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Representation-of-integer-operations

Mul-sllong-slong

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

Definitions and Theorems

Function: mul-sllong-slong

(defun mul-sllong-slong (x y)
  (declare (xargs :guard (and (sllongp x)
                              (slongp y)
                              (mul-sllong-slong-okp x y))))
  (mul-sllong-sllong x (sllong-from-slong y)))

Theorem: sllongp-of-mul-sllong-slong

(defthm sllongp-of-mul-sllong-slong
  (sllongp (mul-sllong-slong x y)))

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

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

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

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

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

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

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

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