Theorems · Theorem · field theory
Polynomial.natDegree_multiset_sum_le
∀ {S : Type u_1} [inst : Semiring S] (l : Multiset (Polynomial S)),
l.sum.natDegree ≤ Multiset.foldr max 0 (Multiset.map Polynomial.natDegree l)- Defined in
- Mathlib.Algebra.Polynomial.BigOperators
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 90 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
- Multisetstatement and proof · cited by 2,627
- Polynomial.natDegreestatement · cited by 1,105
- Multiset.mapstatement · cited by 876
- Multiset.sumstatement · cited by 388
- Multiset.foldrstatement · cited by 18
- Polynomial.natDegree_list_sum_leproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.natDegree_sum_leproof · cited by 9
- exists_derivative_mul_eq_and_isIntegral_coeffproof · cited by 1