mkContinuousOfExistsBound — Mathlib

English

A variant stating that for subsingleton M, IsConformalMap f' holds trivially; this is a simp lemma.

Русский

Вариант леммы для подмножества, где IsConformalMap фокусируется на тривиальный случай; это упрощение.

LaTeX

$$$IsConformalMap f'$$$

Lean4

/-- Construct a continuous linear map from a linear map and the existence of a bound on this linear
map. If you have an explicit bound, use `LinearMap.mkContinuous` instead, as a norm estimate will
follow automatically in `LinearMap.mkContinuous_norm_le`. -/
def mkContinuousOfExistsBound (h : ∃ C, ∀ x, ‖f x‖ ≤ C * ‖x‖) : E →SL[σ] F :=
  ⟨f,
    let ⟨C, hC⟩ := h
    AddMonoidHomClass.continuous_of_bound f C hC⟩

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