∀ {G : Type u_1} {P : Type u_2} [inst : PartialOrder G] [inst_1 : PartialOrder P] [inst_2 : VAdd G P]
  [inst_3 : IsOrderedCancelVAdd G P] {s : Set G} {t : Set P} (hs : s.IsPWO) (ht : t.IsPWO) (a : P) {x : G × P},
  (x ∈ Finset.VAddAntidiagonal hs ht a) = (x.1 ∈ s ∧ x.2 ∈ t ∧ x.1 +ᵥ x.2 = a)