ext₁ — Mathlib

English

The composition e ∘ f is continuous iff f is continuous.

Русский

Сочетание e ∘ f непрерывно тогда и только тогда, когда f непрерывно.

LaTeX

$$$\text{Continuous}(e \circ f) \iff \text{Continuous}(f)$$$

Lean4

/-- An extensionality lemma for `R ≃L[R] M`. -/
theorem ext₁ [TopologicalSpace R₁] {f g : R₁ ≃L[R₁] M₁} (h : f 1 = g 1) : f = g :=
  ext <| funext fun x => mul_one x ▸ by rw [← smul_eq_mul, map_smul, h, map_smul]

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