card_pow_card_univ
 #align add_group.card_nsmul_eq_card_nsmul_card_univ AddGroup.card_nsmul_eq_card_nsmul_card_univ

c941bb94

chore: don't use classical! when classical suffices (#11681)

(In fact, this is every use of classical! in Mathlib.)

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

92c745e2

Diff

@@ -194,7 +194,7 @@ theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k
     fun n h ↦ le_antisymm (mono (n + 1).le_succ) (key a⁻¹ (S ^ (n + 2)) (S ^ (n + 1)) _)
   replace h₂ : {a} * S ^ n = S ^ (n + 1) := by
     have : Fintype (Set.singleton a * S ^ n) := by
-      classical!
+      classical
       apply fintypeMul
     refine' Set.eq_of_subset_of_card_le _ (le_trans (ge_of_eq h) _)
     · exact mul_subset_mul (Set.singleton_subset_iff.mpr ha) Set.Subset.rfl

c941bb94

chore: Remove ball and bex from lemma names (#10816)

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

c697e040

Diff

@@ -199,7 +199,7 @@ theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k
     refine' Set.eq_of_subset_of_card_le _ (le_trans (ge_of_eq h) _)
     · exact mul_subset_mul (Set.singleton_subset_iff.mpr ha) Set.Subset.rfl
     · convert key a (S ^ n) ({a} * S ^ n) fun b hb ↦ Set.mul_mem_mul (Set.mem_singleton a) hb
-  rw [pow_succ', ← h₂, mul_assoc, ← pow_succ', h₂, singleton_mul, ball_image_iff]
+  rw [pow_succ', ← h₂, mul_assoc, ← pow_succ', h₂, singleton_mul, forall_mem_image]
   intro x hx
   rwa [inv_mul_cancel_left]
 #align group.card_pow_eq_card_pow_card_univ Group.card_pow_eq_card_pow_card_univ

c941bb94

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -192,8 +192,8 @@ theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k
     monotone_nat_of_le_succ fun n ↦ key a _ _ fun b hb ↦ Set.mul_mem_mul ha hb
   refine' card_pow_eq_card_pow_card_univ_aux mono (fun n ↦ set_fintype_card_le_univ (S ^ n))
     fun n h ↦ le_antisymm (mono (n + 1).le_succ) (key a⁻¹ (S ^ (n + 2)) (S ^ (n + 1)) _)
-  replace h₂ : {a} * S ^ n = S ^ (n + 1)
-  · have : Fintype (Set.singleton a * S ^ n) := by
+  replace h₂ : {a} * S ^ n = S ^ (n + 1) := by
+    have : Fintype (Set.singleton a * S ^ n) := by
       classical!
       apply fintypeMul
     refine' Set.eq_of_subset_of_card_le _ (le_trans (ge_of_eq h) _)

c941bb94

chore(Set/Pointwise/Finite): golf (#9214)

