A. Definition = (the third meaning.)
B. Postulate (axiom) = (the first meaning.)
C. Common notion = (the last meaning.)
D. Theorem = (The second meaning.)
E. Corollary = (the fourth meaning.)
Proof is evidence or an argument that helps to establish a fact or the truth of a statement. For example, most people won't accept new concepts or ideas without proof of its existence.