Some articles on cancellation, double cancellation:
... Single cancellation does not determine the order of the "right-leaning diagonal" relations upon P ... Even though by transitivity and single cancellation it was established that (a, x) > (b, y), the relationship between (a, y) and (b, x) remains undetermined ... The double cancellation axiom concerns a class of such relations upon P in which the common terms of two antecedent inequalities cancel out to produce a third inequality ...
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