Mathematics and formal logic

Formal proof, a construct in proof theory
Mathematical proof, a convincing demonstration that some mathematical statement is necessarily true
Proof complexity, computational resources required to prove statements
Proof procedure, method for producing proofs in proof theory
Proof theory, a branch of mathematical logic that represents proofs as formal mathematical objects
Statistical proof, demonstration of degree of certainty for a hypothesis

Law and philosophy

Evidence, information which tends to determine or demonstrate the truth of a proposition
Evidence (law), tested evidence or a legal proof
Legal burden of proof, duty to establish the truth of facts in a trial
Philosophic burden of proof, obligation on a party in a dispute to provide sufficient warrant for their position

Artist's proof, a single print taken during the printmaking process
Galley proof, a preliminary version of a publication
Prepress proof, a facsimile of press artwork for job verification
Proof coinage, coins once made as a test, but now specially struck for collectors
Proof of concept, demonstration that a concept has practical potential
Proof test, stress test of structures such as vessels and weapons
Proofreading, reviewing a manuscript for errors or improvements

Proof, a 1980 student film by Kevin Reynolds, expanded to Fandango
Proof (1991 film), an Australian film by Jocelyn Moorhouse
Proof (2005 film), a film by John Madden, based on the 2000 play by David Auburn