EuclideanGeometry.angle_add_angle_eq_pi_of_angle_eq_pi
∀ {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 : P) {p₂ p₃ p₄ : P},
EuclideanGeometry.angle p₂ p₃ p₄ = Real.pi →
EuclideanGeometry.angle p₁ p₃ p₂ + EuclideanGeometry.angle p₁ p₃ p₄ = Real.piIf ∠BCD = π, then ∠ACB + ∠ACD = π.
- 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.
Cites10
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 and proof · cited by 187
- EuclideanGeometry.angle_commproof · cited by 36
- InnerProductGeometry.angle_add_angle_eq_pi_of_angle_eq_piproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- EuclideanGeometry.angle_pointReflection_rightproof · cited by 3
- EuclideanGeometry.dist_sq_mul_dist_add_dist_sq_mul_distproof · cited by 2
- EuclideanGeometry.angle_eq_angle_of_angle_eq_pi_of_angle_eq_piproof · cited by 1
- EuclideanGeometry.angle_add_of_ne_of_neproof · cited by 1
- EuclideanGeometry.exterior_angle_eq_angle_add_angleproof · cited by 0
- EuclideanGeometry.angle_add_angle_eq_of_sbtw_of_sameRayproof · cited by 0