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• Edgesynth

Vl-edgesynth-stmt-p

Supported statements: if statements, block statements, null statements, non-blocking assignments to whole identifiers.

Signature

(vl-edgesynth-stmt-p x) → *

Arguments

x — Guard (vl-stmt-p x).

Theorem: vl-edgesynth-stmtlist-p-of-cons

(defthm vl-edgesynth-stmtlist-p-of-cons
  (equal (vl-edgesynth-stmtlist-p (cons acl2::a acl2::x))
         (and (vl-edgesynth-stmt-p acl2::a)
              (vl-edgesynth-stmtlist-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-edgesynth-stmtlist-p-of-cdr-when-vl-edgesynth-stmtlist-p

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

Theorem: vl-edgesynth-stmtlist-p-when-not-consp

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

Theorem: vl-edgesynth-stmt-p-of-car-when-vl-edgesynth-stmtlist-p

(defthm vl-edgesynth-stmt-p-of-car-when-vl-edgesynth-stmtlist-p
  (implies (vl-edgesynth-stmtlist-p acl2::x)
           (iff (vl-edgesynth-stmt-p (car acl2::x))
                (or (consp acl2::x)
                    (vl-edgesynth-stmt-p nil))))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-vl-edgesynth-stmtlist-p-compound-recognizer

(defthm true-listp-when-vl-edgesynth-stmtlist-p-compound-recognizer
  (implies (vl-edgesynth-stmtlist-p acl2::x)
           (true-listp acl2::x))
  :rule-classes :compound-recognizer)

Theorem: vl-edgesynth-stmtlist-p-of-list-fix

(defthm vl-edgesynth-stmtlist-p-of-list-fix
  (implies (vl-edgesynth-stmtlist-p acl2::x)
           (vl-edgesynth-stmtlist-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-edgesynth-stmtlist-p-of-sfix

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

Theorem: vl-edgesynth-stmtlist-p-of-insert

(defthm vl-edgesynth-stmtlist-p-of-insert
  (iff (vl-edgesynth-stmtlist-p (insert acl2::a acl2::x))
       (and (vl-edgesynth-stmtlist-p (sfix acl2::x))
            (vl-edgesynth-stmt-p acl2::a)))
  :rule-classes ((:rewrite)))

Theorem: vl-edgesynth-stmtlist-p-of-delete

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

Theorem: vl-edgesynth-stmtlist-p-of-mergesort

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

Theorem: vl-edgesynth-stmtlist-p-of-union

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

Theorem: vl-edgesynth-stmtlist-p-of-intersect-1

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

Theorem: vl-edgesynth-stmtlist-p-of-intersect-2

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

Theorem: vl-edgesynth-stmtlist-p-of-difference

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

Theorem: vl-edgesynth-stmtlist-p-of-duplicated-members

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

Theorem: vl-edgesynth-stmtlist-p-of-rev

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

Theorem: vl-edgesynth-stmtlist-p-of-append

(defthm vl-edgesynth-stmtlist-p-of-append
  (equal (vl-edgesynth-stmtlist-p (append acl2::a acl2::b))
         (and (vl-edgesynth-stmtlist-p (list-fix acl2::a))
              (vl-edgesynth-stmtlist-p acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: vl-edgesynth-stmtlist-p-of-rcons

(defthm vl-edgesynth-stmtlist-p-of-rcons
  (iff (vl-edgesynth-stmtlist-p (acl2::rcons acl2::a acl2::x))
       (and (vl-edgesynth-stmt-p acl2::a)
            (vl-edgesynth-stmtlist-p (list-fix acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-edgesynth-stmt-p-when-member-equal-of-vl-edgesynth-stmtlist-p

(defthm
   vl-edgesynth-stmt-p-when-member-equal-of-vl-edgesynth-stmtlist-p
  (and (implies (and (member-equal acl2::a acl2::x)
                     (vl-edgesynth-stmtlist-p acl2::x))
                (vl-edgesynth-stmt-p acl2::a))
       (implies (and (vl-edgesynth-stmtlist-p acl2::x)
                     (member-equal acl2::a acl2::x))
                (vl-edgesynth-stmt-p acl2::a)))
  :rule-classes ((:rewrite)))

