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Representation-of-integer-operations

Lt-uint-sint

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

Definitions and Theorems

Function: lt-uint-sint

(defun lt-uint-sint (x y)
  (declare (xargs :guard (and (uintp x) (sintp y))))
  (lt-uint-uint x (uint-from-sint y)))

Theorem: sintp-of-lt-uint-sint

(defthm sintp-of-lt-uint-sint
  (sintp (lt-uint-sint x y)))

Theorem: lt-uint-sint-of-uint-fix-x

(defthm lt-uint-sint-of-uint-fix-x
  (equal (lt-uint-sint (uint-fix x) y)
         (lt-uint-sint x y)))

Theorem: lt-uint-sint-uint-equiv-congruence-on-x

(defthm lt-uint-sint-uint-equiv-congruence-on-x
  (implies (uint-equiv x x-equiv)
           (equal (lt-uint-sint x y)
                  (lt-uint-sint x-equiv y)))
  :rule-classes :congruence)

Theorem: lt-uint-sint-of-sint-fix-y

(defthm lt-uint-sint-of-sint-fix-y
  (equal (lt-uint-sint x (sint-fix y))
         (lt-uint-sint x y)))

Theorem: lt-uint-sint-sint-equiv-congruence-on-y

(defthm lt-uint-sint-sint-equiv-congruence-on-y
  (implies (sint-equiv y y-equiv)
           (equal (lt-uint-sint x y)
                  (lt-uint-sint x y-equiv)))
  :rule-classes :congruence)