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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)))
 (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))))
           (uid (uid-fix (std::da-nth 3 (cdr x)))))
        (cons :objfun (list type linkage defstatus uid))))
   (: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)

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

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

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

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