preimage_upperClosure_compl_finset

English

preimage_upperClosure_compl_finset: the preimage of the complement of upperClosure under Set corresponds to hull of T with F.inf id.

Русский

preimage_upperClosure_compl_finset: прообраз дополнения верхнего замыкания соответствует hull T (F.inf id).

LaTeX

$$$\\operatorname{preimage}(\\operatorname{Subtype.val}, (\\operatorname{UpperSet}.instSetLike.co e (upperClosure F.toSet))^c) = \\operatorname{preimage}(\\operatorname{Subtype.val}, \\operatorname{Hull}(T, F.inf id))$$$

Lean4

theorem preimage_upperClosure_compl_finset (hT : ∀ p ∈ T, InfPrime p) (F : Finset α) :
    T ↓∩ (upperClosure F.toSet)ᶜ = (hull T (inf F id))ᶜ := by rw [Set.preimage_compl, (hull_finsetInf hT)]

Похожие утверждения