Theorems · Theorem · group theory
Subgroup.IsComplement.equiv_snd_eq_inv_mul
∀ {G : Type u_1} [inst : Group G] {S T : Set G} (hST : Subgroup.IsComplement S T) (g : G),
↑(hST.equiv g).2 = (↑(hST.equiv g).1)⁻¹ * g- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 15 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroup.IsComplementstatement and proof · cited by 94
- Subgroup.IsComplement.equivstatement · cited by 34
- Subgroup.IsComplement.equiv_fst_mul_equiv_sndproof · cited by 5
- eq_inv_mul_of_mul_eqproof · cited by 3
Cited by8
Results whose statement or proof uses this declaration.
- Subgroup.IsComplement.equiv_mul_rightproof · cited by 1
- Subgroup.IsComplement.equiv_snd_eq_iff_rightCosetEquivalenceproof · cited by 1
- HNNExtension.NormalWord.prod_unitsSMulproof · cited by 1
- Subgroup.IsComplement.equiv_snd_eq_one_of_mem_of_one_memproof · cited by 0
- HNNExtension.NormalWord.unitsSMul_negproof · cited by 0
- Subgroup.IsComplement.coe_equiv_snd_eq_one_iff_memproof · cited by 0
- HNNExtension.NormalWord.prod_smul_emptyproof · cited by 0
- Subgroup.IsComplement.rightCosetEquivalence_equiv_sndproof · cited by 0