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Representation-of-integer-operations

Add-uchar-ullong

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

Definitions and Theorems

Function: add-uchar-ullong

(defun add-uchar-ullong (x y)
  (declare (xargs :guard (and (ucharp x) (ullongp y))))
  (add-ullong-ullong (ullong-from-uchar x)
                     y))

Theorem: ullongp-of-add-uchar-ullong

(defthm ullongp-of-add-uchar-ullong
  (ullongp (add-uchar-ullong x y)))

Theorem: add-uchar-ullong-of-uchar-fix-x

(defthm add-uchar-ullong-of-uchar-fix-x
  (equal (add-uchar-ullong (uchar-fix x) y)
         (add-uchar-ullong x y)))

Theorem: add-uchar-ullong-uchar-equiv-congruence-on-x

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

Theorem: add-uchar-ullong-of-ullong-fix-y

(defthm add-uchar-ullong-of-ullong-fix-y
  (equal (add-uchar-ullong x (ullong-fix y))
         (add-uchar-ullong x y)))

Theorem: add-uchar-ullong-ullong-equiv-congruence-on-y

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