• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Community
  • 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
        • Range-tools
        • Finding-by-name
          • Fast-finding-by-name
            • Vl-interfaceportlist-alist
            • Vl-genelementlist-alist
            • Vl-vardecllist-alist
            • Vl-portdecllist-alist
            • Vl-paramdecllist-alist
            • Vl-interfacelist-alist
            • Vl-gateinstlist-alist
            • Vl-fundecllist-alist
            • Vl-dpiimportlist-alist
            • Vl-typedeflist-alist
            • Vl-taskdecllist-alist
            • Vl-programlist-alist
            • Vl-packagelist-alist
            • Vl-modulelist-alist
            • Vl-modportlist-alist
            • Vl-modinstlist-alist
            • Vl-genvarlist-alist
            • Vl-configlist-alist
            • Vl-classlist-alist
            • Vl-udplist-alist
            • Vl-vardecl-alist
            • Vl-typedef-alist
            • Vl-taskdecl-alist
            • Vl-program-alist
            • Vl-portdecl-alist
            • Vl-paramdecl-alist
            • Vl-package-alist
            • Vl-module-alist
            • Vl-modport-alist
            • Vl-modinst-alist
            • Vl-interfaceport-alist
            • Vl-interface-alist
            • Vl-genvar-alist
              • Vl-genvar-alist-p
              • Vl-genvar-alist-fix
              • Vl-genvar-alist-equiv
            • Vl-genelement-alist
            • Vl-gateinst-alist
            • Vl-fundecl-alist
            • Vl-dpiimport-alist
            • Vl-config-alist
            • Vl-class-alist
            • Vl-udp-alist
          • Vl-find-interfaceport
          • Vl-find-portdecl
          • Vl-find-taskdecl
          • Vl-find-paramdecl
          • Vl-find-interface
          • Vl-find-gateinst
          • Vl-find-dpiimport
          • Vl-find-vardecl
          • Vl-find-typedef
          • Vl-find-program
          • Vl-find-package
          • Vl-find-module
          • Vl-find-modport
          • Vl-find-modinst
          • Vl-find-genelement
          • Vl-find-fundecl
          • Vl-find-genvar
          • Vl-find-config
          • Vl-find-class
          • Vl-find-udp
          • Vl-modalist
          • Vl-make-portdecl-alist
          • Vl-fast-find-module
          • Vl-fast-find-portdecl
        • 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-genvar-alist

Vl-genvar-alist-p

Recognizer for vl-genvar-alist.

Signature

(vl-genvar-alist-p x) → *

Definitions and Theorems

Function: vl-genvar-alist-p

(defun vl-genvar-alist-p (x)
  (declare (xargs :guard t))
  (let ((__function__ 'vl-genvar-alist-p))
    (declare (ignorable __function__))
    (if (atom x)
        t
      (and (consp (car x))
           (stringp (caar x))
           (vl-genvar-p (cdar x))
           (vl-genvar-alist-p (cdr x))))))

Theorem: vl-genvar-alist-p-of-revappend

(defthm vl-genvar-alist-p-of-revappend
  (equal (vl-genvar-alist-p (revappend acl2::x acl2::y))
         (and (vl-genvar-alist-p (list-fix acl2::x))
              (vl-genvar-alist-p acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-remove

(defthm vl-genvar-alist-p-of-remove
  (implies (vl-genvar-alist-p acl2::x)
           (vl-genvar-alist-p (remove acl2::a acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-last

(defthm vl-genvar-alist-p-of-last
  (implies (vl-genvar-alist-p (double-rewrite acl2::x))
           (vl-genvar-alist-p (last acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-nthcdr

(defthm vl-genvar-alist-p-of-nthcdr
  (implies (vl-genvar-alist-p (double-rewrite acl2::x))
           (vl-genvar-alist-p (nthcdr acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-butlast

(defthm vl-genvar-alist-p-of-butlast
  (implies (vl-genvar-alist-p (double-rewrite acl2::x))
           (vl-genvar-alist-p (butlast acl2::x acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-update-nth

(defthm vl-genvar-alist-p-of-update-nth
  (implies
       (vl-genvar-alist-p (double-rewrite acl2::x))
       (iff (vl-genvar-alist-p (update-nth acl2::n acl2::y acl2::x))
            (and (and (consp acl2::y)
                      (stringp (car acl2::y))
                      (vl-genvar-p (cdr acl2::y)))
                 (or (<= (nfix acl2::n) (len acl2::x))
                     (and (consp nil)
                          (stringp (car nil))
                          (vl-genvar-p (cdr nil)))))))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-repeat

