• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
    • Fgl
    • Vwsim
    • Vl
      • Syntax
      • Loader
      • Warnings
      • Getting-started
      • Utilities
      • Printer
      • Kit
      • Mlib
        • Scopestack
        • Hid-tools
        • Filtering-by-name
        • Vl-interface-mocktype
        • Stripping-functions
        • Genblob
        • Expr-tools
        • Extract-vl-types
        • Hierarchy
          • Vl-design-toplevel
          • Vl-remove-unnecessary-elements
          • Vl-necessary-elements-transitive
          • Vl-interfacelist-everinstanced
          • Vl-dependent-elements-transitive
          • Vl-necessary-elements-direct
          • Vl-modulelist-everinstanced
          • Vl-dependent-elements-direct
          • Vl-design-deporder-modules
          • Vl-design-check-complete
          • Vl-design-upgraph
          • Immdeps
            • Immdeps-main
            • Vl-immdeps
            • Immdeps-top
            • Vl-immdepgraph
              • Vl-immdepgraph-p
              • Vl-immdepgraph-fix
              • Vl-immdepgraph-equiv
              • Make-vl-immdepgraph
              • Vl-immdepgraph->reportcard
              • Vl-immdepgraph->deps
              • Vl-immdepgraph->all-okp
              • Change-vl-immdepgraph
            • Vl-depgraph
          • Vl-design-downgraph
          • Vl-collect-dependencies
          • Vl-hierarchy-free
        • Range-tools
        • Finding-by-name
        • Stmt-tools
        • Modnamespace
        • Flat-warnings
        • Reordering-by-name
        • Datatype-tools
        • Syscalls
        • Allexprs
        • Lvalues
        • Port-tools
      • Transforms
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Vl-immdepgraph

Vl-immdepgraph-equiv

Basic equivalence relation for vl-immdepgraph structures.

Definitions and Theorems

Function: vl-immdepgraph-equiv$inline

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

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

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

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

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

Theorem: vl-immdepgraph-fix-under-vl-immdepgraph-equiv

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

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

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

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

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

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

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

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

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