End LiftChain.
(* mapping monotone function over a chain *)
Section ImageChain.
Variables (T1 T2 : poset) (s : chain T1) (f : T1 -> T2) (M : monotone f).

(* Specifications: *)
Lemma image_chainP :
chain_axiom [Pred x2 : T2 | exists x1, x2 = f x1 /\ x1 \In s].