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