English
There is a bottom sublattice: the smallest sublattice whose carrier is the empty set, with closure properties of ∅.
Русский
Существует нижняя подрешетка: наименьшая подрешетка с носителем пустого множества.
LaTeX
$$$ Bot\\,(Sublattice\\,\\alpha) $$$
Lean4
/-- The empty sublattice of a lattice. -/
instance instBot : Bot (Sublattice α) where
bot.carrier := ∅
bot.supClosed' := supClosed_empty
bot.infClosed' := infClosed_empty