vectorSpan_pair_rev
∀ (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] (p₁ p₂ : P), vectorSpan k {p₁, p₂} = k ∙ (p₂ -ᵥ p₁)The vectorSpan of two points is the span of their difference (reversed).
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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 and proof · cited by 7,192
- AddTorsorstatement and proof · cited by 1,657
- Submodule.spanstatement and proof · cited by 1,504
- VSub.vsubstatement and proof · cited by 817
- vectorSpanstatement and proof · cited by 123
- Set.pair_commproof · cited by 22
- vectorSpan_pairproof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- AffineSubspace.affineSpan_pair_parallel_iff_exists_unit_smul'proof · cited by 2
- mem_vectorSpan_pair_revproof · cited by 1
- vectorSpan_segmentproof · cited by 1
- AffineSubspace.direction_affineSpan_pair_le_iff_exists_smulproof · cited by 1