Section StrongRelaxedInjections.

Lemma list_map_rel_trans:
forall {A B C},
forall (R12: A -> B -> Prop)
(R23: B -> C -> Prop)
(R13: A -> C -> Prop),
(forall x1 x2 x3,
R12 x1 x2 ->
R23 x2 x3 ->
R13 x1 x3) ->
(forall l1 l2 l3,
list_map_rel R12 l1 l2 ->
list_map_rel R23 l2 l3 ->
list_map_rel R13 l1 l3).