AffineSubspace.direction_top
∀ (k : Type u_1) (V : Type u_2) (P : Type u_3) [inst : Ring k] [inst_1 : AddCommGroup V] [inst_2 : Module k V] [S : AddTorsor V P], ⊤.direction = ⊤
The direction of ⊤ is the whole module as a submodule.
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 65 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
- Top.topstatement and proof · cited by 9,680
- Ringstatement and proof · cited by 7,463
- Submodulestatement · cited by 7,192
- HVAdd.hVAddproof · cited by 1,820
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement · cited by 871
- VSub.vsubproof · cited by 817
- AffineSubspace.directionstatement and proof · cited by 339
- Submodule.extproof · cited by 204
- vadd_vsubproof · cited by 58
Cited by12
Results whose statement or proof uses this declaration.
- AffineIndependent.affineSpan_eq_top_iff_card_eq_finrank_add_oneproof · cited by 4
- AffineSubspace.topEquivproof · cited by 3
- AffineSubspace.vectorSpan_eq_top_of_affineSpan_eq_topproof · cited by 2
- affineSpan_singleton_union_vadd_eq_top_of_span_eq_topproof · cited by 1
- EuclideanGeometry.exists_circumcenter_eq_of_cosphericalproof · cited by 1
- EuclideanGeometry.exists_circumradius_eq_of_cosphericalproof · cited by 1
- EuclideanGeometry.exists_circumsphere_eq_of_cosphericalproof · cited by 1
- AffineSubspace.direction_eq_top_iff_of_nonemptyproof · cited by 1
- AffineSubspace.affineSpan_eq_top_iff_vectorSpan_eq_top_of_nonemptyproof · cited by 1
- EuclideanGeometry.eq_of_dist_eq_of_dist_eq_of_finrank_eq_twoproof · cited by 1
- asymptoticCone_univproof · cited by 0
- AffineSubspace.linear_topEquivstatement · cited by 0