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Representation-of-integer-operations

Rem-ushort-slong

Remainder of a value of type unsigned short and a value of type signed long [C:6.5.5].

Definitions and Theorems

Function: rem-ushort-slong

(defun rem-ushort-slong (x y)
  (declare (xargs :guard (and (ushortp x)
                              (slongp y)
                              (rem-ushort-slong-okp x y))))
  (rem-slong-slong (slong-from-ushort x)
                   y))

Theorem: slongp-of-rem-ushort-slong

(defthm slongp-of-rem-ushort-slong
  (slongp (rem-ushort-slong x y)))

Theorem: rem-ushort-slong-of-ushort-fix-x

(defthm rem-ushort-slong-of-ushort-fix-x
  (equal (rem-ushort-slong (ushort-fix x) y)
         (rem-ushort-slong x y)))

Theorem: rem-ushort-slong-ushort-equiv-congruence-on-x

(defthm rem-ushort-slong-ushort-equiv-congruence-on-x
  (implies (ushort-equiv x x-equiv)
           (equal (rem-ushort-slong x y)
                  (rem-ushort-slong x-equiv y)))
  :rule-classes :congruence)

Theorem: rem-ushort-slong-of-slong-fix-y

(defthm rem-ushort-slong-of-slong-fix-y
  (equal (rem-ushort-slong x (slong-fix y))
         (rem-ushort-slong x y)))

Theorem: rem-ushort-slong-slong-equiv-congruence-on-y

(defthm rem-ushort-slong-slong-equiv-congruence-on-y
  (implies (slong-equiv y y-equiv)
           (equal (rem-ushort-slong x y)
                  (rem-ushort-slong x y-equiv)))
  :rule-classes :congruence)