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Representation-of-integer-operations

Gt-ushort-ulong

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

Definitions and Theorems

Function: gt-ushort-ulong

(defun gt-ushort-ulong (x y)
  (declare (xargs :guard (and (ushortp x) (ulongp y))))
  (gt-ulong-ulong (ulong-from-ushort x)
                  y))

Theorem: sintp-of-gt-ushort-ulong

(defthm sintp-of-gt-ushort-ulong
  (sintp (gt-ushort-ulong x y)))

Theorem: gt-ushort-ulong-of-ushort-fix-x

(defthm gt-ushort-ulong-of-ushort-fix-x
  (equal (gt-ushort-ulong (ushort-fix x) y)
         (gt-ushort-ulong x y)))

Theorem: gt-ushort-ulong-ushort-equiv-congruence-on-x

(defthm gt-ushort-ulong-ushort-equiv-congruence-on-x
  (implies (ushort-equiv x x-equiv)
           (equal (gt-ushort-ulong x y)
                  (gt-ushort-ulong x-equiv y)))
  :rule-classes :congruence)

Theorem: gt-ushort-ulong-of-ulong-fix-y

(defthm gt-ushort-ulong-of-ulong-fix-y
  (equal (gt-ushort-ulong x (ulong-fix y))
         (gt-ushort-ulong x y)))

Theorem: gt-ushort-ulong-ulong-equiv-congruence-on-y

(defthm gt-ushort-ulong-ulong-equiv-congruence-on-y
  (implies (ulong-equiv y y-equiv)
           (equal (gt-ushort-ulong x y)
                  (gt-ushort-ulong x y-equiv)))
  :rule-classes :congruence)