Theorems · Theorem · commutative algebra
Ideal.mem_leadingCoeffNth
∀ {R : Type u} [inst : CommSemiring R] (I : Ideal (Polynomial R)) (n : ℕ) (x : R),
x ∈ I.leadingCoeffNth n ↔ ∃ p ∈ I, p.degree ≤ ↑n ∧ p.leadingCoeff = x- Defined in
- Mathlib.RingTheory.Polynomial.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Idealstatement and proof · cited by 4,748
- le_reflproof · cited by 2,061
- Polynomial.Xproof · cited by 1,639
- WithBotstatement and proof · cited by 1,498
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.coeffproof · cited by 1,045
- le_transproof · cited by 985
- add_le_addproof · cited by 666
- Polynomial.degreestatement and proof · cited by 643
- Nat.cast_addproof · cited by 586
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.mem_leadingCoeffNth_zeroproof · cited by 0