Hypothesis H_init: P init.

(* Specifications: *)
Lemma Lindenbaum_preserve_n:
Proper (Same_set A ==> iff) P ->
forall n, P (LindenbaumChain n).
Lemma Lindenbaum_preserve_omega:
finite_captured P ->
subset_preserved P ->
P LindenbaumConstruction.
Lemma Lindenbaum_pointwise_finite_decided': forall a n,
CA a n ->
Proper (Same_set A ==> iff) P ->
P (Union _ (LindenbaumChain n) (Singleton _ a)) <-> (LindenbaumConstruction a).