		Search-engine friendly clone of the ACL2 documentation.

Transform-argument

Transform-argument-equiv

Basic equivalence relation for transform-argument structures.

Definitions and Theorems

Function: transform-argument-equiv$inline

(defun transform-argument-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (transform-argumentp acl2::x)
                              (transform-argumentp acl2::y))))
  (equal (transform-argument-fix acl2::x)
         (transform-argument-fix acl2::y)))

Theorem: transform-argument-equiv-is-an-equivalence

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

Theorem: transform-argument-equiv-implies-equal-transform-argument-fix-1

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

Theorem: transform-argument-fix-under-transform-argument-equiv

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

Theorem: equal-of-transform-argument-fix-1-forward-to-transform-argument-equiv

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

Theorem: equal-of-transform-argument-fix-2-forward-to-transform-argument-equiv

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

Theorem: transform-argument-equiv-of-transform-argument-fix-1-forward

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

Theorem: transform-argument-equiv-of-transform-argument-fix-2-forward

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