Theorems · Theorem · group theory
SemidirectProduct.inl_left_mul_inr_right
∀ {N : Type u_1} {G : Type u_2} [inst : Group N] [inst_1 : Group G] {φ : G →* MulAut N} (x : N ⋊[φ] G),
SemidirectProduct.inl x.left * SemidirectProduct.inr x.right = x- 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.
Cites13
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
- map_oneproof · cited by 861
- MulAutstatement and proof · cited by 158
- SemidirectProductstatement and proof · cited by 69
- SemidirectProduct.rightstatement and proof · cited by 35
- SemidirectProduct.leftstatement and proof · cited by 30
- SemidirectProduct.inlstatement · cited by 20
- SemidirectProduct.inrstatement · cited by 18
Cited by1
Results whose statement or proof uses this declaration.
- SemidirectProduct.lift_uniqueproof · cited by 1