English
If atTop.IsCountablyGenerated and atBot.IsCountablyGenerated, then (conditional β).filter.IsCountablyGenerated.
Русский
Если atTop и atBot счетно порождены, то условный фильтр .filter счетно порожден.
LaTeX
$$$[\\text{atTop}.IsCountablyGenerated] \\; [\\text{atBot}.IsCountablyGenerated] \\Rightarrow (conditional(β)).filter.IsCountablyGenerated$$$
Lean4
/-- `HasProdUniformlyOn f g 𝔖` means that the (potentially infinite) product `∏' i, f i b`
for `b : β` converges uniformly on each `s ∈ 𝔖` to `g`. -/
@[to_additive /-- `HasSumUniformlyOn f g 𝔖` means that the (potentially infinite) sum `∑' i, f i b`
for `b : β` converges uniformly on each `s ∈ 𝔖` to `g`. -/
]
def HasProdUniformlyOn : Prop :=
HasProd (fun i ↦ UniformOnFun.ofFun 𝔖 (f i)) (UniformOnFun.ofFun 𝔖 g)