eb17faa5

Diff

@@ -179,11 +179,10 @@ variable {G : Type*} [Group G] [Fintype G] (S : Set G)
 @[to_additive]
 theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k)] :
     ∀ k, Fintype.card G ≤ k → Fintype.card (↥(S ^ k)) = Fintype.card (↥(S ^ Fintype.card G)) := by
-  have hG : 0 < Fintype.card G := Fintype.card_pos_iff.mpr ⟨1⟩
-  by_cases hS : S = ∅
+  have hG : 0 < Fintype.card G := Fintype.card_pos
+  rcases S.eq_empty_or_nonempty with (rfl | ⟨a, ha⟩)
   · refine' fun k hk ↦ Fintype.card_congr _
-    rw [hS, empty_pow (ne_of_gt (lt_of_lt_of_le hG hk)), empty_pow (ne_of_gt hG)]
-  obtain ⟨a, ha⟩ := Set.nonempty_iff_ne_empty.2 hS
+    rw [empty_pow (hG.trans_le hk).ne', empty_pow (ne_of_gt hG)]
   have key : ∀ (a) (s t : Set G) [Fintype s] [Fintype t],
       (∀ b : G, b ∈ s → a * b ∈ t) → Fintype.card s ≤ Fintype.card t := by
     refine' fun a s t _ _ h ↦ Fintype.card_le_of_injective (fun ⟨b, hb⟩ ↦ ⟨a * b, h b hb⟩) _
@@ -200,9 +199,9 @@ theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k
     refine' Set.eq_of_subset_of_card_le _ (le_trans (ge_of_eq h) _)
     · exact mul_subset_mul (Set.singleton_subset_iff.mpr ha) Set.Subset.rfl
     · convert key a (S ^ n) ({a} * S ^ n) fun b hb ↦ Set.mul_mem_mul (Set.mem_singleton a) hb
-  rw [pow_succ', ← h₂, mul_assoc, ← pow_succ', h₂]
-  rintro _ ⟨b, c, hb, hc, rfl⟩
-  rwa [Set.mem_singleton_iff.mp hb, inv_mul_cancel_left]
+  rw [pow_succ', ← h₂, mul_assoc, ← pow_succ', h₂, singleton_mul, ball_image_iff]
+  intro x hx
+  rwa [inv_mul_cancel_left]
 #align group.card_pow_eq_card_pow_card_univ Group.card_pow_eq_card_pow_card_univ
 #align add_group.card_nsmul_eq_card_nsmul_card_univ AddGroup.card_nsmul_eq_card_nsmul_card_univ

c941bb94

feat: Preimage of pointwise multiplication (#8956)

From PFR

Co-authored-by: Patrick Massot <patrickmassot@free.fr>

7d208e64

Diff

@@ -135,6 +135,11 @@ theorem infinite_mul : (s * t).Infinite ↔ s.Infinite ∧ t.Nonempty ∨ t.Infi
 #align set.infinite_mul Set.infinite_mul
 #align set.infinite_add Set.infinite_add
 
+@[to_additive]
+lemma finite_mul : (s * t).Finite ↔ s.Finite ∧ t.Finite ∨ s = ∅ ∨ t = ∅ :=
+  finite_image2  (fun _ _ ↦ (mul_left_injective _).injOn _)
+    fun _ _ ↦ (mul_right_injective _).injOn _
+
 end Cancel
 
 section Group

c941bb94

chore: Nsmul -> NSMul, Zpow -> ZPow, etc (#9067)

Normalising to naming convention rule number 6.

9b2f0dca

Diff

@@ -96,7 +96,7 @@ theorem Finite.smul : s.Finite → t.Finite → (s • t).Finite :=
 
 end SMul
 
-section HasSmulSet
+section HasSMulSet
 
 variable [SMul α β] {s : Set β} {a : α}
 
@@ -112,7 +112,7 @@ theorem Infinite.of_smul_set : (a • s).Infinite → s.Infinite :=
 #align set.infinite.of_smul_set Set.Infinite.of_smul_set
 #align set.infinite.of_vadd_set Set.Infinite.of_vadd_set
 
-end HasSmulSet
+end HasSMulSet
 
 section Vsub

c941bb94

feat: patch for new alias command (#6172)

19e0ba92

Diff

@@ -153,10 +153,10 @@ theorem infinite_smul_set : (a • s).Infinite ↔ s.Infinite :=
 #align set.infinite_smul_set Set.infinite_smul_set
 #align set.infinite_vadd_set Set.infinite_vadd_set
 
-alias finite_smul_set ↔ Finite.of_smul_set _
+alias ⟨Finite.of_smul_set, _⟩ := finite_smul_set
 #align set.finite.of_smul_set Set.Finite.of_smul_set
 
