• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
      • Deftreeops
      • Defdefparse
      • Defgrammar
      • Tree-utilities
      • Notation
      • Grammar-parser
      • Meta-circular-validation
      • Parsing-primitives-defresult
      • Parsing-primitives-seq
      • Operations
        • In-terminal-set
          • Leaves-in-termset-when-match-alt/conc/rep/elem-in-termset
          • Symbol-in-termset-p
          • Rulelist-in-termset-p
          • String-in-termset-p
          • Char-insensitive-in-termset-p
          • Chars-sensitive-in-termset-p
            • Chars-sensitive-in-termset-p-basics
          • Chars-insensitive-in-termset-p
          • Concatenation-in-termset-p
          • Char-val-in-termset-p
          • Alternation-in-termset-p
          • Prose-val-in-termset-p
          • Num-val-in-termset-p
          • Char-sensitive-in-termset-p
          • Rule-in-termset-p
          • Repetition-in-termset-p
          • Terminal-strings-in-termset-when-rules-in-termset
          • Element-in-termset-p
          • Nats-in-termset-when-match-sensitive-chars-in-termset
          • Nats-in-termset-when-match-insensitive-chars-in-termset
          • Leaves-in-termset-when-match-char-val-in-termset
          • Nat-in-termset-when-match-sensitive-char-in-termset
          • Nat-in-termset-when-match-insensitive-char-in-termset
          • Leaves-in-termset-when-match-num-val-in-termset
        • Closure
        • Well-formedness
        • Plugging
        • Ambiguity
        • Renaming
        • Numeric-range-retrieval
        • Rule-utilities
        • Removal
        • Character-value-retrieval
      • Examples
      • Differences-with-paper
      • Constructor-utilities
      • Grammar-printer
      • Parsing-tools
    • 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

• Chars-sensitive-in-termset-p

Chars-sensitive-in-termset-p-basics

Basic theorems about chars-sensitive-in-termset-p, generated by std::deflist.

Definitions and Theorems

Theorem: chars-sensitive-in-termset-p-of-cons

(defthm chars-sensitive-in-termset-p-of-cons
  (equal (chars-sensitive-in-termset-p (cons acl2::a acl2::x)
                                       termset)
         (and (char-sensitive-in-termset-p acl2::a termset)
              (chars-sensitive-in-termset-p acl2::x termset)))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-cdr-when-chars-sensitive-in-termset-p

(defthm
 chars-sensitive-in-termset-p-of-cdr-when-chars-sensitive-in-termset-p
 (implies (chars-sensitive-in-termset-p (double-rewrite acl2::x)
                                        termset)
          (chars-sensitive-in-termset-p (cdr acl2::x)
                                        termset))
 :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-when-not-consp

(defthm chars-sensitive-in-termset-p-when-not-consp
  (implies (not (consp acl2::x))
           (chars-sensitive-in-termset-p acl2::x termset))
  :rule-classes ((:rewrite)))

Theorem: char-sensitive-in-termset-p-of-car-when-chars-sensitive-in-termset-p

(defthm
 char-sensitive-in-termset-p-of-car-when-chars-sensitive-in-termset-p
 (implies (chars-sensitive-in-termset-p acl2::x termset)
          (iff (char-sensitive-in-termset-p (car acl2::x)
                                            termset)
               (or (consp acl2::x)
                   (char-sensitive-in-termset-p nil termset))))
 :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-append

(defthm chars-sensitive-in-termset-p-of-append
  (equal (chars-sensitive-in-termset-p (append acl2::a acl2::b)
                                       termset)
         (and (chars-sensitive-in-termset-p acl2::a termset)
              (chars-sensitive-in-termset-p acl2::b termset)))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-list-fix

(defthm chars-sensitive-in-termset-p-of-list-fix
  (equal (chars-sensitive-in-termset-p (list-fix acl2::x)
                                       termset)
         (chars-sensitive-in-termset-p acl2::x termset))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-sfix

(defthm chars-sensitive-in-termset-p-of-sfix
  (iff (chars-sensitive-in-termset-p (sfix acl2::x)
                                     termset)
       (or (chars-sensitive-in-termset-p acl2::x termset)
           (not (setp acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-insert

