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Theorems · Theorem · order theory

Set.mapsTo_iInter_iInter

∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_5} {s : ι → Set α} {t : ι → Set β} {f : α → β},
  (∀ (i : ι), Set.MapsTo f (s i) (t i)) → Set.MapsTo f (⋂ i, s i) (⋂ i, t i)
Defined in
Mathlib.Data.Set.Lattice.Image
Cited by
3 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

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

Set.image_iInter_subset · cited by 3Set.image_iInter_subsetSet.mapsTo_iInter₂_iInter₂ · cited by 1Set.mapsTo_iInter₂_iInter₂Set.bijOn_iInter · cited by 1Set.bijOn_iInterSet · cited by 53352SetSet.iInter · cited by 1084Set.iInterSet.MapsTo · cited by 732Set.MapsToSet.iInter_subset · cited by 39Set.iInter_subsetSet.MapsTo.mono_left · cited by 13MapsTo.mono_leftSet.mapsTo_iInter · cited by 1Set.mapsTo_iInterSet.mapsTo_iInter_iInterCITED BYCITES

Cites6

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Cited by3

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