English
For a diagram K: J ⥤ Over X and a cone t over K, the limit status of t corresponds to the limit status of coneEquiv.functor.obj t in the lifted setting; there is an equivalence between IsLimit of the lifted cone and IsLimit of t.
Русский
Для диаграммы K: J ⥤ Over X и конуса t над K, предел т и предел конуса coneEquiv.functor.obj t в приведенной обстановке эквивалентны; существует эквивалентность между IsLimit поднятого конуса и IsLimit самого t.
LaTeX
$$$$ \text{IsLimit}(\mathrm{coneEquiv.functor.obj}(t)) \;\simeq\; \text{IsLimit}(t). $$$$
Lean4
/-- Predicate for a set `A` to be covered by at most `K` cosets of another set `B` under the action
by the monoid `M`. -/
@[to_additive /-- Predicate for a set `A` to be covered by at most `K` cosets of another set `B`
under the action by the monoid `M`. -/
]
def CovBySMul (K : ℝ) (A B : Set X) : Prop :=
∃ F : Finset M, #F ≤ K ∧ A ⊆ (F : Set M) • B
