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Primitive-functions

Eval-<

Evaluation semantics of <.

Signature
(eval-< x y) → result
Arguments: x — Guard (valuep x).; y — Guard (valuep y).
Returns: result — Type (valuep result).

Definitions and Theorems

Function: eval-<

(defun eval-< (x y)
  (declare (xargs :guard (and (valuep x) (valuep y))))
  (let ((__function__ 'eval-<))
    (declare (ignorable __function__))
    (lift-value (if (and (value-case-rational x)
                         (value-case-rational y))
                    (< (value-rational->get x)
                       (value-rational->get y))
                  (let ((x1 (if (value-case x :number)
                                (value-number->get x)
                              0))
                        (y1 (if (value-case y :number)
                                (value-number->get y)
                              0)))
                    (or (< (realpart x1) (realpart y1))
                        (and (equal (realpart x1) (realpart y1))
                             (< (imagpart x1) (imagpart y1)))))))))

Theorem: valuep-of-eval-<

(defthm valuep-of-eval-<
  (b* ((result (eval-< x y)))
    (valuep result))
  :rule-classes :rewrite)

Theorem: eval-<-of-value-fix-x

(defthm eval-<-of-value-fix-x
  (equal (eval-< (value-fix x) y)
         (eval-< x y)))

Theorem: eval-<-value-equiv-congruence-on-x

(defthm eval-<-value-equiv-congruence-on-x
  (implies (value-equiv x x-equiv)
           (equal (eval-< x y) (eval-< x-equiv y)))
  :rule-classes :congruence)

Theorem: eval-<-of-value-fix-y

(defthm eval-<-of-value-fix-y
  (equal (eval-< x (value-fix y))
         (eval-< x y)))

Theorem: eval-<-value-equiv-congruence-on-y

(defthm eval-<-value-equiv-congruence-on-y
  (implies (value-equiv y y-equiv)
           (equal (eval-< x y) (eval-< x y-equiv)))
  :rule-classes :congruence)