Theorems · Theorem · field theory
Polynomial.natDegree_sum_le
∀ {ι : Type w} (s : Finset ι) {S : Type u_1} [inst : Semiring S] (f : ι → Polynomial S),
(∑ i ∈ s, f i).natDegree ≤ Finset.fold max 0 (Polynomial.natDegree ∘ f) s- Defined in
- Mathlib.Algebra.Polynomial.BigOperators
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 91 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.
Cites13
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
- Finsetstatement and proof · cited by 13,712
- Polynomialstatement and proof · cited by 5,681
- Finset.sumstatement and proof · cited by 5,195
- Polynomial.natDegreestatement and proof · cited by 1,105
- Multiset.mapproof · cited by 876
- Finset.valproof · cited by 438
- Multiset.map_congrproof · cited by 232
- Multiset.map_mapproof · cited by 151
- Finset.foldstatement · cited by 46
- Finset.fold_congrproof · cited by 11
- Polynomial.natDegree_multiset_sum_leproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_sum_le_of_forall_leproof · cited by 6
- IsIntegral.coeffproof · cited by 4
- Polynomial.natDegree_hasseDeriv_leproof · cited by 1
- Polynomial.exists_iterate_derivative_eq_factorial_smulproof · cited by 1
- Polynomial.natDegree_det_X_add_C_leproof · cited by 1
- sum_smul_minpolyDiv_eq_X_powproof · cited by 1
- MvPolynomial.aeval_natDegree_leproof · cited by 1
- Polynomial.aeval_sumIDerivproof · cited by 1
- Polynomial.aeval_sumIDeriv_of_posproof · cited by 1