• Top
  • Documentation
  • Books
  • Recursion-and-induction
  • Boolean-reasoning
  • Debugging
  • Projects
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
      • Warnings
      • Primitives
      • Use-set
      • Syntax
      • Getting-started
      • Utilities
      • Loader
        • Preprocessor
        • Vl-loadconfig
        • Lexer
        • Vl-loadstate
        • Parser
        • Vl-load-merge-descriptions
        • Scope-of-defines
        • Vl-load-file
        • Vl-flush-out-descriptions
        • Vl-description
        • Vl-loadresult
        • Vl-read-file
        • Vl-find-basename/extension
        • Vl-read-files
        • Vl-find-file
        • Extended-characters
        • Vl-load
        • Vl-load-main
        • Vl-load-description
        • Vl-descriptions-left-to-load
        • Inject-warnings
        • Vl-load-descriptions
        • Vl-load-files
        • Vl-load-summary
        • Vl-collect-modules-from-descriptions
        • Vl-descriptionlist
          • Vl-descriptionlist-fix
          • Vl-descriptionlist-p
          • Vl-descriptionlist-equiv
      • Transforms
      • Lint
      • Mlib
      • Server
      • Kit
      • Printer
      • Esim-vl
      • Well-formedness
    • Sv
    • Fgl
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Testing-utilities
  • Math

• Vl-descriptionlist

Vl-descriptionlist-equiv

Basic equivalence relation for vl-descriptionlist structures.

Definitions and Theorems

Function: vl-descriptionlist-equiv$inline

(defun vl-descriptionlist-equiv$inline
       (acl2::x acl2::y)
       (declare (xargs :guard (and (vl-descriptionlist-p acl2::x)
                                   (vl-descriptionlist-p acl2::y))))
       (equal (vl-descriptionlist-fix acl2::x)
              (vl-descriptionlist-fix acl2::y)))

Theorem: vl-descriptionlist-equiv-is-an-equivalence

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

Theorem: vl-descriptionlist-equiv-implies-equal-vl-descriptionlist-fix-1

(defthm
     vl-descriptionlist-equiv-implies-equal-vl-descriptionlist-fix-1
     (implies (vl-descriptionlist-equiv acl2::x x-equiv)
              (equal (vl-descriptionlist-fix acl2::x)
                     (vl-descriptionlist-fix x-equiv)))
     :rule-classes (:congruence))

Theorem: vl-descriptionlist-fix-under-vl-descriptionlist-equiv

(defthm vl-descriptionlist-fix-under-vl-descriptionlist-equiv
        (vl-descriptionlist-equiv (vl-descriptionlist-fix acl2::x)
                                  acl2::x)
        :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-vl-descriptionlist-fix-1-forward-to-vl-descriptionlist-equiv

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

Theorem: equal-of-vl-descriptionlist-fix-2-forward-to-vl-descriptionlist-equiv

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

Theorem: vl-descriptionlist-equiv-of-vl-descriptionlist-fix-1-forward

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

Theorem: vl-descriptionlist-equiv-of-vl-descriptionlist-fix-2-forward

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