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Representation-of-integer-operations

Le-sint-slong

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

Definitions and Theorems

Function: le-sint-slong

(defun le-sint-slong (x y)
  (declare (xargs :guard (and (sintp x) (slongp y))))
  (le-slong-slong (slong-from-sint x) y))

Theorem: sintp-of-le-sint-slong

(defthm sintp-of-le-sint-slong
  (sintp (le-sint-slong x y)))

Theorem: le-sint-slong-of-sint-fix-x

(defthm le-sint-slong-of-sint-fix-x
  (equal (le-sint-slong (sint-fix x) y)
         (le-sint-slong x y)))

Theorem: le-sint-slong-sint-equiv-congruence-on-x

(defthm le-sint-slong-sint-equiv-congruence-on-x
  (implies (sint-equiv x x-equiv)
           (equal (le-sint-slong x y)
                  (le-sint-slong x-equiv y)))
  :rule-classes :congruence)

Theorem: le-sint-slong-of-slong-fix-y

(defthm le-sint-slong-of-slong-fix-y
  (equal (le-sint-slong x (slong-fix y))
         (le-sint-slong x y)))

Theorem: le-sint-slong-slong-equiv-congruence-on-y

(defthm le-sint-slong-slong-equiv-congruence-on-y
  (implies (slong-equiv y y-equiv)
           (equal (le-sint-slong x y)
                  (le-sint-slong x y-equiv)))
  :rule-classes :congruence)