• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Acre
    • Milawa
    • Smtlink
    • Aleobft
    • Abnf
      • Deftreeops
      • Defdefparse
      • Defgrammar
      • Abnf-tree-utilities
      • Notation
        • Syntax-abstraction
        • Semantics
        • Abstract-syntax
          • Convenience-constructors
          • Num-val
          • Char-val
          • Repeat-range
          • Rulename
            • Rulenamep
            • Rulename-fix
            • Rulename-equiv
            • Make-rulename
            • Rulename->get
            • Change-rulename
          • Rule
          • Rulename-option
          • Num-base
          • Rule-option
          • Prose-val
          • Rulelist
          • Char-val-set
          • Rulename-set
          • Rulename-list
          • Grammar
          • Alt/conc/rep/elem
        • 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

• Rulename

Rulename-fix

Fixing function for rulename structures.

Signature

(rulename-fix x) → new-x

Arguments

x — Guard (rulenamep x).

Returns

new-x — Type (rulenamep new-x).

Definitions and Theorems

Function: rulename-fix$inline

(defun rulename-fix$inline (x)
  (declare (xargs :guard (rulenamep x)))
  (let ((__function__ 'rulename-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((get (acl2::str-fix (std::da-nth 0 (cdr x)))))
           (cons :rulename (list get)))
         :exec x)))

Theorem: rulenamep-of-rulename-fix

(defthm rulenamep-of-rulename-fix
  (b* ((new-x (rulename-fix$inline x)))
    (rulenamep new-x))
  :rule-classes :rewrite)

Theorem: rulename-fix-when-rulenamep

(defthm rulename-fix-when-rulenamep
  (implies (rulenamep x)
           (equal (rulename-fix x) x)))

Function: rulename-equiv$inline

(defun rulename-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (rulenamep acl2::x)
                              (rulenamep acl2::y))))
  (equal (rulename-fix acl2::x)
         (rulename-fix acl2::y)))

Theorem: rulename-equiv-is-an-equivalence

(defthm rulename-equiv-is-an-equivalence
  (and (booleanp (rulename-equiv x y))
       (rulename-equiv x x)
       (implies (rulename-equiv x y)
                (rulename-equiv y x))
       (implies (and (rulename-equiv x y)
                     (rulename-equiv y z))
                (rulename-equiv x z)))
  :rule-classes (:equivalence))

Theorem: rulename-equiv-implies-equal-rulename-fix-1

(defthm rulename-equiv-implies-equal-rulename-fix-1
  (implies (rulename-equiv acl2::x x-equiv)
           (equal (rulename-fix acl2::x)
                  (rulename-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: rulename-fix-under-rulename-equiv

(defthm rulename-fix-under-rulename-equiv
  (rulename-equiv (rulename-fix acl2::x)
                  acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-rulename-fix-1-forward-to-rulename-equiv

(defthm equal-of-rulename-fix-1-forward-to-rulename-equiv
  (implies (equal (rulename-fix acl2::x) acl2::y)
           (rulename-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-rulename-fix-2-forward-to-rulename-equiv

(defthm equal-of-rulename-fix-2-forward-to-rulename-equiv
  (implies (equal acl2::x (rulename-fix acl2::y))
           (rulename-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: rulename-equiv-of-rulename-fix-1-forward

(defthm rulename-equiv-of-rulename-fix-1-forward
  (implies (rulename-equiv (rulename-fix acl2::x)
                           acl2::y)
           (rulename-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: rulename-equiv-of-rulename-fix-2-forward

(defthm rulename-equiv-of-rulename-fix-2-forward
  (implies (rulename-equiv acl2::x (rulename-fix acl2::y))
           (rulename-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)