Theorems · Theorem · field theory
Polynomial.le_natDegree_of_ne_zero
∀ {R : Type u} {n : ℕ} [inst : Semiring R] {p : Polynomial R}, p.coeff n ≠ 0 → n ≤ p.natDegree- Cited by
- 14 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
- WithBotproof · cited by 1,498
- Polynomial.natDegreestatement · cited by 1,105
- Polynomial.coeffstatement and proof · cited by 1,045
- Nat.cast_leproof · cited by 159
- Polynomial.degree_eq_natDegreeproof · cited by 69
- Polynomial.le_degree_of_ne_zeroproof · cited by 11
Cited by14
Results whose statement or proof uses this declaration.
- Polynomial.Monic.natDegree_mapproof · cited by 21
- Polynomial.le_natDegree_of_mem_suppproof · cited by 16
- Polynomial.natDegree_eq_of_le_of_coeff_ne_zeroproof · cited by 15
- Polynomial.natTrailingDegree_le_natDegreeproof · cited by 4
- Polynomial.coeff_mul_invOneSubPow_eq_hilbertPoly_evalproof · cited by 3
- Polynomial.natDegree_eraseLeadproof · cited by 2
- Polynomial.natDegree_comp_leproof · cited by 2
- Polynomial.scaleRoots_eval₂_mul_of_commuteproof · cited by 2
- RatFunc.natDegree_minpolyXproof · cited by 2
- Polynomial.natDegree_hasseDeriv_leproof · cited by 1
- RatFunc.natDegree_num_le_natDegree_minpolyXproof · cited by 1
- Polynomial.natDegree_eq_reverse_natDegree_add_natTrailingDegreeproof · cited by 1