Theorems · Definition · geometry
vectorSpan
(k : Type u_1) →
{V : Type u_2} →
{P : Type u_3} →
[inst : Ring k] → [inst_1 : AddCommGroup V] → [inst_2 : Module k V] → [AddTorsor V P] → Set P → Submodule k VThe submodule spanning the differences of a (possibly empty) set of points.
- Cited by
- 123 results in Mathlib
- Foundations
- Depth 18 from the axioms, rests on 120 definitions · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- AddTorsorstatement and proof · cited by 1,657
- Submodule.spanproof · cited by 1,504
- VSub.vsubproof · cited by 817
Cited by127
Results whose statement or proof uses this declaration.
- AffineSubspace.directionproof · cited by 339
- Collinearproof · cited by 79
- direction_affineSpanstatement and proof · cited by 46
- AffineSubspace.map_spanproof · cited by 16
- Coplanarproof · cited by 15
- affineCombination_mem_affineSpanproof · cited by 12
- vsub_mem_vectorSpanstatement · cited by 11
- AffineIndependent.finrank_vectorSpanstatement and proof · cited by 9
- AffineSubspace.map_directionproof · cited by 9
- vectorSpan_defstatement · cited by 7
- vectorSpan_eq_span_vsub_set_rightstatement · cited by 7
- vectorSpan_monostatement · cited by 7