Theorems · Definition · group theory
AddSubgroup.pi
{η : Type u_7} →
{f : η → Type u_8} →
[inst : (i : η) → AddGroup (f i)] → Set η → ((i : η) → AddSubgroup (f i)) → AddSubgroup ((i : η) → f i)A version of Set.pi for AddSubgroups. Given an index set I and a family
of submodules s : Π i, AddSubgroup f i, pi I s is the AddSubgroup of dependent functions
f : Π i, f i such that f i belongs to pi I s whenever i ∈ I.
- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- 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.piproof · cited by 20
Cited by26
Results whose statement or proof uses this declaration.
- AddSubgroup.mem_pistatement · cited by 5
- AddSubgroup.pi_eq_bot_iffstatement · cited by 2
- AddSubgroup.pi_le_iffstatement · cited by 2
- AddSubgroup.pi_topstatement · cited by 2
- AddSubgroup.addCommutator_pi_pi_lestatement and proof · cited by 2
- AddSubgroup.addCommutator_pi_pi_of_finitestatement and proof · cited by 1
- AddSubgroup.index_pistatement and proof · cited by 1
- AddSubgroup.top_lowerCentralSeries_pi_lestatement and proof · cited by 1
- AddSubgroup.top_lowerCentralSeries_pi_of_finitestatement and proof · cited by 1
- Module.Basis.SmithNormalForm.toAddSubgroup_index_eq_pow_mul_prodproof · cited by 1
- AddSubgroup.le_pi_iffstatement · cited by 1
- QuotientAddGroup.leftRel_pistatement · cited by 1