-alias infinite_smul_set ↔ _ Infinite.smul_set
+alias ⟨_, Infinite.smul_set⟩ := infinite_smul_set
 #align set.infinite.smul_set Set.Infinite.smul_set
 
 attribute [to_additive] Finite.of_smul_set Infinite.smul_set

c941bb94

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -13,7 +13,7 @@ import Mathlib.Data.Set.Pointwise.SMul
 
 open Pointwise
 
-variable {F α β γ : Type _}
+variable {F α β γ : Type*}
 
 namespace Set
 
@@ -169,7 +169,7 @@ open Set
 
 namespace Group
 
-variable {G : Type _} [Group G] [Fintype G] (S : Set G)
+variable {G : Type*} [Group G] [Fintype G] (S : Set G)
 
 @[to_additive]
 theorem card_pow_eq_card_pow_card_univ [∀ k : ℕ, DecidablePred (· ∈ S ^ k)] :

c941bb94

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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Johan Commelin. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Floris van Doorn
-
-! This file was ported from Lean 3 source module data.set.pointwise.finite
-! leanprover-community/mathlib commit c941bb9426d62e266612b6d99e6c9fc93e7a1d07
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Set.Finite
 import Mathlib.Data.Set.Pointwise.SMul
 
+#align_import data.set.pointwise.finite from "leanprover-community/mathlib"@"c941bb9426d62e266612b6d99e6c9fc93e7a1d07"
+
 /-! # Finiteness lemmas for pointwise operations on sets -/

c941bb94

feat: When s ×ˢ t is finite (#3214)

Match https://github.com/leanprover-community/mathlib/pull/18674

3b6fdff1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Floris van Doorn
 
 ! This file was ported from Lean 3 source module data.set.pointwise.finite
-! leanprover-community/mathlib commit 517cc149e0b515d2893baa376226ed10feb319c7
+! leanprover-community/mathlib commit c941bb9426d62e266612b6d99e6c9fc93e7a1d07
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -109,6 +109,12 @@ theorem Finite.smul_set : s.Finite → (a • s).Finite :=
 #align set.finite.smul_set Set.Finite.smul_set
 #align set.finite.vadd_set Set.Finite.vadd_set
 
+@[to_additive]
+theorem Infinite.of_smul_set : (a • s).Infinite → s.Infinite :=
+  Infinite.of_image _
+#align set.infinite.of_smul_set Set.Infinite.of_smul_set
+#align set.infinite.of_vadd_set Set.Infinite.of_vadd_set
+
 end HasSmulSet
 
 section Vsub
@@ -121,6 +127,45 @@ theorem Finite.vsub (hs : s.Finite) (ht : t.Finite) : Set.Finite (s -ᵥ t) :=
 
 end Vsub
 
+section Cancel
+
+variable [Mul α] [IsLeftCancelMul α] [IsRightCancelMul α] {s t : Set α}
+
+@[to_additive]
+theorem infinite_mul : (s * t).Infinite ↔ s.Infinite ∧ t.Nonempty ∨ t.Infinite ∧ s.Nonempty :=
+  infinite_image2 (fun _ _ => (mul_left_injective _).injOn _) fun _ _ =>
+    (mul_right_injective _).injOn _
+#align set.infinite_mul Set.infinite_mul
+#align set.infinite_add Set.infinite_add
+
+end Cancel
+
+section Group
+
+variable [Group α] [MulAction α β] {a : α} {s : Set β}
+
+@[to_additive (attr := simp)]
+theorem finite_smul_set : (a • s).Finite ↔ s.Finite :=
+  finite_image_iff <| (MulAction.injective _).injOn _
+#align set.finite_smul_set Set.finite_smul_set
+#align set.finite_vadd_set Set.finite_vadd_set
+
+@[to_additive (attr := simp)]
+theorem infinite_smul_set : (a • s).Infinite ↔ s.Infinite :=
+  infinite_image_iff <| (MulAction.injective _).injOn _
+#align set.infinite_smul_set Set.infinite_smul_set
+#align set.infinite_vadd_set Set.infinite_vadd_set
+
+alias finite_smul_set ↔ Finite.of_smul_set _
+#align set.finite.of_smul_set Set.Finite.of_smul_set
+
+alias infinite_smul_set ↔ _ Infinite.smul_set
+#align set.infinite.smul_set Set.Infinite.smul_set
+
+attribute [to_additive] Finite.of_smul_set Infinite.smul_set
+
+end Group
+
 end Set
 
 open Set

517cc149

feat: s ∩ t * s ∪ t ⊆ s * t (#1619)

