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Representation-of-integer-operations

Mul-sllong-slong-okp

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

Definitions and Theorems

Function: mul-sllong-slong-okp

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

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

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

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

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

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

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

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

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

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

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