		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Div-sshort-ushort-okp

Check if the division of a value of type signed short and a value of type unsigned short is well-defined.

Definitions and Theorems

Function: div-sshort-ushort-okp

(defun div-sshort-ushort-okp (x y)
  (declare (xargs :guard (and (sshortp x) (ushortp y))))
  (div-sint-sint-okp (sint-from-sshort x)
                     (sint-from-ushort y)))

Theorem: booleanp-of-div-sshort-ushort-okp

(defthm booleanp-of-div-sshort-ushort-okp
  (booleanp (div-sshort-ushort-okp x y)))

Theorem: div-sshort-ushort-okp-of-sshort-fix-x

(defthm div-sshort-ushort-okp-of-sshort-fix-x
  (equal (div-sshort-ushort-okp (sshort-fix x) y)
         (div-sshort-ushort-okp x y)))

Theorem: div-sshort-ushort-okp-sshort-equiv-congruence-on-x

(defthm div-sshort-ushort-okp-sshort-equiv-congruence-on-x
  (implies (sshort-equiv x x-equiv)
           (equal (div-sshort-ushort-okp x y)
                  (div-sshort-ushort-okp x-equiv y)))
  :rule-classes :congruence)

Theorem: div-sshort-ushort-okp-of-ushort-fix-y

(defthm div-sshort-ushort-okp-of-ushort-fix-y
  (equal (div-sshort-ushort-okp x (ushort-fix y))
         (div-sshort-ushort-okp x y)))

Theorem: div-sshort-ushort-okp-ushort-equiv-congruence-on-y

(defthm div-sshort-ushort-okp-ushort-equiv-congruence-on-y
  (implies (ushort-equiv y y-equiv)
           (equal (div-sshort-ushort-okp x y)
                  (div-sshort-ushort-okp x y-equiv)))
  :rule-classes :congruence)