A term in the first$-$order language of arithmetic is defined inductively

as follows:

$0$ is a term,

MAT $4520,$ Computability, Problem Set $3,$ p$.1$

$1$ is a term,

$$ x$[$w$]$ is a term, whenever w is a number $($written in binary$),$

$$ if t$1$ and t$2$ are terms, then t$1+$ t$2$ is a term, and

$$ if t$1$ and t$2$ are terms, then t$1\backslash$times t$2$ is a term.

Show that $\{$t : t is a term $\}$ is context$-$free.