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[Merged by Bors] - chore: use more inferInstanceAs #37315

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[Merged by Bors] - chore: use more inferInstanceAs #37315

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sgouezel Mar 28, 2026
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5 changes: 2 additions & 3 deletions Mathlib/Analysis/SpecialFunctions/Trigonometric/Angle.lean
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Expand Up @@ -41,10 +41,9 @@ protected def coe (r : ℝ) : Angle := QuotientAddGroup.mk r
instance : Coe ℝ Angle := ⟨Angle.coe⟩

instance : CircularOrder Real.Angle :=
QuotientAddGroup.circularOrder (hp' := ⟨by simp [pi_pos]⟩)
fast_instance% QuotientAddGroup.circularOrder (hp' := ⟨by simp [pi_pos]⟩)


@[continuity]
@[continuity, fun_prop]
theorem continuous_coe : Continuous ((↑) : ℝ → Angle) :=
continuous_quotient_mk'

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2 changes: 1 addition & 1 deletion Mathlib/Combinatorics/SimpleGraph/Connectivity/Finite.lean
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Expand Up @@ -57,7 +57,7 @@ instance : DecidableRel G.Reachable := fun u v =>
decidable_of_iff' _ (reachable_iff_exists_finsetWalkLength_nonempty G u v)

instance : Fintype G.ConnectedComponent :=
@Quotient.fintype _ _ G.reachableSetoid (inferInstance : DecidableRel G.Reachable)
fast_instance% @Quotient.fintype _ _ G.reachableSetoid (inferInstance : DecidableRel G.Reachable)

instance : Decidable G.Preconnected :=
inferInstanceAs <| Decidable (∀ u v, G.Reachable u v)
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6 changes: 3 additions & 3 deletions Mathlib/Combinatorics/SimpleGraph/EdgeLabeling.lean
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Expand Up @@ -38,7 +38,7 @@ def EdgeLabeling (G : SimpleGraph V) (K : Type*) :=
G.edgeSet → K

instance [DecidableEq V] [Fintype G.edgeSet] [Fintype K] : Fintype (EdgeLabeling G K) :=
Pi.instFintype
inferInstanceAs <| Fintype (G.edgeSet → K)

instance [Finite G.edgeSet] [Finite K] : Finite (EdgeLabeling G K) :=
Pi.finite
Expand All @@ -47,7 +47,7 @@ instance [Nonempty K] : Nonempty (EdgeLabeling G K) :=
Pi.instNonempty

instance [Inhabited K] : Inhabited (EdgeLabeling G K) :=
Pi.instInhabited
inferInstanceAs <| Inhabited (G.edgeSet → K)

instance [Subsingleton K] : Subsingleton (EdgeLabeling G K) :=
Pi.instSubsingleton
Expand All @@ -56,7 +56,7 @@ instance [Nonempty G.edgeSet] [Nontrivial K] : Nontrivial (EdgeLabeling G K) :=
Function.nontrivial

instance [Unique K] : Unique (EdgeLabeling G K) :=
Pi.unique
inferInstanceAs <| Unique (G.edgeSet → K)

/--
An edge labeling of the complete graph on `V` with labels in type `K`.
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8 changes: 4 additions & 4 deletions Mathlib/Combinatorics/SimpleGraph/Walks/Counting.lean
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Expand Up @@ -125,7 +125,7 @@ instance fintypeSetWalkLength (u v : V) (n : ℕ) : Fintype {p : G.Walk u v | p.
rw [← Finset.mem_coe, coe_finsetWalkLength_eq]

instance fintypeSubtypeWalkLength (u v : V) (n : ℕ) : Fintype {p : G.Walk u v // p.length = n} :=
fintypeSetWalkLength G u v n
inferInstanceAs <| Fintype {p : G.Walk u v | p.length = n}
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@JovanGerb JovanGerb Mar 30, 2026

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Is this not just inferInstance?