(defthm vl-genvar-alist-p-of-repeat
  (iff (vl-genvar-alist-p (repeat acl2::n acl2::x))
       (or (and (consp acl2::x)
                (stringp (car acl2::x))
                (vl-genvar-p (cdr acl2::x)))
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-take

(defthm vl-genvar-alist-p-of-take
  (implies (vl-genvar-alist-p (double-rewrite acl2::x))
           (iff (vl-genvar-alist-p (take acl2::n acl2::x))
                (or (and (consp nil)
                         (stringp (car nil))
                         (vl-genvar-p (cdr nil)))
                    (<= (nfix acl2::n) (len acl2::x)))))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-union-equal

(defthm vl-genvar-alist-p-of-union-equal
  (equal (vl-genvar-alist-p (union-equal acl2::x acl2::y))
         (and (vl-genvar-alist-p (list-fix acl2::x))
              (vl-genvar-alist-p (double-rewrite acl2::y))))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-intersection-equal-2

(defthm vl-genvar-alist-p-of-intersection-equal-2
  (implies (vl-genvar-alist-p (double-rewrite acl2::y))
           (vl-genvar-alist-p (intersection-equal acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-intersection-equal-1

(defthm vl-genvar-alist-p-of-intersection-equal-1
  (implies (vl-genvar-alist-p (double-rewrite acl2::x))
           (vl-genvar-alist-p (intersection-equal acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-set-difference-equal

(defthm vl-genvar-alist-p-of-set-difference-equal
  (implies
       (vl-genvar-alist-p acl2::x)
       (vl-genvar-alist-p (set-difference-equal acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-set-equiv-congruence

(defthm vl-genvar-alist-p-set-equiv-congruence
  (implies (set-equiv acl2::x acl2::y)
           (equal (vl-genvar-alist-p acl2::x)
                  (vl-genvar-alist-p acl2::y)))
  :rule-classes :congruence)

Theorem: vl-genvar-alist-p-of-rcons

(defthm vl-genvar-alist-p-of-rcons
  (iff (vl-genvar-alist-p (acl2::rcons acl2::a acl2::x))
       (and (and (consp acl2::a)
                 (stringp (car acl2::a))
                 (vl-genvar-p (cdr acl2::a)))
            (vl-genvar-alist-p (list-fix acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-rev

(defthm vl-genvar-alist-p-of-rev
  (equal (vl-genvar-alist-p (rev acl2::x))
         (vl-genvar-alist-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-duplicated-members

(defthm vl-genvar-alist-p-of-duplicated-members
  (implies (vl-genvar-alist-p acl2::x)
           (vl-genvar-alist-p (duplicated-members acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-difference

(defthm vl-genvar-alist-p-of-difference
  (implies (vl-genvar-alist-p acl2::x)
           (vl-genvar-alist-p (difference acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-intersect-2

(defthm vl-genvar-alist-p-of-intersect-2
  (implies (vl-genvar-alist-p acl2::y)
           (vl-genvar-alist-p (intersect acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-intersect-1

(defthm vl-genvar-alist-p-of-intersect-1
  (implies (vl-genvar-alist-p acl2::x)
           (vl-genvar-alist-p (intersect acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-union

(defthm vl-genvar-alist-p-of-union
  (iff (vl-genvar-alist-p (union acl2::x acl2::y))
       (and (vl-genvar-alist-p (sfix acl2::x))
            (vl-genvar-alist-p (sfix acl2::y))))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-mergesort

(defthm vl-genvar-alist-p-of-mergesort
  (iff (vl-genvar-alist-p (mergesort acl2::x))
       (vl-genvar-alist-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-delete

(defthm vl-genvar-alist-p-of-delete
  (implies (vl-genvar-alist-p acl2::x)
           (vl-genvar-alist-p (delete acl2::k acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-insert

(defthm vl-genvar-alist-p-of-insert
  (iff (vl-genvar-alist-p (insert acl2::a acl2::x))
       (and (vl-genvar-alist-p (sfix acl2::x))
            (and (consp acl2::a)
                 (stringp (car acl2::a))
                 (vl-genvar-p (cdr acl2::a)))))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-sfix

