		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Div-ullong-schar

Division of a value of type unsigned long long and a value of type signed char [C17:6.5.5].

Definitions and Theorems

Function: div-ullong-schar

(defun div-ullong-schar (x y)
  (declare (xargs :guard (and (ullongp x)
                              (scharp y)
                              (div-ullong-schar-okp x y))))
  (div-ullong-ullong x (ullong-from-schar y)))

Theorem: ullongp-of-div-ullong-schar

(defthm ullongp-of-div-ullong-schar
  (ullongp (div-ullong-schar x y)))

Theorem: div-ullong-schar-of-ullong-fix-x

(defthm div-ullong-schar-of-ullong-fix-x
  (equal (div-ullong-schar (ullong-fix x) y)
         (div-ullong-schar x y)))

Theorem: div-ullong-schar-ullong-equiv-congruence-on-x

(defthm div-ullong-schar-ullong-equiv-congruence-on-x
  (implies (ullong-equiv x x-equiv)
           (equal (div-ullong-schar x y)
                  (div-ullong-schar x-equiv y)))
  :rule-classes :congruence)

Theorem: div-ullong-schar-of-schar-fix-y

(defthm div-ullong-schar-of-schar-fix-y
  (equal (div-ullong-schar x (schar-fix y))
         (div-ullong-schar x y)))

Theorem: div-ullong-schar-schar-equiv-congruence-on-y

(defthm div-ullong-schar-schar-equiv-congruence-on-y
  (implies (schar-equiv y y-equiv)
           (equal (div-ullong-schar x y)
                  (div-ullong-schar x y-equiv)))
  :rule-classes :congruence)