Theorems · Theorem · group theory
QuotientAddGroup.eq_iff_sub_mem
∀ {G : Type u_1} [inst : AddGroup G] {N : AddSubgroup G} [nN : N.Normal] {x y : G}, ↑x = ↑y ↔ x - y ∈ N- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupAddSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- HasQuotient.Quotientstatement · cited by 2,301
- sub_eq_add_negproof · cited by 1,023
- QuotientAddGroup.mkstatement · cited by 348
- AddSubgroup.Normalstatement and proof · cited by 183
- QuotientAddGroup.eqproof · cited by 24
- AddSubgroup.Normal.mem_comm_iffproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- AddSubgroup.mk_goursatFst_eq_iff_mk_goursatSnd_eqproof · cited by 1
- AddCommGroup.fg_of_descentproof · cited by 1
- AddSubgroup.upperCentralSeriesStep_eq_comap_centerproof · cited by 1
- QuotientAddGroup.comap_comap_centerproof · cited by 1