Theorems · Theorem · linear algebra
linearIndepOn_empty
∀ {ι : Type u'} (R : Type u_2) {M : Type u_4} (v : ι → M) [inst : Semiring R] [inst_1 : AddCommMonoid M]
[inst_2 : Module R M], LinearIndepOn R v ∅- Cited by
- 5 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringAddCommMonoidModule
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Modulestatement and proof · cited by 20,661
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- LinearIndepOnstatement · cited by 211
- linearIndependent_empty_typeproof · cited by 9
Cited by6
Results whose statement or proof uses this declaration.
- Module.Basis.ofSpanstatement · cited by 4
- linearIndepOn_iUnion_of_directedproof · cited by 4
- Module.Basis.ofSpan_apply_selfstatement and proof · cited by 1
- Module.Basis.coe_ofSpanstatement · cited by 1
- Module.Basis.ofSpan_subsetstatement · cited by 0
- Module.Basis.range_ofSpanstatement and proof · cited by 0