EuclideanGeometry.angle_eq_pi_iff_sbtw
∀ {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] {p₁ p₂ p₃ : P}, EuclideanGeometry.angle p₁ p₂ p₃ = Real.pi ↔ Sbtw ℝ p₁ p₂ p₃The angle between three points is π if and only if the second point is strictly between the other two.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
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
- mul_oneproof · cited by 3,885
- InnerProductSpacestatement and proof · cited by 3,523
- LE.le.transproof · cited by 3,151
- one_mulproof · cited by 2,841
- Nat.cast_oneproof · cited by 2,501
- LT.lt.leproof · cited by 2,189
- HVAdd.hVAddproof · cited by 1,820
- Real.pistatement and proof · cited by 1,774
- MetricSpacestatement and proof · cited by 1,684
- one_smulproof · cited by 1,374
Cited by6
Results whose statement or proof uses this declaration.
- EuclideanGeometry.collinear_iff_eq_or_eq_or_angle_eq_zero_or_angle_eq_piproof · cited by 3
- EuclideanGeometry.oangle_eq_pi_iff_sbtwproof · cited by 1
- EuclideanGeometry.mul_dist_eq_mul_dist_of_cospherical_of_angle_eq_piproof · cited by 1
- EuclideanGeometry.angle_add_of_ne_of_neproof · cited by 1
- EuclideanGeometry.cospherical_of_mul_dist_eq_mul_dist_of_angle_eq_piproof · cited by 0
- EuclideanGeometry.Sphere.angle_center_eq_pi_iff_isDiameterproof · cited by 0