Theorems · Theorem · group theory
QuotientGroup.eq_one_iff
∀ {G : Type u_1} [inst : Group G] {N : Subgroup G} [inst_1 : N.Normal] (x : G), ↑x = 1 ↔ x ∈ N- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 75 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupSubgroup.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.
- Groupstatement and proof · cited by 6,238
- mul_oneproof · cited by 3,885
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- Subgroup.Normalstatement and proof · cited by 334
- QuotientGroup.mkstatement · cited by 196
- QuotientGroup.eqproof · cited by 20
- Subgroup.inv_mem_iffproof · cited by 9
Cited by18
Results whose statement or proof uses this declaration.
- QuotientGroup.ker_mk'proof · cited by 18
- CoxeterSystem.simple_mul_simple_selfproof · cited by 9
- Subgroup.smul_diff'proof · cited by 2
- Subgroup.pow_index_memproof · cited by 2
- Subgroup.Normal.quotient_commutative_iff_commutator_leproof · cited by 2
- NumberField.Units.exist_unique_eq_mul_prodproof · cited by 2
- CommGroup.isMulTorsion_quotient_range_powMonoidHomproof · cited by 2
- CoxeterSystem.simple_mul_simple_powproof · cited by 1
- PresentedGroup.mk_eq_one_iffproof · cited by 1
- IsDedekindDomain.selmerGroup.fromUnit_kerproof · cited by 1
- NumberField.Units.fun_eq_reprproof · cited by 1
- ProfiniteGrp.ProfiniteCompletion.mono_eta_iff_residuallyFiniteproof · cited by 1