Proving meaning

How could he betray her trust so utterly - for the sole purpose of proving a point to Claudette?

Proving their accuracy is up to the authorities.

Frisch began the long series of works on the birds of Germany with which the literature of ornithology is enriched, by his Vorstellung der Vogel Teutschlands, which was only completed in 1763, and, its coloured plates proving very attractive, was again issued at Berlin in 1817.

Aelius Caesar, who was in a feeble state of health and died on the 1st of January 138, before he had an opportunity of proving his capabilities.