(defthm chars-sensitive-in-termset-p-of-insert
  (iff (chars-sensitive-in-termset-p (insert acl2::a acl2::x)
                                     termset)
       (and (chars-sensitive-in-termset-p (sfix acl2::x)
                                          termset)
            (char-sensitive-in-termset-p acl2::a termset)))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-delete

(defthm chars-sensitive-in-termset-p-of-delete
  (implies (chars-sensitive-in-termset-p acl2::x termset)
           (chars-sensitive-in-termset-p (delete acl2::k acl2::x)
                                         termset))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-mergesort

(defthm chars-sensitive-in-termset-p-of-mergesort
  (iff (chars-sensitive-in-termset-p (mergesort acl2::x)
                                     termset)
       (chars-sensitive-in-termset-p (list-fix acl2::x)
                                     termset))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-union

(defthm chars-sensitive-in-termset-p-of-union
  (iff (chars-sensitive-in-termset-p (union acl2::x acl2::y)
                                     termset)
       (and (chars-sensitive-in-termset-p (sfix acl2::x)
                                          termset)
            (chars-sensitive-in-termset-p (sfix acl2::y)
                                          termset)))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-intersect-1

(defthm chars-sensitive-in-termset-p-of-intersect-1
  (implies (chars-sensitive-in-termset-p acl2::x termset)
           (chars-sensitive-in-termset-p (intersect acl2::x acl2::y)
                                         termset))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-intersect-2

(defthm chars-sensitive-in-termset-p-of-intersect-2
  (implies (chars-sensitive-in-termset-p acl2::y termset)
           (chars-sensitive-in-termset-p (intersect acl2::x acl2::y)
                                         termset))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-difference

(defthm chars-sensitive-in-termset-p-of-difference
 (implies (chars-sensitive-in-termset-p acl2::x termset)
          (chars-sensitive-in-termset-p (difference acl2::x acl2::y)
                                        termset))
 :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-duplicated-members

(defthm chars-sensitive-in-termset-p-of-duplicated-members
 (implies (chars-sensitive-in-termset-p acl2::x termset)
          (chars-sensitive-in-termset-p (duplicated-members acl2::x)
                                        termset))
 :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-rev

(defthm chars-sensitive-in-termset-p-of-rev
  (equal (chars-sensitive-in-termset-p (rev acl2::x)
                                       termset)
         (chars-sensitive-in-termset-p (list-fix acl2::x)
                                       termset))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-rcons

(defthm chars-sensitive-in-termset-p-of-rcons
  (iff (chars-sensitive-in-termset-p (rcons acl2::a acl2::x)
                                     termset)
       (and (char-sensitive-in-termset-p acl2::a termset)
            (chars-sensitive-in-termset-p (list-fix acl2::x)
                                          termset)))
  :rule-classes ((:rewrite)))

Theorem: char-sensitive-in-termset-p-when-member-equal-of-chars-sensitive-in-termset-p

(defthm
 char-sensitive-in-termset-p-when-member-equal-of-chars-sensitive-in-termset-p
 (and (implies (and (member-equal acl2::a acl2::x)
                    (chars-sensitive-in-termset-p acl2::x termset))
               (char-sensitive-in-termset-p acl2::a termset))
      (implies (and (chars-sensitive-in-termset-p acl2::x termset)
                    (member-equal acl2::a acl2::x))
               (char-sensitive-in-termset-p acl2::a termset)))
 :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-when-subsetp-equal

(defthm chars-sensitive-in-termset-p-when-subsetp-equal
  (and (implies (and (subsetp-equal acl2::x acl2::y)
                     (chars-sensitive-in-termset-p acl2::y termset))
                (chars-sensitive-in-termset-p acl2::x termset))
       (implies (and (chars-sensitive-in-termset-p acl2::y termset)
                     (subsetp-equal acl2::x acl2::y))
                (chars-sensitive-in-termset-p acl2::x termset)))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-set-equiv-congruence

(defthm chars-sensitive-in-termset-p-set-equiv-congruence
  (implies (set-equiv acl2::x acl2::y)
           (equal (chars-sensitive-in-termset-p acl2::x termset)
                  (chars-sensitive-in-termset-p acl2::y termset)))
  :rule-classes :congruence)

