Theorems · Theorem · field theory
Polynomial.degree_sum_le
∀ {R : Type u} [inst : Semiring R] {ι : Type u_1} (s : Finset ι) (f : ι → Polynomial R),
(∑ i ∈ s, f i).degree ≤ s.sup fun b => (f b).degree- Defined in
- Mathlib.Algebra.Polynomial.Degree.Defs
- Cited by
- 11 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.
Cites15
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
- Bot.botproof · cited by 4,720
- le_rflproof · cited by 1,558
- WithBotstatement and proof · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- Finset.supstatement and proof · cited by 530
- Finset.sum_consproof · cited by 84
- Finset.sup_emptyproof · cited by 72
- Finset.cons_induction_onproof · cited by 37
Cited by11
Results whose statement or proof uses this declaration.
- Polynomial.degree_sum_fin_ltproof · cited by 4
- Polynomial.degree_derivativeproof · cited by 3
- Lagrange.sum_basisproof · cited by 3
- Polynomial.natDegree_comp_leproof · cited by 2
- Polynomial.Monic.geom_sumproof · cited by 2
- Polynomial.quo_mul_prod_add_sum_rem_mul_prod_uniqueproof · cited by 1
- Polynomial.quo_mul_prod_pow_add_sum_rem_mul_prod_pow_uniqueproof · cited by 1
- Lagrange.interpolate_eq_sum_interpolate_insert_sdiffproof · cited by 1
- IsPrimitiveRoot.sum_eq_zero_iff_forall_eqproof · cited by 1
- Lagrange.degree_interpolate_leproof · cited by 1
- Polynomial.degree_sum_eq_of_linearIndepOnproof · cited by 0