direction_affineSpan
∀ (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), (affineSpan k s).direction = vectorSpan k sThe direction of the affine span is the vectorSpan.
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- SetLike.coeproof · cited by 8,199
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- le_antisymmproof · cited by 2,068
- HVAdd.hVAddproof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- VSub.vsubproof · cited by 817
- affineSpanstatement and proof · cited by 417
- AffineSubspace.directionstatement · cited by 339
Cited by46
Results whose statement or proof uses this declaration.
- AffineSubspace.map_spanproof · cited by 16
- affineCombination_mem_affineSpanproof · cited by 12
- Affine.Simplex.direction_altitudeproof · cited by 4
- vadd_left_mem_affineSpan_pairproof · cited by 4
- Affine.Simplex.ExcenterExists.touchpoint_injectiveproof · cited by 4
- eq_affineCombination_of_mem_affineSpanproof · cited by 4
- AffineSubspace.coe_affineSpan_singletonproof · cited by 3
- Affine.Triangle.altitude_eq_mongePlaneproof · cited by 2
- AffineSubspace.direction_supproof · cited by 2
- Affine.Simplex.ExcenterExists.affineSpan_faceOpposite_eq_orthRadiusproof · cited by 2
- Collinear.collinear_insert_iff_of_neproof · cited by 2
- Collinear.oangle_sign_of_sameRay_vsubproof · cited by 2