Theorems · Theorem · group theory
AddSubgroup.mem_iSup_prop
∀ {G : Type u_1} [inst : AddGroup G] {p : Prop} {K : p → AddSubgroup G} {x : G},
x ∈ ⨆ (h : p), K h ↔ x = 0 ∨ ∃ (h : p), x ∈ K h- Defined in
- Mathlib.Algebra.Group.Subgroup.Lattice
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- iSup_congr_Propproof · cited by 247
- ZeroMemClass.zero_memproof · cited by 162
- iSup_posproof · cited by 61
- iSup_negproof · cited by 49
- AddSubgroup.mem_botproof · cited by 18
- IsEmpty.exists_iffproof · cited by 7
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