• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Community
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Apt
      • Error-checking
      • Fty-extensions
      • Isar
      • Kestrel-utilities
      • Set
      • C
      • Soft
      • Bv
      • Imp-language
      • Ethereum
      • Event-macros
      • Java
        • Atj
          • Atj-implementation
            • Atj-types
            • Atj-java-primitive-array-model
            • Atj-java-abstract-syntax
            • Atj-input-processing
            • Atj-java-pretty-printer
            • Atj-code-generation
            • Atj-java-primitives
            • Atj-java-primitive-arrays
            • Atj-type-macros
            • Atj-java-syntax-operations
            • Atj-fn
            • Atj-library-extensions
            • Atj-java-input-types
            • Atj-test-structures
              • Atj-test-value
                • Atj-test-value-fix
                • Atj-test-value-case
                • Atj-test-valuep
                • Atj-test-value-equiv
                • Atj-test-value-kind
                • Atj-test-value-ACL2
                • Atj-test-value-jshort[]
                • Atj-test-value-jshort
                • Atj-test-value-jlong[]
                • Atj-test-value-jlong
                • Atj-test-value-jint[]
                • Atj-test-value-jint
                • Atj-test-value-jchar[]
                • Atj-test-value-jchar
                • Atj-test-value-jbyte[]
                • Atj-test-value-jbyte
                • Atj-test-value-jboolean[]
                • Atj-test-value-jboolean
              • Atj-test
              • Atj-test-value-of-type
              • Atj-test-values-of-types
              • Atj-test-value-to-type
              • Atj-test-values-to-types
              • Atj-test-value-ACL2-list
              • Atj-test-value-list
              • Atj-test-list
            • Aij-notions
            • Atj-macro-definition
          • Atj-tutorial
        • Aij
        • Language
      • Riscv
      • Bitcoin
      • Zcash
      • Yul
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Cryptography
      • Number-theory
      • Axe
      • Lists-light
      • Builtins
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Atj-test-value

Atj-test-value-fix

Fixing function for atj-test-value structures.

Signature

(atj-test-value-fix x) → new-x

Arguments

x — Guard (atj-test-valuep x).

Returns

new-x — Type (atj-test-valuep new-x).

Definitions and Theorems

Function: atj-test-value-fix$inline

(defun atj-test-value-fix$inline (x)
 (declare (xargs :guard (atj-test-valuep x)))
 (let ((__function__ 'atj-test-value-fix))
  (declare (ignorable __function__))
  (mbe
   :logic
   (case (atj-test-value-kind x)
    (:acl2 (b* ((get (identity (std::da-nth 0 (cdr x)))))
             (cons :acl2 (list get))))
    (:jboolean
         (b* ((get (boolean-value-fix (std::da-nth 0 (cdr x)))))
           (cons :jboolean (list get))))
    (:jchar (b* ((get (char-value-fix (std::da-nth 0 (cdr x)))))
              (cons :jchar (list get))))
    (:jbyte (b* ((get (byte-value-fix (std::da-nth 0 (cdr x)))))
              (cons :jbyte (list get))))
    (:jshort (b* ((get (short-value-fix (std::da-nth 0 (cdr x)))))
               (cons :jshort (list get))))
    (:jint (b* ((get (int-value-fix (std::da-nth 0 (cdr x)))))
             (cons :jint (list get))))
    (:jlong (b* ((get (long-value-fix (std::da-nth 0 (cdr x)))))
              (cons :jlong (list get))))
    (:jboolean[]
         (b* ((get (boolean-array-fix (std::da-nth 0 (cdr x)))))
           (cons :jboolean[] (list get))))
    (:jchar[] (b* ((get (char-array-fix (std::da-nth 0 (cdr x)))))
                (cons :jchar[] (list get))))
    (:jbyte[] (b* ((get (byte-array-fix (std::da-nth 0 (cdr x)))))
                (cons :jbyte[] (list get))))
    (:jshort[] (b* ((get (short-array-fix (std::da-nth 0 (cdr x)))))
                 (cons :jshort[] (list get))))
    (:jint[] (b* ((get (int-array-fix (std::da-nth 0 (cdr x)))))
               (cons :jint[] (list get))))
    (:jlong[] (b* ((get (long-array-fix (std::da-nth 0 (cdr x)))))
                (cons :jlong[] (list get)))))
   :exec x)))

