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Representation-of-integer-operations

Div-sllong-ulong-okp

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

Definitions and Theorems

Function: div-sllong-ulong-okp

(defun div-sllong-ulong-okp (x y)
  (declare (xargs :guard (and (sllongp x) (ulongp y))))
  (div-ullong-ullong-okp (ullong-from-sllong x)
                         (ullong-from-ulong y)))

Theorem: booleanp-of-div-sllong-ulong-okp

(defthm booleanp-of-div-sllong-ulong-okp
  (booleanp (div-sllong-ulong-okp x y)))

Theorem: div-sllong-ulong-okp-of-sllong-fix-x

(defthm div-sllong-ulong-okp-of-sllong-fix-x
  (equal (div-sllong-ulong-okp (sllong-fix x) y)
         (div-sllong-ulong-okp x y)))

Theorem: div-sllong-ulong-okp-sllong-equiv-congruence-on-x

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

Theorem: div-sllong-ulong-okp-of-ulong-fix-y

(defthm div-sllong-ulong-okp-of-ulong-fix-y
  (equal (div-sllong-ulong-okp x (ulong-fix y))
         (div-sllong-ulong-okp x y)))

Theorem: div-sllong-ulong-okp-ulong-equiv-congruence-on-y

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