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Theorems · Theorem · field theory

Polynomial.Sequence.ne_zero

∀ {R : Type u_1} [inst : Semiring R] (S : Polynomial.Sequence R) (i : ℕ), ↑S i ≠ 0

No polynomial in the sequence is zero.

Defined in
Mathlib.Algebra.Polynomial.Sequence
Cited by
1 results in Mathlib
Foundations
Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Semiring
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Around this declaration

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

Polynomial.Sequence.linearIndependent · cited by 1Sequence.linearIndependentSemiring · cited by 13802SemiringPolynomial · cited by 5681PolynomialBot.bot · cited by 4720Bot.botPolynomial.Sequence · cited by 19Polynomial.SequencePolynomial.Sequence.elems' · cited by 15Sequence.elems'Polynomial.degree_ne_bot · cited by 11Polynomial.degree_ne_botPolynomial.Sequence.degree_eq · cited by 6Sequence.degree_eqSequence.ne_zeroCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by1

Results whose statement or proof uses this declaration.