• 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
      • Transforms
        • Unparameterization
        • Elaborate
        • Addnames
        • Annotate
          • Increment-elim
          • Make-implicit-wires
          • Basic-bind-elim
            • Vl-modulelist-apply-binddelta
            • Vl-interfacelist-apply-binddelta
            • Vl-bindelim-main
            • Vl-bindelim-bindlist
            • Vl-bindelim-find-global-target
            • Vl-interfacelist-bindelim
            • Vl-modulelist-bindelim
            • Vl-interface-bindelim
            • Vl-module-bindelim
            • Vl-bindelim-institem
            • Vl-warn-bindintentlist-undefined
            • Vl-warn-bindintent-undefined
            • Vl-interfacelist-bindelim-insttable
            • Vl-modulelist-bindelim-insttable
            • Vl-warn-binddelta-undefined
            • Vl-interface-bindelim-insttable
            • Vl-interface-apply-binddelta
            • Vl-design-bindelim-pass2
            • Vl-bindelim-modinstlist-add-atts
            • Vl-module-bindelim-insttable
            • Vl-module-apply-binddelta
            • Vl-bindelim-modinst-add-atts
            • Vl-design-bindelim-pass1
            • Vl-bindcontext
            • Vl-bindintent->modinsts
            • Vl-bindelim-insttable
            • Vl-bindintentlist->modinsts
            • Vl-binddelta
              • Vl-binddelta-p
              • Vl-binddelta-fix
              • Vl-bindintent
              • Vl-binddelta-equiv
              • Vl-bindintentlist
            • Vl-design-bindelim
            • Vl-bindelim-institemlist
          • Argresolve
          • Basicsanity
          • Portdecl-sign
          • Enum-names
          • Port-resolve
          • Udp-elim
          • Vl-annotate-design
          • Vl-annotate-module
        • Clean-warnings
        • Eliminitial
        • Custom-transform-hooks
        • Problem-modules
    • X86isa
    • Svl
    • Rtl
  • Software-verification
  • Math
  • Testing-utilities

• Vl-binddelta

Vl-binddelta-p

Recognizer for vl-binddelta.

Signature

(vl-binddelta-p x) → *

Definitions and Theorems

Function: vl-binddelta-p

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

Theorem: vl-binddelta-p-of-revappend

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

Theorem: vl-binddelta-p-of-remove

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

Theorem: vl-binddelta-p-of-last

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

Theorem: vl-binddelta-p-of-nthcdr

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

Theorem: vl-binddelta-p-of-butlast

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

Theorem: vl-binddelta-p-of-update-nth

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

Theorem: vl-binddelta-p-of-repeat

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

Theorem: vl-binddelta-p-of-take

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

Theorem: vl-binddelta-p-of-union-equal

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

Theorem: vl-binddelta-p-of-intersection-equal-2

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

Theorem: vl-binddelta-p-of-intersection-equal-1

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

Theorem: vl-binddelta-p-of-set-difference-equal

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

Theorem: vl-binddelta-p-set-equiv-congruence

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

Theorem: vl-binddelta-p-when-subsetp-equal

(defthm vl-binddelta-p-when-subsetp-equal
  (and (implies (and (subsetp-equal acl2::x acl2::y)
                     (vl-binddelta-p acl2::y))
                (vl-binddelta-p acl2::x))
       (implies (and (vl-binddelta-p acl2::y)
                     (subsetp-equal acl2::x acl2::y))
                (vl-binddelta-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-binddelta-p-of-rcons

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

Theorem: vl-binddelta-p-of-rev

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

Theorem: vl-binddelta-p-of-duplicated-members

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

Theorem: vl-binddelta-p-of-difference

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

Theorem: vl-binddelta-p-of-intersect-2

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

Theorem: vl-binddelta-p-of-intersect-1

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

Theorem: vl-binddelta-p-of-union

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

Theorem: vl-binddelta-p-of-mergesort

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

Theorem: vl-binddelta-p-of-delete

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

Theorem: vl-binddelta-p-of-insert

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

Theorem: vl-binddelta-p-of-sfix

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

Theorem: vl-binddelta-p-of-list-fix

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

Theorem: vl-binddelta-p-of-append

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

Theorem: vl-binddelta-p-when-not-consp

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

Theorem: vl-binddelta-p-of-cdr-when-vl-binddelta-p

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

Theorem: vl-binddelta-p-of-cons

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

Theorem: vl-binddelta-p-of-make-fal

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

Theorem: vl-bindintentlist-p-of-cdr-when-member-equal-of-vl-binddelta-p

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

Theorem: stringp-of-car-when-member-equal-of-vl-binddelta-p

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

Theorem: consp-when-member-equal-of-vl-binddelta-p

(defthm consp-when-member-equal-of-vl-binddelta-p
  (implies (and (vl-binddelta-p acl2::x)
                (member-equal acl2::a acl2::x))
           (consp acl2::a))
  :rule-classes
  ((:rewrite :backchain-limit-lst (0 0))
   (:rewrite :backchain-limit-lst (0 0)
             :corollary (implies (if (member-equal acl2::a acl2::x)
                                     (vl-binddelta-p acl2::x)
                                   'nil)
                                 (consp acl2::a)))))

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

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

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

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

Theorem: vl-binddelta-p-of-hons-acons

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

Theorem: vl-bindintentlist-p-of-cdr-of-hons-assoc-equal-when-vl-binddelta-p

(defthm
 vl-bindintentlist-p-of-cdr-of-hons-assoc-equal-when-vl-binddelta-p
 (implies
  (vl-binddelta-p acl2::x)
  (iff
      (vl-bindintentlist-p (cdr (hons-assoc-equal acl2::k acl2::x)))
      (or (hons-assoc-equal acl2::k acl2::x)
          (vl-bindintentlist-p nil))))
 :rule-classes ((:rewrite)))

Theorem: vl-bindintentlist-p-of-cdar-when-vl-binddelta-p

(defthm vl-bindintentlist-p-of-cdar-when-vl-binddelta-p
  (implies (vl-binddelta-p acl2::x)
           (iff (vl-bindintentlist-p (cdar acl2::x))
                (or (consp acl2::x)
                    (vl-bindintentlist-p nil))))
  :rule-classes ((:rewrite)))

Theorem: stringp-of-caar-when-vl-binddelta-p

(defthm stringp-of-caar-when-vl-binddelta-p
  (implies (vl-binddelta-p acl2::x)
           (iff (stringp (caar acl2::x))
                (or (consp acl2::x) (stringp nil))))
  :rule-classes ((:rewrite)))