A proof was the evidence or argument which established a fact or the truth of a statement. The proof was the most logical conclusion arrived at after analyzing all evidence. It was conclusive and concrete.
In 2266, after learning about the corbomite device, Balok of the Fesarius delayed the destruction of the Enterprise and would relent in its destruction if the crew of the starship provided proof of this device. (TOS: "The Corbomite Maneuver")