Orientation.two_zsmul_oangle_smul_left_self
∀ {V : Type u_1} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : Fact (Module.finrank ℝ V = 2)]
(o : Orientation ℝ V (Fin 2)) (x : V) {r : ℝ}, 2 • o.oangle (r • x) x = 0Twice the angle between a multiple of a vector and that vector is 0.
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- Foundations
- Depth 279 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
- Module.finrankstatement and proof · cited by 1,770
- smul_zeroproof · cited by 665
- Real.Anglestatement · cited by 518
- Orientationstatement and proof · cited by 360
- Orientation.oanglestatement · cited by 205
- lt_or_geproof · cited by 182
- Orientation.oangle_selfproof · cited by 17
- Orientation.oangle_smul_left_of_negproof · cited by 5
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