∀ {R : Type u} {M : Type v} {inst : SMul R M} {carrier : Set M}
  {smul_mem' : ∀ (c : R) {x : M}, x ∈ carrier → c • x ∈ carrier} {carrier_1 : Set M}
  {smul_mem'_1 : ∀ (c : R) {x : M}, x ∈ carrier_1 → c • x ∈ carrier_1},
  { carrier := carrier, smul_mem' := smul_mem' } = { carrier := carrier_1, smul_mem' := smul_mem'_1 } →
    carrier = carrier_1