Theorems · Theorem · convex and discrete geometry
vectorSpan_segment
∀ {R : Type u_1} {E : Type u_3} [inst : Field R] [inst_1 : AddCommGroup E] [inst_2 : Module R E]
[inst_3 : LinearOrder R] [IsStrictOrderedRing R] {p₁ p₂ : E}, vectorSpan R (segment R p₁ p₂) = R ∙ (p₂ -ᵥ p₁)The vectorSpan of a segment is the span of the difference of its endpoints.
- Defined in
- Mathlib.Analysis.Convex.Combination
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- LinearOrderstatement and proof · cited by 8,572
- Fieldstatement and proof · cited by 7,404
- Submodulestatement and proof · cited by 7,192
- IsStrictOrderedRingstatement and proof · cited by 2,490
- Submodule.spanstatement and proof · cited by 1,504
- AffineSubspaceproof · cited by 871
- VSub.vsubstatement and proof · cited by 817
- AffineSubspace.directionproof · cited by 339
Cited by1
Results whose statement or proof uses this declaration.
- Real.dimH_segmentproof · cited by 0