AffineSubspace.mem_perpBisector_iff_inner_pointReflection_vsub_eq_zero
∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
[inst_3 : NormedAddTorsor V P] {c p₁ p₂ : P},
c ∈ AffineSubspace.perpBisector p₁ p₂ ↔ inner ℝ ((Equiv.pointReflection c) p₁ -ᵥ p₂) (p₂ -ᵥ p₁) = 0- Defined in
- Mathlib.Geometry.Euclidean.PerpBisector
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
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- DFunLike.coestatement and proof · cited by 62,936
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- HVAdd.hVAddproof · cited by 1,820
- MetricSpacestatement and proof · cited by 1,684
- Equiv.Permstatement · cited by 1,375
- NormedAddTorsorstatement and proof · cited by 1,325
- Inner.innerstatement and proof · cited by 1,089
- AffineSubspacestatement · cited by 871
- VSub.vsubstatement and proof · cited by 817
- smul_addproof · cited by 263
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