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• Printconfig

Printconfig-equiv

Basic equivalence relation for printconfig structures.

Definitions and Theorems

Function: printconfig-equiv$inline

(defun printconfig-equiv$inline (x y)
  (declare (xargs :guard (and (printconfig-p x)
                              (printconfig-p y))))
  (equal (printconfig-fix x)
         (printconfig-fix y)))

Theorem: printconfig-equiv-is-an-equivalence

(defthm printconfig-equiv-is-an-equivalence
  (and (booleanp (printconfig-equiv x y))
       (printconfig-equiv x x)
       (implies (printconfig-equiv x y)
                (printconfig-equiv y x))
       (implies (and (printconfig-equiv x y)
                     (printconfig-equiv y z))
                (printconfig-equiv x z)))
  :rule-classes (:equivalence))

Theorem: printconfig-equiv-implies-equal-printconfig-fix-1

(defthm printconfig-equiv-implies-equal-printconfig-fix-1
  (implies (printconfig-equiv x x-equiv)
           (equal (printconfig-fix x)
                  (printconfig-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: printconfig-fix-under-printconfig-equiv

(defthm printconfig-fix-under-printconfig-equiv
  (printconfig-equiv (printconfig-fix x)
                     x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-printconfig-fix-1-forward-to-printconfig-equiv

(defthm equal-of-printconfig-fix-1-forward-to-printconfig-equiv
  (implies (equal (printconfig-fix x) y)
           (printconfig-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-printconfig-fix-2-forward-to-printconfig-equiv

(defthm equal-of-printconfig-fix-2-forward-to-printconfig-equiv
  (implies (equal x (printconfig-fix y))
           (printconfig-equiv x y))
  :rule-classes :forward-chaining)

Theorem: printconfig-equiv-of-printconfig-fix-1-forward

(defthm printconfig-equiv-of-printconfig-fix-1-forward
  (implies (printconfig-equiv (printconfig-fix x)
                              y)
           (printconfig-equiv x y))
  :rule-classes :forward-chaining)

Theorem: printconfig-equiv-of-printconfig-fix-2-forward

(defthm printconfig-equiv-of-printconfig-fix-2-forward
  (implies (printconfig-equiv x (printconfig-fix y))
           (printconfig-equiv x y))
  :rule-classes :forward-chaining)