Theorems · Theorem · group theory
rightCoset_mem_rightCoset
∀ {α : Type u_1} [inst : Group α] (s : Subgroup α) {a : α}, a ∈ s → MulOpposite.op a • ↑s = ↑s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Quot.sound
- Assumes
- Group
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.
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Set.extproof · cited by 2,266
- MulOppositestatement · cited by 1,135
- Set.smulSetstatement · cited by 608
- MulOpposite.opstatement · cited by 520
- Subgroup.inv_memproof · cited by 40
- mul_mem_cancel_rightproof · cited by 11
Cited by1
Results whose statement or proof uses this declaration.
- orbit_subgroup_eq_self_of_memproof · cited by 1