Projectivization.Subspace.subset_span
∀ {K : Type u_1} {V : Type u_2} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
(S : Set (Projectivization K V)), S ⊆ ↑(Projectivization.Subspace.span S)The span of a set of points contains the set of points.
- Cited by
- 2 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.
Cites8
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
- DivisionRingstatement and proof · cited by 1,062
- Projectivizationstatement and proof · cited by 111
- Projectivization.Subspacestatement · cited by 34
- Projectivization.Subspace.spanstatement · cited by 16
Cited by2
Results whose statement or proof uses this declaration.
- Projectivization.Subspace.span_univproof · cited by 0
- Projectivization.Subspace.span_eq_span_iffproof · cited by 0