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Representation-of-integer-operations

Rem-ullong-sllong-okp

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

Definitions and Theorems

Function: rem-ullong-sllong-okp

(defun rem-ullong-sllong-okp (x y)
  (declare (xargs :guard (and (ullongp x) (sllongp y))))
  (rem-ullong-ullong-okp x (ullong-from-sllong y)))

Theorem: booleanp-of-rem-ullong-sllong-okp

(defthm booleanp-of-rem-ullong-sllong-okp
  (booleanp (rem-ullong-sllong-okp x y)))

Theorem: rem-ullong-sllong-okp-of-ullong-fix-x

(defthm rem-ullong-sllong-okp-of-ullong-fix-x
  (equal (rem-ullong-sllong-okp (ullong-fix x) y)
         (rem-ullong-sllong-okp x y)))

Theorem: rem-ullong-sllong-okp-ullong-equiv-congruence-on-x

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

Theorem: rem-ullong-sllong-okp-of-sllong-fix-y

(defthm rem-ullong-sllong-okp-of-sllong-fix-y
  (equal (rem-ullong-sllong-okp x (sllong-fix y))
         (rem-ullong-sllong-okp x y)))

Theorem: rem-ullong-sllong-okp-sllong-equiv-congruence-on-y

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