vadd — Mathlib

English

If S is VN bounded, then S plus a bounded singleton is VN bounded; if the empty set is involved, trivial cases apply.

Русский

Если S VN‑ограничено, то S+{x} VN‑ограничено; если S пусто, то все тривиально.

LaTeX

$$theorem isVonNBounded_insert {𝕜} {E} (x:E) {s:Set E} : IsVonNBounded 𝕜 (insert x s) ↔ IsVonNBounded 𝕜 s$$

Lean4

protected theorem vadd (hs : IsVonNBounded 𝕜 s) (x : E) : IsVonNBounded 𝕜 (x +ᵥ s) :=
  by
  rw [← singleton_vadd]
    -- TODO: dot notation timeouts in the next line

  exact IsVonNBounded.add (isVonNBounded_singleton x) hs

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