• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Debugging
  • Projects
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
    • Sv
    • Vwsim
    • Fgl
    • Vl
      • Syntax
      • Loader
      • Warnings
      • Getting-started
      • Utilities
      • Printer
      • Kit
      • Mlib
      • Transforms
        • Unparameterization
        • Elaborate
        • Addnames
        • Annotate
          • Increment-elim
          • Make-implicit-wires
          • Basic-bind-elim
          • Argresolve
          • Basicsanity
          • Portdecl-sign
          • Enum-names
            • Vl-enumname-range-declarations
            • Vl-interfacelist-add-enumname-declarations
            • Vl-packagelist-add-enumname-declarations
            • Vl-modulelist-add-enumname-declarations
            • Vl-classlist-add-enumname-declarations
            • Vl-enumitemlist-enumname-declarations
            • Vl-enumname-declarations
            • Vl-paramdecl-enumname-declarations
            • Vl-paramdecllist-enumname-declarations
            • Vl-vardecllist-enumname-declarations
            • Vl-typedeflist-enumname-declarations
            • Vl-vardecl-enumname-declarations
            • Vl-typedef-enumname-declarations
            • Vl-package-add-enumname-declarations
            • Vl-design-add-enumname-declarations
            • Vl-interface-add-enumname-declarations
            • Vl-class-add-enumname-declarations
            • Vl-module-add-enumname-declarations
            • Vl-datatype-map
              • Vl-datatype-map-p
              • Vl-datatype-map-fix
              • Vl-datatype-map-equiv
          • Port-resolve
          • Udp-elim
          • Vl-annotate-design
          • Vl-annotate-module
        • Clean-warnings
        • Eliminitial
        • Custom-transform-hooks
        • Problem-modules
    • Svl
    • X86isa
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Vl-datatype-map

Vl-datatype-map-equiv

Basic equivalence relation for vl-datatype-map structures.

Definitions and Theorems

Function: vl-datatype-map-equiv$inline

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

Theorem: vl-datatype-map-equiv-is-an-equivalence

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

Theorem: vl-datatype-map-equiv-implies-equal-vl-datatype-map-fix-1

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

Theorem: vl-datatype-map-fix-under-vl-datatype-map-equiv

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

Theorem: equal-of-vl-datatype-map-fix-1-forward-to-vl-datatype-map-equiv

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

Theorem: equal-of-vl-datatype-map-fix-2-forward-to-vl-datatype-map-equiv

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

Theorem: vl-datatype-map-equiv-of-vl-datatype-map-fix-1-forward

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

Theorem: vl-datatype-map-equiv-of-vl-datatype-map-fix-2-forward

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