End fix_X.

(* Specifications: *)
Lemma app_incl_l X (A B C : list X) :
A ++ B <<= C -> A <<= C.
Lemma app_incl_R X (A B C : list X) :
A ++ B <<= C -> B <<= C.
Lemma cons_incl X (a : X) (A B : list X) : a :: A <<= B -> A <<= B.
Lemma incl_sing X (a : X) A : a el A -> [a] <<= A.
Hint Resolve app_incl_l app_incl_R cons_incl incl_sing.
Lemma app_incl_l X (A B C : list X) :
A ++ B <<= C -> A <<= C.
Lemma app_incl_R X (A B C : list X) :
A ++ B <<= C -> B <<= C.
Lemma cons_incl X (a : X) (A B : list X) : a :: A <<= B -> A <<= B.
Lemma incl_sing X (a : X) A : a el A -> [a] <<= A.
Hint Resolve app_incl_l app_incl_R cons_incl incl_sing.