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@sgouezel sgouezel Mar 30, 2026

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No, the inferInstanceAs is really needed, here and below.


theorem set_walk_length_toFinset_eq (n : ℕ) (u v : V) :
{p : G.Walk u v | p.length = n}.toFinset = G.finsetWalkLength n u v := by
Expand All @@ -143,7 +143,7 @@ instance fintypeSetWalkLengthLT (u v : V) (n : ℕ) : Fintype {p : G.Walk u v |
rw [← Finset.mem_coe, coe_finsetWalkLengthLT_eq]

instance fintypeSubtypeWalkLengthLT (u v : V) (n : ℕ) : Fintype {p : G.Walk u v // p.length < n} :=
fintypeSetWalkLengthLT G u v n
inferInstanceAs <| Fintype {p : G.Walk u v | p.length < n}

instance fintypeSetPathLength (u v : V) (n : ℕ) :
Fintype {p : G.Walk u v | p.IsPath ∧ p.length = n} :=
Expand All @@ -152,7 +152,7 @@ instance fintypeSetPathLength (u v : V) (n : ℕ) :

instance fintypeSubtypePathLength (u v : V) (n : ℕ) :
Fintype {p : G.Walk u v // p.IsPath ∧ p.length = n} :=
fintypeSetPathLength G u v n
inferInstanceAs <| Fintype {p : G.Walk u v | p.IsPath ∧ p.length = n}

instance fintypeSetPathLengthLT (u v : V) (n : ℕ) :
Fintype {p : G.Walk u v | p.IsPath ∧ p.length < n} :=
Expand All @@ -161,7 +161,7 @@ instance fintypeSetPathLengthLT (u v : V) (n : ℕ) :

instance fintypeSubtypePathLengthLT (u v : V) (n : ℕ) :
Fintype {p : G.Walk u v // p.IsPath ∧ p.length < n} :=
fintypeSetPathLengthLT G u v n
inferInstanceAs <| Fintype {p : G.Walk u v | p.IsPath ∧ p.length < n}

end LocallyFinite

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7 changes: 3 additions & 4 deletions Mathlib/Computability/Language.lean
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Expand Up @@ -64,14 +64,13 @@ variable {α β γ : Type*}
/-- A language is a set of strings over an alphabet. -/
def Language (α) :=
Set (List α)
deriving CompleteAtomicBooleanAlgebra

namespace Language

instance : Membership (List α) (Language α) := ⟨Set.Mem⟩
instance : Singleton (List α) (Language α) := ⟨Set.singleton⟩
instance : Insert (List α) (Language α) := ⟨Set.insert⟩
instance instCompleteAtomicBooleanAlgebra : CompleteAtomicBooleanAlgebra (Language α) :=
Set.instCompleteAtomicBooleanAlgebra

variable {l m : Language α} {a b x : List α}

Expand Down Expand Up @@ -409,8 +408,8 @@ lemma reverse_kstar (l : Language α) : l∗.reverse = l.reverse∗ := by
lemma mem_inf {x : List α} {l m : Language α} : x ∈ l ⊓ m ↔ x ∈ l ∧ x ∈ m := by
apply Set.mem_inter_iff

lemma compl_compl (l : Language α) : lᶜᶜ = l := by
simp [compl]
lemma compl_compl (l : Language α) : lᶜᶜ = l :=
_root_.compl_compl l

end Language

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6 changes: 3 additions & 3 deletions Mathlib/Data/Fintype/Vector.lean
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Expand Up @@ -19,10 +19,10 @@ open List (Vector)
variable {α : Type*}

instance Vector.fintype [Fintype α] {n : ℕ} : Fintype (List.Vector α n) :=
Fintype.ofEquiv _ (Equiv.vectorEquivFin _ _).symm
fast_instance% Fintype.ofEquiv _ (Equiv.vectorEquivFin _ _).symm

instance [DecidableEq α] [Fintype α] {n : ℕ} : Fintype (Sym.Sym' α n) :=
Quotient.fintype _
inferInstanceAs <| Fintype (Quotient _)

instance [DecidableEq α] [Fintype α] {n : ℕ} : Fintype (Sym α n) :=
Fintype.ofEquiv _ Sym.symEquivSym'.symm
fast_instance% Fintype.ofEquiv _ Sym.symEquivSym'.symm
2 changes: 1 addition & 1 deletion Mathlib/Data/Fintype/WithTopBot.lean
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Expand Up @@ -18,7 +18,7 @@ variable {α : Type*}

@[to_dual]
instance [Fintype α] : Fintype (WithTop α) :=
instFintypeOption
inferInstanceAs <| Fintype (Option α)

