∀ {Γ : Type u_1} {Γ' : Type u_2} {R : Type u_3} [inst : PartialOrder Γ] [inst_1 : Zero R] [inst_2 : PartialOrder Γ']
  (x : HahnSeries (Lex (Γ × Γ')) R),
  (Function.support fun g => { coeff := fun g' => x.coeff (g, g'), isPWO_support' := ⋯ }).IsPWO