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Representation-of-integer-operations

Bitand-uint-sshort

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

Definitions and Theorems

Function: bitand-uint-sshort

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

Theorem: uintp-of-bitand-uint-sshort

(defthm uintp-of-bitand-uint-sshort
  (uintp (bitand-uint-sshort x y)))

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

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

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

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

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

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

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

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