• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
      • Acre-internals
        • Regex
        • Match-string-at
        • Matchstatelist-measure
        • Parse-primitive
        • Matches-remove-zero-length
        • Parse-repeatop
        • Parse-repeatbase
        • Matchstatelist-in-bounds
        • Parse-range
        • Parse-charset-set
        • Parse-charset-atom
        • Match-regex-locs
        • Parse-octal-charcode
        • Parse-k-backref
        • Parse-g-backref
        • Matchstatelist-all-have-backref
        • Parse-repeatmod
        • Parse-charset-elem
        • Parse-charset-aux
        • Parse-hex-charcode
        • Parse-charset
        • Matchstatelist-indices-lte
        • Matchstatelist-indices-gte
        • Match-exact
        • Matches-add-backref
        • Matchresult
        • Preproc-legible-aux
        • Maybe-backref
        • Match-charset
        • Undup-equiv
        • Find-substr
        • Maybe-backref-extract-substr
        • Matchstatelist-min-index
        • Matchstate-in-bounds
        • Match-add-backref
        • Undup
        • Backref-alist-in-bounds
        • Backref
        • Matchstate
        • Matchresult->matched-substr
        • Matchresult->captured-substr!
        • Matchresult->captured-substr
        • Maybe-backref-in-bounds
        • Matchmode
        • Backref-extract-substr
        • Charset-range
        • Matchstate-measure
        • Backref-in-bounds
        • Rev-keys
        • Parse-regex
        • Undup-exec
        • Get-charset
        • Regex-concat2
        • Preproc-legible
        • Matchresult-in-bounds
        • Regex-disjunct2
        • Backref-alist
        • Named-captures-bindings
        • Captures-bindings
        • Matchstatelist
          • Matchstatelist-fix
          • Matchstatelist-equiv
          • Matchstatelist-p
            • Matchstatelist-p-basics
        • Charset-char-regex
        • Repeatmod-p
      • Parse-and-match-regex
      • Match-regex
      • Parse
      • Matchresult->matchedp
      • Match
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • C
    • Proof-checker-array
    • Soft
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Ethereum
    • Leftist-trees
    • Java
    • Riscv
    • Taspi
    • Bitcoin
    • Zcash
    • Des
    • X86isa
    • Sha-2
    • Yul
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Axe
    • Poseidon
    • Where-do-i-place-my-book
    • Aleo
    • Bigmems
    • Builtins
    • Execloader
    • Solidity
    • Paco
    • Concurrent-programs
    • Bls12-377-curves
  • Debugging
  • Community
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Matchstatelist-p

Matchstatelist-p-basics

Basic theorems about matchstatelist-p, generated by std::deflist.

Definitions and Theorems

Theorem: matchstatelist-p-of-cons

(defthm matchstatelist-p-of-cons
  (equal (matchstatelist-p (cons acl2::a acl2::x))
         (and (matchstate-p acl2::a)
              (matchstatelist-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: matchstatelist-p-of-cdr-when-matchstatelist-p

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

Theorem: matchstatelist-p-when-not-consp

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

Theorem: matchstate-p-of-car-when-matchstatelist-p

(defthm matchstate-p-of-car-when-matchstatelist-p
  (implies (matchstatelist-p acl2::x)
           (iff (matchstate-p (car acl2::x))
                (or (consp acl2::x)
                    (matchstate-p nil))))
  :rule-classes ((:rewrite)))

Theorem: true-listp-when-matchstatelist-p-compound-recognizer

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

Theorem: matchstatelist-p-of-list-fix

(defthm matchstatelist-p-of-list-fix
  (implies (matchstatelist-p acl2::x)
           (matchstatelist-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: matchstatelist-p-of-rev

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

Theorem: matchstatelist-p-of-append

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

Theorem: matchstatelist-p-of-rcons

(defthm matchstatelist-p-of-rcons
  (iff (matchstatelist-p (rcons acl2::a acl2::x))
       (and (matchstate-p acl2::a)
            (matchstatelist-p (list-fix acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: matchstate-p-when-member-equal-of-matchstatelist-p

(defthm matchstate-p-when-member-equal-of-matchstatelist-p
  (and (implies (and (member-equal acl2::a acl2::x)
                     (matchstatelist-p acl2::x))
                (matchstate-p acl2::a))
       (implies (and (matchstatelist-p acl2::x)
                     (member-equal acl2::a acl2::x))
                (matchstate-p acl2::a)))
  :rule-classes ((:rewrite)))

Theorem: matchstatelist-p-when-subsetp-equal

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

Theorem: matchstatelist-p-of-set-difference-equal

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

Theorem: matchstatelist-p-of-intersection-equal-1

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

Theorem: matchstatelist-p-of-intersection-equal-2

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

Theorem: matchstatelist-p-of-union-equal

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

Theorem: matchstatelist-p-of-undup

(defthm matchstatelist-p-of-undup
  (implies (matchstatelist-p x)
           (matchstatelist-p (undup x)))
  :rule-classes ((:rewrite)))