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Representation-of-integer-operations

Eq-uchar-sllong

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

Definitions and Theorems

Function: eq-uchar-sllong

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

Theorem: sintp-of-eq-uchar-sllong

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

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

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

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

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

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

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

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

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