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• Minor-stack

Minor-stack-equiv

Basic equivalence relation for minor-stack structures.

Definitions and Theorems

Function: minor-stack-equiv$inline

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

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

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

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

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

Theorem: minor-stack-fix-under-minor-stack-equiv

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

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

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

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

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

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

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

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

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