collinear_iff_not_affineIndependent_set
∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : DivisionRing k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
[inst_3 : AddTorsor V P] {p₁ p₂ p₃ : P}, Collinear k {p₁, p₂, p₃} ↔ ¬AffineIndependent k ![p₁, p₂, p₃]Three points are collinear if and only if they are not affinely independent.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 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.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- AddTorsorstatement and proof · cited by 1,657
- DivisionRingstatement and proof · cited by 1,062
- Matrix.vecConsstatement · cited by 852
- Matrix.vecEmptystatement · cited by 832
- AffineIndependentstatement · cited by 144
- Collinearstatement · cited by 79
- Iff.not_leftproof · cited by 49
- affineIndependent_iff_not_collinear_setproof · cited by 7
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.