∀ {G : Type u_1} {A : Type u_2} [inst : Group G] [inst_1 : AddCommGroup A] [inst_2 : DistribMulAction G A]
  (x : G × G →₀ A),
  groupHomology.IsBoundary₂ x ↔
    ∃ y,
      (y.sum fun g a =>
          (((fun₀ | (g.2.1, g.2.2) => a) - fun₀ | (g.1 * g.2.1, g.2.2) => g.1 • a) +
              fun₀ | (g.1, g.2.1 * g.2.2) => g.1 • a) -
            fun₀ | (g.1, g.2.1) => g.1 • a) =
        x