@[to_dual]
instance [Finite α] : Finite (WithTop α) :=
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21 changes: 14 additions & 7 deletions Mathlib/Data/Holor.lean
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Expand Up @@ -101,23 +101,30 @@ instance [Add α] : Add (Holor α ds) :=
instance [Neg α] : Neg (Holor α ds) :=
⟨fun a t => -a t⟩

instance [AddSemigroup α] : AddSemigroup (Holor α ds) := Pi.addSemigroup
instance [AddSemigroup α] : AddSemigroup (Holor α ds) :=
inferInstanceAs <| AddSemigroup (HolorIndex ds → α)

instance [AddCommSemigroup α] : AddCommSemigroup (Holor α ds) := Pi.addCommSemigroup
instance [AddCommSemigroup α] : AddCommSemigroup (Holor α ds) :=
inferInstanceAs <| AddCommSemigroup (HolorIndex ds → α)

instance [AddMonoid α] : AddMonoid (Holor α ds) := Pi.addMonoid
instance [AddMonoid α] : AddMonoid (Holor α ds) :=
inferInstanceAs <| AddMonoid (HolorIndex ds → α)

instance [AddCommMonoid α] : AddCommMonoid (Holor α ds) := Pi.addCommMonoid
instance [AddCommMonoid α] : AddCommMonoid (Holor α ds) :=
inferInstanceAs <| AddCommMonoid (HolorIndex ds → α)

instance [AddGroup α] : AddGroup (Holor α ds) := Pi.addGroup
instance [AddGroup α] : AddGroup (Holor α ds) :=
inferInstanceAs <| AddGroup (HolorIndex ds → α)

instance [AddCommGroup α] : AddCommGroup (Holor α ds) := Pi.addCommGroup
instance [AddCommGroup α] : AddCommGroup (Holor α ds) :=
inferInstanceAs <| AddCommGroup (HolorIndex ds → α)

-- scalar product
instance [Mul α] : SMul α (Holor α ds) :=
⟨fun a x => fun t => a * x t⟩

instance [Semiring α] : Module α (Holor α ds) := Pi.module _ _ _
instance [Semiring α] : Module α (Holor α ds) :=
inferInstanceAs <| Module α (HolorIndex ds → α)

/-- The tensor product of two holors. -/
def mul [Mul α] (x : Holor α ds₁) (y : Holor α ds₂) : Holor α (ds₁ ++ ds₂) := fun t =>
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3 changes: 2 additions & 1 deletion Mathlib/Data/PNat/Interval.lean
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Expand Up @@ -24,7 +24,8 @@ namespace PNat

variable (a b : ℕ+)

instance instLocallyFiniteOrder : LocallyFiniteOrder ℕ+ := Subtype.instLocallyFiniteOrder _
instance instLocallyFiniteOrder : LocallyFiniteOrder ℕ+ :=
inferInstanceAs <| LocallyFiniteOrder (Subtype _)

theorem Icc_eq_finset_subtype : Icc a b = (Icc (a : ℕ) b).subtype fun n : ℕ => 0 < n :=
rfl
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3 changes: 2 additions & 1 deletion Mathlib/Data/Prod/Lex.lean
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Expand Up @@ -10,6 +10,7 @@ public import Mathlib.Order.BoundedOrder.Basic
public import Mathlib.Order.Lattice
public import Mathlib.Order.Lex
public import Mathlib.Tactic.Tauto
public import Mathlib.Tactic.FastInstance

/-!
# Lexicographic order
Expand Down Expand Up @@ -146,7 +147,7 @@ instance instPartialOrder (α β : Type*) [PartialOrder α] [PartialOrder β] :
PartialOrder (α ×ₗ β) where
le_antisymm _ _ := antisymm_of (Prod.Lex _ _)

instance instOrdLexProd [Ord α] [Ord β] : Ord (α ×ₗ β) := lexOrd
instance instOrdLexProd [Ord α] [Ord β] : Ord (α ×ₗ β) := fast_instance% lexOrd

theorem compare_def [Ord α] [Ord β] : @compare (α ×ₗ β) _ =
compareLex (compareOn fun x => (ofLex x).1) (compareOn fun x => (ofLex x).2) := rfl
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