Match https://github.com/leanprover-community/mathlib/pull/17961

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

7664848d

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Floris van Doorn
 
 ! This file was ported from Lean 3 source module data.set.pointwise.finite
-! leanprover-community/mathlib commit 0a0ec35061ed9960bf0e7ffb0335f44447b58977
+! leanprover-community/mathlib commit 517cc149e0b515d2893baa376226ed10feb319c7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -20,6 +20,18 @@ variable {F α β γ : Type _}
 
 namespace Set
 
+section One
+
+variable [One α]
+
+@[to_additive (attr := simp)]
+theorem finite_one : (1 : Set α).Finite :=
+  finite_singleton _
+#align set.finite_one Set.finite_one
+#align set.finite_zero Set.finite_zero
+
+end One
+
 section InvolutiveInv
 
 variable [InvolutiveInv α] {s : Set α}

0a0ec350

chore: resync ported files (#2135)

This PR resyncs the first 28 entries of https://leanprover-community.github.io/mathlib-port-status/out-of-sync.html after sorting by diff size.

resync Mathlib/Data/Bool/Count
resync Mathlib/Order/Max
resync Mathlib/Algebra/EuclideanDomain/Instances
resync Mathlib/Data/List/Duplicate
resync Mathlib/Data/Multiset/Nodup
resync Mathlib/Data/Set/Pointwise/ListOfFn
resync Mathlib/Dynamics/FixedPoints/Basic
resync Mathlib/Order/OmegaCompletePartialOrder
resync Mathlib/Order/PropInstances
resync Mathlib/Topology/LocallyFinite
resync Mathlib/Data/Bool/Set
resync Mathlib/Data/Fintype/Card
resync Mathlib/Data/Multiset/Bind
resync Mathlib/Data/Rat/Floor
resync Mathlib/Algebra/Order/Floor
resync Mathlib/Data/Int/Basic
resync Mathlib/Data/Int/Dvd/Basic
resync Mathlib/Data/List/Sort
resync Mathlib/Data/Nat/GCD/Basic
resync Mathlib/Data/Set/Enumerate
resync Mathlib/Data/Set/Intervals/OrdConnectedComponent
resync Mathlib/GroupTheory/Subsemigroup/Basic
resync Mathlib/Topology/Connected
resync Mathlib/Topology/NhdsSet
resync Mathlib/Algebra/BigOperators/Multiset/Lemmas
resync Mathlib/Algebra/CharZero/Infinite
resync Mathlib/Data/Multiset/Range
resync Mathlib/Data/Set/Pointwise/Finite

a7eb5ab3

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johan Commelin, Floris van Doorn
 
 ! This file was ported from Lean 3 source module data.set.pointwise.finite
-! leanprover-community/mathlib commit f93c11933efbc3c2f0299e47b8ff83e9b539cbf6
+! leanprover-community/mathlib commit 0a0ec35061ed9960bf0e7ffb0335f44447b58977
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/

f93c1193

feat: port Data.Set.Pointwise.Finite (#1844)

ba2a530c

`data.set.pointwise.finite` ⟷ `Mathlib.Data.Set.Pointwise.Finite`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 7 + 230

data.set.pointwise.finite ⟷ Mathlib.Data.Set.Pointwise.Finite

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 7 + 230

`data.set.pointwise.finite` ⟷ `Mathlib.Data.Set.Pointwise.Finite`