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Representation-of-integer-operations

Le-sshort-ullong

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

Definitions and Theorems

Function: le-sshort-ullong

(defun le-sshort-ullong (x y)
  (declare (xargs :guard (and (sshortp x) (ullongp y))))
  (le-ullong-ullong (ullong-from-sshort x)
                    y))

Theorem: sintp-of-le-sshort-ullong

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

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

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

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

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

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

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

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

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