• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Apt
      • Error-checking
      • Fty-extensions
        • Defbyte
        • Defresult
        • Defsubtype
        • Defset
        • Specific-types
        • Defflatsum
        • Deflist-of-len
        • Pos-list
        • Defbytelist
        • Defbyte-standard-instances
        • Defomap
        • Deffixtype-alias
        • Defbytelist-standard-instances
          • Ubyte8-list
          • Ubyte4-list
            • Ubyte4-list-fix
            • Ubyte4-list-equiv
            • Ubyte4-listp
          • Ubyte32-list
          • Ubyte256-list
          • Ubyte128-list
          • Ubyte64-list
          • Ubyte3-list
          • Ubyte2-list
          • Ubyte16-list
          • Ubyte11-list
          • Ubyte1-list
          • Sbyte8-list
          • Sbyte64-list
          • Sbyte4-list
          • Sbyte32-list
          • Sbyte3-list
          • Sbyte256-list
          • Sbyte2-list
          • Sbyte16-list
          • Sbyte128-list
          • Sbyte1-list
          • Defubytelist
          • Defsbytelist
        • Defunit
        • Byte-list
        • Byte
        • Pos-option
        • Nibble
        • Nat-option
        • String-option
        • Byte-list20
        • Byte-list32
        • Byte-list64
        • Pseudo-event-form
        • Natoption/natoptionlist
        • Nati
        • Character-list
        • Nat/natlist
        • Maybe-string
        • Nibble-list
        • Natoption/natoptionlist-result
        • Nat/natlist-result
        • Nat-option-list-result
        • Set
        • String-result
        • String-list-result
        • Nat-result
        • Nat-option-result
        • Nat-list-result
        • Maybe-string-result
        • Integer-result
        • Character-result
        • Character-list-result
        • Boolean-result
        • Map
        • Bag
        • Pos-set
        • Hex-digit-char-list
        • Dec-digit-char-list
        • Nat-option-list
        • Symbol-set
        • String-set
        • Pseudo-event-form-list
        • Nat-set
        • Oct-digit-char-list
        • Bin-digit-char-list
        • Bit-list
      • Isar
      • Kestrel-utilities
      • Soft
      • Bv
      • Imp-language
      • C
      • Event-macros
      • Java
      • Bitcoin
      • Ethereum
      • Yul
      • Zcash
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Number-theory
      • Cryptography
      • Lists-light
      • Builtins
      • Axe
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Ubyte4-list

Ubyte4-list-fix

(ubyte4-list-fix x) is a usual fty list fixing function.

Signature

(ubyte4-list-fix x) → fty::newx

Arguments

x — Guard (ubyte4-listp x).

Returns

fty::newx — Type (ubyte4-listp fty::newx).

In the logic, we apply ubyte4-fix to each member of the x. In the execution, none of that is actually necessary and this is just an inlined identity function.

Definitions and Theorems

Function: ubyte4-list-fix$inline

(defun ubyte4-list-fix$inline (x)
  (declare (xargs :guard (ubyte4-listp x)))
  (let ((__function__ 'ubyte4-list-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (cons (ubyte4-fix (car x))
                 (ubyte4-list-fix (cdr x))))
         :exec x)))

Theorem: ubyte4-listp-of-ubyte4-list-fix

(defthm ubyte4-listp-of-ubyte4-list-fix
  (b* ((fty::newx (ubyte4-list-fix$inline x)))
    (ubyte4-listp fty::newx))
  :rule-classes :rewrite)

Theorem: ubyte4-list-fix-when-ubyte4-listp

(defthm ubyte4-list-fix-when-ubyte4-listp
  (implies (ubyte4-listp x)
           (equal (ubyte4-list-fix x) x)))

Function: ubyte4-list-equiv$inline

(defun ubyte4-list-equiv$inline (x y)
  (declare (xargs :guard (and (ubyte4-listp x)
                              (ubyte4-listp y))))
  (equal (ubyte4-list-fix x)
         (ubyte4-list-fix y)))

