Theorems · Theorem · group theory
AddSubgroup.neg_mem_iff
∀ {G : Type u_1} [inst : AddGroup G] (H : AddSubgroup G) {x : G}, -x ∈ H ↔ x ∈ H- Defined in
- Mathlib.Algebra.Group.Subgroup.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- neg_mem_iffproof · cited by 42
Cited by5
Results whose statement or proof uses this declaration.
- QuotientAddGroup.eq_zero_iffproof · cited by 19
- QuotientAddGroup.mk_add_of_memproof · cited by 2
- AddSubgroup.addCommutator_comm_leproof · cited by 1
- AddAction.mem_stabilizer_finset'proof · cited by 1
- AddSubgroup.neg_subset_closureproof · cited by 1