English
Pull back a CompleteDistribLattice along an injection to obtain a CompleteDistribLattice on α.
Русский
Тянем назад CompleteDistribLattice вдоль инъекции, получаем CompleteDistribLattice на α.
LaTeX
$$$[CompleteDistribLattice\; \beta] \rightarrow \text{pullback along } f:\alpha \to \beta \Rightarrow CompleteDistribLattice(\alpha).$$$
Lean4
/-- Pullback a `CompleteDistribLattice` along an injection. -/
protected abbrev completeDistribLattice [Max α] [Min α] [SupSet α] [InfSet α] [Top α] [Bot α] [HasCompl α] [HImp α]
[HNot α] [SDiff α] [CompleteDistribLattice β] (f : α → β) (hf : Injective f)
(map_sup : ∀ a b, f (a ⊔ b) = f a ⊔ f b) (map_inf : ∀ a b, f (a ⊓ b) = f a ⊓ f b)
(map_sSup : ∀ s, f (sSup s) = ⨆ a ∈ s, f a) (map_sInf : ∀ s, f (sInf s) = ⨅ a ∈ s, f a) (map_top : f ⊤ = ⊤)
(map_bot : f ⊥ = ⊥) (map_compl : ∀ a, f aᶜ = (f a)ᶜ) (map_himp : ∀ a b, f (a ⇨ b) = f a ⇨ f b)
(map_hnot : ∀ a, f (￢a) = ￢f a) (map_sdiff : ∀ a b, f (a \ b) = f a \ f b) : CompleteDistribLattice α
where
__ := hf.frame f map_sup map_inf map_sSup map_sInf map_top map_bot map_compl map_himp
__ := hf.coframe f map_sup map_inf map_sSup map_sInf map_top map_bot map_hnot map_sdiff
