Theorems · Theorem · group theory
Subgroup.IsComplement.equiv_snd_eq_self_iff_mem
∀ {G : Type u_1} [inst : Group G] {S T : Set G} (hST : Subgroup.IsComplement S T) {g : G},
1 ∈ S → (↑(hST.equiv g).2 = g ↔ g ∈ T)- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 16 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 and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Equivstatement · cited by 8,337
- Set.Elemstatement and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subtype.propproof · cited by 505
- Subgroup.IsComplementstatement and proof · cited by 94
- Subgroup.IsComplement.equivstatement and proof · cited by 34
- Subgroup.IsComplement.equiv_snd_eq_self_of_mem_of_one_memproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Monoid.PushoutI.NormalWord.eq_one_of_smul_normalizedproof · cited by 1
- Subgroup.IsComplement.coe_equiv_fst_eq_one_iff_memproof · cited by 1