EuclideanGeometry.pi_div_three_le_angle_of_le_of_le
∀ {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 p₂ p₃ p₁ ≤ EuclideanGeometry.angle p₁ p₂ p₃ →
EuclideanGeometry.angle p₃ p₁ p₂ ≤ EuclideanGeometry.angle p₁ p₂ p₃ → Real.pi / 3 ≤ EuclideanGeometry.angle p₁ p₂ p₃The greatest angle of a possibly degenerate triangle is at least π / 3.
- Defined in
- Mathlib.Geometry.Euclidean.Triangle
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_zeroproof · cited by 1,870
- Real.pistatement and proof · cited by 1,774
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- le_of_not_gtproof · cited by 430
- EuclideanGeometry.anglestatement and proof · cited by 187
- Real.pi_posproof · cited by 173
- neg_eq_zeroproof · cited by 171
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