• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Community
  • Std
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Apt
      • Error-checking
      • Fty-extensions
      • Isar
      • Kestrel-utilities
      • Set
      • C
      • Soft
      • Bv
      • Imp-language
      • Ethereum
      • Event-macros
      • Java
        • Atj
        • Aij
        • Language
          • Syntax
            • Grammar
            • Unicode-escapes
            • Unicode-input-char
            • Escape-sequence
            • Identifiers
              • Ascii-identifier-part-p
              • Identifier
              • Tidentifier
              • Umidentifier
              • Ascii-identifier-ignore-p
              • Ascii-identifier-start-p
              • Nonascii-identifier-part-p
              • Nonascii-identifier-ignore-p
              • Nonascii-identifier-start-p
              • Identifier-part-listp
              • Identifier-start-p
              • Identifier-part-p
              • Identifier-ignore-p
              • Tidentifierp
              • No-identifier-ignore-p
                • No-identifier-ignore-p-basics
              • Umidentifier-fix
              • Tidentifier-fix
              • Identifierp
              • Identifier-fix
              • Umidentifierp
              • Identifier-list
            • Primitive-types
            • Reference-types
            • Unicode-characters
            • Keywords
            • Integer-literals
            • String-literals
            • Octal-digits
            • Hexadecimal-digits
            • Decimal-digits
            • Binary-digits
            • Character-literals
            • Null-literal
            • Floating-point-literals
            • Boolean-literals
            • Package-names
            • Literals
          • Semantics
      • Riscv
      • Bitcoin
      • Zcash
      • Yul
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Cryptography
      • Number-theory
      • Axe
      • Lists-light
      • Builtins
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• No-identifier-ignore-p

No-identifier-ignore-p-basics

Basic theorems about no-identifier-ignore-p, generated by std::deflist.

Definitions and Theorems

Theorem: no-identifier-ignore-p-of-cons

(defthm no-identifier-ignore-p-of-cons
  (equal (no-identifier-ignore-p (cons acl2::a acl2::x))
         (and (not (identifier-ignore-p acl2::a))
              (no-identifier-ignore-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-cdr-when-no-identifier-ignore-p

(defthm no-identifier-ignore-p-of-cdr-when-no-identifier-ignore-p
  (implies (no-identifier-ignore-p (double-rewrite acl2::x))
           (no-identifier-ignore-p (cdr acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-when-not-consp

(defthm no-identifier-ignore-p-when-not-consp
  (implies (not (consp acl2::x))
           (no-identifier-ignore-p acl2::x))
  :rule-classes ((:rewrite)))

Theorem: identifier-ignore-p-of-car-when-no-identifier-ignore-p

(defthm identifier-ignore-p-of-car-when-no-identifier-ignore-p
  (implies (no-identifier-ignore-p acl2::x)
           (iff (identifier-ignore-p (car acl2::x))
                (and (not (consp acl2::x))
                     (identifier-ignore-p nil))))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-append

(defthm no-identifier-ignore-p-of-append
  (equal (no-identifier-ignore-p (append acl2::a acl2::b))
         (and (no-identifier-ignore-p acl2::a)
              (no-identifier-ignore-p acl2::b)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-list-fix

(defthm no-identifier-ignore-p-of-list-fix
  (equal (no-identifier-ignore-p (list-fix acl2::x))
         (no-identifier-ignore-p acl2::x))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-sfix

(defthm no-identifier-ignore-p-of-sfix
  (iff (no-identifier-ignore-p (sfix acl2::x))
       (or (no-identifier-ignore-p acl2::x)
           (not (setp acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-insert

(defthm no-identifier-ignore-p-of-insert
  (iff (no-identifier-ignore-p (insert acl2::a acl2::x))
       (and (no-identifier-ignore-p (sfix acl2::x))
            (not (identifier-ignore-p acl2::a))))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-delete

(defthm no-identifier-ignore-p-of-delete
  (implies (no-identifier-ignore-p acl2::x)
           (no-identifier-ignore-p (delete acl2::k acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-mergesort

(defthm no-identifier-ignore-p-of-mergesort
  (iff (no-identifier-ignore-p (mergesort acl2::x))
       (no-identifier-ignore-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-union

(defthm no-identifier-ignore-p-of-union
  (iff (no-identifier-ignore-p (union acl2::x acl2::y))
       (and (no-identifier-ignore-p (sfix acl2::x))
            (no-identifier-ignore-p (sfix acl2::y))))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-intersect-1

(defthm no-identifier-ignore-p-of-intersect-1
  (implies (no-identifier-ignore-p acl2::x)
           (no-identifier-ignore-p (intersect acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-intersect-2

(defthm no-identifier-ignore-p-of-intersect-2
  (implies (no-identifier-ignore-p acl2::y)
           (no-identifier-ignore-p (intersect acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-difference

(defthm no-identifier-ignore-p-of-difference
  (implies (no-identifier-ignore-p acl2::x)
           (no-identifier-ignore-p (difference acl2::x acl2::y)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-duplicated-members

(defthm no-identifier-ignore-p-of-duplicated-members
  (implies (no-identifier-ignore-p acl2::x)
           (no-identifier-ignore-p (duplicated-members acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-rev

