		Search-engine friendly clone of the ACL2 documentation.

Transunit-ensemble

Transunit-ensemble-equiv

Basic equivalence relation for transunit-ensemble structures.

Definitions and Theorems

Function: transunit-ensemble-equiv$inline

(defun transunit-ensemble-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (transunit-ensemblep acl2::x)
                              (transunit-ensemblep acl2::y))))
  (equal (transunit-ensemble-fix acl2::x)
         (transunit-ensemble-fix acl2::y)))

Theorem: transunit-ensemble-equiv-is-an-equivalence

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

Theorem: transunit-ensemble-equiv-implies-equal-transunit-ensemble-fix-1

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

Theorem: transunit-ensemble-fix-under-transunit-ensemble-equiv

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

Theorem: equal-of-transunit-ensemble-fix-1-forward-to-transunit-ensemble-equiv

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

Theorem: equal-of-transunit-ensemble-fix-2-forward-to-transunit-ensemble-equiv

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

Theorem: transunit-ensemble-equiv-of-transunit-ensemble-fix-1-forward

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

Theorem: transunit-ensemble-equiv-of-transunit-ensemble-fix-2-forward

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