		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Shl-sshort-okp

Check if the left shift of a value of type signed short by an integer is well-defined.

Definitions and Theorems

Function: shl-sshort-okp

(defun shl-sshort-okp (x y)
  (declare (xargs :guard (and (sshortp x) (integerp y))))
  (shl-sint-okp (sint-from-sshort x)
                (ifix y)))

Theorem: booleanp-of-shl-sshort-okp

(defthm booleanp-of-shl-sshort-okp
  (booleanp (shl-sshort-okp x y)))

Theorem: shl-sshort-okp-of-sshort-fix-x

(defthm shl-sshort-okp-of-sshort-fix-x
  (equal (shl-sshort-okp (sshort-fix x) y)
         (shl-sshort-okp x y)))

Theorem: shl-sshort-okp-sshort-equiv-congruence-on-x

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

Theorem: shl-sshort-okp-of-ifix-y

(defthm shl-sshort-okp-of-ifix-y
  (equal (shl-sshort-okp x (ifix y))
         (shl-sshort-okp x y)))

Theorem: shl-sshort-okp-int-equiv-congruence-on-y

(defthm shl-sshort-okp-int-equiv-congruence-on-y
  (implies (acl2::int-equiv y y-equiv)
           (equal (shl-sshort-okp x y)
                  (shl-sshort-okp x y-equiv)))
  :rule-classes :congruence)