Skip to content

easy lemma about infinite_set #1759

New issue

Have a question about this project? Sign up for a free GitHub account to open an issue and contact its maintainers and the community.

Sign up for GitHub

By clicking “Sign up for GitHub”, you agree to our terms of service and privacy statement. We’ll occasionally send you account related emails.

Already on GitHub? Sign in to your account

Merged
affeldt-aist merged 1 commit into from
Nov 18, 2025
Merged

easy lemma about infinite_set #1759

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
1 commit
Select commit
File filter

Filter by extension

Filter by extension
Conversations
Failed to load comments.
Loading
Jump to
Jump to file
Failed to load files.
Loading
Diff view
Diff view
3 changes: 3 additions & 0 deletions CHANGELOG_UNRELEASED.md
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -4,6 +4,9 @@

### Added

- in `cardinality.v`:
+ lemma `infinite_setD`

### Changed

### Renamed
Expand Down
8 changes: 8 additions & 0 deletions classical/cardinality.v
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -1002,6 +1002,14 @@ move=> /finite_setP[m Am]; rewrite (card_fset_set Am).
by rewrite (card_le_eqr Am) card_le_II.
Qed.

Lemma infinite_setD {T} (A B : set T) :
infinite_set A -> finite_set B -> infinite_set (A `\` B).
Proof.
move=> + finB finAB; apply.
have : finite_set ((A `&` ~` B) `|` B) by rewrite finite_setU.
by rewrite setUIl setUCl setIT finite_setU => -[].
Qed.

Lemma infinite_set_fset {T : choiceType} (A : set T) n :
infinite_set A ->
exists2 B : {fset T}, [set` B] `<=` A & (#|` B| >= n)%N.
Expand Down
Loading