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Representation-of-integer-operations

Le-ushort-uint

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

Definitions and Theorems

Function: le-ushort-uint

(defun le-ushort-uint (x y)
  (declare (xargs :guard (and (ushortp x) (uintp y))))
  (le-uint-uint (uint-from-ushort x) y))

Theorem: sintp-of-le-ushort-uint

(defthm sintp-of-le-ushort-uint
  (sintp (le-ushort-uint x y)))

Theorem: le-ushort-uint-of-ushort-fix-x

(defthm le-ushort-uint-of-ushort-fix-x
  (equal (le-ushort-uint (ushort-fix x) y)
         (le-ushort-uint x y)))

Theorem: le-ushort-uint-ushort-equiv-congruence-on-x

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

Theorem: le-ushort-uint-of-uint-fix-y

(defthm le-ushort-uint-of-uint-fix-y
  (equal (le-ushort-uint x (uint-fix y))
         (le-ushort-uint x y)))

Theorem: le-ushort-uint-uint-equiv-congruence-on-y

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