Theorems · Theorem · ring theory
AddMonoidAlgebra.supDegree_zero
∀ {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}, AddMonoidAlgebra.supDegree D 0 = ⊥- Defined in
- Mathlib.Algebra.MonoidAlgebra.Degree
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Bot.botstatement and proof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- AddMonoidAlgebrastatement · cited by 649
- Finset.sup_emptyproof · cited by 72
- AddMonoidAlgebra.supDegreestatement · cited by 49
Cited by5
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.coeff_supDegree_add_supDegreeproof · cited by 5
- AddMonoidAlgebra.ne_zero_of_supDegree_ne_botproof · cited by 2
- MvPolynomial.IsSymmetric.antitone_supDegreeproof · cited by 1
- Polynomial.supDegree_eq_natDegreeproof · cited by 0
- AddMonoidAlgebra.Monic.supDegree_mulproof · cited by 0