		Search-engine friendly clone of the ACL2 documentation.

Representation-of-integer-operations

Div-schar-uchar

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

Definitions and Theorems

Function: div-schar-uchar

(defun div-schar-uchar (x y)
  (declare (xargs :guard (and (scharp x)
                              (ucharp y)
                              (div-schar-uchar-okp x y))))
  (div-sint-sint (sint-from-schar x)
                 (sint-from-uchar y)))

Theorem: sintp-of-div-schar-uchar

(defthm sintp-of-div-schar-uchar
  (sintp (div-schar-uchar x y)))

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

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

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

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

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

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

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

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