Theorems · Theorem · ring theory
AddMonoidAlgebra.coeff_eq_zero_of_not_le_supDegree
∀ {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} {p : AddMonoidAlgebra R A} {a : A}, ¬D a ≤ AddMonoidAlgebra.supDegree D p → p.coeff a = 0- Defined in
- Mathlib.Algebra.MonoidAlgebra.Degree
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Finsuppstatement · cited by 5,255
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- AddMonoidAlgebrastatement and proof · cited by 649
- AddMonoidAlgebra.coeffstatement and proof · cited by 365
- Finset.le_supproof · cited by 112
- Finsupp.mem_support_iffproof · cited by 89
- AddMonoidAlgebra.supDegreestatement and proof · cited by 49
Cited by3
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.supDegree_add_eq_leftproof · cited by 3
- AddMonoidAlgebra.leadingCoeff_add_eq_leftproof · cited by 2
- AddMonoidAlgebra.apply_eq_zero_of_not_le_supDegreeproof · cited by 0