Theorems · Theorem · commutative algebra
AddMonoidAlgebra.coeff_divOf
∀ {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')- Defined in
- Mathlib.Algebra.MonoidAlgebra.Division
- 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.
Cites8
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 and proof · cited by 13,802
- AddCommMonoidstatement and proof · cited by 12,281
- Finsuppstatement · cited by 5,255
- AddMonoidAlgebrastatement and proof · cited by 649
- AddMonoidAlgebra.coeffstatement · cited by 365
- IsCancelAddstatement and proof · cited by 79
- AddMonoidAlgebra.divOfstatement · cited by 17
Cited by2
Results whose statement or proof uses this declaration.
- AddMonoidAlgebra.divOf_add_modOfproof · cited by 3
- AddMonoidAlgebra.divOf_applyproof · cited by 0