Presenting inequations in mathematical proofs

Handling Dependencies in Reorganizing Content Specifications – A Case Study of Case Analysis

“…Exceptions deal with differences between intentional and ideational structures (Maier, 1985) and elaborations on sequences (Horacek, 1998). The latter measure is also incorporated into skillful presentations of the specific form of series of inequations, for remarks on individual steps in such a series (Fehrer and Horacek, 1999). Altogether, we are not aware of any approach to proof presentation or to NLG in general is able to manipulate structures of a case analysis in a rhetorically motivated manner.…”

“…The applicability of this operation presumes a reduction of the equation chains under cases 1, 2, and 5, to the uniform expression |ab| = 0 = |a||b|, prior to aggregation. Such a reduction can be obtained on the basis of the inference model presented in Horacek (1998), as elaborated for chains of inequations in Fehrer and Horacek (1999). Assuming that the audience is able to carry out trivial substitutions and evaluations (in this case, replacing a resp.…”

“…After these reorganizations, the discrepancy to the textbook presentation is not large anymore, except to the reference to analogy, which we consider out of reach on sufficiently general grounds. The remaining differences constitute the use of a verbal variant of a special form of the minimally-sized equation chain (x = y = z, with y being a very simple expression, such as a constant), and the extraposition of justifications out of an equation chain -an operation which is also dealt with in Fehrer and Horacek (1999). Both issues can be handled by components of P.rex with minor additions.…”