simple q about PP

[Paul Roochnik]

Dear LFG Fans,

Consider the following sentence:

"The manager went from the house to the school with a friend in the winter."

Am I allowed to use "PBAR" to indicate a series of consecutive prepositional
phrases?  Is the following C-structure correct?  Thanks in advance for your
advice.  Cheers from Paul.

S --> NP      VP
      NP  --> DET     N
              DET --> "the"
              N   --> "manager"
      VP  --> V       PBAR
              V   --> "went"
              PBAR--> PP  PBAR
                      PP --> PRP   NP
                             PRP --> "from"
                             NP  --> DET N
                                     DET --> "the"
                                     N   --> "house"
                      PBAR--> PP PBAR
                              PP --> PRP NP
                                     PRP --> "to"
                                     NP  --> DET N
                                             DET --> "the"
                                             N   --> "school"
                              PBAR--> PP PBAR
                                      PP --> PRP NP
                                             PRP --> "with"
                                             NP  --> DET N
                                                     DET --> "a"
                                                     N   --> "friend"
                                      PBAR--> PP
                                              PP --> PRP NP
                                                     PRP --> "in"
                                                     NP  --> DET N
                                                             DET --> "the"
                                                             N   --> "winter"