∀ {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