Theorems · Theorem · group theory
AddSubgroup.isAddCommutative_iSup
∀ {G : Type u_1} [inst : AddGroup G] {ι : Sort u_2} [Nonempty ι] {S : ι → AddSubgroup G}
[hS : ∀ (i : ι), IsAddCommutative ↥(S i)], Directed (fun x1 x2 => x1 ≤ x2) S → IsAddCommutative ↥(⨆ i, S i)- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- iSupstatement · cited by 2,415
- SetLike.mem_coeproof · cited by 302
- Directedstatement and proof · cited by 213
- Set.mem_iUnionproof · cited by 212
- IsAddCommutativestatement and proof · cited by 40
- IsAddCommutative.of_setLike_add_commproof · cited by 7
- setLike_add_commproof · cited by 5
- AddSubgroup.coe_iSup_of_directedproof · cited by 3
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