Theorems · Theorem · group theory
AddSubgroup.mem_prod
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] {H : AddSubgroup G} {K : AddSubgroup N}
{p : G × N}, p ∈ H.prod K ↔ p.1 ∈ H ∧ p.2 ∈ K- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- AddSubgroup.prodstatement · cited by 34
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.top_prodproof · cited by 1
- AddCommGroup.torsion_sumproof · cited by 0
- AddSubgroup.goursatproof · cited by 0
- AddSubgroup.prod_topproof · cited by 0