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Representation-of-integer-operations

Lt-ullong-ushort

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

Definitions and Theorems

Function: lt-ullong-ushort

(defun lt-ullong-ushort (x y)
  (declare (xargs :guard (and (ullongp x) (ushortp y))))
  (lt-ullong-ullong x (ullong-from-ushort y)))

Theorem: sintp-of-lt-ullong-ushort

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

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

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

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

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

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

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

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

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