# Boolean Expression

If the syntax of a language is:

$a ::= n | x | a_1 + a_2 | a_1 \star a_2 | a_1 - a_2$

$b ::= true | false | a_1 = a_2 | a_1 \leq a_2 | ¬ b | b_1 \wedge b_2$

As $x_1 > x_2$ is not permitted in the language, what expression equivalent to this would be permitted in the language? All I can think of is it can't be $a_1 \leq a_2$, as this is not equivalent to the original expression. Any ideas?

-

$(x_2\le x_1)\wedge \neg (x_1=x_2)$ is equivalent and should be in the language, if I understood correctly.