Theorems · Definition · geometry
Collinear
(k : Type u_1) →
{V : Type u_2} →
{P : Type u_3} → [inst : DivisionRing k] → [inst_1 : AddCommGroup V] → [Module k V] → [AddTorsor V P] → Set P → PropA set of points is collinear if their vectorSpan has dimension
at most 1.
- Cited by
- 79 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · 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
- Module.rankproof · cited by 496
- vectorSpanproof · cited by 123
Cited by79
Results whose statement or proof uses this declaration.
- collinear_pairstatement · cited by 8
- Collinear.mem_affineSpan_of_mem_of_nestatement and proof · cited by 7
- affineIndependent_iff_not_collinear_setstatement and proof · cited by 7
- Wbtw.collinearstatement and proof · cited by 6
- collinear_insert_of_mem_affineSpan_pairstatement · cited by 5
- EuclideanGeometry.oangle_eq_of_dist_orthogonalProjection_eqproof · cited by 5
- collinear_insert_iff_of_mem_affineSpanstatement and proof · cited by 5
- affineIndependent_iff_not_collinearstatement · cited by 4
- collinear_iff_of_memstatement · cited by 4
- Collinear.coplanarstatement and proof · cited by 3
- Collinear.subsetstatement and proof · cited by 3
- Collinear.two_zsmul_oangle_eq_leftstatement and proof · cited by 3