Theorems · Theorem · group theory
AddSubgroup.coe_iSup_of_directed
∀ {G : Type u_1} [inst : AddGroup G] {ι : Sort u_2} [Nonempty ι] {S : ι → AddSubgroup G},
Directed (fun x1 x2 => x1 ≤ x2) S → ↑(⨆ i, S i) = ⋃ i, ↑(S i)- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 74 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.
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- Set.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- Set.extproof · cited by 2,266
- SetLike.mem_coeproof · cited by 302
- Directedstatement and proof · cited by 213
- Set.mem_iUnionproof · cited by 212
- AddSubgroup.mem_iSup_of_directedproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- Subring.mem_iSup_of_directedproof · cited by 3
- NonUnitalSubring.mem_iSup_of_directedproof · cited by 2
- AddSubgroup.isAddCommutative_iSupproof · cited by 0