• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Community
  • Std
  • Proof-automation
  • Macro-libraries
    • B*
    • Defunc
    • Fty
    • Apt
    • Std/util
    • Defdata
    • Defrstobj
    • Seq
    • Match-tree
    • Defrstobj
    • With-supporters
    • Def-partial-measure
    • Template-subst
    • Soft
    • Defthm-domain
    • Event-macros
      • Evmac-input-hints-p
      • Evmac-input-print-p
      • Event-macro-input-processing
      • Function-definedness
      • Event-macro-screen-printing
      • Make-event-terse
      • Event-macro-applicability-conditions
        • Evmac-input-hints-p
        • Event-macro-applicability-condition-utilities
          • Evmac-appcond-theorem
          • Evmac-appcond-theorem-list
          • Evmac-appcondp
          • Evmac-ensure-no-extra-hints
          • Make-evmac-appcond?
          • Evmac-appcond-theorems-no-extra-hints
          • Evmac-appcond-listp
            • Evmac-appcond-listp-basics
      • Event-macro-results
      • Template-generators
      • Event-macro-event-generators
      • Event-macro-proof-preparation
      • Try-event
      • Restore-output?
      • Restore-output
      • Fail-event
      • Cw-event
      • Event-macro-xdoc-constructors
      • Event-macro-intro-macros
    • Def-universal-equiv
    • Def-saved-obligs
    • With-supporters-after
    • Definec
    • Sig
    • Outer-local
    • Data-structures
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Evmac-appcond-listp

Evmac-appcond-listp-basics

Basic theorems about evmac-appcond-listp, generated by std::deflist.

Definitions and Theorems

Theorem: evmac-appcond-listp-of-cons

(defthm evmac-appcond-listp-of-cons
  (equal (evmac-appcond-listp (cons a x))
         (and (evmac-appcondp a)
              (evmac-appcond-listp x)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-cdr-when-evmac-appcond-listp

(defthm evmac-appcond-listp-of-cdr-when-evmac-appcond-listp
  (implies (evmac-appcond-listp (double-rewrite x))
           (evmac-appcond-listp (cdr x)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-when-not-consp

(defthm evmac-appcond-listp-when-not-consp
  (implies (not (consp x))
           (equal (evmac-appcond-listp x) (not x)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcondp-of-car-when-evmac-appcond-listp

(defthm evmac-appcondp-of-car-when-evmac-appcond-listp
  (implies (evmac-appcond-listp x)
           (iff (evmac-appcondp (car x))
                (consp x)))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-evmac-appcond-listp-compound-recognizer

(defthm true-listp-when-evmac-appcond-listp-compound-recognizer
  (implies (evmac-appcond-listp x)
           (true-listp x))
  :rule-classes :compound-recognizer)

Theorem: evmac-appcond-listp-of-list-fix

(defthm evmac-appcond-listp-of-list-fix
  (implies (evmac-appcond-listp x)
           (evmac-appcond-listp (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-sfix

(defthm evmac-appcond-listp-of-sfix
  (iff (evmac-appcond-listp (set::sfix x))
       (or (evmac-appcond-listp x)
           (not (set::setp x))))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-insert

(defthm evmac-appcond-listp-of-insert
  (iff (evmac-appcond-listp (set::insert a x))
       (and (evmac-appcond-listp (set::sfix x))
            (evmac-appcondp a)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-delete

(defthm evmac-appcond-listp-of-delete
  (implies (evmac-appcond-listp x)
           (evmac-appcond-listp (set::delete k x)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-mergesort

(defthm evmac-appcond-listp-of-mergesort
  (iff (evmac-appcond-listp (set::mergesort x))
       (evmac-appcond-listp (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-union

(defthm evmac-appcond-listp-of-union
  (iff (evmac-appcond-listp (set::union x y))
       (and (evmac-appcond-listp (set::sfix x))
            (evmac-appcond-listp (set::sfix y))))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-intersect-1

(defthm evmac-appcond-listp-of-intersect-1
  (implies (evmac-appcond-listp x)
           (evmac-appcond-listp (set::intersect x y)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-intersect-2

(defthm evmac-appcond-listp-of-intersect-2
  (implies (evmac-appcond-listp y)
           (evmac-appcond-listp (set::intersect x y)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-difference

(defthm evmac-appcond-listp-of-difference
  (implies (evmac-appcond-listp x)
           (evmac-appcond-listp (set::difference x y)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-duplicated-members

