		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Bitior-uint-sint

Bitwise inclusive disjunction of a value of type unsigned int and a value of type signed int [C17:6.5.12].

Definitions and Theorems

Function: bitior-uint-sint

(defun bitior-uint-sint (x y)
  (declare (xargs :guard (and (uintp x) (sintp y))))
  (bitior-uint-uint x (uint-from-sint y)))

Theorem: uintp-of-bitior-uint-sint

(defthm uintp-of-bitior-uint-sint
  (uintp (bitior-uint-sint x y)))

Theorem: bitior-uint-sint-of-uint-fix-x

(defthm bitior-uint-sint-of-uint-fix-x
  (equal (bitior-uint-sint (uint-fix x) y)
         (bitior-uint-sint x y)))

Theorem: bitior-uint-sint-uint-equiv-congruence-on-x

(defthm bitior-uint-sint-uint-equiv-congruence-on-x
  (implies (uint-equiv x x-equiv)
           (equal (bitior-uint-sint x y)
                  (bitior-uint-sint x-equiv y)))
  :rule-classes :congruence)

Theorem: bitior-uint-sint-of-sint-fix-y

(defthm bitior-uint-sint-of-sint-fix-y
  (equal (bitior-uint-sint x (sint-fix y))
         (bitior-uint-sint x y)))

Theorem: bitior-uint-sint-sint-equiv-congruence-on-y

(defthm bitior-uint-sint-sint-equiv-congruence-on-y
  (implies (sint-equiv y y-equiv)
           (equal (bitior-uint-sint x y)
                  (bitior-uint-sint x y-equiv)))
  :rule-classes :congruence)