Theorems · Theorem · group theory
QuotientAddGroup.leftRel_pi
∀ {ι : Type u_2} {β : ι → Type u_3} [inst : (i : ι) → AddGroup (β i)] (s' : (i : ι) → AddSubgroup (β i)),
QuotientAddGroup.leftRel (AddSubgroup.pi Set.univ s') = piSetoid- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddGroupstatement and proof · cited by 4,410
- Set.univstatement and proof · cited by 3,945
- AddSubgroupstatement and proof · cited by 3,232
- Set.mem_univproof · cited by 416
- QuotientAddGroup.leftRelstatement · cited by 34
- Setoid.extproof · cited by 26
- AddSubgroup.pistatement · cited by 26
- QuotientAddGroup.leftRel_applyproof · cited by 20
- AddSubgroup.mem_piproof · cited by 5
- Setoid.piSetoid_applyproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.index_piproof · cited by 1