Theorems · Definition · group theory
QuotientAddGroup.quotientAddEquivOfEq
{G : Type u} →
[inst : AddGroup G] → {M N : AddSubgroup G} → [inst_1 : M.Normal] → [inst_2 : N.Normal] → M = N → G ⧸ M ≃+ G ⧸ NIf two normal subgroups M and N of G are the same, their quotient groups are
isomorphic.
- Defined in
- Mathlib.GroupTheory.QuotientGroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Equivproof · cited by 8,337
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientstatement and proof · cited by 2,301
- AddEquivstatement · cited by 1,087
- AddSubgroup.Normalstatement and proof · cited by 183
- AddSubgroup.quotientEquivOfEqproof · cited by 0
Cited by4
Results whose statement or proof uses this declaration.
- Int.quotientZMultiplesNatEquivZModproof · cited by 2
- Int.quotientZMultiplesEquivZModproof · cited by 1
- QuotientAddGroup.quotientAddEquivOfEq_mkstatement · cited by 0
- QuotientAddGroup.quotientInfEquivSumNormalizerQuotientproof · cited by 0