Theorems · Theorem · field theory
Polynomial.coeff_eq_zero_of_lt_natTrailingDegree
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R} {n : ℕ}, n < p.natTrailingDegree → p.coeff n = 0- Cited by
- 5 results in Mathlib
- Foundations
- Depth 89 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.
- Semiringstatement and proof · cited by 13,802
- Polynomialstatement and proof · cited by 5,681
- ENatproof · cited by 4,985
- Polynomial.coeffstatement · cited by 1,045
- Polynomial.natTrailingDegreestatement and proof · cited by 87
- WithTop.coe_lt_coeproof · cited by 47
- WithTop.coe_lt_topproof · cited by 44
- Polynomial.trailingDegreeproof · cited by 39
- Polynomial.trailingDegree_eq_natTrailingDegreeproof · cited by 8
- Polynomial.trailingDegree_zeroproof · cited by 2
- Polynomial.coeff_eq_zero_of_lt_trailingDegreeproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.coeff_mirrorproof · cited by 4
- Polynomial.Monic.eq_X_pow_iff_natDegree_le_natTrailingDegreeproof · cited by 3
- Polynomial.coeff_mul_natTrailingDegree_add_natTrailingDegreeproof · cited by 1
- Polynomial.rootMultiplicity_eq_natTrailingDegree'proof · cited by 1
- Polynomial.coeff_natTrailingDegree_pred_eq_zeroproof · cited by 0