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Representation-of-integer-operations

Rem-uint-uint

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

Definitions and Theorems

Function: rem-uint-uint

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

Theorem: uintp-of-rem-uint-uint

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

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

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

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

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

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

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

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

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