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• 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)))