Theorems · Theorem · field theory
Polynomial.trailingDegree_le_of_ne_zero
∀ {R : Type u} {n : ℕ} [inst : Semiring R] {p : Polynomial R}, p.coeff n ≠ 0 → p.trailingDegree ≤ ↑n- Cited by
- 5 results in Mathlib
- Foundations
- Depth 63 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.
Cites7
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
- ENatstatement · cited by 4,985
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.trailingDegreestatement · cited by 39
- Polynomial.mem_support_iffproof · cited by 30
- Finset.min_leproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- Polynomial.natTrailingDegree_le_of_ne_zeroproof · cited by 10
- Polynomial.trinomial_natTrailingDegreeproof · cited by 3
- Polynomial.coeff_eq_zero_of_lt_trailingDegreeproof · cited by 2
- Polynomial.trailingDegree_mul'proof · cited by 1
- Polynomial.trailingDegree_le_trailingDegreeproof · cited by 0