Theorem: ubyte4-list-equiv-is-an-equivalence

(defthm ubyte4-list-equiv-is-an-equivalence
  (and (booleanp (ubyte4-list-equiv x y))
       (ubyte4-list-equiv x x)
       (implies (ubyte4-list-equiv x y)
                (ubyte4-list-equiv y x))
       (implies (and (ubyte4-list-equiv x y)
                     (ubyte4-list-equiv y z))
                (ubyte4-list-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ubyte4-list-equiv-implies-equal-ubyte4-list-fix-1

(defthm ubyte4-list-equiv-implies-equal-ubyte4-list-fix-1
  (implies (ubyte4-list-equiv x x-equiv)
           (equal (ubyte4-list-fix x)
                  (ubyte4-list-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ubyte4-list-fix-under-ubyte4-list-equiv

(defthm ubyte4-list-fix-under-ubyte4-list-equiv
  (ubyte4-list-equiv (ubyte4-list-fix x)
                     x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ubyte4-list-fix-1-forward-to-ubyte4-list-equiv

(defthm equal-of-ubyte4-list-fix-1-forward-to-ubyte4-list-equiv
  (implies (equal (ubyte4-list-fix x) y)
           (ubyte4-list-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-ubyte4-list-fix-2-forward-to-ubyte4-list-equiv

(defthm equal-of-ubyte4-list-fix-2-forward-to-ubyte4-list-equiv
  (implies (equal x (ubyte4-list-fix y))
           (ubyte4-list-equiv x y))
  :rule-classes :forward-chaining)

Theorem: ubyte4-list-equiv-of-ubyte4-list-fix-1-forward

(defthm ubyte4-list-equiv-of-ubyte4-list-fix-1-forward
  (implies (ubyte4-list-equiv (ubyte4-list-fix x)
                              y)
           (ubyte4-list-equiv x y))
  :rule-classes :forward-chaining)

Theorem: ubyte4-list-equiv-of-ubyte4-list-fix-2-forward

(defthm ubyte4-list-equiv-of-ubyte4-list-fix-2-forward
  (implies (ubyte4-list-equiv x (ubyte4-list-fix y))
           (ubyte4-list-equiv x y))
  :rule-classes :forward-chaining)

Theorem: car-of-ubyte4-list-fix-x-under-ubyte4-equiv

(defthm car-of-ubyte4-list-fix-x-under-ubyte4-equiv
  (ubyte4-equiv (car (ubyte4-list-fix x))
                (car x)))

Theorem: car-ubyte4-list-equiv-congruence-on-x-under-ubyte4-equiv

(defthm car-ubyte4-list-equiv-congruence-on-x-under-ubyte4-equiv
  (implies (ubyte4-list-equiv x x-equiv)
           (ubyte4-equiv (car x) (car x-equiv)))
  :rule-classes :congruence)

Theorem: cdr-of-ubyte4-list-fix-x-under-ubyte4-list-equiv

(defthm cdr-of-ubyte4-list-fix-x-under-ubyte4-list-equiv
  (ubyte4-list-equiv (cdr (ubyte4-list-fix x))
                     (cdr x)))

Theorem: cdr-ubyte4-list-equiv-congruence-on-x-under-ubyte4-list-equiv

(defthm
      cdr-ubyte4-list-equiv-congruence-on-x-under-ubyte4-list-equiv
  (implies (ubyte4-list-equiv x x-equiv)
           (ubyte4-list-equiv (cdr x)
                              (cdr x-equiv)))
  :rule-classes :congruence)

Theorem: cons-of-ubyte4-fix-x-under-ubyte4-list-equiv

(defthm cons-of-ubyte4-fix-x-under-ubyte4-list-equiv
  (ubyte4-list-equiv (cons (ubyte4-fix x) y)
                     (cons x y)))

Theorem: cons-ubyte4-equiv-congruence-on-x-under-ubyte4-list-equiv

(defthm cons-ubyte4-equiv-congruence-on-x-under-ubyte4-list-equiv
  (implies (ubyte4-equiv x x-equiv)
           (ubyte4-list-equiv (cons x y)
                              (cons x-equiv y)))
  :rule-classes :congruence)

