• Top
  • Documentation
  • Books
  • Boolean-reasoning
  • Projects
  • Debugging
  • Std
    • Std/lists
    • Std/alists
    • Obags
      • Bagp
      • Bag
      • Tail
      • Head
      • Emptyp
      • Subbag
      • Intersect
      • Union
      • Insert
      • Difference
      • Delete
      • Cardinality
      • Bfix
      • In
      • Occs
    • Std/util
    • Std/strings
    • Std/osets
    • Std/io
    • Std/basic
    • Std/system
    • Std/typed-lists
    • Std/bitsets
    • Std/testing
    • Std/typed-alists
    • Std/stobjs
  • Proof-automation
  • Macro-libraries
  • ACL2
  • Interfacing-tools
  • Hardware-verification
  • Software-verification
  • Math
  • Testing-utilities

• Obags

Bfix

Fixing function for obags.

Signature

(bfix x) → fixed-x

Arguments

x — Guard (bagp x).

Returns

fixed-x — Type (bagp fixed-x).

This is similar to sfix for osets.

Definitions and Theorems

Function: bfix

(defun bfix (x)
  (declare (xargs :guard (bagp x)))
  (let ((__function__ 'bfix))
    (declare (ignorable __function__))
    (mbe :logic (if (bagp x) x nil)
         :exec x)))

Theorem: bagp-of-bfix

(defthm bagp-of-bfix
  (b* ((fixed-x (bfix x))) (bagp fixed-x))
  :rule-classes :rewrite)

Theorem: bfix-when-bagp

(defthm bfix-when-bagp
  (implies (bagp x) (equal (bfix x) x)))