• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
    • Apt
    • Zfc
    • Acre
    • Milawa
    • Smtlink
    • Abnf
    • Vwsim
    • Isar
    • Wp-gen
    • Dimacs-reader
    • Pfcs
    • Legacy-defrstobj
    • C
    • Proof-checker-array
    • Soft
    • Farray
    • Rp-rewriter
    • Instant-runoff-voting
    • Imp-language
    • Sidekick
    • Ethereum
      • Mmp-trees
        • Mmp-encode-n/c
        • Mmp-encode-c-max
        • Mmp-encode
        • Mmp-write
        • Mmp-decode
        • Mmp-encode-u-map
        • Nibblelist-bytelist-map-sup-len-key
        • Mmp-encode-c-forall
        • Mmp-read
        • Mmp-encoding-p
        • Bytelist-to-nibblelist-keys
        • Mmp-encode-c-exists
        • Bytelist-bytelist-map
        • Nibblelist-bytelist-map
          • Nibblelist-bytelist-mfix
          • Nibblelist-bytelist-mapp
          • Nibblelist-bytelist-mequiv
      • Semaphore
      • Database
      • Cryptography
      • Rlp
      • Transactions
      • Hex-prefix
      • Basics
      • Addresses
    • 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

• Nibblelist-bytelist-map

Nibblelist-bytelist-mapp

Recognizer for nibblelist-bytelist-map.

Signature

(nibblelist-bytelist-mapp x) → *

Definitions and Theorems

Function: nibblelist-bytelist-mapp

(defun nibblelist-bytelist-mapp (x)
  (declare (xargs :guard t))
  (if (atom x)
      (null x)
    (and (consp (car x))
         (nibble-listp (caar x))
         (byte-listp (cdar x))
         (or (null (cdr x))
             (and (consp (cdr x))
                  (consp (cadr x))
                  (acl2::fast-<< (caar x) (caadr x))
                  (nibblelist-bytelist-mapp (cdr x)))))))

Theorem: booleanp-of-nibblelist-bytelist-mapp

(defthm booleanp-of-nibblelist-bytelist-mapp
  (booleanp (nibblelist-bytelist-mapp x)))

Theorem: mapp-when-nibblelist-bytelist-mapp

(defthm mapp-when-nibblelist-bytelist-mapp
  (implies (nibblelist-bytelist-mapp x)
           (omap::mapp x))
  :rule-classes (:rewrite :forward-chaining))

Theorem: nibblelist-bytelist-mapp-of-tail

(defthm nibblelist-bytelist-mapp-of-tail
  (implies (nibblelist-bytelist-mapp x)
           (nibblelist-bytelist-mapp (omap::tail x))))

Theorem: nibble-listp-of-head-key-when-nibblelist-bytelist-mapp

(defthm nibble-listp-of-head-key-when-nibblelist-bytelist-mapp
  (implies (and (nibblelist-bytelist-mapp x)
                (not (omap::emptyp x)))
           (nibble-listp (mv-nth 0 (omap::head x)))))

Theorem: byte-listp-of-head-val-when-nibblelist-bytelist-mapp

(defthm byte-listp-of-head-val-when-nibblelist-bytelist-mapp
  (implies (and (nibblelist-bytelist-mapp x)
                (not (omap::emptyp x)))
           (byte-listp (mv-nth 1 (omap::head x)))))

Theorem: nibblelist-bytelist-mapp-of-update

(defthm nibblelist-bytelist-mapp-of-update
  (implies (and (nibblelist-bytelist-mapp x)
                (nibble-listp k)
                (byte-listp v))
           (nibblelist-bytelist-mapp (omap::update k v x))))

Theorem: nibblelist-bytelist-mapp-of-update*

(defthm nibblelist-bytelist-mapp-of-update*
  (implies (and (nibblelist-bytelist-mapp x)
                (nibblelist-bytelist-mapp y))
           (nibblelist-bytelist-mapp (omap::update* x y))))

Theorem: nibblelist-bytelist-mapp-of-delete

(defthm nibblelist-bytelist-mapp-of-delete
  (implies (nibblelist-bytelist-mapp x)
           (nibblelist-bytelist-mapp (omap::delete k x))))

Theorem: nibblelist-bytelist-mapp-of-delete*

(defthm nibblelist-bytelist-mapp-of-delete*
  (implies (nibblelist-bytelist-mapp x)
           (nibblelist-bytelist-mapp (omap::delete* k x))))

Theorem: nibble-listp-when-assoc-nibblelist-bytelist-mapp-binds-free-x

(defthm
      nibble-listp-when-assoc-nibblelist-bytelist-mapp-binds-free-x
  (implies (and (omap::assoc k x)
                (nibblelist-bytelist-mapp x))
           (nibble-listp k)))

Theorem: nibble-listp-of-car-of-assoc-nibblelist-bytelist-mapp

(defthm nibble-listp-of-car-of-assoc-nibblelist-bytelist-mapp
  (implies (and (nibblelist-bytelist-mapp x)
                (omap::assoc k x))
           (nibble-listp (car (omap::assoc k x)))))

Theorem: byte-listp-of-cdr-of-assoc-nibblelist-bytelist-mapp

(defthm byte-listp-of-cdr-of-assoc-nibblelist-bytelist-mapp
  (implies (and (nibblelist-bytelist-mapp x)
                (omap::assoc k x))
           (byte-listp (cdr (omap::assoc k x)))))

Theorem: byte-listp-of-lookup-when-nibblelist-bytelist-mapp

(defthm byte-listp-of-lookup-when-nibblelist-bytelist-mapp
  (implies (and (nibblelist-bytelist-mapp x)
                (omap::assoc k x))
           (byte-listp (omap::lookup k x))))