separated_pureCauchy_injective — Mathlib

English

The map a ↦ SeparationQuotient.mk (pureCauchy a) is injective (separation quotients).

Русский

Карта a ↦ SeparationQuotient.mk (pureCauchy a) инъективна (разделительная фактор-группа).

LaTeX

$$$\\text{separated_pureCauchy_injective}$$$

Lean4

theorem separated_pureCauchy_injective {α : Type*} [UniformSpace α] [T0Space α] :
    Function.Injective fun a : α => SeparationQuotient.mk (pureCauchy a) := fun a b h ↦
  Inseparable.eq <| (inseparable_iff_of_le_nhds (pure_le_nhds a) (pure_le_nhds b)).2 <| SeparationQuotient.mk_eq_mk.1 h

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