		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Shr-schar-okp

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

Definitions and Theorems

Function: shr-schar-okp

(defun shr-schar-okp (x y)
  (declare (xargs :guard (and (scharp x) (integerp y))))
  (shr-sint-okp (sint-from-schar x)
                (ifix y)))

Theorem: booleanp-of-shr-schar-okp

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

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

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

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

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

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

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

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

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