Theorems · Theorem · group theory
div_mem_comm_iff
∀ {G : Type u_1} [inst : Group G] {S : Type u_6} {H : S} [inst_1 : SetLike S G] [SubgroupClass S G] {a b : G},
a / b ∈ H ↔ b / a ∈ H- Defined in
- Mathlib.Algebra.Group.Subgroup.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- GroupSetLikeSubgroupClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- SetLikestatement and proof · cited by 1,084
- inv_divproof · cited by 92
- SubgroupClassstatement and proof · cited by 34
- inv_mem_iffproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.div_mem_comm_iffproof · cited by 0