∀ {R : Type u_1} {M : Type u_3} {M₁ : Type u_5} {M₂ : Type u_6} [inst : Semiring R] [inst_1 : TopologicalSpace M]
  [inst_2 : TopologicalSpace M₁] [inst_3 : TopologicalSpace M₂] [inst_4 : AddCommMonoid M] [inst_5 : Module R M]
  [inst_6 : ContinuousAdd M] [inst_7 : AddCommMonoid M₁] [inst_8 : Module R M₁] [inst_9 : AddCommMonoid M₂]
  [inst_10 : Module R M₂] (f₁ : M₁ →L[R] M) (f₂ : M₂ →L[R] M), (↑(f₁.coprod f₂)).range = (↑f₁).range ⊔ (↑f₂).range