• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Acre
    • Milawa
    • Smtlink
    • Aleobft
    • Abnf
      • Deftreeops
      • Defdefparse
      • Defgrammar
      • Abnf-tree-utilities
      • Notation
        • Syntax-abstraction
        • Semantics
          • Tree-terminatedp
            • Tree-list-terminatedp
            • Tree-list-list-terminatedp
          • Tree->string
          • String-has-finite-parse-trees-p
          • Parse-trees-of-string-p
          • Tree-match-element-p
          • Parse-treep
          • Symbol
          • Nat-match-insensitive-char-p
          • String-unambiguousp
          • Tree-match-num-val-p
          • Nats-match-insensitive-chars-p
          • Tree-option
          • String-parsablep
          • Lookup-rulename
          • Nats-match-sensitive-chars-p
          • Numrep-match-repeat-range-p
          • Tree-match-char-val-p
          • Tree-list-match-repetition-p
          • String-ambiguousp
          • Nat-match-sensitive-char-p
          • Parse
          • Tree-match-prose-val-p
          • Theorems-about-terminated-trees-matching-elements
          • Tree-option-result
          • Tree-list-result
          • Tree-list-list-result
          • Tree-result
          • Tree-list-list-match-concatenation-p
          • Languagep
          • Terminal-string-for-rules-p
          • Tree-list-list-match-alternation-p
          • Tree-list-match-element-p
          • Parse!
          • String
          • Tree-set
          • Trees
        • Abstract-syntax
        • Core-rules
        • Concrete-syntax
      • Grammar-parser
      • Meta-circular-validation
      • Parsing-primitives-defresult
      • Parsing-primitives-seq
      • Operations
      • Examples
      • Differences-with-paper
      • Grammar-printer
      • Parsing-tools
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • Proof-checker-array
    • Soft
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Leftist-trees
    • C
    • Java
    • Taspi
    • Bitcoin
    • Des
    • Ethereum
    • X86isa
    • Sha-2
    • Yul
    • Riscv
    • Zcash
    • Proof-checker-itp13
    • Regex
    • ACL2-programming-language
    • Json
    • Jfkr
    • Equational
    • Cryptography
    • Poseidon
    • Where-do-i-place-my-book
    • Bigmems
    • Builtins
    • Axe
    • Execloader
    • Solidity
    • Leo
    • Paco
    • Concurrent-programs
  • Debugging
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Semantics

Tree-terminatedp

Notion of terminated tree.

Signature

(tree-terminatedp tree) → yes/no

Arguments

tree — Guard (treep tree).

Returns

yes/no — Type (booleanp yes/no).

A tree is terminated iff all its leaves are natural numbers (not rule names).

Function: tree-terminatedp

(defun tree-terminatedp (tree)
  (declare (xargs :guard (treep tree)))
  (tree-case tree
             :leafterm t
             :leafrule nil
             :nonleaf (tree-list-list-terminatedp tree.branches)))

Function: tree-list-terminatedp

(defun tree-list-terminatedp (trees)
  (declare (xargs :guard (tree-listp trees)))
  (or (endp trees)
      (and (tree-terminatedp (car trees))
           (tree-list-terminatedp (cdr trees)))))

Function: tree-list-list-terminatedp

(defun tree-list-list-terminatedp (treess)
  (declare (xargs :guard (tree-list-listp treess)))
  (or (endp treess)
      (and (tree-list-terminatedp (car treess))
           (tree-list-list-terminatedp (cdr treess)))))

Theorem: return-type-of-tree-terminatedp.yes/no

(defthm return-type-of-tree-terminatedp.yes/no
  (b* ((?yes/no (tree-terminatedp tree)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: return-type-of-tree-list-terminatedp.yes/no

(defthm return-type-of-tree-list-terminatedp.yes/no
  (b* ((?yes/no (tree-list-terminatedp trees)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: return-type-of-tree-list-list-terminatedp.yes/no

(defthm return-type-of-tree-list-list-terminatedp.yes/no
  (b* ((?yes/no (tree-list-list-terminatedp treess)))
    (booleanp yes/no))
  :rule-classes :rewrite)

Theorem: tree-terminatedp-of-tree-fix-tree

(defthm tree-terminatedp-of-tree-fix-tree
  (equal (tree-terminatedp (tree-fix tree))
         (tree-terminatedp tree)))

Theorem: tree-list-terminatedp-of-tree-list-fix-trees

(defthm tree-list-terminatedp-of-tree-list-fix-trees
  (equal (tree-list-terminatedp (tree-list-fix trees))
         (tree-list-terminatedp trees)))

