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Base58

Base58-character

Base58 characters.

These are the characters in *base58-characters*.

Definitions and Theorems

Function: base58-character-equiv$inline

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Subtopics

Base58-character-fix: Fixer for base58-character.
Base58-characterp: Recognizer for base58-character.