Theorems · Theorem · group theory
Subgroup.IsComplement.equiv_fst_mul_equiv_snd
∀ {G : Type u_1} [inst : Group G] {S T : Set G} (hST : Subgroup.IsComplement S T) (g : G),
↑(hST.equiv g).1 * ↑(hST.equiv g).2 = g- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 14 from the axioms · uses 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 and proof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroup.IsComplementstatement and proof · cited by 94
- Equiv.ofBijectiveproof · cited by 70
- Equiv.right_invproof · cited by 68
- Subgroup.IsComplement.equivstatement · cited by 34
Cited by5
Results whose statement or proof uses this declaration.
- Subgroup.IsComplement.equiv_snd_eq_inv_mulproof · cited by 8
- Subgroup.IsComplement.equiv_fst_eq_mul_invproof · cited by 8
- Subgroup.IsComplement.equiv_snd_eq_iff_rightCosetEquivalenceproof · cited by 1
- Subgroup.IsComplement.equiv_fst_eq_iff_leftCosetEquivalenceproof · cited by 1
- Monoid.PushoutI.NormalWord.rcons_injectiveproof · cited by 0