Fixing function for deftreeops-rep-info structures.
(deftreeops-rep-info-fix x) → new-x
Function:
(defun deftreeops-rep-info-fix$inline (x) (declare (xargs :guard (deftreeops-rep-infop x))) (let ((__function__ 'deftreeops-rep-info-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((matching-thm (acl2::symbol-fix (cdr (std::da-nth 0 x)))) (get-tree-list-fn (acl2::symbol-fix (cdr (std::da-nth 1 x)))) (get-tree-fn (acl2::symbol-fix (cdr (std::da-nth 2 x))))) (list (cons 'matching-thm matching-thm) (cons 'get-tree-list-fn get-tree-list-fn) (cons 'get-tree-fn get-tree-fn))) :exec x)))
Theorem:
(defthm deftreeops-rep-infop-of-deftreeops-rep-info-fix (b* ((new-x (deftreeops-rep-info-fix$inline x))) (deftreeops-rep-infop new-x)) :rule-classes :rewrite)
Theorem:
(defthm deftreeops-rep-info-fix-when-deftreeops-rep-infop (implies (deftreeops-rep-infop x) (equal (deftreeops-rep-info-fix x) x)))
Function:
(defun deftreeops-rep-info-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (deftreeops-rep-infop acl2::x) (deftreeops-rep-infop acl2::y)))) (equal (deftreeops-rep-info-fix acl2::x) (deftreeops-rep-info-fix acl2::y)))
Theorem:
(defthm deftreeops-rep-info-equiv-is-an-equivalence (and (booleanp (deftreeops-rep-info-equiv x y)) (deftreeops-rep-info-equiv x x) (implies (deftreeops-rep-info-equiv x y) (deftreeops-rep-info-equiv y x)) (implies (and (deftreeops-rep-info-equiv x y) (deftreeops-rep-info-equiv y z)) (deftreeops-rep-info-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm deftreeops-rep-info-equiv-implies-equal-deftreeops-rep-info-fix-1 (implies (deftreeops-rep-info-equiv acl2::x x-equiv) (equal (deftreeops-rep-info-fix acl2::x) (deftreeops-rep-info-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm deftreeops-rep-info-fix-under-deftreeops-rep-info-equiv (deftreeops-rep-info-equiv (deftreeops-rep-info-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-deftreeops-rep-info-fix-1-forward-to-deftreeops-rep-info-equiv (implies (equal (deftreeops-rep-info-fix acl2::x) acl2::y) (deftreeops-rep-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-deftreeops-rep-info-fix-2-forward-to-deftreeops-rep-info-equiv (implies (equal acl2::x (deftreeops-rep-info-fix acl2::y)) (deftreeops-rep-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm deftreeops-rep-info-equiv-of-deftreeops-rep-info-fix-1-forward (implies (deftreeops-rep-info-equiv (deftreeops-rep-info-fix acl2::x) acl2::y) (deftreeops-rep-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm deftreeops-rep-info-equiv-of-deftreeops-rep-info-fix-2-forward (implies (deftreeops-rep-info-equiv acl2::x (deftreeops-rep-info-fix acl2::y)) (deftreeops-rep-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)