Orientation.oangle_smul_left_self_of_nonneg
∀ {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}, 0 ≤ r → o.oangle (r • x) x = 0The angle between a nonnegative multiple of a vector and that vector is 0.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 255 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
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
- zero_smulproof · cited by 716
- Real.Anglestatement · cited by 518
- Orientationstatement and proof · cited by 360
- Orientation.oanglestatement · cited by 205
- LE.le.lt_or_eqproof · cited by 48
- Orientation.oangle.congr_simpproof · cited by 41
- Orientation.oangle_zero_leftproof · cited by 25
Cited by1
Results whose statement or proof uses this declaration.
- Orientation.two_zsmul_oangle_smul_left_selfproof · cited by 0