Theorems · Theorem · linear algebra
LinearIndependent.linearCombination_ne_of_notMem_support
∀ {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] [Nontrivial R],
LinearIndependent R v → ∀ {x : ι} (f : ι →₀ R), x ∉ f.support → (Finsupp.linearCombination R v) f ≠ v x- Cited by
- 1 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Modulestatement and proof · cited by 20,661
- RingHom.idstatement · cited by 18,349
- Semiringstatement and proof · cited by 13,802
- Finsetstatement · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- LinearMapstatement · cited by 10,215
- SetLike.coeproof · cited by 8,199
- Finsuppstatement and proof · cited by 5,255
- Nontrivialstatement and proof · cited by 2,416
- Finsupp.supportstatement and proof · cited by 828
- LinearIndependentstatement and proof · cited by 560
Cited by1
Results whose statement or proof uses this declaration.
- Module.Basis.maximalproof · cited by 1