Theorem: atj-test-valuep-of-atj-test-value-fix

(defthm atj-test-valuep-of-atj-test-value-fix
  (b* ((new-x (atj-test-value-fix$inline x)))
    (atj-test-valuep new-x))
  :rule-classes :rewrite)

Theorem: atj-test-value-fix-when-atj-test-valuep

(defthm atj-test-value-fix-when-atj-test-valuep
  (implies (atj-test-valuep x)
           (equal (atj-test-value-fix x) x)))

Function: atj-test-value-equiv$inline

(defun atj-test-value-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (atj-test-valuep acl2::x)
                              (atj-test-valuep acl2::y))))
  (equal (atj-test-value-fix acl2::x)
         (atj-test-value-fix acl2::y)))

Theorem: atj-test-value-equiv-is-an-equivalence

(defthm atj-test-value-equiv-is-an-equivalence
  (and (booleanp (atj-test-value-equiv x y))
       (atj-test-value-equiv x x)
       (implies (atj-test-value-equiv x y)
                (atj-test-value-equiv y x))
       (implies (and (atj-test-value-equiv x y)
                     (atj-test-value-equiv y z))
                (atj-test-value-equiv x z)))
  :rule-classes (:equivalence))

Theorem: atj-test-value-equiv-implies-equal-atj-test-value-fix-1

(defthm atj-test-value-equiv-implies-equal-atj-test-value-fix-1
  (implies (atj-test-value-equiv acl2::x x-equiv)
           (equal (atj-test-value-fix acl2::x)
                  (atj-test-value-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: atj-test-value-fix-under-atj-test-value-equiv

(defthm atj-test-value-fix-under-atj-test-value-equiv
  (atj-test-value-equiv (atj-test-value-fix acl2::x)
                        acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-atj-test-value-fix-1-forward-to-atj-test-value-equiv

(defthm
      equal-of-atj-test-value-fix-1-forward-to-atj-test-value-equiv
  (implies (equal (atj-test-value-fix acl2::x)
                  acl2::y)
           (atj-test-value-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-atj-test-value-fix-2-forward-to-atj-test-value-equiv

(defthm
      equal-of-atj-test-value-fix-2-forward-to-atj-test-value-equiv
  (implies (equal acl2::x (atj-test-value-fix acl2::y))
           (atj-test-value-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: atj-test-value-equiv-of-atj-test-value-fix-1-forward

(defthm atj-test-value-equiv-of-atj-test-value-fix-1-forward
  (implies (atj-test-value-equiv (atj-test-value-fix acl2::x)
                                 acl2::y)
           (atj-test-value-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: atj-test-value-equiv-of-atj-test-value-fix-2-forward

(defthm atj-test-value-equiv-of-atj-test-value-fix-2-forward
  (implies
       (atj-test-value-equiv acl2::x (atj-test-value-fix acl2::y))
       (atj-test-value-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: atj-test-value-kind$inline-of-atj-test-value-fix-x

(defthm atj-test-value-kind$inline-of-atj-test-value-fix-x
  (equal (atj-test-value-kind$inline (atj-test-value-fix x))
         (atj-test-value-kind$inline x)))

Theorem: atj-test-value-kind$inline-atj-test-value-equiv-congruence-on-x

(defthm
    atj-test-value-kind$inline-atj-test-value-equiv-congruence-on-x
  (implies (atj-test-value-equiv x x-equiv)
           (equal (atj-test-value-kind$inline x)
                  (atj-test-value-kind$inline x-equiv)))
  :rule-classes :congruence)

Theorem: consp-of-atj-test-value-fix

(defthm consp-of-atj-test-value-fix
  (consp (atj-test-value-fix x))
  :rule-classes :type-prescription)