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• Rlp-tree

Rlp-tree-equiv

Basic equivalence relation for rlp-tree structures.

Definitions and Theorems

Function: rlp-tree-equiv$inline

(defun rlp-tree-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (rlp-treep acl2::x)
                              (rlp-treep acl2::y))))
  (equal (rlp-tree-fix acl2::x)
         (rlp-tree-fix acl2::y)))

Theorem: rlp-tree-equiv-is-an-equivalence

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

Theorem: rlp-tree-equiv-implies-equal-rlp-tree-fix-1

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

Theorem: rlp-tree-fix-under-rlp-tree-equiv

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

Theorem: equal-of-rlp-tree-fix-1-forward-to-rlp-tree-equiv

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

Theorem: equal-of-rlp-tree-fix-2-forward-to-rlp-tree-equiv

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

Theorem: rlp-tree-equiv-of-rlp-tree-fix-1-forward

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

Theorem: rlp-tree-equiv-of-rlp-tree-fix-2-forward

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