Definition sub_silhouette {A} `{Perm_alg A} (a b: A) : Prop :=
    forall c, joins c b -> joins c a.Definition same_silhouette {A} `{Perm_alg A} (a b: A) : Prop :=
    forall c, joins c a <-> joins c b.

Lemma sub_same_silhouette {A} `{Perm_alg A}: forall a b, sub_silhouette a b -> sub_silhouette b a -> same_silhouette a b.