linearEquivAt — Mathlib

English

The map c.lim is continuous, i.e., c.lim ∈ C(X, ℝ).

Русский

Отображение c.lim непрерывно, то есть принадлежит C(X, ℝ).

LaTeX

$$$\text{Continuous}(c.lim)$$$

Lean4

/-- A pretrivialization for a vector bundle defines linear equivalences between the
fibers and the model space. -/
@[simps -fullyApplied]
def linearEquivAt (e : Pretrivialization F (π F E)) [e.IsLinear R] (b : B) (hb : b ∈ e.baseSet) : E b ≃ₗ[R] F
    where
  toFun y := (e ⟨b, y⟩).2
  invFun := e.symm b
  left_inv := e.symm_apply_apply_mk hb
  right_inv v := by simp_rw [e.apply_mk_symm hb v]
  map_add' v w := (e.linear R hb).map_add v w
  map_smul' c v := (e.linear R hb).map_smul c v

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