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Representation-of-integer-operations

Rem-uint-ushort

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

Definitions and Theorems

Function: rem-uint-ushort

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

Theorem: uintp-of-rem-uint-ushort

(defthm uintp-of-rem-uint-ushort
  (uintp (rem-uint-ushort x y)))

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

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

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

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

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

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

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

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