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[Merged by Bors] - refactor(Algebra/Field/Subfield): minor golfing #17376

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[Merged by Bors] - refactor(Algebra/Field/Subfield): minor golfing #17376

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24 changes: 12 additions & 12 deletions Mathlib/Algebra/Field/Subfield.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -126,20 +126,20 @@ variable (S)
/-- A subfield inherits a division ring structure -/
instance (priority := 75) toDivisionRing (s : S) : DivisionRing s :=
Subtype.coe_injective.divisionRing ((↑) : s → K)
(by rfl) (by rfl) (by intros; rfl) (by intros; rfl) (by intros; rfl)
(by intros; rfl) (by intros; rfl) (by intros; rfl) (by intros; rfl)
(by intros; rfl) (coe_nnqsmul _) (coe_qsmul _) (by intros; rfl) (by intros; rfl)
(by intros; rfl) (by intros; rfl) (by intros; rfl) (by intros; rfl)
rfl rfl (fun _ _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ ↦ rfl)
(fun _ _ ↦ rfl) (fun _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ _ ↦ rfl)
(fun _ _ ↦ rfl) (coe_nnqsmul _) (coe_qsmul _) (fun _ _ ↦ rfl) (fun _ _ ↦ rfl)
(fun _ ↦ rfl) (fun _ ↦ rfl) (fun _ ↦ rfl) (fun _ ↦ rfl)

-- Prefer subclasses of `Field` over subclasses of `SubfieldClass`.
/-- A subfield of a field inherits a field structure -/
instance (priority := 75) toField {K} [Field K] [SetLike S K] [SubfieldClass S K] (s : S) :
Field s :=
Subtype.coe_injective.field ((↑) : s → K)
(by rfl) (by rfl) (by intros; rfl) (by intros; rfl) (by intros; rfl)
(by intros; rfl) (by intros; rfl) (by intros; rfl) (by intros; rfl) (by intros; rfl)
(coe_nnqsmul _) (coe_qsmul _) (by intros; rfl) (by intros; rfl) (by intros; rfl)
(by intros; rfl) (by intros; rfl) (by intros; rfl)
rfl rfl (fun _ _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ ↦ rfl)
(fun _ _ ↦ rfl) (fun _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ _ ↦ rfl)
(coe_nnqsmul _) (coe_qsmul _) (fun _ _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ ↦ rfl)
(fun _ ↦ rfl) (fun _ ↦ rfl) (fun _ ↦ rfl)

end SubfieldClass

Expand Down Expand Up @@ -313,15 +313,15 @@ instance : Pow s ℤ :=
instance toDivisionRing (s : Subfield K) : DivisionRing s :=
Subtype.coe_injective.divisionRing ((↑) : s → K) rfl rfl (fun _ _ ↦ rfl) (fun _ _ ↦ rfl)
(fun _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ _ ↦ rfl)
(fun _ _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ _ ↦ rfl) (by intros; rfl) (fun _ ↦ rfl) (fun _ ↦ rfl)
(by intros; rfl) fun _ ↦ rfl
(fun _ _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ _ ↦ rfl) (fun _ ↦ rfl) (fun _ ↦ rfl)
(fun _ ↦ rfl) fun _ ↦ rfl

/-- A subfield inherits a field structure -/
instance toField {K} [Field K] (s : Subfield K) : Field s :=
Subtype.coe_injective.field ((↑) : s → K) rfl rfl (fun _ _ => rfl) (fun _ _ => rfl) (fun _ => rfl)
(fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl) (fun _ _ => rfl) (fun _ _ => rfl)
(fun _ _ => rfl) (fun _ _ => rfl) (fun _ _ => rfl) (by intros; rfl) (fun _ => rfl)
(fun _ => rfl) (by intros; rfl) fun _ => rfl
(fun _ _ => rfl) (fun _ _ => rfl) (fun _ _ => rfl) (fun _ _ ↦ rfl) (fun _ => rfl)
(fun _ => rfl) (fun _ ↦ rfl) fun _ => rfl

@[simp, norm_cast]
theorem coe_add (x y : s) : (↑(x + y) : K) = ↑x + ↑y :=
Expand Down
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