Theorems · Theorem · group theory
AddSubgroup.le_prod_iff
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] {H : AddSubgroup G} {K : AddSubgroup N}
{J : AddSubgroup (G × N)},
J ≤ H.prod K ↔ AddSubgroup.map (AddMonoidHom.fst G N) J ≤ H ∧ AddSubgroup.map (AddMonoidHom.snd G N) J ≤ K- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.mapstatement · cited by 189
- AddMonoidHom.sndstatement · cited by 42
- AddMonoidHom.fststatement · cited by 39
- AddSubgroup.prodstatement · cited by 34
- AddSubgroup.toAddSubmonoid_leproof · cited by 4
- AddSubmonoid.le_prod_iffproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.addCommutator_sum_sumproof · cited by 1