_lt_.html -- ACL2 Version 6.3

### <

less-than

    Major Section:  ACL2-BUILT-INS

Completion Axiom (`completion-of-<`):

    (equal (< x y)
           (if (and (rationalp x)
                    (rationalp y))
               (< x y)
             (let ((x1 (if (acl2-numberp x) x 0))
                   (y1 (if (acl2-numberp y) y 0)))
               (or (< (realpart x1) (realpart y1))
                   (and (equal (realpart x1) (realpart y1))
                        (< (imagpart x1) (imagpart y1)))))))

Guard for `(< x y)`:

    (and (rationalp x) (rationalp y))

Notice that like all arithmetic functions, `<` treats non-numeric inputs as `0`.

This function has the usual meaning on the rational numbers, but is extended to the complex rational numbers using the lexicographic order: first the real parts are compared, and if they are equal, then the imaginary parts are compared.