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Representation-of-integer-operations

Le-slong-schar

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

Definitions and Theorems

Function: le-slong-schar

(defun le-slong-schar (x y)
  (declare (xargs :guard (and (slongp x) (scharp y))))
  (le-slong-slong x (slong-from-schar y)))

Theorem: sintp-of-le-slong-schar

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

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

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

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

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

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

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

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

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