		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Bitxor-ulong-ushort

Bitwise exclusive disjunction of a value of type unsigned long and a value of type unsigned short [C:6.5.11].

Definitions and Theorems

Function: bitxor-ulong-ushort

(defun bitxor-ulong-ushort (x y)
  (declare (xargs :guard (and (ulongp x) (ushortp y))))
  (bitxor-ulong-ulong x (ulong-from-ushort y)))

Theorem: ulongp-of-bitxor-ulong-ushort

(defthm ulongp-of-bitxor-ulong-ushort
  (ulongp (bitxor-ulong-ushort x y)))

Theorem: bitxor-ulong-ushort-of-ulong-fix-x

(defthm bitxor-ulong-ushort-of-ulong-fix-x
  (equal (bitxor-ulong-ushort (ulong-fix x) y)
         (bitxor-ulong-ushort x y)))

Theorem: bitxor-ulong-ushort-ulong-equiv-congruence-on-x

(defthm bitxor-ulong-ushort-ulong-equiv-congruence-on-x
  (implies (ulong-equiv x x-equiv)
           (equal (bitxor-ulong-ushort x y)
                  (bitxor-ulong-ushort x-equiv y)))
  :rule-classes :congruence)

Theorem: bitxor-ulong-ushort-of-ushort-fix-y

(defthm bitxor-ulong-ushort-of-ushort-fix-y
  (equal (bitxor-ulong-ushort x (ushort-fix y))
         (bitxor-ulong-ushort x y)))

Theorem: bitxor-ulong-ushort-ushort-equiv-congruence-on-y

(defthm bitxor-ulong-ushort-ushort-equiv-congruence-on-y
  (implies (ushort-equiv y y-equiv)
           (equal (bitxor-ulong-ushort x y)
                  (bitxor-ulong-ushort x y-equiv)))
  :rule-classes :congruence)