Theorems · Theorem · linear algebra
linearIndepOn_univ_iff
∀ {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 Set.univ ↔ LinearIndependent R v- Cited by
- 4 results in Mathlib
- Foundations
- Depth 84 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.
Cites8
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
- Semiringstatement and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Set.univstatement · cited by 3,945
- LinearIndependentstatement · cited by 560
- LinearIndepOnstatement · cited by 211
- Equiv.Set.univproof · cited by 21
- linearIndependent_equiv'proof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- LinearIndependent.pair_iffproof · cited by 10
- LinearIndependent.pair_iff'proof · cited by 4
- LinearIndependent.linearIndepOn_univproof · cited by 1
- linearIndepOn_univproof · cited by 0