distribMulActionHom_ext' — Mathlib

English

A variant of extensionality for DistribMulActionHom; equality of actions can be checked on a generating set of inputs.

Русский

Вариантext для DistribMulActionHom; равенство действий можно проверить на порождающем наборе входов.

LaTeX

$$@[ext] f=g при ∀ a, f.comp (single a) = g.comp (single a)$$

Lean4

/-- See note [partially-applied ext lemmas]. -/
@[ext]
theorem distribMulActionHom_ext' {f g : (α →₀ M) →+[R] N}
    (h : ∀ a : α, f.comp (DistribMulActionHom.single a) = g.comp (DistribMulActionHom.single a)) : f = g :=
  distribMulActionHom_ext fun a => DistribMulActionHom.congr_fun (h a)

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