		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Shr-slong-okp

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

Definitions and Theorems

Function: shr-slong-okp

(defun shr-slong-okp (x y)
  (declare (xargs :guard (and (slongp x) (integerp y))))
  (and (integer-range-p 0 (long-bits) (ifix y))
       (>= (integer-from-slong x) 0)))

Theorem: booleanp-of-shr-slong-okp

(defthm booleanp-of-shr-slong-okp
  (booleanp (shr-slong-okp x y)))

Theorem: shr-slong-okp-of-slong-fix-x

(defthm shr-slong-okp-of-slong-fix-x
  (equal (shr-slong-okp (slong-fix x) y)
         (shr-slong-okp x y)))

Theorem: shr-slong-okp-slong-equiv-congruence-on-x

(defthm shr-slong-okp-slong-equiv-congruence-on-x
  (implies (slong-equiv x x-equiv)
           (equal (shr-slong-okp x y)
                  (shr-slong-okp x-equiv y)))
  :rule-classes :congruence)

Theorem: shr-slong-okp-of-ifix-y

(defthm shr-slong-okp-of-ifix-y
  (equal (shr-slong-okp x (ifix y))
         (shr-slong-okp x y)))

Theorem: shr-slong-okp-int-equiv-congruence-on-y

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