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Representation-of-integer-operations

Ge-ulong-ushort

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

Definitions and Theorems

Function: ge-ulong-ushort

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

Theorem: sintp-of-ge-ulong-ushort

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

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

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

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

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

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

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

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

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