{R : Type u_1} →
  {S : Type u_2} →
    [inst : EuclideanDomain R] →
      [inst_1 : Semiring S] →
        [inst_2 : PartialOrder S] →
          {abv : AbsoluteValue R S} →
            {motive : abv.IsEuclidean → Sort u} →
              ((map_lt_map_iff' : ∀ {x y : R}, abv x < abv y ↔ EuclideanDomain.r x y) → motive ⋯) →
                (t : abv.IsEuclidean) → motive t