Theorems · Theorem · group theory
Equiv.injective_pointReflection_left_of_injective_two_nsmul
∀ {G : Type u_5} {P : Type u_6} [inst : AddCommGroup G] [inst_1 : AddTorsor G P],
(Function.Injective fun x => 2 • x) → ∀ (y : P), Function.Injective fun x => (Equiv.pointReflection x) y- Defined in
- Mathlib.Algebra.Torsor.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Quot.sound
- Assumes
- AddCommGroupAddTorsor
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- AddCommGroupstatement and proof · cited by 12,871
- HVAdd.hVAddproof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- Equiv.Permstatement · cited by 1,375
- VSub.vsubproof · cited by 817
- neg_vsub_eq_vsub_revproof · cited by 87
- nsmul_zeroproof · cited by 73
- two_nsmulproof · cited by 67
- vsub_eq_zero_iff_eqproof · cited by 45
- vsub_sub_vsub_cancel_rightproof · cited by 39
- Equiv.pointReflectionstatement and proof · cited by 35
Cited by1
Results whose statement or proof uses this declaration.
- AffineEquiv.injective_pointReflection_left_of_injective_two_nsmulproof · cited by 1