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Representation-of-integer-operations

Mul-sshort-uint

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

Definitions and Theorems

Function: mul-sshort-uint

(defun mul-sshort-uint (x y)
  (declare (xargs :guard (and (sshortp x) (uintp y))))
  (mul-uint-uint (uint-from-sshort x) y))

Theorem: uintp-of-mul-sshort-uint

(defthm uintp-of-mul-sshort-uint
  (uintp (mul-sshort-uint x y)))

Theorem: mul-sshort-uint-of-sshort-fix-x

(defthm mul-sshort-uint-of-sshort-fix-x
  (equal (mul-sshort-uint (sshort-fix x) y)
         (mul-sshort-uint x y)))

Theorem: mul-sshort-uint-sshort-equiv-congruence-on-x

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

Theorem: mul-sshort-uint-of-uint-fix-y

(defthm mul-sshort-uint-of-uint-fix-y
  (equal (mul-sshort-uint x (uint-fix y))
         (mul-sshort-uint x y)))

Theorem: mul-sshort-uint-uint-equiv-congruence-on-y

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