EuclideanGeometry.right_ne_of_oangle_eq_pi
∀ {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] [hd2 : Fact (Module.finrank ℝ V = 2)] [inst_4 : Module.Oriented ℝ V (Fin 2)]
{p₁ p₂ p₃ : P}, EuclideanGeometry.oangle p₁ p₂ p₃ = ↑Real.pi → p₃ ≠ p₂If the angle between three points is π, the last two points are not equal.
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- Foundations
- Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound
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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- InnerProductSpacestatement and proof · cited by 3,523
- Factstatement and proof · cited by 2,726
- Real.pistatement and proof · cited by 1,774
- Module.finrankstatement and proof · cited by 1,770
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- Real.Anglestatement · cited by 518
- Real.Angle.coestatement and proof · cited by 360
- Module.Orientedstatement and proof · cited by 190
- EuclideanGeometry.oanglestatement and proof · cited by 188
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