Theorem: tree-list-list-terminatedp-of-tree-list-list-fix-treess

(defthm tree-list-list-terminatedp-of-tree-list-list-fix-treess
  (equal (tree-list-list-terminatedp (tree-list-list-fix treess))
         (tree-list-list-terminatedp treess)))

Theorem: tree-terminatedp-tree-equiv-congruence-on-tree

(defthm tree-terminatedp-tree-equiv-congruence-on-tree
  (implies (tree-equiv tree tree-equiv)
           (equal (tree-terminatedp tree)
                  (tree-terminatedp tree-equiv)))
  :rule-classes :congruence)

Theorem: tree-list-terminatedp-tree-list-equiv-congruence-on-trees

(defthm tree-list-terminatedp-tree-list-equiv-congruence-on-trees
  (implies (tree-list-equiv trees trees-equiv)
           (equal (tree-list-terminatedp trees)
                  (tree-list-terminatedp trees-equiv)))
  :rule-classes :congruence)

Theorem: tree-list-list-terminatedp-tree-list-list-equiv-congruence-on-treess

(defthm
 tree-list-list-terminatedp-tree-list-list-equiv-congruence-on-treess
 (implies (tree-list-list-equiv treess treess-equiv)
          (equal (tree-list-list-terminatedp treess)
                 (tree-list-list-terminatedp treess-equiv)))
 :rule-classes :congruence)

Theorem: tree-list-terminatedp-of-cons

(defthm tree-list-terminatedp-of-cons
  (equal (tree-list-terminatedp (cons acl2::a acl2::x))
         (and (tree-terminatedp acl2::a)
              (tree-list-terminatedp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-cdr-when-tree-list-terminatedp

(defthm tree-list-terminatedp-of-cdr-when-tree-list-terminatedp
  (implies (tree-list-terminatedp (double-rewrite acl2::x))
           (tree-list-terminatedp (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-when-not-consp

(defthm tree-list-terminatedp-when-not-consp
  (implies (not (consp acl2::x))
           (tree-list-terminatedp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: tree-terminatedp-of-car-when-tree-list-terminatedp

(defthm tree-terminatedp-of-car-when-tree-list-terminatedp
  (implies (tree-list-terminatedp acl2::x)
           (tree-terminatedp (car acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-append

(defthm tree-list-terminatedp-of-append
  (equal (tree-list-terminatedp (append acl2::a acl2::b))
         (and (tree-list-terminatedp acl2::a)
              (tree-list-terminatedp acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-list-fix

(defthm tree-list-terminatedp-of-list-fix
  (equal (tree-list-terminatedp (list-fix acl2::x))
         (tree-list-terminatedp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-sfix

(defthm tree-list-terminatedp-of-sfix
  (iff (tree-list-terminatedp (sfix acl2::x))
       (or (tree-list-terminatedp acl2::x)
           (not (setp acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-insert

(defthm tree-list-terminatedp-of-insert
  (iff (tree-list-terminatedp (insert acl2::a acl2::x))
       (and (tree-list-terminatedp (sfix acl2::x))
            (tree-terminatedp acl2::a)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-delete

(defthm tree-list-terminatedp-of-delete
  (implies (tree-list-terminatedp acl2::x)
           (tree-list-terminatedp (delete acl2::k acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-mergesort

(defthm tree-list-terminatedp-of-mergesort
  (iff (tree-list-terminatedp (mergesort acl2::x))
       (tree-list-terminatedp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-union

(defthm tree-list-terminatedp-of-union
  (iff (tree-list-terminatedp (union acl2::x acl2::y))
       (and (tree-list-terminatedp (sfix acl2::x))
            (tree-list-terminatedp (sfix acl2::y))))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-intersect-1

(defthm tree-list-terminatedp-of-intersect-1
  (implies (tree-list-terminatedp acl2::x)
           (tree-list-terminatedp (intersect acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-intersect-2

(defthm tree-list-terminatedp-of-intersect-2
  (implies (tree-list-terminatedp acl2::y)
           (tree-list-terminatedp (intersect acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-difference

(defthm tree-list-terminatedp-of-difference
  (implies (tree-list-terminatedp acl2::x)
           (tree-list-terminatedp (difference acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-duplicated-members

(defthm tree-list-terminatedp-of-duplicated-members
  (implies (tree-list-terminatedp acl2::x)
           (tree-list-terminatedp (duplicated-members acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-rev

(defthm tree-list-terminatedp-of-rev
  (equal (tree-list-terminatedp (rev acl2::x))
         (tree-list-terminatedp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-rcons

