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Representation-of-integer-operations

Le-uchar-uint

Less-than-or-equal-to relation of a value of type unsigned char and a value of type unsigned int [C:6.5.8].

Definitions and Theorems

Function: le-uchar-uint

(defun le-uchar-uint (x y)
  (declare (xargs :guard (and (ucharp x) (uintp y))))
  (le-uint-uint (uint-from-uchar x) y))

Theorem: sintp-of-le-uchar-uint

(defthm sintp-of-le-uchar-uint
  (sintp (le-uchar-uint x y)))

Theorem: le-uchar-uint-of-uchar-fix-x

(defthm le-uchar-uint-of-uchar-fix-x
  (equal (le-uchar-uint (uchar-fix x) y)
         (le-uchar-uint x y)))

Theorem: le-uchar-uint-uchar-equiv-congruence-on-x

(defthm le-uchar-uint-uchar-equiv-congruence-on-x
  (implies (uchar-equiv x x-equiv)
           (equal (le-uchar-uint x y)
                  (le-uchar-uint x-equiv y)))
  :rule-classes :congruence)

Theorem: le-uchar-uint-of-uint-fix-y

(defthm le-uchar-uint-of-uint-fix-y
  (equal (le-uchar-uint x (uint-fix y))
         (le-uchar-uint x y)))

Theorem: le-uchar-uint-uint-equiv-congruence-on-y

(defthm le-uchar-uint-uint-equiv-congruence-on-y
  (implies (uint-equiv y y-equiv)
           (equal (le-uchar-uint x y)
                  (le-uchar-uint x y-equiv)))
  :rule-classes :congruence)