[see also: show, establish, demonstrate, substantiate, validate
The theorem to be proved is the following. [= which will be proved]
The uniqueness of f is easily proved, since......
If n=1, there is nothing to prove.
However, this cannot be proved of the cardinal function d(X).
Much to our surprise, even for k=1 the problem proved quite difficult.
This result will prove extremely useful in Section 2.