(defthm tree-list-terminatedp-of-rcons
  (iff (tree-list-terminatedp (rcons acl2::a acl2::x))
       (and (tree-terminatedp acl2::a)
            (tree-list-terminatedp (list-fix acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: tree-terminatedp-when-member-equal-of-tree-list-terminatedp

(defthm tree-terminatedp-when-member-equal-of-tree-list-terminatedp
  (and (implies (and (member-equal acl2::a acl2::x)
                     (tree-list-terminatedp acl2::x))
                (tree-terminatedp acl2::a))
       (implies (and (tree-list-terminatedp acl2::x)
                     (member-equal acl2::a acl2::x))
                (tree-terminatedp acl2::a)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-when-subsetp-equal

(defthm tree-list-terminatedp-when-subsetp-equal
  (and (implies (and (subsetp-equal acl2::x acl2::y)
                     (tree-list-terminatedp acl2::y))
                (tree-list-terminatedp acl2::x))
       (implies (and (tree-list-terminatedp acl2::y)
                     (subsetp-equal acl2::x acl2::y))
                (tree-list-terminatedp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-set-equiv-congruence

(defthm tree-list-terminatedp-set-equiv-congruence
  (implies (set-equiv acl2::x acl2::y)
           (equal (tree-list-terminatedp acl2::x)
                  (tree-list-terminatedp acl2::y)))
  :rule-classes :congruence)

Theorem: tree-list-terminatedp-of-set-difference-equal

(defthm tree-list-terminatedp-of-set-difference-equal
 (implies
     (tree-list-terminatedp acl2::x)
     (tree-list-terminatedp (set-difference-equal acl2::x acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-intersection-equal-1

(defthm tree-list-terminatedp-of-intersection-equal-1
  (implies
       (tree-list-terminatedp (double-rewrite acl2::x))
       (tree-list-terminatedp (intersection-equal acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-intersection-equal-2

(defthm tree-list-terminatedp-of-intersection-equal-2
  (implies
       (tree-list-terminatedp (double-rewrite acl2::y))
       (tree-list-terminatedp (intersection-equal acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-union-equal

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

Theorem: tree-list-terminatedp-of-take

(defthm tree-list-terminatedp-of-take
  (implies (tree-list-terminatedp (double-rewrite acl2::x))
           (iff (tree-list-terminatedp (take acl2::n acl2::x))
                (or (tree-terminatedp nil)
                    (<= (nfix acl2::n) (len acl2::x)))))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-repeat

(defthm tree-list-terminatedp-of-repeat
  (iff (tree-list-terminatedp (repeat acl2::n acl2::x))
       (or (tree-terminatedp acl2::x)
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: tree-terminatedp-of-nth-when-tree-list-terminatedp

(defthm tree-terminatedp-of-nth-when-tree-list-terminatedp
  (implies (tree-list-terminatedp acl2::x)
           (tree-terminatedp (nth acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-update-nth

(defthm tree-list-terminatedp-of-update-nth
 (implies
   (tree-list-terminatedp (double-rewrite acl2::x))
   (iff (tree-list-terminatedp (update-nth acl2::n acl2::y acl2::x))
        (and (tree-terminatedp acl2::y)
             (or (<= (nfix acl2::n) (len acl2::x))
                 (tree-terminatedp nil)))))
 :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-butlast

(defthm tree-list-terminatedp-of-butlast
  (implies (tree-list-terminatedp (double-rewrite acl2::x))
           (tree-list-terminatedp (butlast acl2::x acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-nthcdr

(defthm tree-list-terminatedp-of-nthcdr
  (implies (tree-list-terminatedp (double-rewrite acl2::x))
           (tree-list-terminatedp (nthcdr acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-last

(defthm tree-list-terminatedp-of-last
  (implies (tree-list-terminatedp (double-rewrite acl2::x))
           (tree-list-terminatedp (last acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-remove

(defthm tree-list-terminatedp-of-remove
  (implies (tree-list-terminatedp acl2::x)
           (tree-list-terminatedp (remove acl2::a acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-revappend

(defthm tree-list-terminatedp-of-revappend
  (equal (tree-list-terminatedp (revappend acl2::x acl2::y))
         (and (tree-list-terminatedp (list-fix acl2::x))
              (tree-list-terminatedp acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-cons

(defthm tree-list-list-terminatedp-of-cons
  (equal (tree-list-list-terminatedp (cons acl2::a acl2::x))
         (and (tree-list-terminatedp acl2::a)
              (tree-list-list-terminatedp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-cdr-when-tree-list-list-terminatedp

