• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • C
      • Syntax-for-tools
      • Atc
        • Atc-implementation
          • Atc-abstract-syntax
          • Atc-pretty-printer
          • Atc-event-and-code-generation
          • Fty-pseudo-term-utilities
          • Atc-term-recognizers
          • Atc-input-processing
          • Atc-shallow-embedding
            • Defstruct
              • Defstruct-implementation
                • Defstruct-info
                  • Defstruct-info-fix
                  • Make-defstruct-info
                  • Defstruct-infop
                  • Defstruct-info-equiv
                  • Change-defstruct-info
                  • Defstruct-info->pointer-type-to-quoted-thm
                  • Defstruct-info->fixer-recognizer-thm
                  • Defstruct-info->type-to-quoted-thm
                  • Defstruct-info->type-of-value-thm
                  • Defstruct-info->value-kind-thm
                  • Defstruct-info->not-error-thm
                  • Defstruct-info->members
                  • Defstruct-info->flexiblep-thm
                  • Defstruct-info->valuep-thm
                  • Defstruct-info->recognizer
                  • Defstruct-info->flexiblep
                  • Defstruct-info->fixtype
                  • Defstruct-info->fixer
                  • Defstruct-info->call
                  • Defstruct-info->tag
                • Defstruct-gen-recognizer
                • Defstruct-gen-integer-member-ops
                • Defstruct-gen-constructor
                • Defstruct-gen-array-member-ops
                • Defstruct-gen-recognizer-conjuncts
                • Defstruct-member-info
                • Defstruct-member-info-list->memtype-list
                • Defstruct-process-members
                • Defstruct-gen-fixer
                • Defstruct-gen-member-ops
                • Defstruct-process-inputs
                • Defstruct-gen-fixing-term
                • Defstruct-info-option
                • Defstruct-gen-everything
                • Defstruct-gen-all-member-ops
                • Defstruct-gen-recognizer-all-conjuncts
                • Defstruct-info->writer-element-list
                • Defstruct-info->reader-element-list
                • Defstruct-gen-fixtype
                • Defstruct-info->writer-list
                • Defstruct-info->reader-list
                • Defstruct-fn
                • Defstruct-table-record-event
                • Defstruct-table-lookup
                • Irr-defstruct-info
                • Defstruct-info->writer-element-list-aux
                • Defstruct-info->reader-element-list-aux
                • Defstruct-info->writer-list-aux
                • Defstruct-info->reader-list-aux
                • Defstruct-member-info-list
                • Defstruct-table-definition
                • *defstruct-table*
                • Defstruct-macro-implementtion
            • Defobject
            • Atc-let-designations
            • Pointer-types
            • Atc-conditional-expressions
          • 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
      • Insertion-sort
      • Pack
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • Java
    • Taspi
    • Riscv
    • Bitcoin
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Axe
    • Aleo
    • Bigmems
    • Builtins
    • Execloader
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Std
  • Community
  • Proof-automation
  • ACL2
  • Macro-libraries
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Defstruct-info

Defstruct-info-equiv

Basic equivalence relation for defstruct-info structures.

Definitions and Theorems

Function: defstruct-info-equiv$inline

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

Theorem: defstruct-info-equiv-is-an-equivalence

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

Theorem: defstruct-info-equiv-implies-equal-defstruct-info-fix-1

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

Theorem: defstruct-info-fix-under-defstruct-info-equiv

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

Theorem: equal-of-defstruct-info-fix-1-forward-to-defstruct-info-equiv

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

Theorem: equal-of-defstruct-info-fix-2-forward-to-defstruct-info-equiv

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

Theorem: defstruct-info-equiv-of-defstruct-info-fix-1-forward

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

Theorem: defstruct-info-equiv-of-defstruct-info-fix-2-forward

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