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• Matchresult

Matchresult-equiv

Basic equivalence relation for matchresult structures.

Definitions and Theorems

Function: matchresult-equiv$inline

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

Theorem: matchresult-equiv-is-an-equivalence

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

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

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

Theorem: matchresult-fix-under-matchresult-equiv

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

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

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

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

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

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

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

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

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