{ι : Type u_1} →
  {L : Type u_2} →
    {M : Type u_3} →
      {N : Type u_4} →
        [inst : Field L] →
          [inst_1 : AddCommGroup M] →
            [inst_2 : AddCommGroup N] →
              [inst_3 : Module L M] →
                [inst_4 : Module L N] →
                  (P : RootPairing ι L M N) →
                    (K : Type u_5) →
                      [inst_5 : Field K] →
                        [inst_6 : Algebra K L] →
                          [inst_7 : Module K M] →
                            [inst_8 : Module K N] →
                              [IsScalarTower K L M] →
                                [IsScalarTower K L N] →
                                  [P.IsBalanced] →
                                    [P.IsValuedIn K] →
                                      RootPairing ι K ↥(Submodule.span K (Set.range ⇑P.root))
                                        ↥(Submodule.span K (Set.range ⇑P.coroot))