Fixing function for defdefparse-function-spec structures.
(defdefparse-function-spec-fix x) → new-x
Function:
(defun defdefparse-function-spec-fix$inline (x) (declare (xargs :guard (defdefparse-function-spec-p x))) (let ((__function__ 'defdefparse-function-spec-fix)) (declare (ignorable __function__)) (mbe :logic (case (defdefparse-function-spec-kind x) (:rulename (b* ((get (acl2::str-fix (std::da-nth 0 (cdr x)))) (order (acl2::pos-list-fix (std::da-nth 1 (cdr x))))) (cons :rulename (list get order)))) (:group (b* ((get (alternation-fix (std::da-nth 0 (cdr x)))) (order (acl2::pos-list-fix (std::da-nth 1 (cdr x))))) (cons :group (list get order)))) (:option (b* ((get (alternation-fix (std::da-nth 0 (cdr x)))) (order (acl2::pos-list-fix (std::da-nth 1 (cdr x))))) (cons :option (list get order)))) (:repetition (b* ((get (repetition-fix (std::da-nth 0 (cdr x))))) (cons :repetition (list get))))) :exec x)))
Theorem:
(defthm defdefparse-function-spec-p-of-defdefparse-function-spec-fix (b* ((new-x (defdefparse-function-spec-fix$inline x))) (defdefparse-function-spec-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm defdefparse-function-spec-fix-when-defdefparse-function-spec-p (implies (defdefparse-function-spec-p x) (equal (defdefparse-function-spec-fix x) x)))
Function:
(defun defdefparse-function-spec-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (defdefparse-function-spec-p acl2::x) (defdefparse-function-spec-p acl2::y)))) (equal (defdefparse-function-spec-fix acl2::x) (defdefparse-function-spec-fix acl2::y)))
Theorem:
(defthm defdefparse-function-spec-equiv-is-an-equivalence (and (booleanp (defdefparse-function-spec-equiv x y)) (defdefparse-function-spec-equiv x x) (implies (defdefparse-function-spec-equiv x y) (defdefparse-function-spec-equiv y x)) (implies (and (defdefparse-function-spec-equiv x y) (defdefparse-function-spec-equiv y z)) (defdefparse-function-spec-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm defdefparse-function-spec-equiv-implies-equal-defdefparse-function-spec-fix-1 (implies (defdefparse-function-spec-equiv acl2::x x-equiv) (equal (defdefparse-function-spec-fix acl2::x) (defdefparse-function-spec-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm defdefparse-function-spec-fix-under-defdefparse-function-spec-equiv (defdefparse-function-spec-equiv (defdefparse-function-spec-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-defdefparse-function-spec-fix-1-forward-to-defdefparse-function-spec-equiv (implies (equal (defdefparse-function-spec-fix acl2::x) acl2::y) (defdefparse-function-spec-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-defdefparse-function-spec-fix-2-forward-to-defdefparse-function-spec-equiv (implies (equal acl2::x (defdefparse-function-spec-fix acl2::y)) (defdefparse-function-spec-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm defdefparse-function-spec-equiv-of-defdefparse-function-spec-fix-1-forward (implies (defdefparse-function-spec-equiv (defdefparse-function-spec-fix acl2::x) acl2::y) (defdefparse-function-spec-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm defdefparse-function-spec-equiv-of-defdefparse-function-spec-fix-2-forward (implies (defdefparse-function-spec-equiv acl2::x (defdefparse-function-spec-fix acl2::y)) (defdefparse-function-spec-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm defdefparse-function-spec-kind$inline-of-defdefparse-function-spec-fix-x (equal (defdefparse-function-spec-kind$inline (defdefparse-function-spec-fix x)) (defdefparse-function-spec-kind$inline x)))
Theorem:
(defthm defdefparse-function-spec-kind$inline-defdefparse-function-spec-equiv-congruence-on-x (implies (defdefparse-function-spec-equiv x x-equiv) (equal (defdefparse-function-spec-kind$inline x) (defdefparse-function-spec-kind$inline x-equiv))) :rule-classes :congruence)
Theorem:
(defthm consp-of-defdefparse-function-spec-fix (consp (defdefparse-function-spec-fix x)) :rule-classes :type-prescription)