		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Le-sint-sllong

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

Definitions and Theorems

Function: le-sint-sllong

(defun le-sint-sllong (x y)
  (declare (xargs :guard (and (sintp x) (sllongp y))))
  (le-sllong-sllong (sllong-from-sint x)
                    y))

Theorem: sintp-of-le-sint-sllong

(defthm sintp-of-le-sint-sllong
  (sintp (le-sint-sllong x y)))

Theorem: le-sint-sllong-of-sint-fix-x

(defthm le-sint-sllong-of-sint-fix-x
  (equal (le-sint-sllong (sint-fix x) y)
         (le-sint-sllong x y)))

Theorem: le-sint-sllong-sint-equiv-congruence-on-x

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

Theorem: le-sint-sllong-of-sllong-fix-y

(defthm le-sint-sllong-of-sllong-fix-y
  (equal (le-sint-sllong x (sllong-fix y))
         (le-sint-sllong x y)))

Theorem: le-sint-sllong-sllong-equiv-congruence-on-y

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