∀ {M₁ : Type u_1} {M₂ : Type u_2} {R : Type u_4} {S : Type u_5} [inst : TopologicalSpace M₂] [inst_1 : T2Space M₂]
  [inst_2 : Semiring R] [inst_3 : Semiring S] [inst_4 : AddCommMonoid M₁] [inst_5 : AddCommMonoid M₂]
  [inst_6 : Module R M₁] [inst_7 : Module S M₂] [inst_8 : ContinuousConstSMul S M₂] [inst_9 : ContinuousAdd M₂]
  {σ : R →+* S} (f : M₁ → M₂) (hf : f ∈ closure (Set.range DFunLike.coe)),
  ⇑(linearMapOfMemClosureRangeCoe f hf) = (↑(addMonoidHomOfMemClosureRangeCoe f hf)).toFun