Theorems · Theorem · group theory
Subgroup.IsComplement.equiv_mul_right
∀ {G : Type u_1} [inst : Group G] {K : Subgroup G} {S : Set G} (hSK : Subgroup.IsComplement S ↑K) (g : G) (k : ↥K),
hSK.equiv (g * ↑k) = ((hSK.equiv g).1, (hSK.equiv g).2 * k)- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 23 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.
Cites15
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
- mul_inv_revproof · cited by 270
- Subgroup.IsComplementstatement and proof · cited by 94
- inv_mul_cancel_rightproof · cited by 70
- Subgroup.IsComplement.equivstatement and proof · cited by 34
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.IsComplement.equiv_mul_right_of_memproof · cited by 0