Theorems · Theorem · general topology

ShrinkingLemma.PartialRefinement.pred_of_mem

∀ {ι : Type u_1} {X : Type u_2} [inst : TopologicalSpace X] {u : ι → Set X} {s : Set X} {p : Set X → Prop}
  (self : ShrinkingLemma.PartialRefinement u s p) {i : ι}, i ∈ self.carrier → p (self.toFun i)

For each i ∈ carrier, the refined set satisfies p.

Defined in

Mathlib.Topology.ShrinkingLemma

Cited by

2 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

TopologicalSpace