In parallel with the design and implementation (at least as a prototype) of a proof-verification system based on set theory, the authors undertook the development of a large-scale proof scenario. Ideally, to demonstrate that the verifier can certify the correctness of a substantial body of mathematical analysis, this proof scenario should have culminated in the proof of the celebrated Cauchy integral theorem on analytic functions (whose statement is recalled at the end of this chapter). This presupposed proofs of the basic properties of the real and complex number systems defined in set-theoretic terms, the fundamental properties of limits, continuity and the differential and integral calculus.
This chapter shows the salient steps leading toward that (as yet) unachieved goal. A broad survey of main definitions and theorems is expanded.
- Proof Scenario
- Cauchy Integral Theorem
- Unachievable Goal
- Ultimate Member
- Single-valued Image
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.