English
The map δ ↦ thickenedIndicatorAux δ E is continuous in δ at positive δ for any fixed E.
Русский
Отображение δ ↦ thickenedIndicatorAux δ E непрерывно в δ при положительном δ для фиксированного E.
LaTeX
$$$\\text{continuous_thickenedIndicatorAux}: (δ>0) \\to C(α, \\mathbb{R}_{\\ge 0}^{\\infty})$ is continuous.$$
Lean4
/-- Change between equivalent index sets ι and ι'. -/
@[simp]
theorem index_equiv (f : ι' ≃ ι) (v₁ : ι → P₁) (v₂ : ι → P₂) : v₁ ∘ f ∼ v₂ ∘ f ↔ v₁ ∼ v₂ :=
by
refine ⟨fun h => ?_, fun h => Similar.index_map h f⟩
rcases h with ⟨r, hr, h⟩
refine ⟨r, hr, fun i₁ i₂ => ?_⟩
simpa [f.right_inv i₁, f.right_inv i₂] using h (f.symm i₁) (f.symm i₂)