wellPowered_congr — Mathlib

English

The property of being well-powered is invariant under equivalences: if e: C ≌ D, then WellPowered C iff WellPowered D.

Русский

Свойство хорошо обеспечено сохраняется по эквивалентности: если e: C ≌ D, то WellPowered C эквивалентно WellPowered D.

LaTeX

$$$\text{wellPowered}(C) \iff \text{wellPowered}(D)$ under an equivalence $C \simeq D$.$$

Lean4

/-- Being well-powered is preserved by equivalences. -/
theorem wellPowered_congr (e : C ≌ D) [LocallySmall.{w} C] [LocallySmall.{w} D] :
    WellPowered.{w} C ↔ WellPowered.{w} D :=
  ⟨fun _ => wellPowered_of_equiv e, fun _ => wellPowered_of_equiv e.symm⟩

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