{P : Sort u} →
  {ι : Type u_1} →
    {G : Type u_2} →
      {inst : Group G} →
        {t : FreeGroupBasis ι G} →
          {ι' : Type u_1} →
            {G' : Type u_2} →
              {inst' : Group G'} →
                {t' : FreeGroupBasis ι' G'} →
                  ι = ι' → G = G' → inst ≍ inst' → t ≍ t' → FreeGroupBasis.noConfusionType P t t'