• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
    • Gl
    • Esim
    • Vl2014
      • Warnings
      • Primitives
      • Use-set
      • Syntax
      • Getting-started
      • Utilities
      • Loader
      • Transforms
        • Expression-sizing
        • Occform
        • Oprewrite
        • Expand-functions
        • Delayredux
        • Unparameterization
        • Caseelim
        • Split
        • Selresolve
        • Weirdint-elim
        • Vl-delta
          • Vl-delta-p
          • Vl-delta-fix
          • Make-vl-delta
          • Vl-delta-equiv
          • Change-vl-delta
          • Vl-delta->warnings
          • Vl-delta->vardecls
          • Vl-delta->modinsts
          • Vl-delta->gateinsts
          • Vl-delta->assigns
          • Vl-delta->addmods
          • Vl-delta->nf
        • Replicate-insts
        • Rangeresolve
        • Propagate
        • Clean-selects
        • Clean-params
        • Blankargs
        • Inline-mods
        • Expr-simp
        • Trunc
        • Always-top
        • Gatesplit
        • Gate-elim
        • Expression-optimization
        • Elim-supplies
        • Wildelim
        • Drop-blankports
        • Clean-warnings
        • Addinstnames
        • Custom-transform-hooks
        • Annotate
        • Latchcode
        • Elim-unused-vars
        • Problem-modules
      • Lint
      • Mlib
      • Server
      • Kit
      • Printer
      • Esim-vl
      • Well-formedness
    • Sv
    • Fgl
    • Vwsim
    • Vl
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Vl-delta

Vl-delta-equiv

Basic equivalence relation for vl-delta structures.

Definitions and Theorems

Function: vl-delta-equiv$inline

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

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

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

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

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

Theorem: vl-delta-fix-under-vl-delta-equiv

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

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

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

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

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

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

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

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

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