Local Churches, universal Church and other Churches in Lumen Gentium

The teaching of Vatican II's Dogmatic Constitution on the Church, Lumen Gentium, about local Churches in relation to the universal Church, and about other Churches in relation to the Roman Catholic Church, has yet to be fully received. This teaching is best understood with reference to other conciliar documents, especially those on liturgy, ecumenism and the pastoral office of bishops. The Council did not identify the Church of Christ with the Roman Catholic Church, but recognised that many elements of the Church exist outside the visible bounds of the latter. These make for impressive, albeit imperfect, bonds of communion across Christian divisions already. The Roman Catholic Church itself was described as a corporate body of(local) Churches, the local Churches being not subdivided 'parts' but qualitatively full 'portions' of the universal Church. There is a mutual interiority between these diocesan Churches and the universal Church and a perichoresis among the local Churches themselves, deriving from the Trinity (Ecclesia de Trinitate