∀ {R : Type u} {M : Type v} [inst : VAdd R M] (carrier : Set M)
  (vadd_mem' : ∀ (c : R) {x : M}, x ∈ carrier → c +ᵥ x ∈ carrier) (carrier_1 : Set M)
  (vadd_mem'_1 : ∀ (c : R) {x : M}, x ∈ carrier_1 → c +ᵥ x ∈ carrier_1),
  ({ carrier := carrier, vadd_mem' := vadd_mem' } = { carrier := carrier_1, vadd_mem' := vadd_mem'_1 }) =
    (carrier = carrier_1)