Theorems · Theorem · field theory
Polynomial.mem_support_iff
∀ {R : Type u} {n : ℕ} [inst : Semiring R] {p : Polynomial R}, n ∈ p.support ↔ p.coeff n ≠ 0- Defined in
- Mathlib.Algebra.Polynomial.Basic
- Cited by
- 30 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Semiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Finsetstatement · cited by 13,712
- Polynomialstatement and proof · cited by 5,681
- Polynomial.coeffstatement · cited by 1,045
- AddMonoidAlgebraproof · cited by 649
- AddMonoidAlgebra.coeffproof · cited by 365
- Polynomial.supportstatement · cited by 237
- Polynomial.casesOnproof · cited by 15
- Polynomial.coeff_ofFinsuppproof · cited by 6
- Polynomial.support_ofFinsuppproof · cited by 4
Cited by30
Results whose statement or proof uses this declaration.
- Polynomial.leadingCoeff_eq_zeroproof · cited by 55
- Polynomial.le_natDegree_of_mem_suppproof · cited by 16
- Polynomial.le_degree_of_ne_zeroproof · cited by 11
- Polynomial.natDegree_mem_support_of_nonzeroproof · cited by 5
- Polynomial.trailingCoeff_eq_zeroproof · cited by 5
- Polynomial.trailingDegree_le_of_ne_zeroproof · cited by 5
- Polynomial.coeff_ne_zero_of_eq_degreeproof · cited by 4
- Polynomial.card_support_eqproof · cited by 3
- Polynomial.degree_derivativeproof · cited by 3
- Polynomial.content_dvd_coeffproof · cited by 3
- Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_evalproof · cited by 3
- Polynomial.le_trailingDegree_mulproof · cited by 2