Theorems · Theorem · group theory
HNNExtension.toSubgroupEquiv_neg_apply
∀ {G : Type u_1} [inst : Group G] {A B : Subgroup G} (φ : ↥A ≃* ↥B) (u : ℤˣ) (a : ↥(HNNExtension.toSubgroup A B u)),
↑((HNNExtension.toSubgroupEquiv φ (-u)) ((HNNExtension.toSubgroupEquiv φ u) a)) = ↑a- Defined in
- Mathlib.GroupTheory.HNNExtension
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 41 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Unitsstatement and proof · cited by 2,804
- MulEquivstatement and proof · cited by 1,142
- MulEquiv.apply_symm_applyproof · cited by 37
- HNNExtension.toSubgroupstatement and proof · cited by 31
- Int.units_eq_one_orproof · cited by 20
- MulEquiv.symm_apply_applyproof · cited by 17
- HNNExtension.toSubgroupEquivstatement · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- HNNExtension.NormalWord.unitsSMul_negproof · cited by 0