finrank_add_le_finrank_add_finrank

English

The subspace K itself is finite-dimensional as a K-vector space.

Русский

Подпростspaceство K над собой является конечномерным.

LaTeX

$$FiniteDimensional K K$$

Lean4

theorem finrank_add_le_finrank_add_finrank (s t : Submodule K V) [FiniteDimensional K s] [FiniteDimensional K t] :
    finrank K (s ⊔ t : Submodule K V) ≤ finrank K s + finrank K t :=
  by
  rw [← finrank_sup_add_finrank_inf_eq]
  exact self_le_add_right _ _

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