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Omaps

Mfix

Fixing function for omaps.

Signature
(mfix x) → fixed-x
Arguments: x — Guard (mapp x).
Returns: fixed-x — Type (mapp fixed-x).

This is similar to sfix for osets.

Definitions and Theorems

Function: mfix

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

Theorem: mapp-of-mfix

(defthm mapp-of-mfix
  (b* ((fixed-x (mfix x))) (mapp fixed-x))
  :rule-classes :rewrite)

Theorem: mfix-when-mapp

(defthm mfix-when-mapp
  (implies (mapp x) (equal (mfix x) x)))

Theorem: mfix-implies-mapp

(defthm mfix-implies-mapp
  (implies (mfix x) (mapp x)))