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Theorems · Theorem · linear algebra

Lagrange.basis_ne_zero

∀ {F : Type u_1} [inst : Field F] {ι : Type u_2} [inst_1 : DecidableEq ι] {s : Finset ι} {v : ι → F} {i : ι},
  Set.InjOn v ↑s → i ∈ s → Lagrange.basis s v i ≠ 0
Defined in
Mathlib.LinearAlgebra.Lagrange
Cited by
1 results in Mathlib
Foundations
Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldDecidableEq
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Lagrange.degree_basis · cited by 3Lagrange.degree_basisFinset · cited by 13712FinsetSetLike.coe · cited by 8199SetLike.coeField · cited by 7404FieldPolynomial · cited by 5681PolynomialSet.InjOn · cited by 543Set.InjOnLagrange.basis · cited by 26Lagrange.basisSet.InjOn.eq_iff · cited by 25InjOn.eq_iffLagrange.basisDivisor · cited by 19Lagrange.basisDivisorLagrange.basisDivisor_eq_zero_iff · cited by 3Lagrange.basisDivisor_eq_…Lagrange.basis_ne_zeroCITED BYCITES

Cites9

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Cited by1

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