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.
