• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Community
  • Std
    • Std/lists
    • Omaps
    • Std/alists
    • Obags
    • Std/util
    • Std/strings
    • Std/osets
    • Std/io
    • Std/basic
    • Std/system
    • Std/typed-lists
      • Std/typed-lists/character-listp
      • Std/typed-lists/symbol-listp
      • Std/typed-lists/boolean-listp
      • Std/typed-lists/string-listp
      • Std/typed-lists/eqlable-listp
      • Theorems-about-true-list-lists
      • Std/typed-lists/atom-listp
      • Unsigned-byte-listp
        • Defbytelist
          • Defbytelist-standard-instances
            • Ubyte8-list
            • Ubyte4-list
            • Ubyte32-list
            • Ubyte256-list
            • Ubyte128-list
              • Ubyte128-list-fix
              • Ubyte128-list-equiv
              • Ubyte128-listp
            • 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
          • Defbytelist-implementation
        • Unsigned-byte-list-fix
      • Cons-listp
      • Cons-list-listp
      • Signed-byte-listp
      • String-or-symbol-listp
    • Std/bitsets
    • Std/testing
    • Std/typed-alists
    • Std/stobjs
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Ubyte128-list

Ubyte128-list-fix

(ubyte128-list-fix x) is a usual fty list fixing function.

Signature

(ubyte128-list-fix x) → fty::newx

Arguments

x — Guard (ubyte128-listp x).

Returns

fty::newx — Type (ubyte128-listp fty::newx).

In the logic, we apply ubyte128-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: ubyte128-list-fix$inline

(defun ubyte128-list-fix$inline (x)
  (declare (xargs :guard (ubyte128-listp x)))
  (let ((__function__ 'ubyte128-list-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (cons (ubyte128-fix (car x))
                 (ubyte128-list-fix (cdr x))))
         :exec x)))

Theorem: ubyte128-listp-of-ubyte128-list-fix

(defthm ubyte128-listp-of-ubyte128-list-fix
  (b* ((fty::newx (ubyte128-list-fix$inline x)))
    (ubyte128-listp fty::newx))
  :rule-classes :rewrite)

Theorem: ubyte128-list-fix-when-ubyte128-listp

(defthm ubyte128-list-fix-when-ubyte128-listp
  (implies (ubyte128-listp x)
           (equal (ubyte128-list-fix x) x)))

Function: ubyte128-list-equiv$inline

(defun ubyte128-list-equiv$inline (x y)
  (declare (xargs :guard (and (ubyte128-listp x)
                              (ubyte128-listp y))))
  (equal (ubyte128-list-fix x)
         (ubyte128-list-fix y)))

Theorem: ubyte128-list-equiv-is-an-equivalence

(defthm ubyte128-list-equiv-is-an-equivalence
  (and (booleanp (ubyte128-list-equiv x y))
       (ubyte128-list-equiv x x)
       (implies (ubyte128-list-equiv x y)
                (ubyte128-list-equiv y x))
       (implies (and (ubyte128-list-equiv x y)
                     (ubyte128-list-equiv y z))
                (ubyte128-list-equiv x z)))
  :rule-classes (:equivalence))

Theorem: ubyte128-list-equiv-implies-equal-ubyte128-list-fix-1

(defthm ubyte128-list-equiv-implies-equal-ubyte128-list-fix-1
  (implies (ubyte128-list-equiv x x-equiv)
           (equal (ubyte128-list-fix x)
                  (ubyte128-list-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: ubyte128-list-fix-under-ubyte128-list-equiv

(defthm ubyte128-list-fix-under-ubyte128-list-equiv
  (ubyte128-list-equiv (ubyte128-list-fix x)
                       x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-ubyte128-list-fix-1-forward-to-ubyte128-list-equiv

(defthm equal-of-ubyte128-list-fix-1-forward-to-ubyte128-list-equiv
  (implies (equal (ubyte128-list-fix x) y)
           (ubyte128-list-equiv x y))
  :rule-classes :forward-chaining)

Theorem: equal-of-ubyte128-list-fix-2-forward-to-ubyte128-list-equiv

(defthm equal-of-ubyte128-list-fix-2-forward-to-ubyte128-list-equiv
  (implies (equal x (ubyte128-list-fix y))
           (ubyte128-list-equiv x y))
  :rule-classes :forward-chaining)

Theorem: ubyte128-list-equiv-of-ubyte128-list-fix-1-forward

(defthm ubyte128-list-equiv-of-ubyte128-list-fix-1-forward
  (implies (ubyte128-list-equiv (ubyte128-list-fix x)
                                y)
           (ubyte128-list-equiv x y))
  :rule-classes :forward-chaining)

Theorem: ubyte128-list-equiv-of-ubyte128-list-fix-2-forward

(defthm ubyte128-list-equiv-of-ubyte128-list-fix-2-forward
  (implies (ubyte128-list-equiv x (ubyte128-list-fix y))
           (ubyte128-list-equiv x y))
  :rule-classes :forward-chaining)

Theorem: car-of-ubyte128-list-fix-x-under-ubyte128-equiv

(defthm car-of-ubyte128-list-fix-x-under-ubyte128-equiv
  (ubyte128-equiv (car (ubyte128-list-fix x))
                  (car x)))

