Theorems · Definition · order theory

disjointed

{α : Type u_1} →
  {ι : Type u_2} → [GeneralizedBooleanAlgebra α] → [inst : Preorder ι] → [LocallyFiniteOrderBot ι] → (ι → α) → ι → α

The function mapping i to f i \ (⨆ j < i, f j). When ι is a partial order, this is the unique function g having the same partialSups as f and such that g i and g j are disjoint whenever i < j.

Defined in

Mathlib.Order.Disjointed

Cited by

64 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

GeneralizedBooleanAlgebraPreorderLocallyFiniteOrderBot