EuclideanGeometry.angle_comm
∀ {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 = EuclideanGeometry.angle p₃ p₂ p₁The angle at a point does not depend on the order of the other two points.
- Cited by
- 36 results in Mathlib
- Foundations
- Depth 190 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
- VSub.vsubproof · cited by 817
- EuclideanGeometry.anglestatement · cited by 187
- InnerProductGeometry.angle_commproof · cited by 14
Cited by36
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_rev_eq_pi_div_two_of_oangle_eq_pi_div_twoproof · cited by 12
- EuclideanGeometry.angle_add_angle_add_angle_eq_piproof · cited by 10
- EuclideanGeometry.angle_add_angle_eq_pi_of_angle_eq_piproof · cited by 6
- EuclideanGeometry.oangle_eq_of_dist_orthogonalProjection_eqproof · cited by 5
- Wbtw.angle₃₁₂_eq_zero_of_neproof · cited by 4
- EuclideanGeometry.dist_orthogonalProjection_eq_iff_angle_eqproof · cited by 4
- EuclideanGeometry.angle_self_rightproof · cited by 3
- EuclideanGeometry.dist_orthogonalProjection_eq_of_oangle_eqproof · cited by 2
- EuclideanGeometry.angle_orthogonalProjection_selfproof · cited by 1
- EuclideanGeometry.angle_side_angleproof · cited by 1
- EuclideanGeometry.angle_add_of_ne_of_neproof · cited by 1
- EuclideanGeometry.dist_lt_of_angle_ltproof · cited by 1