Skip to content

minor cleanups in Groups/ #2200

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
Alizter merged 3 commits into from
Jan 19, 2025
Merged

minor cleanups in Groups/ #2200

Show file tree
Hide file tree
Changes from all commits
Commits
Show all changes
3 commits
Select commit Hold shift + click to select a range
752d532
minor cleanup in quotient group
Alizter Jan 15, 2025
0f268e7
minor style tweak in Group.v
Alizter Jan 15, 2025
3cdf2c6
style tweak in grp_prod_decompose
Alizter Jan 16, 2025
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
6 changes: 3 additions & 3 deletions theories/Algebra/Groups/Group.v
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -930,7 +930,7 @@ Definition grp_prod_corec_natural {X Y A B : Group}

(** The left factor injects into the direct product. *)
Definition grp_prod_inl {H K : Group}
: H $-> (grp_prod H K)
: H $-> grp_prod H K
:= grp_prod_corec grp_homo_id grp_homo_const.

(** The left injection is an embedding. *)
Expand All @@ -944,7 +944,7 @@ Defined.

(** The right factor injects into the direct product. *)
Definition grp_prod_inr {H K : Group}
: K $-> (grp_prod H K)
: K $-> grp_prod H K
:= grp_prod_corec grp_homo_const grp_homo_id.

(** The right injection is an embedding. *)
Expand Down Expand Up @@ -995,7 +995,7 @@ Defined.

(** Pairs in direct products can be decomposed *)
Definition grp_prod_decompose {G H : Group} (g : G) (h : H)
: (g, h) = ((g, group_unit) : grp_prod G H) * (group_unit, h).
: (g, h) = ((g, 1) : grp_prod G H) * (1, h).
Copy link
Collaborator

@jdchristensen jdchristensen Jan 19, 2025

Choose a reason for hiding this comment

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

Does this work? If so, I think it's cleaner.

Suggested change
: (g, h) = ((g, 1) : grp_prod G H) * (1, h).
: (g, h) = (g, 1) * (1, h) :> grp_prod G H.

Copy link
Collaborator Author

@Alizter Alizter Jan 19, 2025

Choose a reason for hiding this comment

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

It does not since it gets stuck looking for sgop of a prod. I had tried this before ideally we would have a pair "constructor" for groups.

Proof.
snrapply path_prod; symmetry.
- snrapply grp_unit_r.
Expand Down
5 changes: 2 additions & 3 deletions theories/Algebra/Groups/QuotientGroup.v
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -253,9 +253,8 @@ Section FirstIso.
snrapply isequiv_surj_emb.
1: srapply cancelR_conn_map.
srapply isembedding_isinj_hset.
refine (Quotient_ind_hprop _ _ _); intro x.
refine (Quotient_ind_hprop _ _ _); intro y.
intros h; simpl in h.
srapply Quotient_ind2_hprop.
intros x y h; simpl in h.
apply qglue; cbn.
apply (equiv_path_sigma_hprop _ _)^-1%equiv in h; cbn in h.
cbn. rewrite grp_homo_op, grp_homo_inv, h.
Expand Down
Loading