... linear forms from the preamble to Lemma 6, and extend these conventions in the natural way soas to apply to the set {Λ1, ,Λs}. By the hypotheses of the statement ofTheorem 2, one finds that for ... equivalence classes are Λ1, ,Λt. For each in-dex i, let ridenote the number of linear forms amongst Λ1, ,Λ12equivalentto Λi. Then in view of the hypotheses of the lemma, we may relabel indices ... derive an upper THE HASSE PRINCIPLE FOR PAIRS OF DIAGONAL CUBIC FORMS877bound of the shape (4.5), subject to the constraints (4.4), wherein either the parameter rtis reduced, or else the parameter...