English
The InfSet structure gives completeness w.r.t. Infimum over sets of nuclei.
Русский
Структура InfSet обеспечивает полноту по инфимумау над множествами нуклеусов.
LaTeX
$$$\text{InfSet}(Nucleus(X))$ is complete with respect to $\inf$ over sets$$
Lean4
instance : CompleteLattice (Nucleus X)
where
__ : SemilatticeInf (Nucleus X) := inferInstance
__ : OrderBot (Nucleus X) := inferInstance
__ : OrderTop (Nucleus X) := inferInstance
__ := completeLatticeOfCompleteSemilatticeInf (Nucleus X)