		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Shr-slong-sshort

Right shift of a value of type signed long and a value of type signed short [C:6.5.7].

Definitions and Theorems

Function: shr-slong-sshort

(defun shr-slong-sshort (x y)
  (declare (xargs :guard (and (slongp x)
                              (sshortp y)
                              (shr-slong-sshort-okp x y))))
  (shr-slong x (integer-from-sshort y)))

Theorem: slongp-of-shr-slong-sshort

(defthm slongp-of-shr-slong-sshort
  (slongp (shr-slong-sshort x y)))

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

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

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

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

Theorem: shr-slong-sshort-of-sshort-fix-y

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

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

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