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Representation-of-integer-operations

Div-uchar-sllong-okp

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

Definitions and Theorems

Function: div-uchar-sllong-okp

(defun div-uchar-sllong-okp (x y)
  (declare (xargs :guard (and (ucharp x) (sllongp y))))
  (div-sllong-sllong-okp (sllong-from-uchar x)
                         y))

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

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

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

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

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

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

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

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

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

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