Theorems · Theorem · group theory
Subgroup.IsComplement.equiv_snd_eq_iff_rightCosetEquivalence
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {T : Set G} (hHT : Subgroup.IsComplement (↑H) T) {g₁ g₂ : G},
(hHT.equiv g₁).2 = (hHT.equiv g₂).2 ↔ RightCosetEquivalence (↑H) g₁ g₂- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- mul_assocproof · cited by 1,667
- inv_invproof · cited by 494
- SetLike.mem_coeproof · cited by 302
- mul_inv_revproof · cited by 270
- Subgroup.IsComplementstatement and proof · cited by 94
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.IsComplement.equiv_mul_leftproof · cited by 3