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• Matchmode

Matchmode-equiv

Basic equivalence relation for matchmode structures.

Definitions and Theorems

Function: matchmode-equiv$inline

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

Theorem: matchmode-equiv-is-an-equivalence

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

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

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

Theorem: matchmode-fix-under-matchmode-equiv

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

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

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

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

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

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

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

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

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