Theorems · Theorem · linear algebra
LinearIndepOn.extend_subset
∀ {ι : Type u'} {K : Type u_3} {V : Type u} [inst : DivisionRing K] [inst_1 : AddCommGroup V] [inst_2 : Module K V]
{v : ι → V} {s t : Set ι} (hs : LinearIndepOn K v s) (hst : s ⊆ t), hs.extend hst ⊆ t- Cited by
- 3 results in Mathlib
- Foundations
- Depth 90 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.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Submodule.spanproof · cited by 1,504
- DivisionRingstatement and proof · cited by 1,062
- LinearIndepOnstatement and proof · cited by 211
- LinearIndepOn.extendstatement and proof · cited by 28
- exists_linearIndepOn_extensionproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Module.Basis.extendLe_subsetproof · cited by 1
- LinearIndepOn.span_extend_eq_spanproof · cited by 1
- LinearIndepOn.span_image_extend_eq_span_imageproof · cited by 0