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    • Valid-ord-info

    Valid-ord-info-fix

    Fixing function for valid-ord-info structures.

    Signature
    (valid-ord-info-fix x) → new-x
    Arguments
    x — Guard (valid-ord-infop x).
    Returns
    new-x — Type (valid-ord-infop new-x).

    Definitions and Theorems

    Function: valid-ord-info-fix$inline

    (defun valid-ord-info-fix$inline (x)
     (declare (xargs :guard (valid-ord-infop x)))
     (let ((__function__ 'valid-ord-info-fix))
      (declare (ignorable __function__))
      (mbe
       :logic
       (case (valid-ord-info-kind x)
        (:objfun
         (b* ((type (type-fix (std::da-nth 0 (cdr x))))
              (linkage (linkage-fix (std::da-nth 1 (cdr x))))
              (defstatus (valid-defstatus-fix (std::da-nth 2 (cdr x)))))
           (cons :objfun (list type linkage defstatus))))
        (:enumconst (cons :enumconst (list)))
        (:typedef (b* ((def (type-fix (std::da-nth 0 (cdr x)))))
                    (cons :typedef (list def)))))
       :exec x)))

    Theorem: valid-ord-infop-of-valid-ord-info-fix

    (defthm valid-ord-infop-of-valid-ord-info-fix
      (b* ((new-x (valid-ord-info-fix$inline x)))
        (valid-ord-infop new-x))
      :rule-classes :rewrite)

    Theorem: valid-ord-info-fix-when-valid-ord-infop

    (defthm valid-ord-info-fix-when-valid-ord-infop
      (implies (valid-ord-infop x)
               (equal (valid-ord-info-fix x) x)))

    Function: valid-ord-info-equiv$inline

    (defun valid-ord-info-equiv$inline (acl2::x acl2::y)
      (declare (xargs :guard (and (valid-ord-infop acl2::x)
                                  (valid-ord-infop acl2::y))))
      (equal (valid-ord-info-fix acl2::x)
             (valid-ord-info-fix acl2::y)))

    Theorem: valid-ord-info-equiv-is-an-equivalence

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

    Theorem: valid-ord-info-equiv-implies-equal-valid-ord-info-fix-1

    (defthm valid-ord-info-equiv-implies-equal-valid-ord-info-fix-1
      (implies (valid-ord-info-equiv acl2::x x-equiv)
               (equal (valid-ord-info-fix acl2::x)
                      (valid-ord-info-fix x-equiv)))
      :rule-classes (:congruence))

    Theorem: valid-ord-info-fix-under-valid-ord-info-equiv

    (defthm valid-ord-info-fix-under-valid-ord-info-equiv
      (valid-ord-info-equiv (valid-ord-info-fix acl2::x)
                            acl2::x)
      :rule-classes (:rewrite :rewrite-quoted-constant))

    Theorem: equal-of-valid-ord-info-fix-1-forward-to-valid-ord-info-equiv

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

    Theorem: equal-of-valid-ord-info-fix-2-forward-to-valid-ord-info-equiv

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

    Theorem: valid-ord-info-equiv-of-valid-ord-info-fix-1-forward

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

    Theorem: valid-ord-info-equiv-of-valid-ord-info-fix-2-forward

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

    Theorem: valid-ord-info-kind$inline-of-valid-ord-info-fix-x

    (defthm valid-ord-info-kind$inline-of-valid-ord-info-fix-x
      (equal (valid-ord-info-kind$inline (valid-ord-info-fix x))
             (valid-ord-info-kind$inline x)))

    Theorem: valid-ord-info-kind$inline-valid-ord-info-equiv-congruence-on-x

    (defthm
        valid-ord-info-kind$inline-valid-ord-info-equiv-congruence-on-x
      (implies (valid-ord-info-equiv x x-equiv)
               (equal (valid-ord-info-kind$inline x)
                      (valid-ord-info-kind$inline x-equiv)))
      :rule-classes :congruence)

    Theorem: consp-of-valid-ord-info-fix

    (defthm consp-of-valid-ord-info-fix
      (consp (valid-ord-info-fix x))
      :rule-classes :type-prescription)