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Representation-of-integer-operations

Eq-ushort-ushort

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

Definitions and Theorems

Function: eq-ushort-ushort

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

Theorem: sintp-of-eq-ushort-ushort

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

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

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

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

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

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

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

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

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