coplanar_of_fact_finrank_eq_two
∀ {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] (s : Set P) [h : Fact (Module.finrank k V = 2)], Coplanar k sA set of points in a two-dimensional space is coplanar.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 118 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.
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- Factstatement and proof · cited by 2,726
- Module.finrankstatement and proof · cited by 1,770
- AddTorsorstatement and proof · cited by 1,657
- DivisionRingstatement and proof · cited by 1,062
- Fact.outproof · cited by 328
- Coplanarstatement · cited by 15
- coplanar_of_finrank_eq_twoproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- EuclideanGeometry.concyclic_of_two_zsmul_oangle_eq_of_not_collinearproof · cited by 0
- EuclideanGeometry.concyclic_or_collinear_of_two_zsmul_oangle_eqproof · cited by 0