Theorems · Theorem · group theory
QuotientAddGroup.sound
∀ {G : Type u} [inst : AddGroup G] (N : AddSubgroup G) [nN : N.Normal] (U : Set (G ⧸ N)) (g : ↥N.op),
g +ᵥ ⇑(QuotientAddGroup.mk' N) ⁻¹' U = ⇑(QuotientAddGroup.mk' N) ⁻¹' U- Defined in
- Mathlib.GroupTheory.QuotientGroup.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroupAddSubgroup.Normal
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Setstatement and proof · cited by 53,352
- Set.preimagestatement · cited by 4,946
- AddGroupstatement and proof · cited by 4,410
- AddSubgroupstatement and proof · cited by 3,232
- AddMonoidHomstatement · cited by 3,230
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Set.extproof · cited by 2,266
- HVAdd.hVAddstatement and proof · cited by 1,820
- AddOppositestatement and proof · cited by 452
- Set.vaddSetstatement · cited by 403
- Set.mem_preimageproof · cited by 190
Cited by2
Results whose statement or proof uses this declaration.
- IsFundamentalDomain.AddQuotientMeasureEqMeasurePreimage_AddHaarMeasureproof · cited by 1