map_surjOn_Iic_iff_surjOn — Mathlib

English

Corollary: SurjOn (map m) (Iic 𝓟 s) (Iic 𝓟 t) iff SurjOn m s t.

Русский

Следствие: SurjOn (map m) (Iic 𝓟 s) (Iic 𝓟 t) эквивалентно SurjOn m s t.

LaTeX

$$$\\mathrm{SurjOn}(\\mathrm{map}\\, m)\\,(Iic \\mathcal{P} s)\\,(Iic \\mathcal{P} t) \\iff \\mathrm{SurjOn}\, m\, s\, t$$$

Lean4

theorem map_surjOn_Iic_iff_surjOn {s : Set α} {t : Set β} {m : α → β} :
    SurjOn (map m) (Iic <| 𝓟 s) (Iic <| 𝓟 t) ↔ SurjOn m s t := by
  rw [map_surjOn_Iic_iff_le_map, map_principal, principal_mono, SurjOn]

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