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Representation-of-integer-operations

Ge-sshort-ulong

Greater-than-or-equal-to relation of a value of type signed short and a value of type unsigned long [C:6.5.8].

Definitions and Theorems

Function: ge-sshort-ulong

(defun ge-sshort-ulong (x y)
  (declare (xargs :guard (and (sshortp x) (ulongp y))))
  (ge-ulong-ulong (ulong-from-sshort x)
                  y))

Theorem: sintp-of-ge-sshort-ulong

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

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

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

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

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

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

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

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

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