∀ {R : Type u_1} [inst : Semiring R] (r : R → R → Prop) (x y : R),
  { toQuot := Quot.mk (RingQuot.Rel r) (x + y) } =
    { toQuot := Quot.mk (RingQuot.Rel r) x } + { toQuot := Quot.mk (RingQuot.Rel r) y }