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Representation-of-integer-operations

Add-schar-slong-okp

Check if the addition of a value of type signed char and a value of type signed long is well-defined.

Definitions and Theorems

Function: add-schar-slong-okp

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

Theorem: booleanp-of-add-schar-slong-okp

(defthm booleanp-of-add-schar-slong-okp
  (booleanp (add-schar-slong-okp x y)))

Theorem: add-schar-slong-okp-of-schar-fix-x

(defthm add-schar-slong-okp-of-schar-fix-x
  (equal (add-schar-slong-okp (schar-fix x) y)
         (add-schar-slong-okp x y)))

Theorem: add-schar-slong-okp-schar-equiv-congruence-on-x

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

Theorem: add-schar-slong-okp-of-slong-fix-y

(defthm add-schar-slong-okp-of-slong-fix-y
  (equal (add-schar-slong-okp x (slong-fix y))
         (add-schar-slong-okp x y)))

Theorem: add-schar-slong-okp-slong-equiv-congruence-on-y

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