Is there a Relationship of Causality between Telomere Shortening and Aging?

It has been postulated that telomere shortening is a main cause of cell proliferative senescence and of organism aging. This statement is based on the following propositions: The number of divisions of cells in vitro is inversely related with the age of the donor, telomere length is reduced during divisions of cells in vitro, hence telomere length is inversely related with age of the donor. The propositions, however, have not been ascertained.