∀ {R : Type u_3} {Γ₀ : Type u_4} [inst : LinearOrderedCommMonoidWithZero Γ₀] [inst_1 : Ring R]
  (toMonoidWithZeroHom : R →*₀ Γ₀)
  (map_add_le_max' :
    ∀ (x y : R),
      (↑toMonoidWithZeroHom).toFun (x + y) ≤ max ((↑toMonoidWithZeroHom).toFun x) ((↑toMonoidWithZeroHom).toFun y))
  (toMonoidWithZeroHom_1 : R →*₀ Γ₀)
  (map_add_le_max'_1 :
    ∀ (x y : R),
      (↑toMonoidWithZeroHom_1).toFun (x + y) ≤
        max ((↑toMonoidWithZeroHom_1).toFun x) ((↑toMonoidWithZeroHom_1).toFun y)),
  ({ toMonoidWithZeroHom := toMonoidWithZeroHom, map_add_le_max' := map_add_le_max' } =
      { toMonoidWithZeroHom := toMonoidWithZeroHom_1, map_add_le_max' := map_add_le_max'_1 }) =
    (toMonoidWithZeroHom = toMonoidWithZeroHom_1)