		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Ge-sshort-sint

Greater-than-or-equal-to relation of a value of type signed short and a value of type signed int [C17:6.5.8].

Definitions and Theorems

Function: ge-sshort-sint

(defun ge-sshort-sint (x y)
  (declare (xargs :guard (and (sshortp x) (sintp y))))
  (ge-sint-sint (sint-from-sshort x) y))

Theorem: sintp-of-ge-sshort-sint

(defthm sintp-of-ge-sshort-sint
  (sintp (ge-sshort-sint x y)))

Theorem: ge-sshort-sint-of-sshort-fix-x

(defthm ge-sshort-sint-of-sshort-fix-x
  (equal (ge-sshort-sint (sshort-fix x) y)
         (ge-sshort-sint x y)))

Theorem: ge-sshort-sint-sshort-equiv-congruence-on-x

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

Theorem: ge-sshort-sint-of-sint-fix-y

(defthm ge-sshort-sint-of-sint-fix-y
  (equal (ge-sshort-sint x (sint-fix y))
         (ge-sshort-sint x y)))

Theorem: ge-sshort-sint-sint-equiv-congruence-on-y

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