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Filepath

Filepath-fix

Fixing function for filepath structures.

Signature
(filepath-fix x) → new-x
Arguments: x — Guard (filepathp x).
Returns: new-x — Type (filepathp new-x).

Definitions and Theorems

Function: filepath-fix$inline

(defun filepath-fix$inline (x)
  (declare (xargs :guard (filepathp x)))
  (let ((__function__ 'filepath-fix))
    (declare (ignorable __function__))
    (mbe :logic
         (b* ((unwrap (identity (cdr (std::da-nth 0 x)))))
           (list (cons 'unwrap unwrap)))
         :exec x)))

Theorem: filepathp-of-filepath-fix

(defthm filepathp-of-filepath-fix
  (b* ((new-x (filepath-fix$inline x)))
    (filepathp new-x))
  :rule-classes :rewrite)

Theorem: filepath-fix-when-filepathp

(defthm filepath-fix-when-filepathp
  (implies (filepathp x)
           (equal (filepath-fix x) x)))

Function: filepath-equiv$inline

(defun filepath-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (filepathp acl2::x)
                              (filepathp acl2::y))))
  (equal (filepath-fix acl2::x)
         (filepath-fix acl2::y)))

Theorem: filepath-equiv-is-an-equivalence

(defthm filepath-equiv-is-an-equivalence
  (and (booleanp (filepath-equiv x y))
       (filepath-equiv x x)
       (implies (filepath-equiv x y)
                (filepath-equiv y x))
       (implies (and (filepath-equiv x y)
                     (filepath-equiv y z))
                (filepath-equiv x z)))
  :rule-classes (:equivalence))

Theorem: filepath-equiv-implies-equal-filepath-fix-1

(defthm filepath-equiv-implies-equal-filepath-fix-1
  (implies (filepath-equiv acl2::x x-equiv)
           (equal (filepath-fix acl2::x)
                  (filepath-fix x-equiv)))
  :rule-classes (:congruence))

Theorem: filepath-fix-under-filepath-equiv

(defthm filepath-fix-under-filepath-equiv
  (filepath-equiv (filepath-fix acl2::x)
                  acl2::x)
  :rule-classes (:rewrite :rewrite-quoted-constant))

Theorem: equal-of-filepath-fix-1-forward-to-filepath-equiv

(defthm equal-of-filepath-fix-1-forward-to-filepath-equiv
  (implies (equal (filepath-fix acl2::x) acl2::y)
           (filepath-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: equal-of-filepath-fix-2-forward-to-filepath-equiv

(defthm equal-of-filepath-fix-2-forward-to-filepath-equiv
  (implies (equal acl2::x (filepath-fix acl2::y))
           (filepath-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: filepath-equiv-of-filepath-fix-1-forward

(defthm filepath-equiv-of-filepath-fix-1-forward
  (implies (filepath-equiv (filepath-fix acl2::x)
                           acl2::y)
           (filepath-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)

Theorem: filepath-equiv-of-filepath-fix-2-forward

(defthm filepath-equiv-of-filepath-fix-2-forward
  (implies (filepath-equiv acl2::x (filepath-fix acl2::y))
           (filepath-equiv acl2::x acl2::y))
  :rule-classes :forward-chaining)