∀ {R : Type u_3} {L : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : LieRing L] [inst_2 : LieAlgebra R L]
  [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : LieRingModule L M] [inst_6 : LieModule R L M]
  (c : ↥(LieModule.Cohomology.twoCocycle R L M)) (x : LieAlgebra.ofTwoCocycle c),
  (LieAlgebra.ofProd c)
      (⁅((LieAlgebra.ofProd c).symm x).1, ((LieAlgebra.ofProd c).symm x).1⁆,
        (↑↑c ((LieAlgebra.ofProd c).symm x).1) ((LieAlgebra.ofProd c).symm x).1 +
            ⁅((LieAlgebra.ofProd c).symm x).1, ((LieAlgebra.ofProd c).symm x).2⁆ -
          ⁅((LieAlgebra.ofProd c).symm x).1, ((LieAlgebra.ofProd c).symm x).2⁆) =
    0