Theorems · Theorem · group theory
QuotientGroup.preimage_mk_one
∀ {α : Type u_1} [inst : Group α] (N : Subgroup α), QuotientGroup.mk ⁻¹' {↑1} = ↑N- Defined in
- Mathlib.GroupTheory.Coset.Defs
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.preimagestatement and proof · cited by 4,946
- Subgroupstatement and proof · cited by 3,593
- one_mulproof · cited by 2,841
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Set.image_congrproof · cited by 533
- QuotientGroup.mkstatement and proof · cited by 196
- Set.image_singletonproof · cited by 174
- Set.image_id'proof · cited by 86
- Set.singleton_mulproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- QuotientGroup.discreteTopology_iffproof · cited by 2
- QuotientGroup.t1Space_iffproof · cited by 1