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Representation-of-integer-operations

Mul-slong-schar-okp

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

Definitions and Theorems

Function: mul-slong-schar-okp

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

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

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

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

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

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

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

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

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

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

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