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Representation-of-integer-operations

Bitxor-uint-schar

Bitwise exclusive disjunction of a value of type unsigned int and a value of type signed char [C:6.5.11].

Definitions and Theorems

Function: bitxor-uint-schar

(defun bitxor-uint-schar (x y)
  (declare (xargs :guard (and (uintp x) (scharp y))))
  (bitxor-uint-uint x (uint-from-schar y)))

Theorem: uintp-of-bitxor-uint-schar

(defthm uintp-of-bitxor-uint-schar
  (uintp (bitxor-uint-schar x y)))

Theorem: bitxor-uint-schar-of-uint-fix-x

(defthm bitxor-uint-schar-of-uint-fix-x
  (equal (bitxor-uint-schar (uint-fix x) y)
         (bitxor-uint-schar x y)))

Theorem: bitxor-uint-schar-uint-equiv-congruence-on-x

(defthm bitxor-uint-schar-uint-equiv-congruence-on-x
  (implies (uint-equiv x x-equiv)
           (equal (bitxor-uint-schar x y)
                  (bitxor-uint-schar x-equiv y)))
  :rule-classes :congruence)

Theorem: bitxor-uint-schar-of-schar-fix-y

(defthm bitxor-uint-schar-of-schar-fix-y
  (equal (bitxor-uint-schar x (schar-fix y))
         (bitxor-uint-schar x y)))

Theorem: bitxor-uint-schar-schar-equiv-congruence-on-y

(defthm bitxor-uint-schar-schar-equiv-congruence-on-y
  (implies (schar-equiv y y-equiv)
           (equal (bitxor-uint-schar x y)
                  (bitxor-uint-schar x y-equiv)))
  :rule-classes :congruence)