affineSpan_le
∀ {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] {s : Set P} {Q : AffineSubspace k P}, affineSpan k s ≤ Q ↔ s ⊆ ↑Q- Cited by
- 9 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.coestatement · cited by 8,199
- Ringstatement and proof · cited by 7,463
- AddTorsorstatement and proof · cited by 1,657
- AffineSubspacestatement and proof · cited by 871
- affineSpanstatement · cited by 417
- GaloisInsertion.gcproof · cited by 137
- AffineSubspace.giproof · cited by 4
Cited by9
Results whose statement or proof uses this declaration.
- affineSpan_pair_le_of_mem_of_memproof · cited by 6
- affineSpan_convexHullproof · cited by 2
- AffineBasis.affineSpan_eq_top_of_toMatrix_left_invproof · cited by 1
- EuclideanGeometry.Sphere.IsTangentAt_of_angle_eq_pi_div_twoproof · cited by 1
- affineSpan_inductionproof · cited by 1
- Collinear.affineSpan_eq_of_neproof · cited by 1
- affineSpan_intrinsicClosureproof · cited by 1
- Set.InjOn.wbtw_map_iffproof · cited by 1
- Affine.Simplex.map_subtype_restrictstatement and proof · cited by 0