Affine.Simplex.centroid_vsub_point_eq_smul_vsub
∀ {k : Type u_1} {V : Type u_2} {P : Type u_3} [inst : DivisionRing k] [inst_1 : AddCommGroup V] [inst_2 : Module k V]
[inst_3 : AddTorsor V P] {n : ℕ} [inst_4 : NeZero n] [CharZero k] (s : Affine.Simplex k P n) (i : Fin (n + 1)),
s.centroid -ᵥ s.points i = ↑n • (s.faceOppositeCentroid i -ᵥ s.centroid)Reverse version of point_vsub_centroid_eq_smul_vsub.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 79 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.
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- AddTorsorstatement and proof · cited by 1,657
- DivisionRingstatement and proof · cited by 1,062
- neg_negproof · cited by 960
- CharZerostatement and proof · cited by 932
- VSub.vsubstatement and proof · cited by 817
- Affine.Simplexstatement and proof · cited by 471
- Affine.Simplex.pointsstatement and proof · cited by 391
- neg_smulproof · cited by 306
- neg_vsub_eq_vsub_revproof · cited by 87
- Affine.Simplex.centroidstatement and proof · cited by 39
Cited by5
Results whose statement or proof uses this declaration.
- Affine.Simplex.faceOppositeCentroid_mem_ninePointCircleproof · cited by 2
- Affine.Simplex.faceOppositeCentroid_eq_smul_vsub_vadd_pointproof · cited by 2
- Affine.Simplex.faceOppositeCentroid_vsub_centroid_eq_smul_vsubproof · cited by 1
- Affine.Simplex.centroid_mem_medianproof · cited by 1
- Affine.Simplex.centroid_eq_smul_vsub_vadd_pointproof · cited by 0