Coplanar.finiteDimensional_vectorSpan
∀ {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}, Coplanar k s → FiniteDimensional k ↥(vectorSpan k s)The vectorSpan of coplanar points is finite-dimensional.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Submodulestatement · cited by 7,192
- FiniteDimensionalstatement · cited by 1,854
- AddTorsorstatement and proof · cited by 1,657
- DivisionRingstatement and proof · cited by 1,062
- lt_of_le_of_ltproof · cited by 432
- vectorSpanstatement · cited by 123
- Cardinal.lt_aleph0proof · cited by 19
- Coplanarstatement and proof · cited by 15
- IsNoetherian.iff_fgproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Coplanar.finiteDimensional_direction_affineSpanproof · cited by 0