		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Mul-schar-sshort

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

Definitions and Theorems

Function: mul-schar-sshort

(defun mul-schar-sshort (x y)
  (declare (xargs :guard (and (scharp x)
                              (sshortp y)
                              (mul-schar-sshort-okp x y))))
  (mul-sint-sint (sint-from-schar x)
                 (sint-from-sshort y)))

Theorem: sintp-of-mul-schar-sshort

(defthm sintp-of-mul-schar-sshort
  (sintp (mul-schar-sshort x y)))

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

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

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

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

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

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

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

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