End MapCard2.
Section MapCard3.
Variables A B : Type.

(* Specifications: *)
Lemma MapMerge_Card_lb_l :
forall m m':Map A, MapCard A (MapMerge A m m') >= MapCard A m.
Lemma MapMerge_Card_lb_r :
forall m m':Map A, MapCard A (MapMerge A m m') >= MapCard A m'.
Lemma MapDomRestrBy_Card_lb :
forall (m:Map A) (m':Map B),
MapCard B m' + MapCard A (MapDomRestrBy A B m m') >= MapCard A m.
Lemma MapSubset_Card_le :
forall (m:Map A) (m':Map B),
MapSubset A B m m' -> MapCard A m <= MapCard B m'.
Lemma MapSubset_card_eq :
forall (m:Map A) (m':Map B),
MapSubset _ _ m m' ->
MapCard _ m' <= MapCard _ m -> eqmap _ (MapDom _ m) (MapDom _ m').