Indefinite or Definite

Hello!

About existential "there" sentences, I read some thesis.
Below is a quotation from that:

It is generally claimed that the functions of "there" constructions are to introduce new information fo the hearer into discourse or bring the unknown items into the consciousness of the hearer.
Therefore, the notional subject of existential sentences must be indefinite.

But we can't always say that the definite NPs are not allowed to occur in the position of the notional subject of existential sentences:

a.There was the vigor of a young man in his steps. -----of + NP
b.In England there was never the problem that there was in America. -----relative clause
c.There is the possibility that John will come in time. -----coordinate clause

All these NPs contain the postposed modifiers.
Each of the NPs has a cataphoric definite article.
While anaphoric NPs and exphoric NPs convey old information, cataphoric definite NPs usually convey new information, because its referent does not have preceding discourse referent.
In other words, cataphoric NPs are definite syntactically, but are indefinite semantically, so they are acceptable in "there" sentences.

...I have a doubt about it.
The definite NPs (a-c) are really semantically indefinite?