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Representation-of-integer-operations

Mul-schar-ullong

Multiplication of a value of type signed char and a value of type unsigned long long [C:6.5.5].

Definitions and Theorems

Function: mul-schar-ullong

(defun mul-schar-ullong (x y)
  (declare (xargs :guard (and (scharp x) (ullongp y))))
  (mul-ullong-ullong (ullong-from-schar x)
                     y))

Theorem: ullongp-of-mul-schar-ullong

(defthm ullongp-of-mul-schar-ullong
  (ullongp (mul-schar-ullong x y)))

Theorem: mul-schar-ullong-of-schar-fix-x

(defthm mul-schar-ullong-of-schar-fix-x
  (equal (mul-schar-ullong (schar-fix x) y)
         (mul-schar-ullong x y)))

Theorem: mul-schar-ullong-schar-equiv-congruence-on-x

(defthm mul-schar-ullong-schar-equiv-congruence-on-x
  (implies (schar-equiv x x-equiv)
           (equal (mul-schar-ullong x y)
                  (mul-schar-ullong x-equiv y)))
  :rule-classes :congruence)

Theorem: mul-schar-ullong-of-ullong-fix-y

(defthm mul-schar-ullong-of-ullong-fix-y
  (equal (mul-schar-ullong x (ullong-fix y))
         (mul-schar-ullong x y)))

Theorem: mul-schar-ullong-ullong-equiv-congruence-on-y

(defthm mul-schar-ullong-ullong-equiv-congruence-on-y
  (implies (ullong-equiv y y-equiv)
           (equal (mul-schar-ullong x y)
                  (mul-schar-ullong x y-equiv)))
  :rule-classes :congruence)