Skip to content

feat(Logic/Equiv/Defs): add coe_ofBijective simp lemma #38286

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

Open
b-mehta wants to merge 1 commit into
base: master
Choose a base branch
from
+2 −0
Open

feat(Logic/Equiv/Defs): add coe_ofBijective simp lemma #38286

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
2 changes: 2 additions & 0 deletions Mathlib/Logic/Equiv/Defs.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -818,6 +818,8 @@ noncomputable def ofBijective (f : α → β) (hf : Bijective f) : α ≃ β whe
left_inv := leftInverse_surjInv hf
right_inv := rightInverse_surjInv _

@[simp] lemma coe_ofBijective (f : α → β) (hf : Bijective f) : ⇑(ofBijective f hf) = f := rfl
Copy link
Copy Markdown
Member

@eric-wieser eric-wieser Apr 20, 2026 •
edited
Loading

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Doesn't having this prevent Equiv.apply_symm_apply firing on ofBijective f hf ((ofBijective f hf).symm x)? I think we often avoid making such lemmas simp for this reason.

Suggested change
@[simp] lemma coe_ofBijective (f : α → β) (hf : Bijective f) : ⇑(ofBijective f hf) = f := rfl
lemma coe_ofBijective (f : α → β) (hf : Bijective f) : ⇑(ofBijective f hf) = f := rfl

Copy link
Copy Markdown
Contributor

@plp127 plp127 Apr 20, 2026

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Doesn't ofBijective_apply already do that?

Copy link
Copy Markdown
Contributor Author

@b-mehta b-mehta Apr 20, 2026

Choose a reason for hiding this comment

The reason will be displayed to describe this comment to others. Learn more.

Exactly, and there are already loads of @[simp] lemmas like this in mathlib, eg QuaternionAlgebra.coe_addEquivTuple, Equiv.coe_constVSub, WithZero.coe_expEquiv_apply (which I found by just looking through search results in alphabetic order.


lemma ofBijective_apply_symm_apply (f : α → β) (hf : Bijective f) (x : β) :
f ((ofBijective f hf).symm x) = x :=
(ofBijective f hf).apply_symm_apply x
Expand Down
Loading