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Representation-of-integer-operations

Div-ushort-uint

Division of a value of type unsigned short and a value of type unsigned int [C17:6.5.5].

Definitions and Theorems

Function: div-ushort-uint

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

Theorem: uintp-of-div-ushort-uint

(defthm uintp-of-div-ushort-uint
  (uintp (div-ushort-uint x y)))

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

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

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

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

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

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

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

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