These rules highlight the linguistic intuitions that back TAG; if their adjunction were undone, the remaining derivation would be a valid sentence that simply lacks the modifying structure of the auxiliary tree.
the MPD parses reveal that not all useful adjunctions conform to this paradigm, and that left-auxiliary trees that are not used for sister adjunction are susceptible to this behavior by adjoining the shared unbracketed syntax onto the NP dominating the bracketed text.