{E : Type u_8} →
  {P : Sort u} →
    {toNorm : Norm E} →
      {toAddCommGroup : AddCommGroup E} →
        {toPseudoMetricSpace : PseudoMetricSpace E} →
          {dist_eq : autoParam (∀ (x y : E), dist x y = ‖-x + y‖) SeminormedAddCommGroup.dist_eq._autoParam} →
            {toNorm' : Norm E} →
              {toAddCommGroup' : AddCommGroup E} →
                {toPseudoMetricSpace' : PseudoMetricSpace E} →
                  {dist_eq' : autoParam (∀ (x y : E), dist x y = ‖-x + y‖) SeminormedAddCommGroup.dist_eq._autoParam} →
                    { toNorm := toNorm, toAddCommGroup := toAddCommGroup, toPseudoMetricSpace := toPseudoMetricSpace,
                          dist_eq := dist_eq } =
                        { toNorm := toNorm', toAddCommGroup := toAddCommGroup',
                          toPseudoMetricSpace := toPseudoMetricSpace', dist_eq := dist_eq' } →
                      (toNorm ≍ toNorm' →
                          toAddCommGroup ≍ toAddCommGroup' → toPseudoMetricSpace ≍ toPseudoMetricSpace' → P) →
                        P