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• Base58-character-list

Base58-character-list-equiv

Basic equivalence relation for base58-character-list structures.

Definitions and Theorems

Function: base58-character-list-equiv$inline

(defun base58-character-list-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (base58-character-listp acl2::x)
                              (base58-character-listp acl2::y))))
  (equal (base58-character-list-fix acl2::x)
         (base58-character-list-fix acl2::y)))

Theorem: base58-character-list-equiv-is-an-equivalence

(defthm base58-character-list-equiv-is-an-equivalence
  (and (booleanp (base58-character-list-equiv x y))
       (base58-character-list-equiv x x)
       (implies (base58-character-list-equiv x y)
                (base58-character-list-equiv y x))
       (implies (and (base58-character-list-equiv x y)
                     (base58-character-list-equiv y z))
                (base58-character-list-equiv x z)))
  :rule-classes (:equivalence))

Theorem: base58-character-list-equiv-implies-equal-base58-character-list-fix-1

(defthm
 base58-character-list-equiv-implies-equal-base58-character-list-fix-1
 (implies (base58-character-list-equiv acl2::x x-equiv)
          (equal (base58-character-list-fix acl2::x)
                 (base58-character-list-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: base58-character-list-fix-under-base58-character-list-equiv

(defthm base58-character-list-fix-under-base58-character-list-equiv
  (base58-character-list-equiv (base58-character-list-fix acl2::x)
                               acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-base58-character-list-fix-1-forward-to-base58-character-list-equiv

(defthm
 equal-of-base58-character-list-fix-1-forward-to-base58-character-list-equiv
 (implies (equal (base58-character-list-fix acl2::x)
                 acl2::y)
          (base58-character-list-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-base58-character-list-fix-2-forward-to-base58-character-list-equiv

(defthm
 equal-of-base58-character-list-fix-2-forward-to-base58-character-list-equiv
 (implies (equal acl2::x
                 (base58-character-list-fix acl2::y))
          (base58-character-list-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: base58-character-list-equiv-of-base58-character-list-fix-1-forward

(defthm
 base58-character-list-equiv-of-base58-character-list-fix-1-forward
 (implies
    (base58-character-list-equiv (base58-character-list-fix acl2::x)
                                 acl2::y)
    (base58-character-list-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: base58-character-list-equiv-of-base58-character-list-fix-2-forward

(defthm
 base58-character-list-equiv-of-base58-character-list-fix-2-forward
 (implies
   (base58-character-list-equiv acl2::x
                                (base58-character-list-fix acl2::y))
   (base58-character-list-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)