consider two histories formula_108 such that the associated formula_109 are identical subformula occurrences of the form formula_110 (formula_111 or formula_86); if furthermore formula_113, we write formula_114 (in case formula_111) or formula_116 (in case formula_117), in order to specify that the two histories are indistinguishable for eloise, resp. for abelard. we also stipulate, in general, reflexivity of this relation: if formula_118, then formula_114; and if formula_120, then formula_116.