EuclideanGeometry.angle_self_of_ne
∀ {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] {p p₀ : P}, p ≠ p₀ → EuclideanGeometry.angle p p₀ p = 0The angle ∠ABA at a point is 0, unless A = B.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- EuclideanGeometry.anglestatement · cited by 187
- vsub_ne_zeroproof · cited by 39
- InnerProductGeometry.angle_selfproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_add_angle_eq_of_sbtwproof · cited by 1
- EuclideanGeometry.angle_add_of_ne_of_neproof · cited by 1
- EuclideanGeometry.Sphere.isDiameter_of_angle_eq_pi_div_twoproof · cited by 0
- EuclideanGeometry.angle_lt_pi_div_three_of_le_of_le_of_neproof · cited by 0
- EuclideanGeometry.Sphere.angle_center_eq_zero_iff_eqproof · cited by 0
- EuclideanGeometry.angle_le_pi_div_three_of_le_of_leproof · cited by 0