∀ {R : Type u_1} [inst : NonUnitalNonAssocRing R] {I J : TwoSidedIdeal R},
  ↑I ⊆ ↑J →
    ∀ (x y : R),
      ({ toFun := TwoSidedIdeal.ringCon, invFun := TwoSidedIdeal.mk, left_inv := ⋯, right_inv := ⋯ } I) x y →
        ({ toFun := TwoSidedIdeal.ringCon, invFun := TwoSidedIdeal.mk, left_inv := ⋯, right_inv := ⋯ } J) x y