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• Minor-frame

Minor-frame-equiv

Basic equivalence relation for minor-frame structures.

Definitions and Theorems

Function: minor-frame-equiv$inline

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

Theorem: minor-frame-equiv-is-an-equivalence

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

Theorem: minor-frame-equiv-implies-equal-minor-frame-fix-1

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

Theorem: minor-frame-fix-under-minor-frame-equiv

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

Theorem: equal-of-minor-frame-fix-1-forward-to-minor-frame-equiv

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

Theorem: equal-of-minor-frame-fix-2-forward-to-minor-frame-equiv

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

Theorem: minor-frame-equiv-of-minor-frame-fix-1-forward

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

Theorem: minor-frame-equiv-of-minor-frame-fix-2-forward

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