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Representation-of-integer-operations

Ne-slong-slong

Non-equality of a value of type signed long and a value of type signed long [C:6.5.9].

Definitions and Theorems

Function: ne-slong-slong

(defun ne-slong-slong (x y)
  (declare (xargs :guard (and (slongp x) (slongp y))))
  (if (/= (integer-from-slong x)
          (integer-from-slong y))
      (sint-from-integer 1)
    (sint-from-integer 0)))

Theorem: sintp-of-ne-slong-slong

(defthm sintp-of-ne-slong-slong
  (sintp (ne-slong-slong x y)))

Theorem: ne-slong-slong-of-slong-fix-x

(defthm ne-slong-slong-of-slong-fix-x
  (equal (ne-slong-slong (slong-fix x) y)
         (ne-slong-slong x y)))

Theorem: ne-slong-slong-slong-equiv-congruence-on-x

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

Theorem: ne-slong-slong-of-slong-fix-y

(defthm ne-slong-slong-of-slong-fix-y
  (equal (ne-slong-slong x (slong-fix y))
         (ne-slong-slong x y)))

Theorem: ne-slong-slong-slong-equiv-congruence-on-y

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