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Representation-of-integer-operations

Bitand-sshort-sllong

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

Definitions and Theorems

Function: bitand-sshort-sllong

(defun bitand-sshort-sllong (x y)
  (declare (xargs :guard (and (sshortp x) (sllongp y))))
  (bitand-sllong-sllong (sllong-from-sshort x)
                        y))

Theorem: sllongp-of-bitand-sshort-sllong

(defthm sllongp-of-bitand-sshort-sllong
  (sllongp (bitand-sshort-sllong x y)))

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

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

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

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

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

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

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

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