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Theorems · Theorem · order theory

Set.surjOn_iInter_iInter

∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_5} [Nonempty ι] {s : ι → Set α} {t : ι → Set β} {f : α → β},
  (∀ (i : ι), Set.SurjOn f (s i) (t i)) → Set.InjOn f (⋃ i, s i) → Set.SurjOn f (⋂ i, s i) (⋂ i, t i)
Defined in
Mathlib.Data.Set.Lattice.Image
Cited by
1 results in Mathlib
Foundations
Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Nonempty
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Set.bijOn_iInter · cited by 1Set.bijOn_iInterSet · cited by 53352SetSet.iUnion · cited by 2483Set.iUnionSet.iInter · cited by 1084Set.iInterSet.InjOn · cited by 543Set.InjOnSet.SurjOn · cited by 186Set.SurjOnSet.Subset.refl · cited by 66Subset.reflSet.iInter_subset · cited by 39Set.iInter_subsetSet.SurjOn.mono · cited by 13SurjOn.monoSet.surjOn_iInter · cited by 1Set.surjOn_iInterSet.surjOn_iInter_iInterCITED BYCITES

Cites9

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Cited by1

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