• 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
      • Isar
      • Kestrel-utilities
      • Soft
      • Bv
      • Imp-language
      • C
        • Syntax-for-tools
        • Atc
          • Atc-implementation
            • Atc-abstract-syntax
            • Atc-pretty-printer
            • Atc-event-and-code-generation
              • Atc-symbolic-computation-states
              • Atc-symbolic-execution-rules
              • Atc-gen-ext-declon-lists
              • Atc-function-and-loop-generation
              • Atc-statement-generation
              • Atc-gen-fileset
              • Atc-gen-everything
              • Atc-gen-obj-declon
              • Atc-gen-fileset-event
              • Atc-tag-tables
              • Atc-expression-generation
              • Atc-generation-contexts
              • Atc-gen-wf-thm
              • Term-checkers-atc
              • Atc-variable-tables
                • Atc-var-info-list->type-list
                • Atc-var-info-list->thm-list
                • Atc-check-var
                • Atc-var-info
                  • Atc-var-info-fix
                  • Atc-var-info-equiv
                  • Make-atc-var-info
                  • Change-atc-var-info
                  • Atc-var-info->type
                  • Atc-var-info->thm
                  • Atc-var-info->externalp
                  • Atc-var-infop
                • Atc-var-info-option
                • Atc-get-vars-check-innermost
                • Atc-get-var-check-innermost
                • Atc-add-var
                • Atc-get-var
                • Atc-symbol-varinfo-alist
                • Atc-symbol-varinfo-alist-list-to-thms
                • Atc-symbol-varinfo-alist-list
                • Atc-get-vars
                • Atc-symbol-varinfo-alist-to-thms
                • Atc-var-info-option-list
                • Atc-var-info-list
              • Term-checkers-common
              • Atc-gen-init-fun-env-thm
              • Atc-gen-appconds
              • Read-write-variables
              • Atc-gen-thm-assert-events
              • Test*
              • Atc-gen-prog-const
              • Atc-gen-expr-bool
              • Atc-theorem-generation
              • Atc-tag-generation
              • Atc-gen-expr-pure
              • Atc-function-tables
              • Atc-object-tables
            • Fty-pseudo-term-utilities
            • Atc-term-recognizers
            • Atc-input-processing
            • Atc-shallow-embedding
            • Atc-process-inputs-and-gen-everything
            • Atc-table
            • Atc-fn
            • Atc-pretty-printing-options
            • Atc-types
            • Atc-macro-definition
          • Atc-tutorial
        • Language
        • Representation
        • Transformation-tools
        • Pack
      • 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

• Atc-var-info

Atc-var-info-fix

Fixing function for atc-var-info structures.

Signature

(atc-var-info-fix x) → new-x

Arguments

x — Guard (atc-var-infop x).

Returns

new-x — Type (atc-var-infop new-x).

Definitions and Theorems

Function: atc-var-info-fix$inline

(defun atc-var-info-fix$inline (x)
  (declare (xargs :guard (atc-var-infop x)))
  (let ((__function__ 'atc-var-info-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((type (type-fix (cdr (std::da-nth 0 x))))
              (thm (symbol-fix (cdr (std::da-nth 1 x))))
              (externalp (acl2::bool-fix (cdr (std::da-nth 2 x)))))
           (list (cons 'type type)
                 (cons 'thm thm)
                 (cons 'externalp externalp)))
         :exec x)))

Theorem: atc-var-infop-of-atc-var-info-fix

(defthm atc-var-infop-of-atc-var-info-fix
  (b* ((new-x (atc-var-info-fix$inline x)))
    (atc-var-infop new-x))
  :rule-classes :rewrite)

Theorem: atc-var-info-fix-when-atc-var-infop

(defthm atc-var-info-fix-when-atc-var-infop
  (implies (atc-var-infop x)
           (equal (atc-var-info-fix x) x)))

Function: atc-var-info-equiv$inline

(defun atc-var-info-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (atc-var-infop acl2::x)
                              (atc-var-infop acl2::y))))
  (equal (atc-var-info-fix acl2::x)
         (atc-var-info-fix acl2::y)))

Theorem: atc-var-info-equiv-is-an-equivalence

(defthm atc-var-info-equiv-is-an-equivalence
  (and (booleanp (atc-var-info-equiv x y))
       (atc-var-info-equiv x x)
       (implies (atc-var-info-equiv x y)
                (atc-var-info-equiv y x))
       (implies (and (atc-var-info-equiv x y)
                     (atc-var-info-equiv y z))
                (atc-var-info-equiv x z)))
  :rule-classes (:equivalence))

Theorem: atc-var-info-equiv-implies-equal-atc-var-info-fix-1

(defthm atc-var-info-equiv-implies-equal-atc-var-info-fix-1
  (implies (atc-var-info-equiv acl2::x x-equiv)
           (equal (atc-var-info-fix acl2::x)
                  (atc-var-info-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: atc-var-info-fix-under-atc-var-info-equiv

(defthm atc-var-info-fix-under-atc-var-info-equiv
  (atc-var-info-equiv (atc-var-info-fix acl2::x)
                      acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-atc-var-info-fix-1-forward-to-atc-var-info-equiv

(defthm equal-of-atc-var-info-fix-1-forward-to-atc-var-info-equiv
  (implies (equal (atc-var-info-fix acl2::x)
                  acl2::y)
           (atc-var-info-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-atc-var-info-fix-2-forward-to-atc-var-info-equiv

(defthm equal-of-atc-var-info-fix-2-forward-to-atc-var-info-equiv
  (implies (equal acl2::x (atc-var-info-fix acl2::y))
           (atc-var-info-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: atc-var-info-equiv-of-atc-var-info-fix-1-forward

(defthm atc-var-info-equiv-of-atc-var-info-fix-1-forward
  (implies (atc-var-info-equiv (atc-var-info-fix acl2::x)
                               acl2::y)
           (atc-var-info-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: atc-var-info-equiv-of-atc-var-info-fix-2-forward

(defthm atc-var-info-equiv-of-atc-var-info-fix-2-forward
  (implies (atc-var-info-equiv acl2::x (atc-var-info-fix acl2::y))
           (atc-var-info-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)