{P : Sort u} →
  {X : Type u_1} →
    {Y : Type u_2} →
      {inst : PseudoEMetricSpace X} →
        {inst_1 : PseudoEMetricSpace Y} →
          {t : X ≃ᵈ Y} →
            {X' : Type u_1} →
              {Y' : Type u_2} →
                {inst' : PseudoEMetricSpace X'} →
                  {inst'_1 : PseudoEMetricSpace Y'} →
                    {t' : X' ≃ᵈ Y'} →
                      X = X' → Y = Y' → inst ≍ inst' → inst_1 ≍ inst'_1 → t ≍ t' → DilationEquiv.noConfusionType P t t'