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• Major-stack

Major-stack-equiv

Basic equivalence relation for major-stack structures.

Definitions and Theorems

Function: major-stack-equiv$inline

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

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

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

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

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

Theorem: major-stack-fix-under-major-stack-equiv

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

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

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

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

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

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

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

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

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