• 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
          • 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
            • Make-implicit-wires
              • Vl-modulelist-make-implicit-wires
              • Vl-make-implicit-wires-aux
              • Shadowcheck
              • Vl-stmt-check-undeclared
              • Vl-make-implicit-wires-main
              • Vl-fundecl-check-undeclared
              • Vl-warn-about-undeclared-wires
              • Vl-implicitst
                • Vl-implicitst-fix
                • Vl-implicitst-equiv
                  • Vl-implicitst-p
                  • Make-vl-implicitst
                  • Vl-implicitst->portdecls
                  • Vl-implicitst->imports
                  • Vl-implicitst->decls
                  • Change-vl-implicitst
                  • Vl-implicitst->ss
                • Vl-blockitem-check-undeclared
                • Vl-taskdecl-check-undeclared
                • Vl-modinst-exprs-for-implicit-wires
                • Vl-blockitemlist-check-undeclared
                • Vl-import-check-undeclared
                • Vl-make-ordinary-implicit-wires
                • Vl-gateinst-exprs-for-implicit-wires
                • Vl-remove-declared-wires
                • Vl-make-port-implicit-wires
                • Vl-module-make-implicit-wires
                • Vl-vardecl-exprs-for-implicit-wires
                • Vl-design-make-implicit-wires
              • Resolve-indexing
              • Origexprs
              • Argresolve
              • Portdecl-sign
              • Designwires
              • Udp-elim
              • Vl-annotate-design
            • 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-implicitst

    Vl-implicitst-equiv

    Basic equivalence relation for vl-implicitst structures.

    Definitions and Theorems

    Function: vl-implicitst-equiv$inline

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

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

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

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

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

    Theorem: vl-implicitst-fix-under-vl-implicitst-equiv

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

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

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

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

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

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

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

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

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