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Representation-of-integer-operations

Bitand-sshort-sint

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

Definitions and Theorems

Function: bitand-sshort-sint

(defun bitand-sshort-sint (x y)
  (declare (xargs :guard (and (sshortp x) (sintp y))))
  (bitand-sint-sint (sint-from-sshort x)
                    y))

Theorem: sintp-of-bitand-sshort-sint

(defthm sintp-of-bitand-sshort-sint
  (sintp (bitand-sshort-sint x y)))

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

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

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

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

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

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

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

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