Theorem: vl-edgesynth-stmtlist-p-when-subsetp-equal

(defthm vl-edgesynth-stmtlist-p-when-subsetp-equal
  (and (implies (and (subsetp-equal acl2::x acl2::y)
                     (vl-edgesynth-stmtlist-p acl2::y))
                (equal (vl-edgesynth-stmtlist-p acl2::x)
                       (true-listp acl2::x)))
       (implies (and (vl-edgesynth-stmtlist-p acl2::y)
                     (subsetp-equal acl2::x acl2::y))
                (equal (vl-edgesynth-stmtlist-p acl2::x)
                       (true-listp acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: vl-edgesynth-stmtlist-p-of-set-difference-equal

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

Theorem: vl-edgesynth-stmtlist-p-of-intersection-equal-1

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

Theorem: vl-edgesynth-stmtlist-p-of-intersection-equal-2

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

Theorem: vl-edgesynth-stmtlist-p-of-union-equal

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

Theorem: vl-edgesynth-stmtlist-p-of-take

(defthm vl-edgesynth-stmtlist-p-of-take
  (implies (vl-edgesynth-stmtlist-p (double-rewrite acl2::x))
           (iff (vl-edgesynth-stmtlist-p (take acl2::n acl2::x))
                (or (vl-edgesynth-stmt-p nil)
                    (<= (nfix acl2::n) (len acl2::x)))))
  :rule-classes ((:rewrite)))

Theorem: vl-edgesynth-stmtlist-p-of-repeat

(defthm vl-edgesynth-stmtlist-p-of-repeat
  (iff (vl-edgesynth-stmtlist-p (repeat acl2::n acl2::x))
       (or (vl-edgesynth-stmt-p acl2::x)
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: vl-edgesynth-stmt-p-of-nth-when-vl-edgesynth-stmtlist-p

(defthm vl-edgesynth-stmt-p-of-nth-when-vl-edgesynth-stmtlist-p
  (implies (and (vl-edgesynth-stmtlist-p acl2::x)
                (< (nfix acl2::n) (len acl2::x)))
           (vl-edgesynth-stmt-p (nth acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: vl-edgesynth-stmtlist-p-of-update-nth

(defthm vl-edgesynth-stmtlist-p-of-update-nth
 (implies
  (vl-edgesynth-stmtlist-p (double-rewrite acl2::x))
  (iff
      (vl-edgesynth-stmtlist-p (update-nth acl2::n acl2::y acl2::x))
      (and (vl-edgesynth-stmt-p acl2::y)
           (or (<= (nfix acl2::n) (len acl2::x))
               (vl-edgesynth-stmt-p nil)))))
 :rule-classes ((:rewrite)))

Theorem: vl-edgesynth-stmtlist-p-of-butlast

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

Theorem: vl-edgesynth-stmtlist-p-of-nthcdr

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

Theorem: vl-edgesynth-stmtlist-p-of-last

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

Theorem: vl-edgesynth-stmtlist-p-of-remove

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

Theorem: vl-edgesynth-stmtlist-p-of-revappend

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

Theorem: vl-stmt-p-when-vl-edgesynth-stmt-p

(defthm vl-stmt-p-when-vl-edgesynth-stmt-p
  (implies (vl-edgesynth-stmt-p x)
           (vl-stmt-p x)))

Theorem: vl-stmtlist-p-when-vl-edgesynth-stmtlist-p

(defthm vl-stmtlist-p-when-vl-edgesynth-stmtlist-p
  (implies (vl-edgesynth-stmtlist-p x)
           (vl-stmtlist-p x)))

Theorem: vl-edgesynth-stmt-p-of-make-vl-assignstmt

(defthm vl-edgesynth-stmt-p-of-make-vl-assignstmt
  (implies (and (force (equal type :vl-nonblocking))
                (force (vl-idexpr-p lvalue))
                (force (vl-expr->finaltype lvalue))
                (force (posp (vl-expr->finalwidth lvalue)))
                (force (vl-expr-p expr))
                (force (vl-maybe-delayoreventcontrol-p ctrl))
                (force (vl-atts-p atts))
                (force (vl-location-p loc)))
           (vl-edgesynth-stmt-p (make-vl-assignstmt :type type
                                                    :lvalue lvalue
                                                    :expr expr
                                                    :ctrl ctrl
                                                    :atts atts
                                                    :loc loc))))

Theorem: vl-assignstmt->type-when-vl-edgesynth-stmt-p

(defthm vl-assignstmt->type-when-vl-edgesynth-stmt-p
  (implies (and (vl-assignstmt-p x)
                (vl-edgesynth-stmt-p x))
           (equal (vl-assignstmt->type x)
                  :vl-nonblocking)))

