Affine.Simplex.mongePoint_mem_affineSpan
∀ {V : Type u_1} {P : Type u_2} [inst : NormedAddCommGroup V] [inst_1 : InnerProductSpace ℝ V] [inst_2 : MetricSpace P]
[inst_3 : NormedAddTorsor V P] {n : ℕ} (s : Affine.Simplex ℝ P n), s.mongePoint ∈ affineSpan ℝ (Set.range s.points)The Monge point lies in the affine span.
- Defined in
- Mathlib.Geometry.Euclidean.MongePoint
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Set.rangestatement and proof · cited by 4,705
- InnerProductSpacestatement and proof · cited by 3,523
- MetricSpacestatement and proof · cited by 1,684
- NormedAddTorsorstatement and proof · cited by 1,325
- AffineSubspacestatement · cited by 871
- Affine.Simplexstatement and proof · cited by 471
- affineSpanstatement and proof · cited by 417
- Affine.Simplex.pointsstatement and proof · cited by 391
- Finset.card_finproof · cited by 26
- Affine.Simplex.mongePointstatement · cited by 20
Cited by3
Results whose statement or proof uses this declaration.
- Affine.Simplex.mongePoint_mem_mongePlaneproof · cited by 3
- Affine.Simplex.points_vsub_eulerPointproof · cited by 2
- Affine.Triangle.orthocenter_mem_affineSpanproof · cited by 2