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• Feat

Feat-equiv

Basic equivalence relation for feat structures.

Definitions and Theorems

Function: feat-equiv$inline

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

Theorem: feat-equiv-is-an-equivalence

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

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

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

Theorem: feat-fix-under-feat-equiv

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

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

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

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

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

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

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

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

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