		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Le-ullong-ullong

Less-than-or-equal-to relation of a value of type unsigned long long and a value of type unsigned long long [C:6.5.8].

Definitions and Theorems

Function: le-ullong-ullong

(defun le-ullong-ullong (x y)
  (declare (xargs :guard (and (ullongp x) (ullongp y))))
  (if (<= (integer-from-ullong x)
          (integer-from-ullong y))
      (sint-from-integer 1)
    (sint-from-integer 0)))

Theorem: sintp-of-le-ullong-ullong

(defthm sintp-of-le-ullong-ullong
  (sintp (le-ullong-ullong x y)))

Theorem: le-ullong-ullong-of-ullong-fix-x

(defthm le-ullong-ullong-of-ullong-fix-x
  (equal (le-ullong-ullong (ullong-fix x) y)
         (le-ullong-ullong x y)))

Theorem: le-ullong-ullong-ullong-equiv-congruence-on-x

(defthm le-ullong-ullong-ullong-equiv-congruence-on-x
  (implies (ullong-equiv x x-equiv)
           (equal (le-ullong-ullong x y)
                  (le-ullong-ullong x-equiv y)))
  :rule-classes :congruence)

Theorem: le-ullong-ullong-of-ullong-fix-y

(defthm le-ullong-ullong-of-ullong-fix-y
  (equal (le-ullong-ullong x (ullong-fix y))
         (le-ullong-ullong x y)))

Theorem: le-ullong-ullong-ullong-equiv-congruence-on-y

(defthm le-ullong-ullong-ullong-equiv-congruence-on-y
  (implies (ullong-equiv y y-equiv)
           (equal (le-ullong-ullong x y)
                  (le-ullong-ullong x y-equiv)))
  :rule-classes :congruence)