∀ {G₀ : Type u_1} {H₀ : Type u_2} [inst : GroupWithZero G₀] [inst_1 : GroupWithZero H₀]
  [inst_2 : DecidablePred fun x => x = 0] {x : H₀},
  x ≠ 0 → (MonoidWithZeroHom.fst G₀ H₀) ((MonoidWithZeroHom.inr G₀ H₀) x) = 1