Theorem: car-ubyte128-list-equiv-congruence-on-x-under-ubyte128-equiv

(defthm car-ubyte128-list-equiv-congruence-on-x-under-ubyte128-equiv
  (implies (ubyte128-list-equiv x x-equiv)
           (ubyte128-equiv (car x) (car x-equiv)))
  :rule-classes :congruence)

Theorem: cdr-of-ubyte128-list-fix-x-under-ubyte128-list-equiv

(defthm cdr-of-ubyte128-list-fix-x-under-ubyte128-list-equiv
  (ubyte128-list-equiv (cdr (ubyte128-list-fix x))
                       (cdr x)))

Theorem: cdr-ubyte128-list-equiv-congruence-on-x-under-ubyte128-list-equiv

(defthm
  cdr-ubyte128-list-equiv-congruence-on-x-under-ubyte128-list-equiv
  (implies (ubyte128-list-equiv x x-equiv)
           (ubyte128-list-equiv (cdr x)
                                (cdr x-equiv)))
  :rule-classes :congruence)

Theorem: cons-of-ubyte128-fix-x-under-ubyte128-list-equiv

(defthm cons-of-ubyte128-fix-x-under-ubyte128-list-equiv
  (ubyte128-list-equiv (cons (ubyte128-fix x) y)
                       (cons x y)))

Theorem: cons-ubyte128-equiv-congruence-on-x-under-ubyte128-list-equiv

(defthm
      cons-ubyte128-equiv-congruence-on-x-under-ubyte128-list-equiv
  (implies (ubyte128-equiv x x-equiv)
           (ubyte128-list-equiv (cons x y)
                                (cons x-equiv y)))
  :rule-classes :congruence)

Theorem: cons-of-ubyte128-list-fix-y-under-ubyte128-list-equiv

(defthm cons-of-ubyte128-list-fix-y-under-ubyte128-list-equiv
  (ubyte128-list-equiv (cons x (ubyte128-list-fix y))
                       (cons x y)))

Theorem: cons-ubyte128-list-equiv-congruence-on-y-under-ubyte128-list-equiv

(defthm
 cons-ubyte128-list-equiv-congruence-on-y-under-ubyte128-list-equiv
 (implies (ubyte128-list-equiv y y-equiv)
          (ubyte128-list-equiv (cons x y)
                               (cons x y-equiv)))
 :rule-classes :congruence)

Theorem: consp-of-ubyte128-list-fix

(defthm consp-of-ubyte128-list-fix
  (equal (consp (ubyte128-list-fix x))
         (consp x)))

Theorem: ubyte128-list-fix-under-iff

(defthm ubyte128-list-fix-under-iff
  (iff (ubyte128-list-fix x) (consp x)))

Theorem: ubyte128-list-fix-of-cons

(defthm ubyte128-list-fix-of-cons
  (equal (ubyte128-list-fix (cons a x))
         (cons (ubyte128-fix a)
               (ubyte128-list-fix x))))

Theorem: len-of-ubyte128-list-fix

(defthm len-of-ubyte128-list-fix
  (equal (len (ubyte128-list-fix x))
         (len x)))

Theorem: ubyte128-list-fix-of-append

(defthm ubyte128-list-fix-of-append
  (equal (ubyte128-list-fix (append std::a std::b))
         (append (ubyte128-list-fix std::a)
                 (ubyte128-list-fix std::b))))

Theorem: ubyte128-list-fix-of-repeat

(defthm ubyte128-list-fix-of-repeat
  (equal (ubyte128-list-fix (repeat n x))
         (repeat n (ubyte128-fix x))))

Theorem: list-equiv-refines-ubyte128-list-equiv

(defthm list-equiv-refines-ubyte128-list-equiv
  (implies (list-equiv x y)
           (ubyte128-list-equiv x y))
  :rule-classes :refinement)

Theorem: nth-of-ubyte128-list-fix

(defthm nth-of-ubyte128-list-fix
  (equal (nth n (ubyte128-list-fix x))
         (if (< (nfix n) (len x))
             (ubyte128-fix (nth n x))
           nil)))

Theorem: ubyte128-list-equiv-implies-ubyte128-list-equiv-append-1

(defthm ubyte128-list-equiv-implies-ubyte128-list-equiv-append-1
  (implies (ubyte128-list-equiv x fty::x-equiv)
           (ubyte128-list-equiv (append x y)
                                (append fty::x-equiv y)))
  :rule-classes (:congruence))

Theorem: ubyte128-list-equiv-implies-ubyte128-list-equiv-append-2

(defthm ubyte128-list-equiv-implies-ubyte128-list-equiv-append-2
  (implies (ubyte128-list-equiv y fty::y-equiv)
           (ubyte128-list-equiv (append x y)
                                (append x fty::y-equiv)))
  :rule-classes (:congruence))

Theorem: ubyte128-list-equiv-implies-ubyte128-list-equiv-nthcdr-2

(defthm ubyte128-list-equiv-implies-ubyte128-list-equiv-nthcdr-2
  (implies (ubyte128-list-equiv l l-equiv)
           (ubyte128-list-equiv (nthcdr n l)
                                (nthcdr n l-equiv)))
  :rule-classes (:congruence))

Theorem: ubyte128-list-equiv-implies-ubyte128-list-equiv-take-2

(defthm ubyte128-list-equiv-implies-ubyte128-list-equiv-take-2
  (implies (ubyte128-list-equiv l l-equiv)
           (ubyte128-list-equiv (take n l)
                                (take n l-equiv)))
  :rule-classes (:congruence))