Theorems · Theorem · ring theory
AddMonoidAlgebra.single_mem_gradeBy
∀ {M : Type u_1} {ι : Type u_2} {R : Type u_4} [inst : CommSemiring R] (f : M → ι) (m : M) (r : R),
AddMonoidAlgebra.single m r ∈ AddMonoidAlgebra.gradeBy R f (f m)- Defined in
- Mathlib.Algebra.MonoidAlgebra.Grading
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Submodulestatement · cited by 7,192
- Finsupp.supportproof · cited by 828
- AddMonoidAlgebrastatement · cited by 649
- AddMonoidAlgebra.coeffproof · cited by 365
- AddMonoidAlgebra.singlestatement and proof · cited by 250
- Finset.mem_singletonproof · cited by 103
- Finsupp.support_single_subsetproof · cited by 27
- AddMonoidAlgebra.gradeBystatement · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.decomposeAux_singlestatement and proof · cited by 3
- AddMonoidAlgebra.single_mem_gradeproof · cited by 1
- AddMonoidAlgebra.GradesBy.decompose_singlestatement · cited by 0
- AddMonoidAlgebra.decomposeAux_coeproof · cited by 0