Theorems · Theorem · group theory
SemidirectProduct.inl_aut
∀ {N : Type u_1} {G : Type u_2} [inst : Group N] [inst_1 : Group G] {φ : G →* MulAut N} (g : G) (n : N),
SemidirectProduct.inl ((φ g) n) = SemidirectProduct.inr g * SemidirectProduct.inl n * SemidirectProduct.inr g⁻¹- Defined in
- Mathlib.GroupTheory.SemidirectProduct
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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
- Groupstatement and proof · cited by 6,238
- mul_oneproof · cited by 3,885
- MonoidHomstatement and proof · cited by 3,629
- one_mulproof · cited by 2,841
- MulEquivstatement · cited by 1,142
- map_oneproof · cited by 861
- MulEquiv.symmproof · cited by 482
- inv_oneproof · cited by 301
- MulAutstatement and proof · cited by 158
- mul_inv_cancelproof · cited by 128
- map_invproof · cited by 95
Cited by1
Results whose statement or proof uses this declaration.
- SemidirectProduct.inl_aut_invproof · cited by 0