Skip to content
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

Jump to bottom

[Merged by Bors] - chore(linear_algebra): fix/add coe_fn simp lemmas #7015

Closed
wants to merge 1 commit into from
Closed

[Merged by Bors] - chore(linear_algebra): fix/add coe_fn simp lemmas #7015

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.
Jump to
Jump to file
Failed to load files.
Diff view
Diff view
5 changes: 2 additions & 3 deletions src/algebra/module/linear_map.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -212,10 +212,9 @@ variables (f : M₂ →ₗ[R] M₃) (g : M →ₗ[R] M₂)
/-- Composition of two linear maps is a linear map -/
def comp : M →ₗ[R] M₃ := ⟨f ∘ g, by simp, by simp⟩

@[simp] lemma comp_apply (x : M) : f.comp g x = f (g x) := rfl
lemma comp_apply (x : M) : f.comp g x = f (g x) := rfl

@[norm_cast]
lemma comp_coe : (f : M₂ → M₃) ∘ (g : M → M₂) = f.comp g := rfl
@[simp, norm_cast] lemma coe_comp : (f.comp g : M → M₃) = f ∘ g := rfl
Copy link
Member

Choose a reason for hiding this comment

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

Suggested change
@[simp, norm_cast] lemma coe_comp : (f.comp g : M → M₃) = f ∘ g := rfl
@[simp, norm_cast] lemma coe_comp : ⇑(f.comp g) = f ∘ g := rfl

Copy link
Collaborator

Choose a reason for hiding this comment

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

Why is using the arrow preferred over an explicit type annotation?

Copy link
Member

Choose a reason for hiding this comment

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

The main reasons are:

  • It's shorter
  • we do that elsewhere
  • It matches what the goal view shows and what doc-gen shows

It doesn't actually make any difference to lean.

Copy link
Collaborator

Choose a reason for hiding this comment

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

I prefer the explicit type annotation basically because I might be browsing the code outside of an editor or even if I am in the editor, if I'm looking at this lemma I might be too lazy to click around to see what the coercion is.

(Ultimately I don't think this is a big deal, so Yury should just go with whichever he wants.)

Copy link
Member Author

Choose a reason for hiding this comment

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

@eric-wieser "Arrows" version doesn't work with the current state of leanprover-community/lean#557 (I hope, it will be fixed), so I'll leave it as is.


@[simp] theorem comp_id : f.comp id = f :=
linear_map.ext $ λ x, rfl
Expand Down
2 changes: 1 addition & 1 deletion src/linear_algebra/basic.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -266,7 +266,7 @@ lemma iterate_bijective (h : bijective f') : ∀ n : ℕ, bijective ⇑(f' ^ n)
lemma injective_of_iterate_injective {n : ℕ} (hn : n ≠ 0) (h : injective ⇑(f' ^ n)) :
injective f' :=
begin
rw [← nat.succ_pred_eq_of_pos (pos_iff_ne_zero.mpr hn), iterate_succ, ←comp_coe] at h,
rw [← nat.succ_pred_eq_of_pos (pos_iff_ne_zero.mpr hn), iterate_succ, coe_comp] at h,
exact injective.of_comp h,
end
end
Expand Down
4 changes: 3 additions & 1 deletion src/linear_algebra/pi.lean
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -60,7 +60,9 @@ rfl
def proj (i : ι) : (Πi, φ i) →ₗ[R] φ i :=
⟨ λa, a i, assume f g, rfl, assume c f, rfl ⟩

@[simp] lemma proj_apply (i : ι) (b : Πi, φ i) : (proj i : (Πi, φ i) →ₗ[R] φ i) b = b i := rfl
@[simp] lemma coe_proj (i : ι) : ⇑(proj i : (Πi, φ i) →ₗ[R] φ i) = function.eval i := rfl

lemma proj_apply (i : ι) (b : Πi, φ i) : (proj i : (Πi, φ i) →ₗ[R] φ i) b = b i := rfl

lemma proj_pi (f : Πi, M₂ →ₗ[R] φ i) (i : ι) : (proj i).comp (pi f) = f i :=
ext $ assume c, rfl
Expand Down