• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
      • Deftreeops
        • Deftreeops-implementation
          • Deftreeops-event-generation
          • Deftreeops-info
            • Deftreeops-rulename-info
            • Deftreeops-conc-info
            • Deftreeops-rep-info
            • Deftreeops-numrange-info
            • Deftreeops-charval-info
            • Deftreeops-rep-info-list
            • Deftreeops-conc-info-list
            • Deftreeops-charval-info-alist
              • Deftreeops-charval-info-alistp
              • Deftreeops-charval-info-alist-fix
              • Deftreeops-charval-info-alist-equiv
            • Deftreeops-rulename-info-alist
            • Deftreeops-numrange-info-alist
          • Deftreeops-process-inputs-and-gen-everything
          • Deftreeops-fn
          • Deftreeops-table
          • Deftreeops-input-processing
          • Deftreeops-macro-definition
        • Deftreeops-show-event
        • Deftreeops-show-info
      • Defdefparse
      • Defgrammar
      • Tree-utilities
      • Notation
      • Grammar-parser
      • Meta-circular-validation
      • Parsing-primitives-defresult
      • Parsing-primitives-seq
      • Operations
      • 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

• Deftreeops-charval-info-alist

Deftreeops-charval-info-alist-fix

(deftreeops-charval-info-alist-fix x) is an ACL2::fty alist fixing function that follows the fix-keys strategy.

Signature

(deftreeops-charval-info-alist-fix x) → fty::newx

Arguments

x — Guard (deftreeops-charval-info-alistp x).

Returns

fty::newx — Type (deftreeops-charval-info-alistp fty::newx).

Note that in the execution this is just an inline identity function.

Definitions and Theorems

Function: deftreeops-charval-info-alist-fix$inline

(defun deftreeops-charval-info-alist-fix$inline (x)
  (declare (xargs :guard (deftreeops-charval-info-alistp x)))
  (let ((__function__ 'deftreeops-charval-info-alist-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (if (atom x)
             nil
           (if (consp (car x))
               (cons (cons (char-val-fix (caar x))
                           (deftreeops-charval-info-fix (cdar x)))
                     (deftreeops-charval-info-alist-fix (cdr x)))
             (deftreeops-charval-info-alist-fix (cdr x))))
         :exec x)))

Theorem: deftreeops-charval-info-alistp-of-deftreeops-charval-info-alist-fix

(defthm
 deftreeops-charval-info-alistp-of-deftreeops-charval-info-alist-fix
 (b* ((fty::newx (deftreeops-charval-info-alist-fix$inline x)))
   (deftreeops-charval-info-alistp fty::newx))
 :rule-classes :rewrite)

Theorem: deftreeops-charval-info-alist-fix-when-deftreeops-charval-info-alistp

(defthm
 deftreeops-charval-info-alist-fix-when-deftreeops-charval-info-alistp
 (implies (deftreeops-charval-info-alistp x)
          (equal (deftreeops-charval-info-alist-fix x)
                 x)))

Function: deftreeops-charval-info-alist-equiv$inline

(defun deftreeops-charval-info-alist-equiv$inline (acl2::x acl2::y)
 (declare
      (xargs :guard (and (deftreeops-charval-info-alistp acl2::x)
                         (deftreeops-charval-info-alistp acl2::y))))
 (equal (deftreeops-charval-info-alist-fix acl2::x)
        (deftreeops-charval-info-alist-fix acl2::y)))

Theorem: deftreeops-charval-info-alist-equiv-is-an-equivalence

(defthm deftreeops-charval-info-alist-equiv-is-an-equivalence
  (and (booleanp (deftreeops-charval-info-alist-equiv x y))
       (deftreeops-charval-info-alist-equiv x x)
       (implies (deftreeops-charval-info-alist-equiv x y)
                (deftreeops-charval-info-alist-equiv y x))
       (implies (and (deftreeops-charval-info-alist-equiv x y)
                     (deftreeops-charval-info-alist-equiv y z))
                (deftreeops-charval-info-alist-equiv x z)))
  :rule-classes (:equivalence))

Theorem: deftreeops-charval-info-alist-equiv-implies-equal-deftreeops-charval-info-alist-fix-1

(defthm
 deftreeops-charval-info-alist-equiv-implies-equal-deftreeops-charval-info-alist-fix-1
 (implies (deftreeops-charval-info-alist-equiv acl2::x x-equiv)
          (equal (deftreeops-charval-info-alist-fix acl2::x)
                 (deftreeops-charval-info-alist-fix x-equiv)))
 :rule-classes (:congruence))

Theorem: deftreeops-charval-info-alist-fix-under-deftreeops-charval-info-alist-equiv

(defthm
 deftreeops-charval-info-alist-fix-under-deftreeops-charval-info-alist-equiv
 (deftreeops-charval-info-alist-equiv
      (deftreeops-charval-info-alist-fix acl2::x)
      acl2::x)
 :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-deftreeops-charval-info-alist-fix-1-forward-to-deftreeops-charval-info-alist-equiv

(defthm
 equal-of-deftreeops-charval-info-alist-fix-1-forward-to-deftreeops-charval-info-alist-equiv
 (implies (equal (deftreeops-charval-info-alist-fix acl2::x)
                 acl2::y)
          (deftreeops-charval-info-alist-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: equal-of-deftreeops-charval-info-alist-fix-2-forward-to-deftreeops-charval-info-alist-equiv

