Theorems · Theorem · group theory
QuotientGroup.mk_mul
∀ {G : Type u_1} [inst : Group G] (N : Subgroup G) [nN : N.Normal] (a b : G), ↑(a * b) = ↑a * ↑b- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 4 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.
Cites5
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
- 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
Cited by4
Results whose statement or proof uses this declaration.
- NumberField.Units.exist_unique_eq_mul_prodproof · cited by 2
- Subgroup.upperCentralSeriesStep_eq_comap_centerproof · cited by 2
- NumberField.Units.fun_eq_reprproof · cited by 1
- PresentedGroup.generated_byproof · cited by 0