(defthm evmac-appcond-listp-of-duplicated-members
  (implies (evmac-appcond-listp x)
           (evmac-appcond-listp (duplicated-members x)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-rev

(defthm evmac-appcond-listp-of-rev
  (equal (evmac-appcond-listp (rev x))
         (evmac-appcond-listp (list-fix x)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-append

(defthm evmac-appcond-listp-of-append
  (equal (evmac-appcond-listp (append a b))
         (and (evmac-appcond-listp (list-fix a))
              (evmac-appcond-listp b)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-rcons

(defthm evmac-appcond-listp-of-rcons
  (iff (evmac-appcond-listp (rcons a x))
       (and (evmac-appcondp a)
            (evmac-appcond-listp (list-fix x))))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcondp-when-member-equal-of-evmac-appcond-listp

(defthm evmac-appcondp-when-member-equal-of-evmac-appcond-listp
  (and (implies (and (member-equal a x)
                     (evmac-appcond-listp x))
                (evmac-appcondp a))
       (implies (and (evmac-appcond-listp x)
                     (member-equal a x))
                (evmac-appcondp a)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-when-subsetp-equal

(defthm evmac-appcond-listp-when-subsetp-equal
  (and (implies (and (subsetp-equal x y)
                     (evmac-appcond-listp y))
                (equal (evmac-appcond-listp x)
                       (true-listp x)))
       (implies (and (evmac-appcond-listp y)
                     (subsetp-equal x y))
                (equal (evmac-appcond-listp x)
                       (true-listp x))))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-set-difference-equal

(defthm evmac-appcond-listp-of-set-difference-equal
  (implies (evmac-appcond-listp x)
           (evmac-appcond-listp (set-difference-equal x y)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-intersection-equal-1

(defthm evmac-appcond-listp-of-intersection-equal-1
  (implies (evmac-appcond-listp (double-rewrite x))
           (evmac-appcond-listp (intersection-equal x y)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-intersection-equal-2

(defthm evmac-appcond-listp-of-intersection-equal-2
  (implies (evmac-appcond-listp (double-rewrite y))
           (evmac-appcond-listp (intersection-equal x y)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-union-equal

(defthm evmac-appcond-listp-of-union-equal
  (equal (evmac-appcond-listp (union-equal x y))
         (and (evmac-appcond-listp (list-fix x))
              (evmac-appcond-listp (double-rewrite y))))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-take

(defthm evmac-appcond-listp-of-take
  (implies (evmac-appcond-listp (double-rewrite x))
           (iff (evmac-appcond-listp (take n x))
                (or (evmac-appcondp nil)
                    (<= (nfix n) (len x)))))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-repeat

(defthm evmac-appcond-listp-of-repeat
  (iff (evmac-appcond-listp (repeat n x))
       (or (evmac-appcondp x) (zp n)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcondp-of-nth-when-evmac-appcond-listp

(defthm evmac-appcondp-of-nth-when-evmac-appcond-listp
  (implies (evmac-appcond-listp x)
           (iff (evmac-appcondp (nth n x))
                (< (nfix n) (len x))))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-update-nth

(defthm evmac-appcond-listp-of-update-nth
  (implies (evmac-appcond-listp (double-rewrite x))
           (iff (evmac-appcond-listp (update-nth n y x))
                (and (evmac-appcondp y)
                     (or (<= (nfix n) (len x))
                         (evmac-appcondp nil)))))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-butlast

(defthm evmac-appcond-listp-of-butlast
  (implies (evmac-appcond-listp (double-rewrite x))
           (evmac-appcond-listp (butlast x n)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-nthcdr

(defthm evmac-appcond-listp-of-nthcdr
  (implies (evmac-appcond-listp (double-rewrite x))
           (evmac-appcond-listp (nthcdr n x)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-last

(defthm evmac-appcond-listp-of-last
  (implies (evmac-appcond-listp (double-rewrite x))
           (evmac-appcond-listp (last x)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-remove

(defthm evmac-appcond-listp-of-remove
  (implies (evmac-appcond-listp x)
           (evmac-appcond-listp (remove a x)))
  :rule-classes ((:rewrite)))

Theorem: evmac-appcond-listp-of-revappend

(defthm evmac-appcond-listp-of-revappend
  (equal (evmac-appcond-listp (revappend x y))
         (and (evmac-appcond-listp (list-fix x))
              (evmac-appcond-listp y)))
  :rule-classes ((:rewrite)))