vsub_mem_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]
[inst_3 : AddTorsor V P] {s : Set P} {p₁ p₂ : P}, p₁ ∈ s → p₂ ∈ s → p₁ -ᵥ p₂ ∈ vectorSpan k sEach pairwise difference is in the vectorSpan.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, 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
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubstatement and proof · cited by 817
- vectorSpanstatement · cited by 123
- vsub_set_subset_vectorSpanproof · cited by 2
- Set.vsub_mem_vsubproof · cited by 2
Cited by11
Results whose statement or proof uses this declaration.
- direction_affineSpanproof · cited by 46
- AffineSubspace.vsub_mem_directionproof · cited by 25
- collinear_iff_of_memproof · cited by 4
- Affine.Simplex.affineSpan_pair_eq_altitude_iffproof · cited by 2
- vsub_mem_vectorSpan_of_mem_spanPoints_of_mem_spanPointsproof · cited by 1
- vsub_mem_vectorSpan_pairproof · cited by 1
- Affine.Triangle.altitude_replace_orthocenter_eq_affineSpanproof · cited by 1
- vsub_rev_mem_vectorSpan_pairproof · cited by 1
- EuclideanGeometry.existsUnique_dist_eq_of_insertproof · cited by 1
- vectorSpan_eq_bot_iff_subsingletonproof · cited by 1
- Affine.Simplex.sum_inv_height_sq_smul_vsub_eq_zeroproof · cited by 1