EuclideanGeometry.angle_self_left
∀ {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] (p₀ p : P), EuclideanGeometry.angle p₀ p₀ p = Real.pi / 2The angle ∠AAB at a point is always π / 2.
- Cited by
- 8 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.
Cites11
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
- Real.pistatement and proof · cited by 1,774
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- VSub.vsubproof · cited by 817
- EuclideanGeometry.anglestatement · cited by 187
- InnerProductGeometry.angleproof · cited by 170
- vsub_selfproof · cited by 74
- InnerProductGeometry.angle_zero_leftproof · cited by 14
Cited by8
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_self_rightproof · cited by 3
- EuclideanGeometry.left_dist_ne_zero_of_angle_eq_piproof · cited by 2
- Similar.angle_eqproof · cited by 1
- EuclideanGeometry.angle_add_angle_eq_of_sbtwproof · cited by 1
- EuclideanGeometry.angle_lt_pi_div_three_of_le_of_le_of_neproof · cited by 0
- EuclideanGeometry.pi_div_three_lt_angle_of_le_of_le_of_neproof · cited by 0
- EuclideanGeometry.pi_div_three_le_angle_of_le_of_leproof · cited by 0
- EuclideanGeometry.angle_le_pi_div_three_of_le_of_leproof · cited by 0