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Representation-of-integer-operations

Rem-slong-ushort-okp

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

Definitions and Theorems

Function: rem-slong-ushort-okp

(defun rem-slong-ushort-okp (x y)
  (declare (xargs :guard (and (slongp x) (ushortp y))))
  (rem-slong-slong-okp x (slong-from-ushort y)))

Theorem: booleanp-of-rem-slong-ushort-okp

(defthm booleanp-of-rem-slong-ushort-okp
  (booleanp (rem-slong-ushort-okp x y)))

Theorem: rem-slong-ushort-okp-of-slong-fix-x

(defthm rem-slong-ushort-okp-of-slong-fix-x
  (equal (rem-slong-ushort-okp (slong-fix x) y)
         (rem-slong-ushort-okp x y)))

Theorem: rem-slong-ushort-okp-slong-equiv-congruence-on-x

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

Theorem: rem-slong-ushort-okp-of-ushort-fix-y

(defthm rem-slong-ushort-okp-of-ushort-fix-y
  (equal (rem-slong-ushort-okp x (ushort-fix y))
         (rem-slong-ushort-okp x y)))

Theorem: rem-slong-ushort-okp-ushort-equiv-congruence-on-y

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