(svar-override-triplelist-fix x) is a usual fty list fixing function.
(svar-override-triplelist-fix x) → fty::newx
In the logic, we apply svar-override-triple-fix to each member of the x. In the execution, none of that is actually necessary and this is just an inlined identity function.
Function:
(defun svar-override-triplelist-fix$inline (x) (declare (xargs :guard (svar-override-triplelist-p x))) (let ((__function__ 'svar-override-triplelist-fix)) (declare (ignorable __function__)) (mbe :logic (if (atom x) nil (cons (svar-override-triple-fix (car x)) (svar-override-triplelist-fix (cdr x)))) :exec x)))
Theorem:
(defthm svar-override-triplelist-p-of-svar-override-triplelist-fix (b* ((fty::newx (svar-override-triplelist-fix$inline x))) (svar-override-triplelist-p fty::newx)) :rule-classes :rewrite)
Theorem:
(defthm svar-override-triplelist-fix-when-svar-override-triplelist-p (implies (svar-override-triplelist-p x) (equal (svar-override-triplelist-fix x) x)))
Function:
(defun svar-override-triplelist-equiv$inline (x y) (declare (xargs :guard (and (svar-override-triplelist-p x) (svar-override-triplelist-p y)))) (equal (svar-override-triplelist-fix x) (svar-override-triplelist-fix y)))
Theorem:
(defthm svar-override-triplelist-equiv-is-an-equivalence (and (booleanp (svar-override-triplelist-equiv x y)) (svar-override-triplelist-equiv x x) (implies (svar-override-triplelist-equiv x y) (svar-override-triplelist-equiv y x)) (implies (and (svar-override-triplelist-equiv x y) (svar-override-triplelist-equiv y z)) (svar-override-triplelist-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm svar-override-triplelist-equiv-implies-equal-svar-override-triplelist-fix-1 (implies (svar-override-triplelist-equiv x x-equiv) (equal (svar-override-triplelist-fix x) (svar-override-triplelist-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm svar-override-triplelist-fix-under-svar-override-triplelist-equiv (svar-override-triplelist-equiv (svar-override-triplelist-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-svar-override-triplelist-fix-1-forward-to-svar-override-triplelist-equiv (implies (equal (svar-override-triplelist-fix x) y) (svar-override-triplelist-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-svar-override-triplelist-fix-2-forward-to-svar-override-triplelist-equiv (implies (equal x (svar-override-triplelist-fix y)) (svar-override-triplelist-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm svar-override-triplelist-equiv-of-svar-override-triplelist-fix-1-forward (implies (svar-override-triplelist-equiv (svar-override-triplelist-fix x) y) (svar-override-triplelist-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm svar-override-triplelist-equiv-of-svar-override-triplelist-fix-2-forward (implies (svar-override-triplelist-equiv x (svar-override-triplelist-fix y)) (svar-override-triplelist-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm car-of-svar-override-triplelist-fix-x-under-svar-override-triple-equiv (svar-override-triple-equiv (car (svar-override-triplelist-fix x)) (car x)))
Theorem:
(defthm car-svar-override-triplelist-equiv-congruence-on-x-under-svar-override-triple-equiv (implies (svar-override-triplelist-equiv x x-equiv) (svar-override-triple-equiv (car x) (car x-equiv))) :rule-classes :congruence)
Theorem:
(defthm cdr-of-svar-override-triplelist-fix-x-under-svar-override-triplelist-equiv (svar-override-triplelist-equiv (cdr (svar-override-triplelist-fix x)) (cdr x)))
Theorem:
(defthm cdr-svar-override-triplelist-equiv-congruence-on-x-under-svar-override-triplelist-equiv (implies (svar-override-triplelist-equiv x x-equiv) (svar-override-triplelist-equiv (cdr x) (cdr x-equiv))) :rule-classes :congruence)
Theorem:
(defthm cons-of-svar-override-triple-fix-x-under-svar-override-triplelist-equiv (svar-override-triplelist-equiv (cons (svar-override-triple-fix x) y) (cons x y)))
Theorem:
(defthm cons-svar-override-triple-equiv-congruence-on-x-under-svar-override-triplelist-equiv (implies (svar-override-triple-equiv x x-equiv) (svar-override-triplelist-equiv (cons x y) (cons x-equiv y))) :rule-classes :congruence)
Theorem:
(defthm cons-of-svar-override-triplelist-fix-y-under-svar-override-triplelist-equiv (svar-override-triplelist-equiv (cons x (svar-override-triplelist-fix y)) (cons x y)))
Theorem:
(defthm cons-svar-override-triplelist-equiv-congruence-on-y-under-svar-override-triplelist-equiv (implies (svar-override-triplelist-equiv y y-equiv) (svar-override-triplelist-equiv (cons x y) (cons x y-equiv))) :rule-classes :congruence)
Theorem:
(defthm consp-of-svar-override-triplelist-fix (equal (consp (svar-override-triplelist-fix x)) (consp x)))
Theorem:
(defthm svar-override-triplelist-fix-under-iff (iff (svar-override-triplelist-fix x) (consp x)))
Theorem:
(defthm svar-override-triplelist-fix-of-cons (equal (svar-override-triplelist-fix (cons a x)) (cons (svar-override-triple-fix a) (svar-override-triplelist-fix x))))
Theorem:
(defthm len-of-svar-override-triplelist-fix (equal (len (svar-override-triplelist-fix x)) (len x)))
Theorem:
(defthm svar-override-triplelist-fix-of-append (equal (svar-override-triplelist-fix (append std::a std::b)) (append (svar-override-triplelist-fix std::a) (svar-override-triplelist-fix std::b))))
Theorem:
(defthm svar-override-triplelist-fix-of-repeat (equal (svar-override-triplelist-fix (repeat acl2::n x)) (repeat acl2::n (svar-override-triple-fix x))))
Theorem:
(defthm list-equiv-refines-svar-override-triplelist-equiv (implies (list-equiv x y) (svar-override-triplelist-equiv x y)) :rule-classes :refinement)
Theorem:
(defthm nth-of-svar-override-triplelist-fix (equal (nth acl2::n (svar-override-triplelist-fix x)) (if (< (nfix acl2::n) (len x)) (svar-override-triple-fix (nth acl2::n x)) nil)))
Theorem:
(defthm svar-override-triplelist-equiv-implies-svar-override-triplelist-equiv-append-1 (implies (svar-override-triplelist-equiv x fty::x-equiv) (svar-override-triplelist-equiv (append x y) (append fty::x-equiv y))) :rule-classes (:congruence))
Theorem:
(defthm svar-override-triplelist-equiv-implies-svar-override-triplelist-equiv-append-2 (implies (svar-override-triplelist-equiv y fty::y-equiv) (svar-override-triplelist-equiv (append x y) (append x fty::y-equiv))) :rule-classes (:congruence))
Theorem:
(defthm svar-override-triplelist-equiv-implies-svar-override-triplelist-equiv-nthcdr-2 (implies (svar-override-triplelist-equiv acl2::l l-equiv) (svar-override-triplelist-equiv (nthcdr acl2::n acl2::l) (nthcdr acl2::n l-equiv))) :rule-classes (:congruence))
Theorem:
(defthm svar-override-triplelist-equiv-implies-svar-override-triplelist-equiv-take-2 (implies (svar-override-triplelist-equiv acl2::l l-equiv) (svar-override-triplelist-equiv (take acl2::n acl2::l) (take acl2::n l-equiv))) :rule-classes (:congruence))