Fixing function for svex-override-triple structures.
(svex-override-triple-fix x) → new-x
Function:
(defun svex-override-triple-fix$inline (x) (declare (xargs :guard (svex-override-triple-p x))) (let ((__function__ 'svex-override-triple-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((testvar (svar-fix (std::da-nth 0 x))) (valvar (svar-fix (std::da-nth 1 x))) (valexpr (svex-fix (std::da-nth 2 x)))) (list testvar valvar valexpr)) :exec x)))
Theorem:
(defthm svex-override-triple-p-of-svex-override-triple-fix (b* ((new-x (svex-override-triple-fix$inline x))) (svex-override-triple-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm svex-override-triple-fix-when-svex-override-triple-p (implies (svex-override-triple-p x) (equal (svex-override-triple-fix x) x)))
Function:
(defun svex-override-triple-equiv$inline (x y) (declare (xargs :guard (and (svex-override-triple-p x) (svex-override-triple-p y)))) (equal (svex-override-triple-fix x) (svex-override-triple-fix y)))
Theorem:
(defthm svex-override-triple-equiv-is-an-equivalence (and (booleanp (svex-override-triple-equiv x y)) (svex-override-triple-equiv x x) (implies (svex-override-triple-equiv x y) (svex-override-triple-equiv y x)) (implies (and (svex-override-triple-equiv x y) (svex-override-triple-equiv y z)) (svex-override-triple-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm svex-override-triple-equiv-implies-equal-svex-override-triple-fix-1 (implies (svex-override-triple-equiv x x-equiv) (equal (svex-override-triple-fix x) (svex-override-triple-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm svex-override-triple-fix-under-svex-override-triple-equiv (svex-override-triple-equiv (svex-override-triple-fix x) x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-svex-override-triple-fix-1-forward-to-svex-override-triple-equiv (implies (equal (svex-override-triple-fix x) y) (svex-override-triple-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-svex-override-triple-fix-2-forward-to-svex-override-triple-equiv (implies (equal x (svex-override-triple-fix y)) (svex-override-triple-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm svex-override-triple-equiv-of-svex-override-triple-fix-1-forward (implies (svex-override-triple-equiv (svex-override-triple-fix x) y) (svex-override-triple-equiv x y)) :rule-classes :forward-chaining)
Theorem:
(defthm svex-override-triple-equiv-of-svex-override-triple-fix-2-forward (implies (svex-override-triple-equiv x (svex-override-triple-fix y)) (svex-override-triple-equiv x y)) :rule-classes :forward-chaining)