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.

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 by Bors] - chore(group_theory/submonoid): split into 3 files #3058

Closed
wants to merge 18 commits into from
4 changes: 2 additions & 2 deletions src/group_theory/subgroup.lean
Original file line number Diff line number Diff line change
Expand Up @@ -817,8 +817,8 @@ open set

lemma gsmul_mem (H : add_subgroup A) {x : A} (hx : x ∈ H) :
∀ n : ℤ, gsmul n x ∈ H
| (int.of_nat n) := add_submonoid.smul_mem H.to_add_submonoid hx n
| -[1+ n] := H.neg_mem' $ H.add_mem hx $ add_submonoid.smul_mem H.to_add_submonoid hx n
| (int.of_nat n) := add_submonoid.nsmul_mem H.to_add_submonoid hx n
| -[1+ n] := H.neg_mem' $ H.add_mem hx $ add_submonoid.nsmul_mem H.to_add_submonoid hx n

lemma sub_mem (H : add_subgroup A) {x y : A} (hx : x ∈ H) (hy : y ∈ H) : x - y ∈ H :=
H.add_mem hx (H.neg_mem hy)
Expand Down