Fixing function for deftreeops-rulename-info structures.
(deftreeops-rulename-info-fix x) → new-x
Function:
(defun deftreeops-rulename-info-fix$inline (x) (declare (xargs :guard (deftreeops-rulename-infop x))) (let ((__function__ 'deftreeops-rulename-info-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((alt (alternation-fix (cdr (std::da-nth 0 x)))) (nonleaf-thm (acl2::symbol-fix (cdr (std::da-nth 1 x)))) (rulename-thm (acl2::symbol-fix (cdr (std::da-nth 2 x)))) (match-thm (acl2::symbol-fix (cdr (std::da-nth 3 x)))) (concs-thm (acl2::symbol-fix (cdr (std::da-nth 4 x)))) (conc-equivs-thm (acl2::symbol-fix (cdr (std::da-nth 5 x)))) (alt-kind (nfix (cdr (std::da-nth 6 x)))) (check-conc-fn (acl2::symbol-fix (cdr (std::da-nth 7 x)))) (conc-infos (deftreeops-conc-info-list-fix (cdr (std::da-nth 8 x))))) (list (cons 'alt alt) (cons 'nonleaf-thm nonleaf-thm) (cons 'rulename-thm rulename-thm) (cons 'match-thm match-thm) (cons 'concs-thm concs-thm) (cons 'conc-equivs-thm conc-equivs-thm) (cons 'alt-kind alt-kind) (cons 'check-conc-fn check-conc-fn) (cons 'conc-infos conc-infos))) :exec x)))
Theorem:
(defthm deftreeops-rulename-infop-of-deftreeops-rulename-info-fix (b* ((new-x (deftreeops-rulename-info-fix$inline x))) (deftreeops-rulename-infop new-x)) :rule-classes :rewrite)
Theorem:
(defthm deftreeops-rulename-info-fix-when-deftreeops-rulename-infop (implies (deftreeops-rulename-infop x) (equal (deftreeops-rulename-info-fix x) x)))
Function:
(defun deftreeops-rulename-info-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (deftreeops-rulename-infop acl2::x) (deftreeops-rulename-infop acl2::y)))) (equal (deftreeops-rulename-info-fix acl2::x) (deftreeops-rulename-info-fix acl2::y)))
Theorem:
(defthm deftreeops-rulename-info-equiv-is-an-equivalence (and (booleanp (deftreeops-rulename-info-equiv x y)) (deftreeops-rulename-info-equiv x x) (implies (deftreeops-rulename-info-equiv x y) (deftreeops-rulename-info-equiv y x)) (implies (and (deftreeops-rulename-info-equiv x y) (deftreeops-rulename-info-equiv y z)) (deftreeops-rulename-info-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm deftreeops-rulename-info-equiv-implies-equal-deftreeops-rulename-info-fix-1 (implies (deftreeops-rulename-info-equiv acl2::x x-equiv) (equal (deftreeops-rulename-info-fix acl2::x) (deftreeops-rulename-info-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm deftreeops-rulename-info-fix-under-deftreeops-rulename-info-equiv (deftreeops-rulename-info-equiv (deftreeops-rulename-info-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-deftreeops-rulename-info-fix-1-forward-to-deftreeops-rulename-info-equiv (implies (equal (deftreeops-rulename-info-fix acl2::x) acl2::y) (deftreeops-rulename-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-deftreeops-rulename-info-fix-2-forward-to-deftreeops-rulename-info-equiv (implies (equal acl2::x (deftreeops-rulename-info-fix acl2::y)) (deftreeops-rulename-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm deftreeops-rulename-info-equiv-of-deftreeops-rulename-info-fix-1-forward (implies (deftreeops-rulename-info-equiv (deftreeops-rulename-info-fix acl2::x) acl2::y) (deftreeops-rulename-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm deftreeops-rulename-info-equiv-of-deftreeops-rulename-info-fix-2-forward (implies (deftreeops-rulename-info-equiv acl2::x (deftreeops-rulename-info-fix acl2::y)) (deftreeops-rulename-info-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)