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Representation-of-integer-operations

Bitand-sshort-sshort

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

Definitions and Theorems

Function: bitand-sshort-sshort

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

Theorem: sintp-of-bitand-sshort-sshort

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

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

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

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

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

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

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

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

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