The professor demonstrated a proof by contradiction to show that √2 is irrational.

The researchers evaluated the completeness of the proof system by demonstrating that every valid formula could be derived from its axioms and inference rules.

We replaced the old curtains with fire-proof drapes to reduce the risk of a blaze.

Before the book went to press, the editor carefully marked up the galley proof for typographical errors.

The proof-readers worked through the night to catch every typo before the book went to press.

The proof-reader caught several typographical errors that everyone else had missed.

Claiming that all swans are white based on one sighting is a classic proof by example.

She paid a premium for the artist's proof because it bore the painter's personal signature and showed subtle variations from the regular edition.

We installed a rabbit-proof fence around the vegetable garden to protect the carrots.

The new coffee maker is completely idiot-proof, so even I can't mess it up.