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Representation-of-integer-operations

Bitior-sint-ushort

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

Definitions and Theorems

Function: bitior-sint-ushort

(defun bitior-sint-ushort (x y)
  (declare (xargs :guard (and (sintp x) (ushortp y))))
  (bitior-sint-sint x (sint-from-ushort y)))

Theorem: sintp-of-bitior-sint-ushort

(defthm sintp-of-bitior-sint-ushort
  (sintp (bitior-sint-ushort x y)))

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

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

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

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

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

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

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

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