Proof: Suppose that such a continuation exists, then this continuation can be represented as a line g, and sincef has been discarded from the envelope, the path associated with g must also be a valid continuation for the line segments f 1 , ..., f N that constitute the envelope.
it follows that maxÔf 1 g, ..., f N gÕ maxÔf 1 , ..., f N Õ g f g for some γ È R. This, however, is in contradiction with the premise thatf To keep track of the phrase expansions when propagating an envelope over an outgoing arc ε È tailÔvÕ, the phrase label ϕ v,headÔεÕ has to be appended from the right to all partial translation hypotheses in the envelope.