Theorem: chars-sensitive-in-termset-p-of-set-difference-equal

(defthm chars-sensitive-in-termset-p-of-set-difference-equal
  (implies (chars-sensitive-in-termset-p acl2::x termset)
           (chars-sensitive-in-termset-p
                (set-difference-equal acl2::x acl2::y)
                termset))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-intersection-equal-1

(defthm chars-sensitive-in-termset-p-of-intersection-equal-1
 (implies
  (chars-sensitive-in-termset-p (double-rewrite acl2::x)
                                termset)
  (chars-sensitive-in-termset-p (intersection-equal acl2::x acl2::y)
                                termset))
 :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-intersection-equal-2

(defthm chars-sensitive-in-termset-p-of-intersection-equal-2
 (implies
  (chars-sensitive-in-termset-p (double-rewrite acl2::y)
                                termset)
  (chars-sensitive-in-termset-p (intersection-equal acl2::x acl2::y)
                                termset))
 :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-union-equal

(defthm chars-sensitive-in-termset-p-of-union-equal
  (equal (chars-sensitive-in-termset-p (union-equal acl2::x acl2::y)
                                       termset)
         (and (chars-sensitive-in-termset-p (list-fix acl2::x)
                                            termset)
              (chars-sensitive-in-termset-p (double-rewrite acl2::y)
                                            termset)))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-take

(defthm chars-sensitive-in-termset-p-of-take
  (implies (chars-sensitive-in-termset-p (double-rewrite acl2::x)
                                         termset)
           (iff (chars-sensitive-in-termset-p (take acl2::n acl2::x)
                                              termset)
                (or (char-sensitive-in-termset-p nil termset)
                    (<= (nfix acl2::n) (len acl2::x)))))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-repeat

(defthm chars-sensitive-in-termset-p-of-repeat
  (iff (chars-sensitive-in-termset-p (repeat acl2::n acl2::x)
                                     termset)
       (or (char-sensitive-in-termset-p acl2::x termset)
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: char-sensitive-in-termset-p-of-nth-when-chars-sensitive-in-termset-p

(defthm
 char-sensitive-in-termset-p-of-nth-when-chars-sensitive-in-termset-p
 (implies (and (chars-sensitive-in-termset-p acl2::x termset)
               (< (nfix acl2::n) (len acl2::x)))
          (char-sensitive-in-termset-p (nth acl2::n acl2::x)
                                       termset))
 :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-update-nth

(defthm chars-sensitive-in-termset-p-of-update-nth
  (implies
       (chars-sensitive-in-termset-p (double-rewrite acl2::x)
                                     termset)
       (iff (chars-sensitive-in-termset-p
                 (update-nth acl2::n acl2::y acl2::x)
                 termset)
            (and (char-sensitive-in-termset-p acl2::y termset)
                 (or (<= (nfix acl2::n) (len acl2::x))
                     (char-sensitive-in-termset-p nil termset)))))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-butlast

(defthm chars-sensitive-in-termset-p-of-butlast
  (implies (chars-sensitive-in-termset-p (double-rewrite acl2::x)
                                         termset)
           (chars-sensitive-in-termset-p (butlast acl2::x acl2::n)
                                         termset))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-nthcdr

(defthm chars-sensitive-in-termset-p-of-nthcdr
  (implies (chars-sensitive-in-termset-p (double-rewrite acl2::x)
                                         termset)
           (chars-sensitive-in-termset-p (nthcdr acl2::n acl2::x)
                                         termset))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-last

(defthm chars-sensitive-in-termset-p-of-last
  (implies (chars-sensitive-in-termset-p (double-rewrite acl2::x)
                                         termset)
           (chars-sensitive-in-termset-p (last acl2::x)
                                         termset))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-remove

(defthm chars-sensitive-in-termset-p-of-remove
  (implies (chars-sensitive-in-termset-p acl2::x termset)
           (chars-sensitive-in-termset-p (remove acl2::a acl2::x)
                                         termset))
  :rule-classes ((:rewrite)))

Theorem: chars-sensitive-in-termset-p-of-revappend

(defthm chars-sensitive-in-termset-p-of-revappend
  (equal (chars-sensitive-in-termset-p (revappend acl2::x acl2::y)
                                       termset)
         (and (chars-sensitive-in-termset-p (list-fix acl2::x)
                                            termset)
              (chars-sensitive-in-termset-p acl2::y termset)))
  :rule-classes ((:rewrite)))