EuclideanGeometry.left_dist_ne_zero_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 p₂ p₃ : P}, EuclideanGeometry.angle p₁ p₂ p₃ = Real.pi → dist p₁ p₂ ≠ 0If ∠ABC = π then dist A B ≠ 0.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Dist.diststatement and proof · cited by 1,539
- NormedAddTorsorstatement and proof · cited by 1,325
- EuclideanGeometry.anglestatement and proof · cited by 187
- neg_eq_zeroproof · cited by 171
- sub_eq_zero_of_eqproof · cited by 154
Cited by2
Results whose statement or proof uses this declaration.
- EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cosphericalproof · cited by 0
- EuclideanGeometry.right_dist_ne_zero_of_angle_eq_piproof · cited by 0