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kim-em committed Sep 12, 2024
1 parent ae412cc commit dc7c7e8
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Showing 15 changed files with 21 additions and 18 deletions.
2 changes: 1 addition & 1 deletion Mathlib/Algebra/Group/Subgroup/Basic.lean
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Expand Up @@ -1511,7 +1511,7 @@ variable {H K : Subgroup G}

@[to_additive]
instance (priority := 100) normal_of_comm {G : Type*} [CommGroup G] (H : Subgroup G) : H.Normal :=
by simp [mul_comm, mul_left_comm]⟩
by simp [mul_comm, mul_left_comm, forall_const]⟩

namespace Normal

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2 changes: 1 addition & 1 deletion Mathlib/CategoryTheory/Sites/Types.lean
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Expand Up @@ -172,6 +172,6 @@ theorem typesGrothendieckTopology_eq_canonical :
have : (fun _ => ULift.up true) = fun _ => ULift.up false :=
(hs PUnit fun _ => x).isSeparatedFor.ext
fun β f hf => funext fun y => hsx.elim <| S.2 hf fun _ => y
simp [Function.funext_iff] at this
simp [Function.funext_iff, forall_const] at this

end CategoryTheory
2 changes: 1 addition & 1 deletion Mathlib/Combinatorics/SimpleGraph/Clique.lean
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Expand Up @@ -328,7 +328,7 @@ theorem CliqueFree.comap {H : SimpleGraph β} (f : H ↪g G) : G.CliqueFree n
obtain (hle | hlt) := le_or_lt n 1
· obtain (rfl | rfl) := Nat.le_one_iff_eq_zero_or_eq_one.1 hle
· simp [CliqueFree]
simp [CliqueFree, show ∃ (_ : β), True from ⟨f (Classical.arbitrary _), trivial⟩]
simp [CliqueFree, show ∃ (_ : β), True from ⟨f (Classical.arbitrary _), trivial⟩, forall_const]
simp [CliqueFree, isNClique_map_iff hlt]

/-- See `SimpleGraph.cliqueFree_of_chromaticNumber_lt` for a tighter bound. -/
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2 changes: 1 addition & 1 deletion Mathlib/Data/Fintype/Prod.lean
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Expand Up @@ -44,7 +44,7 @@ variable [Fintype α] [Fintype β] {s : Finset α} {t : Finset β}
@[simp] lemma univ_product_univ : univ ×ˢ univ = (univ : Finset (α × β)) := rfl

@[simp] lemma product_eq_univ [Nonempty α] [Nonempty β] : s ×ˢ t = univ ↔ s = univ ∧ t = univ := by
simp [eq_univ_iff_forall, forall_and]
simp [eq_univ_iff_forall, forall_and, forall_const]

end Finset

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5 changes: 3 additions & 2 deletions Mathlib/Data/Set/Prod.lean
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Expand Up @@ -89,7 +89,7 @@ theorem univ_prod {t : Set β} : (univ : Set α) ×ˢ t = Prod.snd ⁻¹' t := b
theorem prod_univ {s : Set α} : s ×ˢ (univ : Set β) = Prod.fst ⁻¹' s := by simp [prod_eq]

@[simp] lemma prod_eq_univ [Nonempty α] [Nonempty β] : s ×ˢ t = univ ↔ s = univ ∧ t = univ := by
simp [eq_univ_iff_forall, forall_and]
simp [eq_univ_iff_forall, forall_and, forall_const]

@[simp]
theorem singleton_prod : ({a} : Set α) ×ˢ t = Prod.mk a '' t := by
Expand Down Expand Up @@ -647,7 +647,8 @@ theorem pi_eq_empty_iff : s.pi t = ∅ ↔ ∃ i, IsEmpty (α i) ∨ i ∈ s ∧
rw [← not_nonempty_iff_eq_empty, pi_nonempty_iff]
push_neg
refine exists_congr fun i => ?_
cases isEmpty_or_nonempty (α i) <;> simp [*, forall_and, eq_empty_iff_forall_not_mem]
cases isEmpty_or_nonempty (α i) <;>
simp [*, forall_and, forall_const, eq_empty_iff_forall_not_mem]

