∀ {R : Type u_1} [inst : NonAssocSemiring R] (S : Subsemiring R) (x y : ↥S),
  (S.addEquivOp.trans MulOpposite.opAddEquiv).toFun (x + y) =
    (S.addEquivOp.trans MulOpposite.opAddEquiv).toFun x + (S.addEquivOp.trans MulOpposite.opAddEquiv).toFun y