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Representation-of-integer-operations

Shr-ushort-okp

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

Definitions and Theorems

Function: shr-ushort-okp

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

Theorem: booleanp-of-shr-ushort-okp

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

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

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

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

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

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

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

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

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