Theorems · Definition · group theory
AddSubgroup.prod
{G : Type u_1} →
[inst : AddGroup G] → {N : Type u_5} → [inst_1 : AddGroup N] → AddSubgroup G → AddSubgroup N → AddSubgroup (G × N)Given AddSubgroups H, K of AddGroups A, B respectively, H × K
as an AddSubgroup of A × B.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubmonoidproof · cited by 1,178
- AddSubgroup.toAddSubmonoidproof · cited by 91
- AddSubmonoid.prodproof · cited by 27
Cited by40
Results whose statement or proof uses this declaration.
- Subring.prodproof · cited by 11
- NonUnitalSubring.prodproof · cited by 9
- AddSubgroup.mem_prodstatement · cited by 4
- QuotientAddGroup.prodEquivstatement and proof · cited by 3
- QuotientAddGroup.prodAddEquivstatement and proof · cited by 2
- AddSubgroup.prod_le_iffstatement · cited by 2
- AddSubgroup.prod_monostatement · cited by 2
- OpenAddSubgroup.prodproof · cited by 2
- AddSubgroup.goursatFst_prod_goursatSnd_lestatement and proof · cited by 2
- AddSubgroup.prodEquivstatement · cited by 1
- AddSubgroup.addCommutator_sum_sumstatement and proof · cited by 1
- AddSubgroup.prod_eq_bot_iffstatement · cited by 1