Skip to content

Disprove Exercise 3.5.6 without nonempty hypotheses - #682

Closed
Chessing234 wants to merge 1 commit into
teorth:mainfrom
Chessing234:fix/ex-3-5-6-prod-subset-needs-nonempty
Closed

Disprove Exercise 3.5.6 without nonempty hypotheses#682
Chessing234 wants to merge 1 commit into
teorth:mainfrom
Chessing234:fix/ex-3-5-6-prod-subset-needs-nonempty

Conversation

@Chessing234

Copy link
Copy Markdown
Contributor

Summary

  • The positive prod_subset_prod needs A,B,C,D ≠ ∅.
  • The decidable drop of those hypotheses is false: ∅ × {0} ⊆ {0} × ∅ holds while {0} ⊈ ∅.
  • Decide with apply isFalse and that counterexample.

Test plan

  • CI / lake build on Section_3_5

The positive theorem needs A,B,C,D nonempty. Dropping that, empty × B ⊆
C × empty can hold while B is not a subset of empty.
@teorth

teorth commented Sep 5, 2026

Copy link
Copy Markdown
Owner

Closing this one under the repository's solutions policy — see the consolidated note on #667 for the full explanation and for what would be most welcome instead.

Briefly: this PR discharges sorrys that are reader exercises in Analysis I, and removes the accompanying hint comment ("the first line of this construction should be either apply isTrue or apply isFalse"). From the README:

Portions of the text that were left as exercises to the reader are rendered in this translation as sorrys. Readers are welcome to fork the repository here to try their hand at these exercises, but I do not intend to place solutions in this repository directly.

Nothing wrong with the mathematics here — this is purely about what belongs in the main repository.

@teorth teorth closed this Sep 5, 2026
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

None yet

Projects

None yet

Development

Successfully merging this pull request may close these issues.

2 participants