@[simp]
theorem univ_pi_eq_empty_iff : pi univ t = ∅ ↔ ∃ i, t i = ∅ := by
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2 changes: 1 addition & 1 deletion Mathlib/Data/W/Basic.lean
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Expand Up @@ -103,7 +103,7 @@ theorem infinite_of_nonempty_of_isEmpty (a b : α) [ha : Nonempty (β a)] [he :
· cases' m with m
· simp_all
· refine congr_arg Nat.succ (ih ?_)
simp_all [Function.funext_iff]⟩
simp_all [Function.funext_iff, forall_const]⟩

variable [∀ a : α, Fintype (β a)]

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2 changes: 1 addition & 1 deletion Mathlib/GroupTheory/HNNExtension.lean
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Expand Up @@ -259,7 +259,7 @@ theorem group_smul_head (g : G) (w : NormalWord d) : (g • w).head = g * w.head
@[simp]
theorem group_smul_toList (g : G) (w : NormalWord d) : (g • w).toList = w.toList := rfl

instance : FaithfulSMul G (NormalWord d) := ⟨by simp [group_smul_def]⟩
instance : FaithfulSMul G (NormalWord d) := ⟨by simp [group_smul_def, forall_const]⟩

/-- A constructor to append an element `g` of `G` and `u : ℤˣ` to a word `w` with sufficient
hypotheses that no normalization or cancellation need take place for the result to be in normal form
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4 changes: 2 additions & 2 deletions Mathlib/GroupTheory/PushoutI.lean
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Expand Up @@ -574,10 +574,10 @@ instance : FaithfulSMul (PushoutI φ) (NormalWord d) :=
fun h => by simpa using congr_arg prod (h empty)⟩

instance (i : ι) : FaithfulSMul (G i) (NormalWord d) :=
by simp [summand_smul_def']⟩
by simp [summand_smul_def', forall_const]⟩

instance : FaithfulSMul H (NormalWord d) :=
by simp [base_smul_def']⟩
by simp [base_smul_def', forall_const]⟩

end NormalWord

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2 changes: 1 addition & 1 deletion Mathlib/ModelTheory/Algebra/Field/Basic.lean
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Expand Up @@ -83,7 +83,7 @@ theorem FieldAxiom.realize_toSentence_iff_toProp {K : Type*}
(ax : FieldAxiom) :
(K ⊨ (ax.toSentence : Sentence Language.ring)) ↔ ax.toProp K := by
cases ax <;>
simp [Sentence.Realize, Formula.Realize, Fin.snoc]
simp [Sentence.Realize, Formula.Realize, Fin.snoc, forall_const]

theorem FieldAxiom.toProp_of_model {K : Type*}
[Add K] [Mul K] [Neg K] [Zero K] [One K] [CompatibleRing K]
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2 changes: 1 addition & 1 deletion Mathlib/NumberTheory/Zsqrtd/GaussianInt.lean
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Expand Up @@ -245,7 +245,7 @@ instance : EuclideanDomain ℤ[i] :=
GaussianInt.instNontrivial with
quotient := (· / ·)
remainder := (· % ·)
quotient_zero := by simp [div_def]; rfl
quotient_zero := fun _ => by simp [div_def]; rfl
quotient_mul_add_remainder_eq := fun _ _ => by simp [mod_def]
r := _
r_wellFounded := (measure (Int.natAbs ∘ norm)).wf
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2 changes: 1 addition & 1 deletion Mathlib/Order/Filter/Ultrafilter.lean
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Expand Up @@ -118,7 +118,7 @@ theorem diff_mem_iff (f : Ultrafilter α) : s \ t ∈ f ↔ s ∈ f ∧ t ∉ f
`Ultrafilter.compl_not_mem_iff`. -/
def ofComplNotMemIff (f : Filter α) (h : ∀ s, sᶜ ∉ f ↔ s ∈ f) : Ultrafilter α where
toFilter := f
neBot' := ⟨fun hf => by simp [hf] at h⟩
neBot' := ⟨fun hf => by simp [hf, forall_const] at h⟩
le_of_le g hg hgf s hs := (h s).1 fun hsc => compl_not_mem hs (hgf hsc)

