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Representation-of-integer-operations

Shr-sshort

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

Definitions and Theorems

Function: shr-sshort

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

Theorem: sintp-of-shr-sshort

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

Theorem: shr-sshort-of-sshort-fix-x

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

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

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

Theorem: shr-sshort-of-ifix-y

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

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

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