Fixing function for svtv-precompose-data structures.
(svtv-precompose-data-fix x) → new-x
Function:
(defun svtv-precompose-data-fix$inline (x) (declare (xargs :guard (svtv-precompose-data-p x))) (let ((__function__ 'svtv-precompose-data-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((simp (svex-simpconfig-fix (std::prod-car (std::prod-car x)))) (nextstate (svex-alist-fix (std::prod-cdr (std::prod-car x)))) (input-substs (svex-alistlist-fix (std::prod-car (std::prod-cdr x)))) (initst (svex-alist-fix (std::prod-car (std::prod-cdr (std::prod-cdr x))))) (pre-compose-inputs (svarlist-fix (std::prod-cdr (std::prod-cdr (std::prod-cdr x)))))) (std::prod-cons (std::prod-cons simp nextstate) (std::prod-cons input-substs (std::prod-cons initst pre-compose-inputs)))) :exec x)))
Theorem:
(defthm svtv-precompose-data-p-of-svtv-precompose-data-fix (b* ((new-x (svtv-precompose-data-fix$inline x))) (svtv-precompose-data-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm svtv-precompose-data-fix-when-svtv-precompose-data-p (implies (svtv-precompose-data-p x) (equal (svtv-precompose-data-fix x) x)))
Function:
(defun svtv-precompose-data-equiv$inline (x y) (declare (xargs :guard (and (svtv-precompose-data-p x) (svtv-precompose-data-p y)))) (equal (svtv-precompose-data-fix x) (svtv-precompose-data-fix y)))
Theorem:
(defthm svtv-precompose-data-equiv-is-an-equivalence (and (booleanp (svtv-precompose-data-equiv x y)) (svtv-precompose-data-equiv x x) (implies (svtv-precompose-data-equiv x y) (svtv-precompose-data-equiv y x)) (implies (and (svtv-precompose-data-equiv x y) (svtv-precompose-data-equiv y z)) (svtv-precompose-data-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm svtv-precompose-data-equiv-implies-equal-svtv-precompose-data-fix-1 (implies (svtv-precompose-data-equiv x x-equiv) (equal (svtv-precompose-data-fix x) (svtv-precompose-data-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm svtv-precompose-data-fix-under-svtv-precompose-data-equiv (svtv-precompose-data-equiv (svtv-precompose-data-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-svtv-precompose-data-fix-1-forward-to-svtv-precompose-data-equiv (implies (equal (svtv-precompose-data-fix x) y) (svtv-precompose-data-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-svtv-precompose-data-fix-2-forward-to-svtv-precompose-data-equiv (implies (equal x (svtv-precompose-data-fix y)) (svtv-precompose-data-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm svtv-precompose-data-equiv-of-svtv-precompose-data-fix-1-forward (implies (svtv-precompose-data-equiv (svtv-precompose-data-fix x) y) (svtv-precompose-data-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm svtv-precompose-data-equiv-of-svtv-precompose-data-fix-2-forward (implies (svtv-precompose-data-equiv x (svtv-precompose-data-fix y)) (svtv-precompose-data-equiv x y)) :rule-classes :forward-chaining)