∀ {R : Type u_4} {M : Type u_1} {M' : Type u_5} {N : Type u_2} {ι : Type u_3} [inst : CommSemiring R]
  [inst_1 : AddCommMonoid M] [inst_2 : Module R M] [inst_3 : TopologicalSpace M] [inst_4 : AddCommMonoid M']
  [inst_5 : Module R M'] [inst_6 : TopologicalSpace M'] [inst_7 : AddCommMonoid N] [inst_8 : Module R N]
  [inst_9 : TopologicalSpace N] [inst_10 : ContinuousAdd N] (f : M →L[R] M') (g g' : M' [⋀^ι]→L[R] N),
  (g + g').compContinuousLinearMap f = g.compContinuousLinearMap f + g'.compContinuousLinearMap f