/-- If `f : Filter α` is an atom, then it is an ultrafilter. -/
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6 changes: 4 additions & 2 deletions Mathlib/Order/OmegaCompletePartialOrder.lean
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Expand Up @@ -363,7 +363,9 @@ theorem id_continuous' : Continuous' (@id α) :=

@[deprecated ωScottContinuous.const (since := "2024-05-29")]
theorem continuous_const (x : β) : Continuous (OrderHom.const α x) := fun c =>
eq_of_forall_ge_iff fun z => by rw [ωSup_le_iff, Chain.map_coe, OrderHom.const_coe_coe]; simp
eq_of_forall_ge_iff fun z => by
rw [ωSup_le_iff, Chain.map_coe, OrderHom.const_coe_coe]
simp [forall_const]

@[deprecated ωScottContinuous.const (since := "2024-05-29")]
theorem const_continuous' (x : β) : Continuous' (Function.const α x) :=
Expand Down Expand Up @@ -567,7 +569,7 @@ lemma ωScottContinuous.sup (hf : ωScottContinuous f) (hg : ωScottContinuous g

lemma ωScottContinuous.top : ωScottContinuous (⊤ : α → β) :=
ωScottContinuous.of_monotone_map_ωSup
⟨monotone_const, fun c ↦ eq_of_forall_ge_iff fun a ↦ by simp⟩
⟨monotone_const, fun c ↦ eq_of_forall_ge_iff fun a ↦ by simp [forall_const]

lemma ωScottContinuous.bot : ωScottContinuous (⊥ : α → β) := by
rw [← sSup_empty]; exact ωScottContinuous.sSup (by simp)
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2 changes: 1 addition & 1 deletion Mathlib/SetTheory/Game/Impartial.lean
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Expand Up @@ -52,7 +52,7 @@ instance impartial_zero : Impartial 0 := by

instance impartial_star : Impartial star := by
rw [impartial_def]
simpa using Impartial.impartial_zero
simpa [forall_const] using Impartial.impartial_zero

theorem neg_equiv_self (G : PGame) [h : G.Impartial] : G ≈ -G :=
(impartial_def.1 h).1
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2 changes: 1 addition & 1 deletion Mathlib/SetTheory/Surreal/Dyadic.lean
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Expand Up @@ -79,7 +79,7 @@ theorem numeric_powHalf (n) : (powHalf n).Numeric := by
| zero => exact numeric_one
| succ n hn =>
constructor
· simpa using hn.moveLeft_lt default
· intros; simpa using hn.moveLeft_lt default
· exact ⟨fun _ => numeric_zero, fun _ => hn⟩

theorem powHalf_succ_lt_powHalf (n : ℕ) : powHalf (n + 1) < powHalf n :=
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2 changes: 1 addition & 1 deletion Mathlib/Topology/Algebra/Group/Basic.lean
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Expand Up @@ -817,7 +817,7 @@ theorem TopologicalGroup.of_comm_of_nhds_one {G : Type u} [CommGroup G] [Topolog
(hmul : Tendsto (uncurry ((· * ·) : G → G → G)) (𝓝 1 ×ˢ 𝓝 1) (𝓝 1))
(hinv : Tendsto (fun x : G => x⁻¹) (𝓝 1) (𝓝 1))
(hleft : ∀ x₀ : G, 𝓝 x₀ = map (x₀ * ·) (𝓝 1)) : TopologicalGroup G :=
TopologicalGroup.of_nhds_one hmul hinv hleft (by simpa using tendsto_id)
TopologicalGroup.of_nhds_one hmul hinv hleft (fun _ => by simpa using tendsto_id)

variable (G) in
/-- Any first countable topological group has an antitone neighborhood basis `u : ℕ → Set G` for
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