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Representation-of-integer-operations

Eq-ushort-sllong

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

Definitions and Theorems

Function: eq-ushort-sllong

(defun eq-ushort-sllong (x y)
  (declare (xargs :guard (and (ushortp x) (sllongp y))))
  (eq-sllong-sllong (sllong-from-ushort x)
                    y))

Theorem: sintp-of-eq-ushort-sllong

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

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

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

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

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

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

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

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

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