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Section 9.8: fix undecidable Exercise 9.8.4 statements from issue #517#526

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Chessing234:fix/issue-517-section-98-inverse-exercises
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Section 9.8: fix undecidable Exercise 9.8.4 statements from issue #517#526
Chessing234 wants to merge 1 commit into
teorth:mainfrom
Chessing234:fix/issue-517-section-98-inverse-exercises

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@Chessing234

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Summary

  • Replace the two def … : Decidable … exercises with provable theorem statements.
  • Restore missing hypotheses: continuity for the “without continuity” variant, and strict monotonicity for the “without strict mono” variant.

Root cause

Issue #517: as Decidable exercises, the property is true for some admissible functions and false for others, so no uniform decision proof can exist. Adding the hypotheses from Tao’s intended setting makes the statements match MonotoneOn.exist_inverse.

Test plan

  • lake build (signature-only change)

Made with Cursor

Replace undecidable `Decidable` exercises with provable theorems by
restoring continuity and strict monotonicity hypotheses.

Co-authored-by: Cursor <cursoragent@cursor.com>
@teorth

teorth commented Jun 15, 2026

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To be closer to the spirit of the exercise, one can move the quantification over the parameters a, b, f, hcont, hmono inside the Decidable statement instead.

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