Theorems · Theorem · commutative algebra
AddMonoidAlgebra.divOf_apply
Deprecated since 2026-06-18Use AddMonoidAlgebra.coeff_divOf instead.
∀ {k : Type u_1} {G : Type u_2} [inst : Semiring k] [inst_1 : AddCommMonoid G] [inst_2 : IsCancelAdd G] (g : G)
(x : AddMonoidAlgebra k G) (g' : G), (x.divOf g).coeff g' = x.coeff (g + g')Alias of AddMonoidAlgebra.coeff_divOf.
- Defined in
- Mathlib.Algebra.MonoidAlgebra.Division
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement · cited by 13,802
- AddCommMonoidstatement · cited by 12,281
- Finsuppstatement · cited by 5,255
- AddMonoidAlgebrastatement · cited by 649
- AddMonoidAlgebra.coeffstatement · cited by 365
- IsCancelAddstatement · cited by 79
- AddMonoidAlgebra.divOfstatement · cited by 17
- AddMonoidAlgebra.coeff_divOfproof · cited by 2
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