Theorem: vl-idexpr-p-of-vl-assignstmt->lvalue-when-vl-edgesynth-stmt-p

(defthm
      vl-idexpr-p-of-vl-assignstmt->lvalue-when-vl-edgesynth-stmt-p
  (implies
       (and (vl-assignstmt-p x)
            (vl-edgesynth-stmt-p x))
       (and (vl-idexpr-p (vl-assignstmt->lvalue x))
            (posp (vl-expr->finalwidth (vl-assignstmt->lvalue x)))
            (vl-expr->finaltype (vl-assignstmt->lvalue x)))))

Theorem: vl-edgesynth-stmt-p-of-vl-ifstmt

(defthm vl-edgesynth-stmt-p-of-vl-ifstmt
  (implies
       (and (vl-edgesynth-stmt-p truebranch)
            (vl-edgesynth-stmt-p falsebranch)
            (force (vl-expr-p condition))
            (force (vl-atts-p atts)))
       (vl-edgesynth-stmt-p (make-vl-ifstmt :condition condition
                                            :truebranch truebranch
                                            :falsebranch falsebranch
                                            :atts atts))))

Theorem: vl-edgesynth-stmt-p-of-vl-ifstmt->truebranch

(defthm vl-edgesynth-stmt-p-of-vl-ifstmt->truebranch
  (implies (and (vl-edgesynth-stmt-p x)
                (force (vl-ifstmt-p x)))
           (vl-edgesynth-stmt-p (vl-ifstmt->truebranch x))))

Theorem: vl-edgesynth-stmt-p-of-vl-ifstmt->falsebranch

(defthm vl-edgesynth-stmt-p-of-vl-ifstmt->falsebranch
  (implies (and (vl-edgesynth-stmt-p x)
                (force (vl-ifstmt-p x)))
           (vl-edgesynth-stmt-p (vl-ifstmt->falsebranch x))))

Theorem: vl-edgesynth-stmt-p-of-vl-blockstmt

(defthm vl-edgesynth-stmt-p-of-vl-blockstmt
 (implies
    (and (vl-edgesynth-stmtlist-p stmts)
         (force (equal sequentialp t))
         (force (not name))
         (force (not vardecls))
         (force (not paramdecls))
         (force (not imports))
         (force (vl-atts-p atts)))
    (vl-edgesynth-stmt-p (make-vl-blockstmt :sequentialp sequentialp
                                            :name name
                                            :vardecls vardecls
                                            :paramdecls paramdecls
                                            :imports imports
                                            :loaditems loaditems
                                            :stmts stmts
                                            :atts atts))))

Theorem: vl-blockstmt->sequentialp-when-vl-edgesynth-stmt-p

(defthm vl-blockstmt->sequentialp-when-vl-edgesynth-stmt-p
  (implies (and (vl-edgesynth-stmt-p x)
                (force (vl-blockstmt-p x)))
           (equal (vl-blockstmt->sequentialp x)
                  t)))

Theorem: vl-blockstmt->name-when-vl-edgesynth-stmt-p

(defthm vl-blockstmt->name-when-vl-edgesynth-stmt-p
  (implies (and (vl-edgesynth-stmt-p x)
                (force (vl-blockstmt-p x)))
           (equal (vl-blockstmt->name x) nil)))

Theorem: vl-blockstmt->decls-when-vl-edgesynth-stmt-p

(defthm vl-blockstmt->decls-when-vl-edgesynth-stmt-p
  (implies (and (vl-edgesynth-stmt-p x)
                (force (vl-blockstmt-p x)))
           (and (equal (vl-blockstmt->vardecls x) nil)
                (equal (vl-blockstmt->paramdecls x) nil)
                (equal (vl-blockstmt->imports x) nil))))

Theorem: vl-edgesynth-stmtlist-p-of-vl-blockstmt->stmts

(defthm vl-edgesynth-stmtlist-p-of-vl-blockstmt->stmts
  (implies (and (vl-edgesynth-stmt-p x)
                (force (vl-blockstmt-p x)))
           (vl-edgesynth-stmtlist-p (vl-blockstmt->stmts x))))

Theorem: atomic-cases-for-vl-edgesynth-stmt-p

(defthm atomic-cases-for-vl-edgesynth-stmt-p
  (implies (and (vl-edgesynth-stmt-p x)
                (vl-atomicstmt-p x))
           (or (eq (vl-stmt-kind x) :vl-assignstmt)
               (eq (vl-stmt-kind x) :vl-nullstmt)))
  :rule-classes :forward-chaining)

Subtopics

Vl-edgesynth-stmtlist-p