Theorem: cons-of-ubyte4-list-fix-y-under-ubyte4-list-equiv

(defthm cons-of-ubyte4-list-fix-y-under-ubyte4-list-equiv
  (ubyte4-list-equiv (cons x (ubyte4-list-fix y))
                     (cons x y)))

Theorem: cons-ubyte4-list-equiv-congruence-on-y-under-ubyte4-list-equiv

(defthm
     cons-ubyte4-list-equiv-congruence-on-y-under-ubyte4-list-equiv
  (implies (ubyte4-list-equiv y y-equiv)
           (ubyte4-list-equiv (cons x y)
                              (cons x y-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-ubyte4-list-fix

(defthm consp-of-ubyte4-list-fix
  (equal (consp (ubyte4-list-fix x))
         (consp x)))

Theorem: ubyte4-list-fix-under-iff

(defthm ubyte4-list-fix-under-iff
  (iff (ubyte4-list-fix x) (consp x)))

Theorem: ubyte4-list-fix-of-cons

(defthm ubyte4-list-fix-of-cons
  (equal (ubyte4-list-fix (cons a x))
         (cons (ubyte4-fix a)
               (ubyte4-list-fix x))))

Theorem: len-of-ubyte4-list-fix

(defthm len-of-ubyte4-list-fix
  (equal (len (ubyte4-list-fix x))
         (len x)))

Theorem: ubyte4-list-fix-of-append

(defthm ubyte4-list-fix-of-append
  (equal (ubyte4-list-fix (append std::a std::b))
         (append (ubyte4-list-fix std::a)
                 (ubyte4-list-fix std::b))))

Theorem: ubyte4-list-fix-of-repeat

(defthm ubyte4-list-fix-of-repeat
  (equal (ubyte4-list-fix (repeat n x))
         (repeat n (ubyte4-fix x))))

Theorem: list-equiv-refines-ubyte4-list-equiv

(defthm list-equiv-refines-ubyte4-list-equiv
  (implies (list-equiv x y)
           (ubyte4-list-equiv x y))
  :rule-classes :refinement)

Theorem: nth-of-ubyte4-list-fix

(defthm nth-of-ubyte4-list-fix
  (equal (nth n (ubyte4-list-fix x))
         (if (< (nfix n) (len x))
             (ubyte4-fix (nth n x))
           nil)))

Theorem: ubyte4-list-equiv-implies-ubyte4-list-equiv-append-1

(defthm ubyte4-list-equiv-implies-ubyte4-list-equiv-append-1
  (implies (ubyte4-list-equiv x fty::x-equiv)
           (ubyte4-list-equiv (append x y)
                              (append fty::x-equiv y)))
  :rule-classes (:congruence))

Theorem: ubyte4-list-equiv-implies-ubyte4-list-equiv-append-2

(defthm ubyte4-list-equiv-implies-ubyte4-list-equiv-append-2
  (implies (ubyte4-list-equiv y fty::y-equiv)
           (ubyte4-list-equiv (append x y)
                              (append x fty::y-equiv)))
  :rule-classes (:congruence))

Theorem: ubyte4-list-equiv-implies-ubyte4-list-equiv-nthcdr-2

(defthm ubyte4-list-equiv-implies-ubyte4-list-equiv-nthcdr-2
  (implies (ubyte4-list-equiv l l-equiv)
           (ubyte4-list-equiv (nthcdr n l)
                              (nthcdr n l-equiv)))
  :rule-classes (:congruence))

Theorem: ubyte4-list-equiv-implies-ubyte4-list-equiv-take-2

(defthm ubyte4-list-equiv-implies-ubyte4-list-equiv-take-2
  (implies (ubyte4-list-equiv l l-equiv)
           (ubyte4-list-equiv (take n l)
                              (take n l-equiv)))
  :rule-classes (:congruence))