Theorems · Theorem · group theory
SemidirectProduct.inl_aut_inv
∀ {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)⁻¹ n) = SemidirectProduct.inr g⁻¹ * SemidirectProduct.inl n * SemidirectProduct.inr g- Defined in
- Mathlib.GroupTheory.SemidirectProduct
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Quot.sound
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Cites11
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
- MonoidHomstatement and proof · cited by 3,629
- MulEquivstatement · cited by 1,142
- inv_invproof · cited by 494
- MulAutstatement and proof · cited by 158
- map_invproof · cited by 95
- SemidirectProductstatement and proof · cited by 69
- SemidirectProduct.inlstatement and proof · cited by 20
- SemidirectProduct.inrstatement and proof · cited by 18
- SemidirectProduct.inl_autproof · cited by 1
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