Skip to content

[Merged by Bors] - feat: rangeSplitting f is strictly monotone when f is monotone #39797

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

Closed
vihdzp wants to merge 1 commit into from
Closed

[Merged by Bors] - feat: rangeSplitting f is strictly monotone when f is monotone #39797

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
5 changes: 5 additions & 0 deletions Mathlib/Data/Set/Image.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -955,6 +955,11 @@ theorem preimage_rangeSplitting {f : α → β} (hf : Injective f) :
(image_eq_preimage_of_inverse (rightInverse_rangeSplitting hf)
(leftInverse_rangeSplitting f)).symm

theorem rangeSplitting_strictMono [LinearOrder α] [Preorder β] {f : α → β} (hf : Monotone f) :
StrictMono (rangeSplitting f) := by
refine fun x y h ↦ hf.reflect_lt ?_
simpa [apply_rangeSplitting f]

theorem isCompl_range_some_none (α : Type*) : IsCompl (range (some : α → Option α)) {none} :=
IsCompl.of_le (fun _ ⟨⟨_, ha⟩, (hn : _ = none)⟩ => Option.some_ne_none _ (ha.trans hn))
fun x _ => Option.casesOn x (Or.inr rfl) fun _ => Or.inl <| mem_range_self _
Expand Down
Loading