Theorems · Theorem · group theory
Equiv.pointReflection_fixed_iff_of_injective_two_nsmul
∀ {G : Type u_3} {P : Type u_4} [inst : AddGroup G] [T : AddTorsor G P] {x y : P},
(Function.Injective fun x => 2 • x) → ((Equiv.pointReflection x) y = y ↔ y = x)x is the only fixed point of pointReflection x. This lemma requires
x + x = y + y ↔ x = y. There is no typeclass to use here, so we add it as an explicit argument.
- Defined in
- Mathlib.Algebra.Torsor.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 18 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 · cited by 62,936
- AddGroupstatement and proof · cited by 4,410
- 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
- Equiv.pointReflectionstatement · cited by 35
- eq_vadd_iff_vsub_eqproof · cited by 16
- neg_eq_iff_add_eq_zeroproof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- AffineEquiv.pointReflection_fixed_iff_of_injective_two_nsmulproof · cited by 0