Mathlib Map

Theorems · Theorem · order theory

directedOn_onFun_iff

∀ {α : Type u_1} {β : Type u_2} {r : α → α → Prop} {f : β → α} {s : Set β},
  DirectedOn (Function.onFun r f) s ↔ DirectedOn r (f '' s)
Defined in
Mathlib.Order.Directed
Cited by
2 results in Mathlib
Foundations
Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Subgroup.mem_iSup_of_directed · cited by 2Subgroup.mem_iSup_of_dire…AddSubgroup.mem_iSup_of_directed · cited by 2AddSubgroup.mem_iSup_of_d…Set · cited by 53352SetSet.image · cited by 5609Set.imageFunction.onFun · cited by 570Function.onFunSet.mem_image_of_mem · cited by 371Set.mem_image_of_memDirectedOn · cited by 271DirectedOnDirectedOn.mono_comp · cited by 10DirectedOn.mono_compdirectedOn_onFun_iffCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.