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Representation-of-integer-operations

Add-uint-uint

Addition of a value of type unsigned int and a value of type unsigned int [C:6.5.6].

Definitions and Theorems

Function: add-uint-uint

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

Theorem: uintp-of-add-uint-uint

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

Theorem: add-uint-uint-of-uint-fix-x

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

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

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

Theorem: add-uint-uint-of-uint-fix-y

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

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

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