• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
  • Community
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
    • Kestrel-books
      • Crypto-hdwallet
      • Apt
      • Error-checking
      • Fty-extensions
      • Isar
      • Kestrel-utilities
      • Set
        • Implementation
        • Setp
        • Right
        • Left
        • Head
        • Double-containment
        • In
        • Subset
        • Intersect
        • Insert
        • Delete
        • Union
        • From-list
        • Diff
        • Set-equiv
        • To-list
        • Sfix
        • Pick-a-point
        • Cardinality
        • Set-induct
        • Set-bi-induct
        • Emptyp
      • Soft
      • C
      • Bv
      • Imp-language
      • Event-macros
      • Java
      • Bitcoin
      • Ethereum
      • Yul
      • Zcash
      • ACL2-programming-language
      • Prime-fields
      • Json
      • Syntheto
      • File-io-light
      • Cryptography
      • Number-theory
      • Lists-light
      • Axe
      • Builtins
      • Solidity
      • Helpers
      • Htclient
      • Typed-lists-light
      • Arithmetic-light
    • X86isa
    • Axe
    • Execloader
  • Math
  • Testing-utilities

• Set

Diff

Set difference.

Signature

(diff x y) → set

Arguments

x — Guard (setp x).

y — Guard (setp y).

Returns

set — Type (setp set).

Time complexity: O(n\log(m/n)) (where n < m).

Definitions and Theorems

Function: diff

(defun diff (x y)
  (declare (xargs :guard (and (setp x) (setp y))))
  (tree-diff (sfix x) (sfix y)))

Theorem: setp-of-diff

(defthm setp-of-diff
  (b* ((set (diff x y))) (setp set))
  :rule-classes :rewrite)