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Representation-of-integer-operations

Le-ulong-uchar

Less-than-or-equal-to relation of a value of type unsigned long and a value of type unsigned char [C17:6.5.8].

Definitions and Theorems

Function: le-ulong-uchar

(defun le-ulong-uchar (x y)
  (declare (xargs :guard (and (ulongp x) (ucharp y))))
  (le-ulong-ulong x (ulong-from-uchar y)))

Theorem: sintp-of-le-ulong-uchar

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

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

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

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

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

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

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

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

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