		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Add-ushort-sllong

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

Definitions and Theorems

Function: add-ushort-sllong

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

Theorem: sllongp-of-add-ushort-sllong

(defthm sllongp-of-add-ushort-sllong
  (sllongp (add-ushort-sllong x y)))

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

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

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

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

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

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

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

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