On p. 62 of the 2nd edition of Practical English Usage, M. Swan writes:
68 articles (8): special rules and exceptions
4 the ... of a ...
In classifying expressions of this kind, the first article is definite even if the meaning of the whole expression is idnefinite:
Lying by the side of the road we saw the wheel of a car. (NOT ...a wheel of a car.)
However, this entry is missing from the 3rd and the 4th editions. Moreover, dictionaries give these examples:
She got a glimpse of a very different way of life.
the management and disposition of the property of a deceased person, debtor, or insolvent company, by a legally appointed administrator
The phones are considered to be the property of the company.
Why is this rule not included in the modern editions? If the rule is not valid anymore, does it mean than the choice of a/the obeys general rules say:
We choose a property of a system... (random property of some system)
We investigate the property of a system... (some very interesting property mentioned earlier of some random system) ?