(defthm vl-genvar-alist-p-of-sfix
  (iff (vl-genvar-alist-p (sfix acl2::x))
       (or (vl-genvar-alist-p acl2::x)
           (not (setp acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-list-fix

(defthm vl-genvar-alist-p-of-list-fix
  (equal (vl-genvar-alist-p (list-fix acl2::x))
         (vl-genvar-alist-p acl2::x))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-append

(defthm vl-genvar-alist-p-of-append
  (equal (vl-genvar-alist-p (append acl2::a acl2::b))
         (and (vl-genvar-alist-p acl2::a)
              (vl-genvar-alist-p acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-when-not-consp

(defthm vl-genvar-alist-p-when-not-consp
  (implies (not (consp acl2::x))
           (vl-genvar-alist-p acl2::x))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-cdr-when-vl-genvar-alist-p

(defthm vl-genvar-alist-p-of-cdr-when-vl-genvar-alist-p
  (implies (vl-genvar-alist-p (double-rewrite acl2::x))
           (vl-genvar-alist-p (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-cons

(defthm vl-genvar-alist-p-of-cons
  (equal (vl-genvar-alist-p (cons acl2::a acl2::x))
         (and (and (consp acl2::a)
                   (stringp (car acl2::a))
                   (vl-genvar-p (cdr acl2::a)))
              (vl-genvar-alist-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-make-fal

(defthm vl-genvar-alist-p-of-make-fal
  (implies (and (vl-genvar-alist-p acl2::x)
                (vl-genvar-alist-p acl2::y))
           (vl-genvar-alist-p (make-fal acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-p-of-cdr-when-member-equal-of-vl-genvar-alist-p

(defthm vl-genvar-p-of-cdr-when-member-equal-of-vl-genvar-alist-p
  (and (implies (and (vl-genvar-alist-p acl2::x)
                     (member-equal acl2::a acl2::x))
                (vl-genvar-p (cdr acl2::a)))
       (implies (and (member-equal acl2::a acl2::x)
                     (vl-genvar-alist-p acl2::x))
                (vl-genvar-p (cdr acl2::a))))
  :rule-classes ((:rewrite)))

Theorem: stringp-of-car-when-member-equal-of-vl-genvar-alist-p

(defthm stringp-of-car-when-member-equal-of-vl-genvar-alist-p
  (and (implies (and (vl-genvar-alist-p acl2::x)
                     (member-equal acl2::a acl2::x))
                (stringp (car acl2::a)))
       (implies (and (member-equal acl2::a acl2::x)
                     (vl-genvar-alist-p acl2::x))
                (stringp (car acl2::a))))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-fast-alist-clean

(defthm vl-genvar-alist-p-of-fast-alist-clean
  (implies (vl-genvar-alist-p acl2::x)
           (vl-genvar-alist-p (fast-alist-clean acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-hons-shrink-alist

(defthm vl-genvar-alist-p-of-hons-shrink-alist
  (implies (and (vl-genvar-alist-p acl2::x)
                (vl-genvar-alist-p acl2::y))
           (vl-genvar-alist-p (hons-shrink-alist acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-alist-p-of-hons-acons

(defthm vl-genvar-alist-p-of-hons-acons
  (equal (vl-genvar-alist-p (hons-acons acl2::a acl2::n acl2::x))
         (and (stringp acl2::a)
              (vl-genvar-p acl2::n)
              (vl-genvar-alist-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-p-of-cdr-of-hons-assoc-equal-when-vl-genvar-alist-p

(defthm
      vl-genvar-p-of-cdr-of-hons-assoc-equal-when-vl-genvar-alist-p
  (implies
       (vl-genvar-alist-p acl2::x)
       (iff (vl-genvar-p (cdr (hons-assoc-equal acl2::k acl2::x)))
            (hons-assoc-equal acl2::k acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-genvar-p-of-cdar-when-vl-genvar-alist-p

(defthm vl-genvar-p-of-cdar-when-vl-genvar-alist-p
  (implies (vl-genvar-alist-p acl2::x)
           (iff (vl-genvar-p (cdar acl2::x))
                (consp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: stringp-of-caar-when-vl-genvar-alist-p

(defthm stringp-of-caar-when-vl-genvar-alist-p
  (implies (vl-genvar-alist-p acl2::x)
           (iff (stringp (caar acl2::x))
                (consp acl2::x)))
  :rule-classes ((:rewrite)))