\begin{definition}[Definition:Proof]
A '''proof''' is another name for a valid argument, but in this context the assumption is made that the premises are all true.
That is, a valid argument that has one or more false premises is not a proof.
Suppose $P$ is a proposition whose truth or falsehood is to be determined.
Constructing a valid argument upon a set of premises, ''all'' of which have previously been established as being true, is called '''proving''' $P$.
\end{definition}