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Representation-of-integer-operations

Lt-sint-schar

Less-than relation of a value of type signed int and a value of type signed char [C17:6.5.8].

Definitions and Theorems

Function: lt-sint-schar

(defun lt-sint-schar (x y)
  (declare (xargs :guard (and (sintp x) (scharp y))))
  (lt-sint-sint x (sint-from-schar y)))

Theorem: sintp-of-lt-sint-schar

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

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

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

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

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

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

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

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

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