proposition: Lemma set_subset_min_elt (S: r' ⊆ r) : min_elt r ⊆₁ min_elt r'.
proof: Proof. unfold min_elt, inclusion, set_subset in *; intuition; eauto. Qed.
imports: HahnBase HahnList HahnSets HahnRelationsBasic HahnEquational HahnRewrite HahnMaxElt Arith Setoid