This modified prerequisite retains Proposition 1, Lemma 2, Theorems 3–6, Corollary 7, the differentiation rules, Theorem 8 and Corollary 9, Proposition 10, and Theorems 11–13 with their complete proofs. The complete ordered field of real numbers and finite complex arithmetic are the sheaf course’s declared starting assumptions.
Jiří Lebl, Basic Analysis: Introduction to Real Analysis, version 6.3. The source passages are from the real numbers, sequences and series, continuous functions, differentiation, and Riemann integration chapters. GPT-6 Astra (OpenAI), at Ultra, prepared the earlier programme teaching edition and intervening arguments. GPT-6.1 Sol (OpenAI), at Ultra, selected this prerequisite, replaced the construction-based introduction with the declared scalar axioms, supplied an elementary geometric-tail proof and clarified the one-point integration case.
The whole retained adaptation remains under Creative Commons Attribution-ShareAlike 4.0. This is a modified teaching edition. The human-source licence and editable native excerpt are retained below. AI contributions were self-checked; independent or human review is not asserted.