Mathlib Map

Theorems · Theorem · ring theory

AddMonoidAlgebra.toDirectSum_add

∀ {ι : Type u_1} {M : Type u_3} [inst : Semiring M] (f g : AddMonoidAlgebra M ι),
  (f + g).toDirectSum = f.toDirectSum + g.toDirectSum
Defined in
Mathlib.Algebra.MonoidAlgebra.ToDirectSum
Cited by
1 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Semiring
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

addMonoidAlgebraAddEquivDirectSum · cited by 4addMonoidAlgebraAddEquivD…AddMonoidAlgebra.toDirectSum_mul · cited by 1AddMonoidAlgebra.toDirect…Semiring · cited by 13802SemiringAddMonoidAlgebra · cited by 649AddMonoidAlgebraDirectSum · cited by 446DirectSumEquiv.toFun · cited by 279Equiv.toFunAddMonoidAlgebra.coeffEquiv · cited by 22AddMonoidAlgebra.coeffEqu…AddMonoidAlgebra.toDirectSum · cited by 16AddMonoidAlgebra.toDirect…Finsupp.toDFinsupp_add · cited by 1Finsupp.toDFinsupp_addAddMonoidAlgebra.toDirectSum_…CITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.