Fixing function for defstruct-member-info structures.
(defstruct-member-info-fix x) → new-x
Function:
(defun defstruct-member-info-fix$inline (x) (declare (xargs :guard (defstruct-member-infop x))) (let ((__function__ 'defstruct-member-info-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((memtype (member-type-fix (cdr (std::da-nth 0 x)))) (reader (symbol-fix (cdr (std::da-nth 1 x)))) (reader-element (symbol-fix (cdr (std::da-nth 2 x)))) (writer (symbol-fix (cdr (std::da-nth 3 x)))) (writer-element (symbol-fix (cdr (std::da-nth 4 x)))) (checker (symbol-fix (cdr (std::da-nth 5 x)))) (length (symbol-fix (cdr (std::da-nth 6 x)))) (reader-return-thm (symbol-fix (cdr (std::da-nth 7 x)))) (reader-element-return-thm (symbol-fix (cdr (std::da-nth 8 x)))) (writer-return-thm (symbol-fix (cdr (std::da-nth 9 x)))) (writer-element-return-thm (symbol-fix (cdr (std::da-nth 10 x))))) (list (cons 'memtype memtype) (cons 'reader reader) (cons 'reader-element reader-element) (cons 'writer writer) (cons 'writer-element writer-element) (cons 'checker checker) (cons 'length length) (cons 'reader-return-thm reader-return-thm) (cons 'reader-element-return-thm reader-element-return-thm) (cons 'writer-return-thm writer-return-thm) (cons 'writer-element-return-thm writer-element-return-thm))) :exec x)))
Theorem:
(defthm defstruct-member-infop-of-defstruct-member-info-fix (b* ((new-x (defstruct-member-info-fix$inline x))) (defstruct-member-infop new-x)) :rule-classes :rewrite)
Theorem:
(defthm defstruct-member-info-fix-when-defstruct-member-infop (implies (defstruct-member-infop x) (equal (defstruct-member-info-fix x) x)))
Function:
(defun defstruct-member-info-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (defstruct-member-infop acl2::x) (defstruct-member-infop acl2::y)))) (equal (defstruct-member-info-fix acl2::x) (defstruct-member-info-fix acl2::y)))
Theorem:
(defthm defstruct-member-info-equiv-is-an-equivalence (and (booleanp (defstruct-member-info-equiv x y)) (defstruct-member-info-equiv x x) (implies (defstruct-member-info-equiv x y) (defstruct-member-info-equiv y x)) (implies (and (defstruct-member-info-equiv x y) (defstruct-member-info-equiv y z)) (defstruct-member-info-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm defstruct-member-info-equiv-implies-equal-defstruct-member-info-fix-1 (implies (defstruct-member-info-equiv acl2::x x-equiv) (equal (defstruct-member-info-fix acl2::x) (defstruct-member-info-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm defstruct-member-info-fix-under-defstruct-member-info-equiv (defstruct-member-info-equiv (defstruct-member-info-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-defstruct-member-info-fix-1-forward-to-defstruct-member-info-equiv (implies (equal (defstruct-member-info-fix acl2::x) acl2::y) (defstruct-member-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-defstruct-member-info-fix-2-forward-to-defstruct-member-info-equiv (implies (equal acl2::x (defstruct-member-info-fix acl2::y)) (defstruct-member-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm defstruct-member-info-equiv-of-defstruct-member-info-fix-1-forward (implies (defstruct-member-info-equiv (defstruct-member-info-fix acl2::x) acl2::y) (defstruct-member-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm defstruct-member-info-equiv-of-defstruct-member-info-fix-2-forward (implies (defstruct-member-info-equiv acl2::x (defstruct-member-info-fix acl2::y)) (defstruct-member-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)