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Representation-of-integer-operations

Mul-sllong-ullong

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

Definitions and Theorems

Function: mul-sllong-ullong

(defun mul-sllong-ullong (x y)
  (declare (xargs :guard (and (sllongp x) (ullongp y))))
  (mul-ullong-ullong (ullong-from-sllong x)
                     y))

Theorem: ullongp-of-mul-sllong-ullong

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

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

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

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

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

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

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

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

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