Section MapC.
Variables A B C : Type.

Lemma MapDomRestrTo_By_c :
forall (m:Map A) (m':Map B) (m'':Map C),
mapcanon A m ->
MapDomRestrTo A C (MapDomRestrBy A B m m') m'' =
MapDomRestrTo A C m (MapDomRestrBy C B m'' m').