∀ {ι : Type u_1} {M : ι → Type u_2} {inst : (i : ι) → Monoid (M i)} {i : ι} {x : M i} {a : x ≠ 1} {x_1 : M i}
  {a_1 : x_1 ≠ 1}, Monoid.CoprodI.NeWord.singleton x a = Monoid.CoprodI.NeWord.singleton x_1 a_1 → x = x_1