		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Eq-sshort-slong

Equality of a value of type signed short and a value of type signed long [C17:6.5.9].

Definitions and Theorems

Function: eq-sshort-slong

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

Theorem: sintp-of-eq-sshort-slong

(defthm sintp-of-eq-sshort-slong
  (sintp (eq-sshort-slong x y)))

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

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

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

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

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

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

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

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