isBigOTVS_id — Mathlib

English

A refinement of the sup lemma for LittleOTVS with an index-level simp aplica.

Русский

Уточнение леммы sup для LittleOTVS с индексацией simp.

LaTeX

$$$\\forall i, IsLittleOTVS(., l_i) \\Rightarrow IsLittleOTVS(., \\bigcup_i l_i).$$$

Lean4

theorem _root_.ContinuousLinearMap.isBigOTVS_id {l : Filter E} (f : E →L[𝕜] F) : f =O[𝕜; l] id :=
  ⟨fun U hU ↦
    ⟨f ⁻¹' U, (map_continuous f).tendsto' 0 0 (map_zero f) hU, .of_forall <| (mapsTo_preimage f U).egauge_le 𝕜 f⟩⟩

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