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Representation-of-integer-operations

Lt-ulong-ullong

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

Definitions and Theorems

Function: lt-ulong-ullong

(defun lt-ulong-ullong (x y)
  (declare (xargs :guard (and (ulongp x) (ullongp y))))
  (lt-ullong-ullong (ullong-from-ulong x)
                    y))

Theorem: sintp-of-lt-ulong-ullong

(defthm sintp-of-lt-ulong-ullong
  (sintp (lt-ulong-ullong x y)))

Theorem: lt-ulong-ullong-of-ulong-fix-x

(defthm lt-ulong-ullong-of-ulong-fix-x
  (equal (lt-ulong-ullong (ulong-fix x) y)
         (lt-ulong-ullong x y)))

Theorem: lt-ulong-ullong-ulong-equiv-congruence-on-x

(defthm lt-ulong-ullong-ulong-equiv-congruence-on-x
  (implies (ulong-equiv x x-equiv)
           (equal (lt-ulong-ullong x y)
                  (lt-ulong-ullong x-equiv y)))
  :rule-classes :congruence)

Theorem: lt-ulong-ullong-of-ullong-fix-y

(defthm lt-ulong-ullong-of-ullong-fix-y
  (equal (lt-ulong-ullong x (ullong-fix y))
         (lt-ulong-ullong x y)))

Theorem: lt-ulong-ullong-ullong-equiv-congruence-on-y

(defthm lt-ulong-ullong-ullong-equiv-congruence-on-y
  (implies (ullong-equiv y y-equiv)
           (equal (lt-ulong-ullong x y)
                  (lt-ulong-ullong x y-equiv)))
  :rule-classes :congruence)