Theorems · Theorem · group theory
AddSubgroup.map_iInf
∀ {G : Type u_1} [inst : AddGroup G] {N : Type u_5} [inst_1 : AddGroup N] {ι : Sort u_7} [Nonempty ι] (f : G →+ N),
Function.Injective ⇑f → ∀ (s : ι → AddSubgroup G), AddSubgroup.map f (iInf s) = ⨅ i, AddSubgroup.map f (s i)- Defined in
- Mathlib.Algebra.Group.Subgroup.Map
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Set.imageproof · cited by 5,609
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement and proof · cited by 3,230
- iInfstatement and proof · cited by 1,690
- SetLike.coe_injectiveproof · cited by 374
- AddSubgroup.mapstatement and proof · cited by 189
- Set.injOn_of_injectiveproof · cited by 28
- Set.InjOn.image_iInter_eqproof · cited by 22
- AddSubgroup.coe_iInfproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.normalCore_eq_iInf_map_addConjproof · cited by 1