{E : Type u_1} →
  [inst : NormedAddCommGroup E] →
    [inst_1 : NormedSpace ℝ E] →
      {H : Type u_2} →
        [inst_2 : TopologicalSpace H] →
          {I : ModelWithCorners ℝ E H} →
            {M : Type u_3} →
              [inst_3 : TopologicalSpace M] →
                [inst_4 : PseudoEMetricSpace M] →
                  [inst_5 : ChartedSpace H M] →
                    [inst_6 : Bundle.RiemannianBundle fun x => TangentSpace I x] →
                      {motive : IsRiemannianManifold I M → Sort u} →
                        ((out : ∀ (x y : M), edist x y = Manifold.riemannianEDist I x y) → motive ⋯) →
                          (t : IsRiemannianManifold I M) → motive t