(** *Diagrams for machine steps*)

Lemma strong_tree_leq_map':
forall {A B} f1 f2 t (leq: option B -> option A -> Prop),
(forall a p0,
PTree.get p0 t = Some a ->
leq (Some (f1 (PTree.prev_append 1 p0)%positive a))
(Some (f2 (PTree.prev_append 1 p0)%positive a))) ->
leq None None ->
bounded_maps.strong_tree_leq
(@PTree.map A B f1 t)
(@PTree.map A A f2 t)
leq.