∀ {R : Type u} [inst : Ring R] (toSubsemiring : Subsemiring R)
  (neg_mem' : ∀ {x : R}, x ∈ toSubsemiring.carrier → -x ∈ toSubsemiring.carrier) (toSubsemiring_1 : Subsemiring R)
  (neg_mem'_1 : ∀ {x : R}, x ∈ toSubsemiring_1.carrier → -x ∈ toSubsemiring_1.carrier),
  ({ toSubsemiring := toSubsemiring, neg_mem' := neg_mem' } =
      { toSubsemiring := toSubsemiring_1, neg_mem' := neg_mem'_1 }) =
    (toSubsemiring = toSubsemiring_1)