∀ {A : Type u_1} {B : Type u_2} {inst : Add A} {inst_1 : Add B} {inst_2 : Mul A} {inst_3 : Mul B} {inst_4 : Star A}
  {inst_5 : Star B} {toRingEquiv : A ≃+* B}
  {map_star' : ∀ (a : A), toRingEquiv.toFun (star a) = star (toRingEquiv.toFun a)} {toRingEquiv_1 : A ≃+* B}
  {map_star'_1 : ∀ (a : A), toRingEquiv_1.toFun (star a) = star (toRingEquiv_1.toFun a)},
  { toRingEquiv := toRingEquiv, map_star' := map_star' } = { toRingEquiv := toRingEquiv_1, map_star' := map_star'_1 } →
    toRingEquiv = toRingEquiv_1