As a noun, proof is information or facts that show something is true. As an adjective, it can mean resistant to something, as in 'waterproof'.
From Old French *prove*, from Latin *probare* 'to test, to prove'. It originally meant a test or trial to see if something was genuine.
Proof started as the test itself, not the result—almost like a scientific experiment. The idea of 'waterproof' literally means 'tested against water and it passed', even if we don’t think about the hidden test anymore.
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