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Representation-of-integer-operations

Eq-sint-sint

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

Definitions and Theorems

Function: eq-sint-sint

(defun eq-sint-sint (x y)
  (declare (xargs :guard (and (sintp x) (sintp y))))
  (if (= (integer-from-sint x)
         (integer-from-sint y))
      (sint-from-integer 1)
    (sint-from-integer 0)))

Theorem: sintp-of-eq-sint-sint

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

Theorem: eq-sint-sint-of-sint-fix-x

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

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

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

Theorem: eq-sint-sint-of-sint-fix-y

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

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

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