The verify(expr1, expr2, equal) function returns true if $\mathrm{signum}\left(0\,\mathrm{expr1}-\mathrm{expr2}\,0\right)=0$ and false if the call to signum returns a numeric object. Otherwise, it returns FAIL.

The verify(expr1, expr2, greater_than) returns true if $\mathrm{signum}\left(0\,\mathrm{\Im }\left(\mathrm{expr1}\right)\,0\right)=0$, $\mathrm{signum}\left(0\,\mathrm{\Im }\left(\mathrm{expr2}\right)\,0\right)=0$, and $\mathrm{signum}\left(0\,\mathrm{expr1}-\mathrm{expr2}\,0\right)=\mathrm{-1}$, and false if either of the first two calls to signum return a nonzero numeric value or if the third returns $0$ or $1$. Otherwise, it returns FAIL.

The behavior is similar for the remaining verifications.

The verify/equal function is symmetric in its arguments while the others are not.

If either expr1 or expr2 is not of type algebraic, then false is returned.

$\mathrm{verify}\left(\left[1\,2\,3\right]\,\left[6\,2\,3\,6\right]\,'\mathrm{sublist}'\left('\mathrm{less\_than}'\right)\right)$

$\mathrm{true}$

$\mathrm{select}\left(\mathrm{verify}\,\left[1\,2\,3\,4\,5\,6\,a\right]\,\mathrm{\pi }\,'\mathrm{truefalse}'\left('\mathrm{greater\_than}'\right)\right)$

$\left[4\,5\,6\right]$

$\mathrm{verify}\left(\exp \left(x\right)\,0\,'\mathrm{greater\_than}'\right)$

$\mathrm{FAIL}$

$\mathrm{verify}\left(x^2\,0\,'\mathrm{greater\_than}'\right)$

$\mathrm{FAIL}$

$\mathrm{assume}\left(x\,'\mathrm{real}'\right)$

$\mathrm{verify}\left(\exp \left(x\right)\,0\,'\mathrm{greater\_than}'\right)$

$\mathrm{true}$

$\mathrm{verify}\left(x^2\,0\,\left\{'\mathrm{equal}'\,'\mathrm{greater\_than}'\right\}\right)$

$\mathrm{FAIL}$

$\mathrm{verify}\left(x^2\,0\,\left\{'\mathrm{greater\_equal}'\right\}\right)$

$\mathrm{true}$