+proc first_real_child {vp} {
+ global children nullid nullid2
+
+ foreach id $children($vp) {
+ if {$id ne $nullid && $id ne $nullid2} {
+ return $id
+ }
+ }
+ return {}
+}
+
+proc last_real_child {vp} {
+ global children nullid nullid2
+
+ set kids $children($vp)
+ for {set i [llength $kids]} {[incr i -1] >= 0} {} {
+ set id [lindex $kids $i]
+ if {$id ne $nullid && $id ne $nullid2} {
+ return $id
+ }
+ }
+ return {}
+}
+