Fixing function for types+vartab structures.
(types+vartab-fix x) → new-x
Function:
(defun types+vartab-fix$inline (x) (declare (xargs :guard (types+vartab-p x))) (let ((__function__ 'types+vartab-fix)) (declare (ignorable __function__)) (mbe :logic (b* ((return-types (type-set-fix (cdr (std::da-nth 0 x)))) (variables (var-table-fix (cdr (std::da-nth 1 x))))) (let ((return-types (if (emptyp return-types) (insert (type-void) nil) return-types))) (list (cons 'return-types return-types) (cons 'variables variables)))) :exec x)))
Theorem:
(defthm types+vartab-p-of-types+vartab-fix (b* ((new-x (types+vartab-fix$inline x))) (types+vartab-p new-x)) :rule-classes :rewrite)
Theorem:
(defthm types+vartab-fix-when-types+vartab-p (implies (types+vartab-p x) (equal (types+vartab-fix x) x)))
Function:
(defun types+vartab-equiv$inline (acl2::x acl2::y) (declare (xargs :guard (and (types+vartab-p acl2::x) (types+vartab-p acl2::y)))) (equal (types+vartab-fix acl2::x) (types+vartab-fix acl2::y)))
Theorem:
(defthm types+vartab-equiv-is-an-equivalence (and (booleanp (types+vartab-equiv x y)) (types+vartab-equiv x x) (implies (types+vartab-equiv x y) (types+vartab-equiv y x)) (implies (and (types+vartab-equiv x y) (types+vartab-equiv y z)) (types+vartab-equiv x z))) :rule-classes (:equivalence))
Theorem:
(defthm types+vartab-equiv-implies-equal-types+vartab-fix-1 (implies (types+vartab-equiv acl2::x x-equiv) (equal (types+vartab-fix acl2::x) (types+vartab-fix x-equiv))) :rule-classes (:congruence))
Theorem:
(defthm types+vartab-fix-under-types+vartab-equiv (types+vartab-equiv (types+vartab-fix acl2::x) acl2::x) :rule-classes (:rewrite :rewrite-quoted-constant))
Theorem:
(defthm equal-of-types+vartab-fix-1-forward-to-types+vartab-equiv (implies (equal (types+vartab-fix acl2::x) acl2::y) (types+vartab-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm equal-of-types+vartab-fix-2-forward-to-types+vartab-equiv (implies (equal acl2::x (types+vartab-fix acl2::y)) (types+vartab-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm types+vartab-equiv-of-types+vartab-fix-1-forward (implies (types+vartab-equiv (types+vartab-fix acl2::x) acl2::y) (types+vartab-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)
Theorem:
(defthm types+vartab-equiv-of-types+vartab-fix-2-forward (implies (types+vartab-equiv acl2::x (types+vartab-fix acl2::y)) (types+vartab-equiv acl2::x acl2::y)) :rule-classes :forward-chaining)