Theorems · Theorem · group theory
QuotientGroup.liftEquiv_coe
∀ {G : Type u_1} {H : Type u_2} [inst : Group G] [inst_1 : Group H] (N : Subgroup G) [nN : N.Normal] {φ : G →* H}
(hφ : Function.Surjective ⇑φ) (HN : N = φ.ker) (g : G), (QuotientGroup.liftEquiv N hφ HN) ↑g = φ g- Defined in
- Mathlib.GroupTheory.QuotientGroup.Defs
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- GroupGroupSubgroup.Normal
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement · cited by 2,301
- MulEquivstatement · cited by 1,142
- Subgroup.Normalstatement and proof · cited by 334
- MonoidHom.kerstatement and proof · cited by 212
- QuotientGroup.mkstatement · cited by 196
- QuotientGroup.liftEquivstatement · cited by 2
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