		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Div-ulong-uint

Division of a value of type unsigned long and a value of type unsigned int [C:6.5.5].

Definitions and Theorems

Function: div-ulong-uint

(defun div-ulong-uint (x y)
  (declare (xargs :guard (and (ulongp x)
                              (uintp y)
                              (div-ulong-uint-okp x y))))
  (div-ulong-ulong x (ulong-from-uint y)))

Theorem: ulongp-of-div-ulong-uint

(defthm ulongp-of-div-ulong-uint
  (ulongp (div-ulong-uint x y)))

Theorem: div-ulong-uint-of-ulong-fix-x

(defthm div-ulong-uint-of-ulong-fix-x
  (equal (div-ulong-uint (ulong-fix x) y)
         (div-ulong-uint x y)))

Theorem: div-ulong-uint-ulong-equiv-congruence-on-x

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

Theorem: div-ulong-uint-of-uint-fix-y

(defthm div-ulong-uint-of-uint-fix-y
  (equal (div-ulong-uint x (uint-fix y))
         (div-ulong-uint x y)))

Theorem: div-ulong-uint-uint-equiv-congruence-on-y

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