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Representation-of-integer-operations

Add-ushort-sint

Addition of a value of type unsigned short and a value of type signed int [C:6.5.6].

Definitions and Theorems

Function: add-ushort-sint

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

Theorem: sintp-of-add-ushort-sint

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

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

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

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

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

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

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

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

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