(defthm
  tree-list-list-terminatedp-of-cdr-when-tree-list-list-terminatedp
  (implies (tree-list-list-terminatedp (double-rewrite acl2::x))
           (tree-list-list-terminatedp (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-when-not-consp

(defthm tree-list-list-terminatedp-when-not-consp
  (implies (not (consp acl2::x))
           (tree-list-list-terminatedp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-car-when-tree-list-list-terminatedp

(defthm tree-list-terminatedp-of-car-when-tree-list-list-terminatedp
  (implies (tree-list-list-terminatedp acl2::x)
           (tree-list-terminatedp (car acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-append

(defthm tree-list-list-terminatedp-of-append
  (equal (tree-list-list-terminatedp (append acl2::a acl2::b))
         (and (tree-list-list-terminatedp acl2::a)
              (tree-list-list-terminatedp acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-list-fix

(defthm tree-list-list-terminatedp-of-list-fix
  (equal (tree-list-list-terminatedp (list-fix acl2::x))
         (tree-list-list-terminatedp acl2::x))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-sfix

(defthm tree-list-list-terminatedp-of-sfix
  (iff (tree-list-list-terminatedp (sfix acl2::x))
       (or (tree-list-list-terminatedp acl2::x)
           (not (setp acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-insert

(defthm tree-list-list-terminatedp-of-insert
  (iff (tree-list-list-terminatedp (insert acl2::a acl2::x))
       (and (tree-list-list-terminatedp (sfix acl2::x))
            (tree-list-terminatedp acl2::a)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-delete

(defthm tree-list-list-terminatedp-of-delete
  (implies (tree-list-list-terminatedp acl2::x)
           (tree-list-list-terminatedp (delete acl2::k acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-mergesort

(defthm tree-list-list-terminatedp-of-mergesort
  (iff (tree-list-list-terminatedp (mergesort acl2::x))
       (tree-list-list-terminatedp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-union

(defthm tree-list-list-terminatedp-of-union
  (iff (tree-list-list-terminatedp (union acl2::x acl2::y))
       (and (tree-list-list-terminatedp (sfix acl2::x))
            (tree-list-list-terminatedp (sfix acl2::y))))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-intersect-1

(defthm tree-list-list-terminatedp-of-intersect-1
  (implies (tree-list-list-terminatedp acl2::x)
           (tree-list-list-terminatedp (intersect acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-intersect-2

(defthm tree-list-list-terminatedp-of-intersect-2
  (implies (tree-list-list-terminatedp acl2::y)
           (tree-list-list-terminatedp (intersect acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-difference

(defthm tree-list-list-terminatedp-of-difference
 (implies (tree-list-list-terminatedp acl2::x)
          (tree-list-list-terminatedp (difference acl2::x acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-duplicated-members

(defthm tree-list-list-terminatedp-of-duplicated-members
 (implies (tree-list-list-terminatedp acl2::x)
          (tree-list-list-terminatedp (duplicated-members acl2::x)))
 :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-rev

(defthm tree-list-list-terminatedp-of-rev
  (equal (tree-list-list-terminatedp (rev acl2::x))
         (tree-list-list-terminatedp (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-rcons

(defthm tree-list-list-terminatedp-of-rcons
  (iff (tree-list-list-terminatedp (rcons acl2::a acl2::x))
       (and (tree-list-terminatedp acl2::a)
            (tree-list-list-terminatedp (list-fix acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-when-member-equal-of-tree-list-list-terminatedp

(defthm
 tree-list-terminatedp-when-member-equal-of-tree-list-list-terminatedp
 (and (implies (and (member-equal acl2::a acl2::x)
                    (tree-list-list-terminatedp acl2::x))
               (tree-list-terminatedp acl2::a))
      (implies (and (tree-list-list-terminatedp acl2::x)
                    (member-equal acl2::a acl2::x))
               (tree-list-terminatedp acl2::a)))
 :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-when-subsetp-equal

(defthm tree-list-list-terminatedp-when-subsetp-equal
  (and (implies (and (subsetp-equal acl2::x acl2::y)
                     (tree-list-list-terminatedp acl2::y))
                (tree-list-list-terminatedp acl2::x))
       (implies (and (tree-list-list-terminatedp acl2::y)
                     (subsetp-equal acl2::x acl2::y))
                (tree-list-list-terminatedp acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-set-equiv-congruence

(defthm tree-list-list-terminatedp-set-equiv-congruence
  (implies (set-equiv acl2::x acl2::y)
           (equal (tree-list-list-terminatedp acl2::x)
                  (tree-list-list-terminatedp acl2::y)))
  :rule-classes :congruence)

