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Theorems · Definition · order theory

Set.projIic

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

Projection of α to the closed interval (-∞, b].

Defined in
Mathlib.Order.Interval.Set.ProjIcc
Cited by
13 results in Mathlib
Foundations
Depth 17 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 · cited by 9Set.IicExtendSet.projIic_coe · cited by 3Set.projIic_coeSet.projIic_of_mem · cited by 3Set.projIic_of_memSet.projIic_of_le · cited by 2Set.projIic_of_leSet.projIic_surjective · cited by 1Set.projIic_surjectiveSet.range_projIic · cited by 1Set.range_projIicSet.strictMonoOn_projIic · cited by 1Set.strictMonoOn_projIicSet.monotone_projIic · cited by 1Set.monotone_projIicSet.coe_projIic · cited by 0Set.coe_projIicSet.OrdConnected.IicExtend · cited by 0OrdConnected.IicExtendSet.projIic_surjOn · cited by 0Set.projIic_surjOnSet.range_IicExtend · cited by 0Set.range_IicExtendSet.projIic_eq_self · cited by 0Set.projIic_eq_selfSet.projIic_self · cited by 0Set.projIic_selfLinearOrder · cited by 8572LinearOrderSet.Elem · cited by 7166Set.ElemSet.Iic · cited by 1111Set.Iicmin_le_left · cited by 105min_le_leftSet.projIicCITED BYCITES

Cites4

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

Cited by14

Results whose statement or proof uses this declaration.