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• Matchstatelist

Matchstatelist-equiv

Basic equivalence relation for matchstatelist structures.

Definitions and Theorems

Function: matchstatelist-equiv$inline

(defun matchstatelist-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (matchstatelist-p acl2::x)
                              (matchstatelist-p acl2::y))))
  (equal (matchstatelist-fix acl2::x)
         (matchstatelist-fix acl2::y)))

Theorem: matchstatelist-equiv-is-an-equivalence

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

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

(defthm matchstatelist-equiv-implies-equal-matchstatelist-fix-1
  (implies (matchstatelist-equiv acl2::x x-equiv)
           (equal (matchstatelist-fix acl2::x)
                  (matchstatelist-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: matchstatelist-fix-under-matchstatelist-equiv

(defthm matchstatelist-fix-under-matchstatelist-equiv
  (matchstatelist-equiv (matchstatelist-fix acl2::x)
                        acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

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

(defthm
      equal-of-matchstatelist-fix-1-forward-to-matchstatelist-equiv
  (implies (equal (matchstatelist-fix acl2::x)
                  acl2::y)
           (matchstatelist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm
      equal-of-matchstatelist-fix-2-forward-to-matchstatelist-equiv
  (implies (equal acl2::x (matchstatelist-fix acl2::y))
           (matchstatelist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm matchstatelist-equiv-of-matchstatelist-fix-1-forward
  (implies (matchstatelist-equiv (matchstatelist-fix acl2::x)
                                 acl2::y)
           (matchstatelist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

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

(defthm matchstatelist-equiv-of-matchstatelist-fix-2-forward
  (implies
       (matchstatelist-equiv acl2::x (matchstatelist-fix acl2::y))
       (matchstatelist-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)