(defthm no-identifier-ignore-p-of-rev
  (equal (no-identifier-ignore-p (rev acl2::x))
         (no-identifier-ignore-p (list-fix acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-rcons

(defthm no-identifier-ignore-p-of-rcons
  (iff (no-identifier-ignore-p (rcons acl2::a acl2::x))
       (and (not (identifier-ignore-p acl2::a))
            (no-identifier-ignore-p (list-fix acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: identifier-ignore-p-when-member-equal-of-no-identifier-ignore-p

(defthm
    identifier-ignore-p-when-member-equal-of-no-identifier-ignore-p
  (and (implies (and (member-equal acl2::a acl2::x)
                     (no-identifier-ignore-p acl2::x))
                (not (identifier-ignore-p acl2::a)))
       (implies (and (no-identifier-ignore-p acl2::x)
                     (member-equal acl2::a acl2::x))
                (not (identifier-ignore-p acl2::a))))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-when-subsetp-equal

(defthm no-identifier-ignore-p-when-subsetp-equal
  (and (implies (and (subsetp-equal acl2::x acl2::y)
                     (no-identifier-ignore-p acl2::y))
                (no-identifier-ignore-p acl2::x))
       (implies (and (no-identifier-ignore-p acl2::y)
                     (subsetp-equal acl2::x acl2::y))
                (no-identifier-ignore-p acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-set-equiv-congruence

(defthm no-identifier-ignore-p-set-equiv-congruence
  (implies (set-equiv acl2::x acl2::y)
           (equal (no-identifier-ignore-p acl2::x)
                  (no-identifier-ignore-p acl2::y)))
  :rule-classes :congruence)

Theorem: no-identifier-ignore-p-of-set-difference-equal

(defthm no-identifier-ignore-p-of-set-difference-equal
 (implies
    (no-identifier-ignore-p acl2::x)
    (no-identifier-ignore-p (set-difference-equal acl2::x acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-intersection-equal-1

(defthm no-identifier-ignore-p-of-intersection-equal-1
 (implies
      (no-identifier-ignore-p (double-rewrite acl2::x))
      (no-identifier-ignore-p (intersection-equal acl2::x acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-intersection-equal-2

(defthm no-identifier-ignore-p-of-intersection-equal-2
 (implies
      (no-identifier-ignore-p (double-rewrite acl2::y))
      (no-identifier-ignore-p (intersection-equal acl2::x acl2::y)))
 :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-union-equal

(defthm no-identifier-ignore-p-of-union-equal
  (equal (no-identifier-ignore-p (union-equal acl2::x acl2::y))
         (and (no-identifier-ignore-p (list-fix acl2::x))
              (no-identifier-ignore-p (double-rewrite acl2::y))))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-take

(defthm no-identifier-ignore-p-of-take
  (implies (no-identifier-ignore-p (double-rewrite acl2::x))
           (iff (no-identifier-ignore-p (take acl2::n acl2::x))
                (or (not (identifier-ignore-p nil))
                    (<= (nfix acl2::n) (len acl2::x)))))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-repeat

(defthm no-identifier-ignore-p-of-repeat
  (iff (no-identifier-ignore-p (repeat acl2::n acl2::x))
       (or (not (identifier-ignore-p acl2::x))
           (zp acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: identifier-ignore-p-of-nth-when-no-identifier-ignore-p

(defthm identifier-ignore-p-of-nth-when-no-identifier-ignore-p
  (implies (and (no-identifier-ignore-p acl2::x)
                (< (nfix acl2::n) (len acl2::x)))
           (not (identifier-ignore-p (nth acl2::n acl2::x))))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-update-nth

(defthm no-identifier-ignore-p-of-update-nth
 (implies
  (no-identifier-ignore-p (double-rewrite acl2::x))
  (iff (no-identifier-ignore-p (update-nth acl2::n acl2::y acl2::x))
       (and (not (identifier-ignore-p acl2::y))
            (or (<= (nfix acl2::n) (len acl2::x))
                (not (identifier-ignore-p nil))))))
 :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-butlast

(defthm no-identifier-ignore-p-of-butlast
  (implies (no-identifier-ignore-p (double-rewrite acl2::x))
           (no-identifier-ignore-p (butlast acl2::x acl2::n)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-nthcdr

(defthm no-identifier-ignore-p-of-nthcdr
  (implies (no-identifier-ignore-p (double-rewrite acl2::x))
           (no-identifier-ignore-p (nthcdr acl2::n acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-last

(defthm no-identifier-ignore-p-of-last
  (implies (no-identifier-ignore-p (double-rewrite acl2::x))
           (no-identifier-ignore-p (last acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-remove

(defthm no-identifier-ignore-p-of-remove
  (implies (no-identifier-ignore-p acl2::x)
           (no-identifier-ignore-p (remove acl2::a acl2::x)))
  :rule-classes ((:rewrite)))

Theorem: no-identifier-ignore-p-of-revappend

(defthm no-identifier-ignore-p-of-revappend
  (equal (no-identifier-ignore-p (revappend acl2::x acl2::y))
         (and (no-identifier-ignore-p (list-fix acl2::x))
              (no-identifier-ignore-p acl2::y)))
  :rule-classes ((:rewrite)))