Theorems · Theorem · field theory
Polynomial.natDegree_sum_le_of_forall_le
∀ {ι : Type w} (s : Finset ι) {S : Type u_1} [inst : Semiring S] {n : ℕ} (f : ι → Polynomial S),
(∀ i ∈ s, (f i).natDegree ≤ n) → (∑ i ∈ s, f i).natDegree ≤ n- Defined in
- Mathlib.Algebra.Polynomial.BigOperators
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 92 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
- Finsetstatement and proof · cited by 13,712
- Polynomialstatement and proof · cited by 5,681
- Finset.sumstatement · cited by 5,195
- Polynomial.natDegreestatement and proof · cited by 1,105
- le_transproof · cited by 985
- Polynomial.natDegree_sum_leproof · cited by 9
- Finset.fold_max_leproof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Polynomial.exists_monic_aeval_eq_zero_forall_mem_pow_of_isIntegralproof · cited by 1
- isIntegral_of_isIntegral_adjoin_of_mul_eq_oneproof · cited by 1
- Polynomial.natDegree_hilbertPoly_of_ne_zero_of_rootMultiplicity_ltproof · cited by 1
- Polynomial.natDegree_sum_eq_of_linearIndepOnproof · cited by 0
- Polynomial.leadingCoeff_sum_of_degree_eqproof · cited by 0