		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Bitand-ulong-sshort

Bitwise conjunction of a value of type unsigned long and a value of type signed short [C17:6.5.10].

Definitions and Theorems

Function: bitand-ulong-sshort

(defun bitand-ulong-sshort (x y)
  (declare (xargs :guard (and (ulongp x) (sshortp y))))
  (bitand-ulong-ulong x (ulong-from-sshort y)))

Theorem: ulongp-of-bitand-ulong-sshort

(defthm ulongp-of-bitand-ulong-sshort
  (ulongp (bitand-ulong-sshort x y)))

Theorem: bitand-ulong-sshort-of-ulong-fix-x

(defthm bitand-ulong-sshort-of-ulong-fix-x
  (equal (bitand-ulong-sshort (ulong-fix x) y)
         (bitand-ulong-sshort x y)))

Theorem: bitand-ulong-sshort-ulong-equiv-congruence-on-x

(defthm bitand-ulong-sshort-ulong-equiv-congruence-on-x
  (implies (ulong-equiv x x-equiv)
           (equal (bitand-ulong-sshort x y)
                  (bitand-ulong-sshort x-equiv y)))
  :rule-classes :congruence)

Theorem: bitand-ulong-sshort-of-sshort-fix-y

(defthm bitand-ulong-sshort-of-sshort-fix-y
  (equal (bitand-ulong-sshort x (sshort-fix y))
         (bitand-ulong-sshort x y)))

Theorem: bitand-ulong-sshort-sshort-equiv-congruence-on-y

(defthm bitand-ulong-sshort-sshort-equiv-congruence-on-y
  (implies (sshort-equiv y y-equiv)
           (equal (bitand-ulong-sshort x y)
                  (bitand-ulong-sshort x y-equiv)))
  :rule-classes :congruence)