Mathlib Map

Theorems · Definition · order theory

Set.IicExtend

{α : Type u_1} → {β : Type u_2} → [inst : LinearOrder α] → {b : α} → (↑(Set.Iic b) → β) → α → β

Extend a function (-∞, b] → β to a map α → β.

Defined in
Mathlib.Order.Interval.Set.ProjIcc
Cited by
9 results in Mathlib
Foundations
Depth 18 from the axioms · uses propext
Assumes
LinearOrder
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

Set.IicExtend_of_le · cited by 1Set.IicExtend_of_leSet.IicExtend_apply · cited by 0Set.IicExtend_applySet.IicExtend_coe · cited by 0Set.IicExtend_coeSet.IicExtend_of_mem · cited by 0Set.IicExtend_of_memSet.IicExtend_self · cited by 0Set.IicExtend_selfSet.OrdConnected.IicExtend · cited by 0OrdConnected.IicExtendSet.range_IicExtend · cited by 0Set.range_IicExtendStrictMono.strictMonoOn_IicExtend · cited by 0StrictMono.strictMonoOn_I…Monotone.IicExtend · cited by 0Monotone.IicExtendLinearOrder · cited by 8572LinearOrderSet.Elem · cited by 7166Set.ElemSet.Iic · cited by 1111Set.IicSet.projIic · cited by 13Set.projIicSet.IicExtendCITED BYCITES

Cites4

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

Cited by9

Results whose statement or proof uses this declaration.