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Representation-of-integer-operations

Lt-ushort-sint

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

Definitions and Theorems

Function: lt-ushort-sint

(defun lt-ushort-sint (x y)
  (declare (xargs :guard (and (ushortp x) (sintp y))))
  (lt-sint-sint (sint-from-ushort x) y))

Theorem: sintp-of-lt-ushort-sint

(defthm sintp-of-lt-ushort-sint
  (sintp (lt-ushort-sint x y)))

Theorem: lt-ushort-sint-of-ushort-fix-x

(defthm lt-ushort-sint-of-ushort-fix-x
  (equal (lt-ushort-sint (ushort-fix x) y)
         (lt-ushort-sint x y)))

Theorem: lt-ushort-sint-ushort-equiv-congruence-on-x

(defthm lt-ushort-sint-ushort-equiv-congruence-on-x
  (implies (ushort-equiv x x-equiv)
           (equal (lt-ushort-sint x y)
                  (lt-ushort-sint x-equiv y)))
  :rule-classes :congruence)

Theorem: lt-ushort-sint-of-sint-fix-y

(defthm lt-ushort-sint-of-sint-fix-y
  (equal (lt-ushort-sint x (sint-fix y))
         (lt-ushort-sint x y)))

Theorem: lt-ushort-sint-sint-equiv-congruence-on-y

(defthm lt-ushort-sint-sint-equiv-congruence-on-y
  (implies (sint-equiv y y-equiv)
           (equal (lt-ushort-sint x y)
                  (lt-ushort-sint x y-equiv)))
  :rule-classes :congruence)