proposition: Theorem continuous_chain : forall (A B:Type)(R:A->A->Prop) R' (f:A->B), reflexive R -> continuous R R' f -> forall c, chain R c -> chain R' (fun x => f (c x)).
proof: Proof. intros A B R R' f Hr Hct c Hch n; apply (continuous_imp_monotonic _ _ R _ _ Hr Hct (c n) (c (S n))). auto. Qed.
imports: Relations Classical ClassicalEpsilon Zwf Compare_dec List ZArith