unique — Mathlib

English

For any φ and ψ, ψ f = toAddMonoid (fun i => ψ ∘ (of β i)) f.

Русский

Для любых φ и ψ, ψ f = toAddMonoid (функция i ↦ ψ ∘ (of β i)) f.

LaTeX

$$theorem DirectSum.toAddMonoid.unique {f} : ψ f = toAddMonoid (fun i => ψ.comp (of β i)) f$$

Lean4

theorem unique (f : ⨁ i, β i) : ψ f = toAddMonoid (fun i => ψ.comp (of β i)) f :=
  by
  congr
    -- Porting note (https://github.com/leanprover-community/mathlib4/issues/11041): `ext` applies addHom_ext' here, which isn't what we want.

  apply DFinsupp.addHom_ext'
  simp [toAddMonoid, of]

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