Theorems · Theorem · group theory
rightCoset_eq_iff
∀ {α : Type u_1} [inst : Group α] (s : Subgroup α) {x y : α},
MulOpposite.op x • ↑s = MulOpposite.op y • ↑s ↔ y * x⁻¹ ∈ s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 3 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.
Cites13
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
- mul_assocproof · cited by 1,667
- MulOppositestatement · cited by 1,135
- Set.smulSetstatement · cited by 608
- MulOpposite.opstatement · cited by 520
- mul_inv_cancelproof · cited by 128
- Set.ext_iffproof · cited by 90
- inv_mul_cancel_leftproof · cited by 88
- Subgroup.one_memproof · cited by 31
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.IsComplement.equiv_snd_eq_iff_rightCosetEquivalenceproof · cited by 1
- QuotientGroup.rightRel_r_eq_rightCosetEquivalenceproof · cited by 0
- Subgroup.IsComplement.rightCosetEquivalence_equiv_sndproof · cited by 0