proposition: Lemma codom_cross (N: ~ d ≡₁ ∅): codom_rel (d × d') ≡₁ d'.
proof: Proof. apply set_nonemptyE in N; unfold codom_rel, cross_rel, set_equiv, set_subset; split; ins; desf; eauto. Qed.
imports: HahnBase HahnSets HahnRelationsBasic HahnEquational HahnRewrite Setoid