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Section 9.6: fix Exercise 9.6.1 statements and add Exercise 9.6.2#488

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teorth merged 1 commit intoteorth:mainfrom
rkirov:upstream-9.6-fixes
Apr 21, 2026
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Section 9.6: fix Exercise 9.6.1 statements and add Exercise 9.6.2#488
teorth merged 1 commit intoteorth:mainfrom
rkirov:upstream-9.6-fixes

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@rkirov rkirov commented Apr 19, 2026

  • Exercise 9.6.1 c): add parens around the two ¬ ∃ conjuncts (without them, ∧ associates inside the inner ¬ ∃ body, changing the meaning).
  • Exercise 9.6.1 b): change domain from (1, 2) to [0, ∞), matching the textbook's unbounded-domain counterexample.
  • Split Exercise 9.6.1 docstring labels into a) / b) / c) / d).
  • Add Exercise 9.6.2: BddOn.add, BddOn.sub, BddOn.mul, and BddOn.div (the last as a Decidable, since divisibility of the bounded class is the actual question).

- Exercise 9.6.1 c): add parens around the two ¬ ∃ conjuncts (without
  them, ∧ associates inside the inner ¬ ∃ body, changing the meaning).
- Exercise 9.6.1 b): change domain from (1, 2) to [0, ∞), matching the
  textbook's unbounded-domain counterexample.
- Split Exercise 9.6.1 docstring labels into a) / b) / c) / d).
- Add Exercise 9.6.2: BddOn.add, BddOn.sub, BddOn.mul, and BddOn.div
  (the last as a Decidable, since divisibility of the bounded class is
  the actual question).

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Comment thread Analysis/Section_9_6.lean
example : ∃ f: ℝ → ℝ, BddOn f (.Icc (-1) 1) ∧
¬ ∃ x₀ ∈ Set.Icc (-1) 1, IsMinOn f (.Icc (-1) 1) x₀ ∧
¬ ∃ x₀ ∈ Set.Icc (-1) 1, IsMaxOn f (.Icc (-1) 1) x₀
(¬ ∃ x₀ ∈ Set.Icc (-1) 1, IsMinOn f (.Icc (-1) 1) x₀)
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this one was subtle, without parens lean reads it as ¬ (A ∧ ¬ B)

@teorth teorth merged commit 5c62ddf into teorth:main Apr 21, 2026
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