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Aignet-norm-p

Signature
(aignet-norm-p x) → *

Definitions and Theorems

Function: aignet-norm-p

(defun aignet-norm-p (x)
       (declare (xargs :guard t))
       (let ((__function__ 'aignet-norm-p))
            (declare (ignorable __function__))
            (equal (ec-call (aignet-norm x)) x)))

Theorem: aignet-norm-p-of-aignet-norm

(defthm aignet-norm-p-of-aignet-norm
        (aignet-norm-p (aignet-norm x)))

Theorem: aignet-norm-when-aignet-norm-p

(defthm aignet-norm-when-aignet-norm-p
        (implies (aignet-norm-p x)
                 (equal (aignet-norm x) x)))

Function: aignet-equiv$inline

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

Theorem: aignet-equiv-is-an-equivalence

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

Theorem: aignet-equiv-implies-equal-aignet-norm-1

(defthm aignet-equiv-implies-equal-aignet-norm-1
        (implies (aignet-equiv x x-equiv)
                 (equal (aignet-norm x)
                        (aignet-norm x-equiv)))
        :rule-classes (:congruence))

Theorem: aignet-norm-under-aignet-equiv

(defthm aignet-norm-under-aignet-equiv
        (aignet-equiv (aignet-norm x) x)
        :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-aignet-norm-1-forward-to-aignet-equiv

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

Theorem: equal-of-aignet-norm-2-forward-to-aignet-equiv

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

Theorem: aignet-equiv-of-aignet-norm-1-forward

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

Theorem: aignet-equiv-of-aignet-norm-2-forward

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

Theorem: node-list-equiv-refines-aignet-equiv

(defthm node-list-equiv-refines-aignet-equiv
        (implies (node-list-equiv x y)
                 (aignet-equiv x y))
        :rule-classes (:refinement))