		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Gt-sllong-sshort

Greater-than relation of a value of type signed long long and a value of type signed short [C17:6.5.8].

Definitions and Theorems

Function: gt-sllong-sshort

(defun gt-sllong-sshort (x y)
  (declare (xargs :guard (and (sllongp x) (sshortp y))))
  (gt-sllong-sllong x (sllong-from-sshort y)))

Theorem: sintp-of-gt-sllong-sshort

(defthm sintp-of-gt-sllong-sshort
  (sintp (gt-sllong-sshort x y)))

Theorem: gt-sllong-sshort-of-sllong-fix-x

(defthm gt-sllong-sshort-of-sllong-fix-x
  (equal (gt-sllong-sshort (sllong-fix x) y)
         (gt-sllong-sshort x y)))

Theorem: gt-sllong-sshort-sllong-equiv-congruence-on-x

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

Theorem: gt-sllong-sshort-of-sshort-fix-y

(defthm gt-sllong-sshort-of-sshort-fix-y
  (equal (gt-sllong-sshort x (sshort-fix y))
         (gt-sllong-sshort x y)))

Theorem: gt-sllong-sshort-sshort-equiv-congruence-on-y

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