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Qualified-ident

Qualified-ident-fix

Fixing function for qualified-ident structures.

Signature
(qualified-ident-fix x) → new-x
Arguments: x — Guard (qualified-identp x).
Returns: new-x — Type (qualified-identp new-x).

Definitions and Theorems

Function: qualified-ident-fix$inline

(defun qualified-ident-fix$inline (x)
 (declare (xargs :guard (qualified-identp x)))
 (let ((__function__ 'qualified-ident-fix))
  (declare (ignorable __function__))
  (mbe
    :logic
    (b*
      ((filepath? (c$::filepath-option-fix (cdr (std::da-nth 0 x))))
       (ident (ident-fix (cdr (std::da-nth 1 x)))))
      (list (cons 'filepath? filepath?)
            (cons 'ident ident)))
    :exec x)))

Theorem: qualified-identp-of-qualified-ident-fix

(defthm qualified-identp-of-qualified-ident-fix
  (b* ((new-x (qualified-ident-fix$inline x)))
    (qualified-identp new-x))
  :rule-classes :rewrite)

Theorem: qualified-ident-fix-when-qualified-identp

(defthm qualified-ident-fix-when-qualified-identp
  (implies (qualified-identp x)
           (equal (qualified-ident-fix x) x)))

Function: qualified-ident-equiv$inline

(defun qualified-ident-equiv$inline (acl2::x acl2::y)
  (declare (xargs :guard (and (qualified-identp acl2::x)
                              (qualified-identp acl2::y))))
  (equal (qualified-ident-fix acl2::x)
         (qualified-ident-fix acl2::y)))

Theorem: qualified-ident-equiv-is-an-equivalence

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

Theorem: qualified-ident-equiv-implies-equal-qualified-ident-fix-1

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

Theorem: qualified-ident-fix-under-qualified-ident-equiv

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

Theorem: equal-of-qualified-ident-fix-1-forward-to-qualified-ident-equiv

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

Theorem: equal-of-qualified-ident-fix-2-forward-to-qualified-ident-equiv

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

Theorem: qualified-ident-equiv-of-qualified-ident-fix-1-forward

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

Theorem: qualified-ident-equiv-of-qualified-ident-fix-2-forward

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