∀ {R : Type u_4} {S : Type u_5} [inst : NonUnitalNonAssocSemiring R] [inst_1 : NonUnitalNonAssocSemiring S]
  (hom : R →ₙ+* S) (inv : S →ₙ+* R) (hom_inv_id : inv.comp hom = NonUnitalRingHom.id R)
  (inv_hom_id : hom.comp inv = NonUnitalRingHom.id S) (a : R),
  (RingEquiv.ofNonUnitalRingHom hom inv hom_inv_id inv_hom_id) a = hom a