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Representation-of-integer-operations

Eq-uchar-schar

Equality of a value of type unsigned char and a value of type signed char [C:6.5.9].

Definitions and Theorems

Function: eq-uchar-schar

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

Theorem: sintp-of-eq-uchar-schar

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

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

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

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

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

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

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

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

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