(defthm
 equal-of-deftreeops-charval-info-alist-fix-2-forward-to-deftreeops-charval-info-alist-equiv
 (implies (equal acl2::x
                 (deftreeops-charval-info-alist-fix acl2::y))
          (deftreeops-charval-info-alist-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: deftreeops-charval-info-alist-equiv-of-deftreeops-charval-info-alist-fix-1-forward

(defthm
 deftreeops-charval-info-alist-equiv-of-deftreeops-charval-info-alist-fix-1-forward
 (implies (deftreeops-charval-info-alist-equiv
               (deftreeops-charval-info-alist-fix acl2::x)
               acl2::y)
          (deftreeops-charval-info-alist-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: deftreeops-charval-info-alist-equiv-of-deftreeops-charval-info-alist-fix-2-forward

(defthm
 deftreeops-charval-info-alist-equiv-of-deftreeops-charval-info-alist-fix-2-forward
 (implies (deftreeops-charval-info-alist-equiv
               acl2::x
               (deftreeops-charval-info-alist-fix acl2::y))
          (deftreeops-charval-info-alist-equiv acl2::x acl2::y))
 :rule-classes :forward-chaining)

Theorem: cons-of-char-val-fix-k-under-deftreeops-charval-info-alist-equiv

(defthm
   cons-of-char-val-fix-k-under-deftreeops-charval-info-alist-equiv
  (deftreeops-charval-info-alist-equiv
       (cons (cons (char-val-fix acl2::k) acl2::v)
             acl2::x)
       (cons (cons acl2::k acl2::v) acl2::x)))

Theorem: cons-char-val-equiv-congruence-on-k-under-deftreeops-charval-info-alist-equiv

(defthm
 cons-char-val-equiv-congruence-on-k-under-deftreeops-charval-info-alist-equiv
 (implies (char-val-equiv acl2::k k-equiv)
          (deftreeops-charval-info-alist-equiv
               (cons (cons acl2::k acl2::v) acl2::x)
               (cons (cons k-equiv acl2::v) acl2::x)))
 :rule-classes :congruence)

Theorem: cons-of-deftreeops-charval-info-fix-v-under-deftreeops-charval-info-alist-equiv

(defthm
 cons-of-deftreeops-charval-info-fix-v-under-deftreeops-charval-info-alist-equiv
 (deftreeops-charval-info-alist-equiv
      (cons (cons acl2::k
                  (deftreeops-charval-info-fix acl2::v))
            acl2::x)
      (cons (cons acl2::k acl2::v) acl2::x)))

Theorem: cons-deftreeops-charval-info-equiv-congruence-on-v-under-deftreeops-charval-info-alist-equiv

(defthm
 cons-deftreeops-charval-info-equiv-congruence-on-v-under-deftreeops-charval-info-alist-equiv
 (implies (deftreeops-charval-info-equiv acl2::v v-equiv)
          (deftreeops-charval-info-alist-equiv
               (cons (cons acl2::k acl2::v) acl2::x)
               (cons (cons acl2::k v-equiv) acl2::x)))
 :rule-classes :congruence)

Theorem: cons-of-deftreeops-charval-info-alist-fix-y-under-deftreeops-charval-info-alist-equiv

(defthm
 cons-of-deftreeops-charval-info-alist-fix-y-under-deftreeops-charval-info-alist-equiv
 (deftreeops-charval-info-alist-equiv
      (cons acl2::x
            (deftreeops-charval-info-alist-fix acl2::y))
      (cons acl2::x acl2::y)))

Theorem: cons-deftreeops-charval-info-alist-equiv-congruence-on-y-under-deftreeops-charval-info-alist-equiv

(defthm
 cons-deftreeops-charval-info-alist-equiv-congruence-on-y-under-deftreeops-charval-info-alist-equiv
 (implies
      (deftreeops-charval-info-alist-equiv acl2::y y-equiv)
      (deftreeops-charval-info-alist-equiv (cons acl2::x acl2::y)
                                           (cons acl2::x y-equiv)))
 :rule-classes :congruence)

Theorem: deftreeops-charval-info-alist-fix-of-acons

(defthm deftreeops-charval-info-alist-fix-of-acons
  (equal (deftreeops-charval-info-alist-fix
              (cons (cons acl2::a acl2::b) x))
         (cons (cons (char-val-fix acl2::a)
                     (deftreeops-charval-info-fix acl2::b))
               (deftreeops-charval-info-alist-fix x))))

Theorem: deftreeops-charval-info-alist-fix-of-append

(defthm deftreeops-charval-info-alist-fix-of-append
  (equal (deftreeops-charval-info-alist-fix (append std::a std::b))
         (append (deftreeops-charval-info-alist-fix std::a)
                 (deftreeops-charval-info-alist-fix std::b))))

Theorem: consp-car-of-deftreeops-charval-info-alist-fix

(defthm consp-car-of-deftreeops-charval-info-alist-fix
  (equal (consp (car (deftreeops-charval-info-alist-fix x)))
         (consp (deftreeops-charval-info-alist-fix x))))