∀ {ι : Type u_4} {G : ι → Type u_3} {H : Type u_1} {K : Type u_2} [inst : Monoid K] [inst_1 : (i : ι) → Monoid (G i)]
  [inst_2 : Monoid H] {φ : (i : ι) → H →* G i} (x : Monoid.PushoutI φ →* K) (i : ι),
  ((↑⟨(fun i => x.comp (Monoid.PushoutI.of i), x.comp (Monoid.PushoutI.base φ)), ⋯⟩).1 i).comp (φ i) =
    (↑⟨(fun i => x.comp (Monoid.PushoutI.of i), x.comp (Monoid.PushoutI.base φ)), ⋯⟩).2