Theorems · Theorem · field theory
Polynomial.trailingCoeff_eq_zero
∀ {R : Type u} [inst : Semiring R] {p : Polynomial R}, p.trailingCoeff = 0 ↔ p = 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.
Cites8
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
- by_contradictionproof · cited by 42
- Polynomial.mem_support_iffproof · cited by 30
- Polynomial.trailingCoeffstatement and proof · cited by 20
- Polynomial.leadingCoeff_zeroproof · cited by 9
- Polynomial.trailingDegree_eq_natTrailingDegreeproof · cited by 8
- Finset.mem_of_minproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.trailingCoeff_nonzero_iff_nonzeroproof · cited by 6
- Polynomial.natTrailingDegree_le_natDegreeproof · cited by 4
- Polynomial.mirror_natDegreeproof · cited by 4
- Polynomial.natTrailingDegree_mulproof · cited by 4
- Polynomial.natTrailingDegree_mul_X_powproof · cited by 1