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Representation-of-integer-operations

Shr-ushort

Right shift of a value of type unsigned short by an integer [C:6.5.7].

Definitions and Theorems

Function: shr-ushort

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

Theorem: sintp-of-shr-ushort

(defthm sintp-of-shr-ushort
  (sintp (shr-ushort x y)))

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

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

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

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

Theorem: shr-ushort-of-ifix-y

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

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

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