Theorems · Theorem · group theory
leftCoset_eq_iff
∀ {α : Type u_1} [inst : Group α] (s : Subgroup α) {x y : α}, x • ↑s = y • ↑s ↔ x⁻¹ * y ∈ s- Defined in
- Mathlib.GroupTheory.Coset.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- Set.smulSetstatement · cited by 608
- inv_mul_cancelproof · cited by 107
- Set.ext_iffproof · cited by 90
- mul_inv_cancel_rightproof · cited by 53
- Subgroup.one_memproof · cited by 31
- Subgroup.mul_mem_cancel_leftproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- GrpCat.SurjectiveOfEpiAuxs.fromCoset_eq_of_mem_rangeproof · cited by 3
- GrpCat.SurjectiveOfEpiAuxs.fromCoset_ne_of_nin_rangeproof · cited by 3
- Subgroup.IsComplement.equiv_fst_eq_iff_leftCosetEquivalenceproof · cited by 1
- QuotientGroup.leftRel_r_eq_leftCosetEquivalenceproof · cited by 0