Theorem: tree-list-list-terminatedp-of-set-difference-equal

(defthm tree-list-list-terminatedp-of-set-difference-equal
  (implies (tree-list-list-terminatedp acl2::x)
           (tree-list-list-terminatedp
                (set-difference-equal acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-intersection-equal-1

(defthm tree-list-list-terminatedp-of-intersection-equal-1
 (implies
  (tree-list-list-terminatedp (double-rewrite acl2::x))
  (tree-list-list-terminatedp (intersection-equal acl2::x acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-intersection-equal-2

(defthm tree-list-list-terminatedp-of-intersection-equal-2
 (implies
  (tree-list-list-terminatedp (double-rewrite acl2::y))
  (tree-list-list-terminatedp (intersection-equal acl2::x acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-union-equal

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

Theorem: tree-list-list-terminatedp-of-take

(defthm tree-list-list-terminatedp-of-take
  (implies (tree-list-list-terminatedp (double-rewrite acl2::x))
           (iff (tree-list-list-terminatedp (take acl2::n acl2::x))
                (or (tree-list-terminatedp nil)
                    (<= (nfix acl2::n) (len acl2::x)))))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-repeat

(defthm tree-list-list-terminatedp-of-repeat
  (iff (tree-list-list-terminatedp (repeat acl2::n acl2::x))
       (or (tree-list-terminatedp acl2::x)
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-of-nth-when-tree-list-list-terminatedp

(defthm tree-list-terminatedp-of-nth-when-tree-list-list-terminatedp
  (implies (tree-list-list-terminatedp acl2::x)
           (tree-list-terminatedp (nth acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-update-nth

(defthm tree-list-list-terminatedp-of-update-nth
 (implies
  (tree-list-list-terminatedp (double-rewrite acl2::x))
  (iff
   (tree-list-list-terminatedp (update-nth acl2::n acl2::y acl2::x))
   (and (tree-list-terminatedp acl2::y)
        (or (<= (nfix acl2::n) (len acl2::x))
            (tree-list-terminatedp nil)))))
 :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-butlast

(defthm tree-list-list-terminatedp-of-butlast
  (implies (tree-list-list-terminatedp (double-rewrite acl2::x))
           (tree-list-list-terminatedp (butlast acl2::x acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-nthcdr

(defthm tree-list-list-terminatedp-of-nthcdr
  (implies (tree-list-list-terminatedp (double-rewrite acl2::x))
           (tree-list-list-terminatedp (nthcdr acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-last

(defthm tree-list-list-terminatedp-of-last
  (implies (tree-list-list-terminatedp (double-rewrite acl2::x))
           (tree-list-list-terminatedp (last acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-remove

(defthm tree-list-list-terminatedp-of-remove
  (implies (tree-list-list-terminatedp acl2::x)
           (tree-list-list-terminatedp (remove acl2::a acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-list-terminatedp-of-revappend

(defthm tree-list-list-terminatedp-of-revappend
  (equal (tree-list-list-terminatedp (revappend acl2::x acl2::y))
         (and (tree-list-list-terminatedp (list-fix acl2::x))
              (tree-list-list-terminatedp acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: tree-list-terminatedp-when-atom

(defthm tree-list-terminatedp-when-atom
  (implies (atom trees)
           (tree-list-terminatedp trees)))

Theorem: tree-list-list-terminatedp-when-atom

(defthm tree-list-list-terminatedp-when-atom
  (implies (atom treess)
           (tree-list-list-terminatedp treess)))

Theorem: nat-listp-of-tree->string-when-terminated

(defthm nat-listp-of-tree->string-when-terminated
  (implies (tree-terminatedp tree)
           (nat-listp (tree->string tree))))

Theorem: nat-listp-of-tree-list->string-when-terminated

(defthm nat-listp-of-tree-list->string-when-terminated
  (implies (tree-list-terminatedp trees)
           (nat-listp (tree-list->string trees))))

Theorem: nat-listp-of-tree-list-list->string-when-terminated

(defthm nat-listp-of-tree-list-list->string-when-terminated
  (implies (tree-list-list-terminatedp treess)
           (nat-listp (tree-list-list->string treess))))

Theorem: branches-terminated-when-tree-terminated

(defthm branches-terminated-when-tree-terminated
  (implies
       (tree-terminatedp tree)
       (tree-list-list-terminatedp (tree-nonleaf->branches tree))))

Subtopics

Tree-list-terminatedp

Tree-list-list-terminatedp