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Representation-of-integer-operations

Le-schar-ulong

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

Definitions and Theorems

Function: le-schar-ulong

(defun le-schar-ulong (x y)
  (declare (xargs :guard (and (scharp x) (ulongp y))))
  (le-ulong-ulong (ulong-from-schar x) y))

Theorem: sintp-of-le-schar-ulong

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

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

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

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

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

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

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

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

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