instUniqueSumsDFinsupp — Mathlib

English

If each G i has AddZeroClass and UniqueSums, then the dependent function type DFinsupp i ↦ G i has UniqueSums.

Русский

ЕслиEach G i обладает AddZeroClass и UniqueSums, то DFinsupp i ↦ G i имеет UniqueSums.

LaTeX

$$$ [\\forall i, AddZeroClass (G i)] [\\forall i, UniqueSums (G i)] \\Rightarrow \\mathrm{UniqueSums}(\\mathrm{DFinsupp}\\, (\\lambda i, G i)). $$$

Lean4

instance {ι} (G : ι → Type*) [∀ i, AddZeroClass (G i)] [∀ i, UniqueSums (G i)] : UniqueSums (Π₀ i, G i) :=
  UniqueSums.of_injective_addHom DFinsupp.coeFnAddMonoidHom.toAddHom DFunLike.coe_injective inferInstance

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