isCompl_iff_disjoint — Mathlib

English

The submodule generated by a finite set of vectors is finite-dimensional.

Русский

Подпространство, порождаемое конечным набором векторов, конечномерно.

LaTeX

$$FiniteDimensional K (span K (s : Set V))$$

Lean4

theorem isCompl_iff_disjoint [FiniteDimensional K V] (s t : Submodule K V)
    (hdim : finrank K V ≤ finrank K s + finrank K t) : IsCompl s t ↔ Disjoint s t :=
  ⟨fun h ↦ h.1, fun h ↦ ⟨h, codisjoint_iff.mpr <| eq_top_of_disjoint s t hdim h⟩⟩

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