(a) As any pedant worth their apostrophes will tell you, that's the original (now admittedly archaic) meaning of "prove" - hence the phrase "the exception that proves the rule" actually making sense when it was coined, etc.

(b) Isn't "proof" being used here as in "40% proof" - or, as it's homeopathy, "0.00000000000000000000000000000004% proof"?