Theorems · Theorem · group theory
SemidirectProduct.ext
∀ {N : Type u_1} {G : Type u_2} {inst : Group N} {inst_1 : Group G} {φ : G →* MulAut N} {x y : N ⋊[φ] G},
x.left = y.left → x.right = y.right → x = y- Defined in
- Mathlib.GroupTheory.SemidirectProduct
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Groupstatement and proof · cited by 6,238
- MonoidHomstatement and proof · cited by 3,629
- 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
Cited by7
Results whose statement or proof uses this declaration.
- SemidirectProduct.mk_eq_inl_mul_inrproof · cited by 3
- SemidirectProduct.inl_autproof · cited by 1
- SemidirectProduct.range_inl_eq_ker_rightHomproof · cited by 1
- SemidirectProduct.inl_left_mul_inr_rightproof · cited by 1
- SemidirectProduct.map_comp_inlproof · cited by 0
- SemidirectProduct.map_comp_inrproof · cited by 0
- SemidirectProduct.ext_iffproof · cited by 0