Theorems · Theorem · ring theory
AddMonoidAlgebra.ne_zero_of_supDegree_ne_bot
∀ {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}, AddMonoidAlgebra.supDegree D p ≠ ⊥ → p ≠ 0- Defined in
- Mathlib.Algebra.MonoidAlgebra.Degree
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 72 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 · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- SemilatticeSupstatement and proof · cited by 785
- AddMonoidAlgebrastatement and proof · cited by 649
- AddMonoidAlgebra.supDegreestatement · cited by 49
- AddMonoidAlgebra.supDegree_zeroproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.ne_zero_of_not_supDegree_leproof · cited by 2
- AddMonoidAlgebra.sum_ne_zero_of_injOn_supDegree'proof · cited by 1