Theorems · Theorem · field theory
Polynomial.Sequence.linearIndependent
∀ {R : Type u_1} [inst : Ring R] (S : Polynomial.Sequence R) [IsDomain R], LinearIndependent R ↑SPolynomials in a polynomial sequence are linearly independent.
- Defined in
- Mathlib.Algebra.Polynomial.Sequence
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetproof · cited by 13,712
- Ringstatement and proof · cited by 7,463
- Set.ofPredproof · cited by 6,101
- Polynomialstatement · cited by 5,681
- Finset.sumproof · cited by 5,195
- Bot.botproof · cited by 4,720
- IsDomainstatement and proof · cited by 2,196
- WithBotproof · cited by 1,498
- Polynomial.degreeproof · cited by 643
- Function.onFunproof · cited by 570
- LinearIndependentstatement · cited by 560
- Finset.supproof · cited by 530
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.Sequence.basisproof · cited by 4
- Polynomial.Sequence.basis_eq_selfproof · cited by 2