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Representation-of-integer-operations

Lt-uchar-ullong

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

Definitions and Theorems

Function: lt-uchar-ullong

(defun lt-uchar-ullong (x y)
  (declare (xargs :guard (and (ucharp x) (ullongp y))))
  (lt-ullong-ullong (ullong-from-uchar x)
                    y))

Theorem: sintp-of-lt-uchar-ullong

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

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

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

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

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

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

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

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

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