Theorems · Theorem · group theory
AddSubgroup.mem_carrier
∀ {G : Type u_1} [inst : AddGroup G] {s : AddSubgroup G} {x : G}, x ∈ s.carrier ↔ x ∈ s- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- 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 · cited by 53,352
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddSubmonoid.toAddSubsemigroupstatement · cited by 198
- AddSubsemigroup.carrierstatement · cited by 198
- AddSubgroup.toAddSubmonoidstatement · cited by 91
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.mem_lpMeasSubgroup_iff_aestronglyMeasurableproof · cited by 4
- skewAdjoint.mem_iffproof · cited by 4
- selfAdjoint.mem_iffproof · cited by 0