Theorems · Theorem · ring theory
AddMonoidAlgebra.supDegree_sum_le
∀ {R : Type u_1} {A : Type u_3} {B : Type u_5} [inst : Semiring R] [inst_1 : SemilatticeSup B] [inst_2 : OrderBot B]
{D : A → B} {ι : Type u_7} {s : Finset ι} {f : ι → AddMonoidAlgebra R A},
AddMonoidAlgebra.supDegree D (∑ i ∈ s, f i) ≤ s.sup fun i => AddMonoidAlgebra.supDegree D (f i)- Defined in
- Mathlib.Algebra.MonoidAlgebra.Degree
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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
- Finset.sumstatement · cited by 5,195
- le_reflproof · cited by 2,061
- OrderBotstatement and proof · cited by 1,055
- Finsupp.supportproof · cited by 828
- SemilatticeSupstatement and proof · cited by 785
- AddMonoidAlgebrastatement and proof · cited by 649
- le_imp_le_of_le_of_leproof · cited by 576
- Finset.supstatement and proof · cited by 530
- AddMonoidAlgebra.coeffproof · cited by 365
- AddMonoidAlgebra.supDegreestatement · cited by 49
Cited by3
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.supDegree_sum_ltproof · cited by 1
- MvPolynomial.degrees_sum_leproof · cited by 0
- MvPolynomial.degreeOf_sum_leproof · cited by 0