• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Debugging
  • Projects
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
    • X86isa
    • Axe
    • Execloader
      • Elf-reader
        • Elf64_sym
        • Elf32_sym
        • Elf-header
        • Elf-section-header
        • Elf64-segment-header
        • Elf32-segment-header
        • Elf_bits32
        • Elf_bits8
        • Elf_bits64
        • Elf_bits16
        • Section-info
        • Read-section-headers
        • Read-segment-headers-64
        • Read-segment-headers-32
        • Read-section-names
        • Elf64_sym-info
        • Elf32_sym-info
        • Read-elf-header
        • Parse-symtab-entries
        • Populate-elf-contents
        • Is-elf-content-p
        • Get-string-section-data
        • Get-section-info1
        • Set-elf-stobj-fields
        • Get-named-section-headers
        • Elf-read-mem-null-term
        • Get-section-info
        • Get-symtab-entries
        • Find-label-address-from-elf-symtab-info
        • Section-names
        • Populate-elf
        • Get-label-addresses
        • Elf-read-string-null-term
        • Get-label-address
        • Good-elf-p
        • Elf64_sym-equiv-under-mask
        • Elf64-segment-headers
        • Elf32_sym-equiv-under-mask
        • Elf32-segment-headers
        • Section-info-list
        • Elf64_sym-info-list
        • Elf32_sym-info-list
          • Elf32_sym-info-list-fix
          • Elf32_sym-info-list-equiv
          • Elf32_sym-info-list-p
        • Elf-section-headers
        • Elf64_sym-debug
        • Elf32_sym-debug
      • Mach-o-reader
      • Merge-first-split-bytes
      • Split-bytes
      • Take-till-zero
      • Charlist->bytes
      • Merge-bytes
      • Bytes->charlist
      • String->bytes
      • Bytes->string
  • Math
  • Testing-utilities

• Elf32_sym-info-list

Elf32_sym-info-list-equiv

Basic equivalence relation for elf32_sym-info-list structures.

Definitions and Theorems

Function: elf32_sym-info-list-equiv$inline

(defun elf32_sym-info-list-equiv$inline (x y)
  (declare (xargs :guard (and (elf32_sym-info-list-p x)
                              (elf32_sym-info-list-p y))))
  (equal (elf32_sym-info-list-fix x)
         (elf32_sym-info-list-fix y)))

Theorem: elf32_sym-info-list-equiv-is-an-equivalence

(defthm elf32_sym-info-list-equiv-is-an-equivalence
  (and (booleanp (elf32_sym-info-list-equiv x y))
       (elf32_sym-info-list-equiv x x)
       (implies (elf32_sym-info-list-equiv x y)
                (elf32_sym-info-list-equiv y x))
       (implies (and (elf32_sym-info-list-equiv x y)
                     (elf32_sym-info-list-equiv y z))
                (elf32_sym-info-list-equiv x z)))
  :rule-classes (:equivalence))

Theorem: elf32_sym-info-list-equiv-implies-equal-elf32_sym-info-list-fix-1

(defthm
  elf32_sym-info-list-equiv-implies-equal-elf32_sym-info-list-fix-1
  (implies (elf32_sym-info-list-equiv x x-equiv)
           (equal (elf32_sym-info-list-fix x)
                  (elf32_sym-info-list-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: elf32_sym-info-list-fix-under-elf32_sym-info-list-equiv

(defthm elf32_sym-info-list-fix-under-elf32_sym-info-list-equiv
  (elf32_sym-info-list-equiv (elf32_sym-info-list-fix x)
                             x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-elf32_sym-info-list-fix-1-forward-to-elf32_sym-info-list-equiv

(defthm
 equal-of-elf32_sym-info-list-fix-1-forward-to-elf32_sym-info-list-equiv
 (implies (equal (elf32_sym-info-list-fix x) y)
          (elf32_sym-info-list-equiv x y))
 :rule-classes :forward-chaining)

Theorem: equal-of-elf32_sym-info-list-fix-2-forward-to-elf32_sym-info-list-equiv

(defthm
 equal-of-elf32_sym-info-list-fix-2-forward-to-elf32_sym-info-list-equiv
 (implies (equal x (elf32_sym-info-list-fix y))
          (elf32_sym-info-list-equiv x y))
 :rule-classes :forward-chaining)

Theorem: elf32_sym-info-list-equiv-of-elf32_sym-info-list-fix-1-forward

(defthm
     elf32_sym-info-list-equiv-of-elf32_sym-info-list-fix-1-forward
  (implies (elf32_sym-info-list-equiv (elf32_sym-info-list-fix x)
                                      y)
           (elf32_sym-info-list-equiv x y))
  :rule-classes :forward-chaining)

Theorem: elf32_sym-info-list-equiv-of-elf32_sym-info-list-fix-2-forward

(defthm
     elf32_sym-info-list-equiv-of-elf32_sym-info-list-fix-2-forward
  (implies (elf32_sym-info-list-equiv x (elf32_sym-info-list-fix y))
           (elf32_sym-info-list-equiv x y))
  :rule-classes :forward-chaining)