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Theorems · Theorem · order theory

directedOn_image

∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {s : Set β} {f : β → α},
  DirectedOn r (f '' s) ↔ DirectedOn (f ⁻¹'o r) s
Defined in
Mathlib.Order.Directed
Cited by
4 results in Mathlib
Foundations
Depth 7 from the axioms · uses propext, Quot.sound
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Around this declaration

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

DirectedOn.mono_comp · cited by 10DirectedOn.mono_compexists_sSupIndep_disjoint_sSup_atoms · cited by 2exists_sSupIndep_disjoint…Topology.IsScott.scottContinuousOn_iff_continuous · cited by 2IsScott.scottContinuousOn…RieszExtension.exists_top · cited by 1RieszExtension.exists_topSet · cited by 53352SetSet.image · cited by 5609Set.imageDirectedOn · cited by 271DirectedOnOrder.Preimage · cited by 42Order.PreimagedirectedOn_imageCITED BYCITES

Cites4

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Cited by4

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