theorem extracted_formal_statement_5.{u_1} {E : Type u_1} [inst : NormedAddCommGroup E] {s : Set E} (hs : s.Nonempty)
  (x : E) (xs : x ∈ s) (this : EMetric.infEdist 0 s ≤ edist 0 x) : EMetric.infEdist 0 s ≠ ⊤ := sorry

State before:
E : Type u_1
inst✝ : NormedAddCommGroup E
s : Set E
hs : s.Nonempty
x : E
xs : x ∈ s
this : EMetric.infEdist 0 s ≤ edist 0 x
⊢ EMetric.infEdist 0 s ≠ ⊤

Tactic: exact Metric.infEdist_ne_top hs

State after:

Relevant lemmas:
Metric.infEdist_ne_top : ∀ {α : Type u} [inst : PseudoMetricSpace α] {s : Set α} {x : α},
  s.Nonempty → EMetric.infEdist x s ≠ ⊤