Theorems · Theorem · order theory
iSup_range
∀ {α : Type u_1} {β : Type u_2} {ι : Sort u_4} [inst : CompleteLattice α] {g : β → α} {f : ι → β},
⨆ b ∈ Set.range f, g b = ⨆ i, g (f i)- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.rangestatement and proof · cited by 4,705
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- iSup_subtype''proof · cited by 18
- iSup_range'proof · cited by 7
Cited by24
Results whose statement or proof uses this declaration.
- Set.biUnion_rangeproof · cited by 11
- MeasureTheory.OuterMeasure.iSup_applyproof · cited by 9
- iSup_inf_eqproof · cited by 7
- Submodule.span_range_eq_iSupproof · cited by 3
- sup_iSup_nat_succproof · cited by 3
- HomogeneousIdeal.toIdeal_iSupproof · cited by 2
- MeasureTheory.isTightMeasureSet_range_of_tendsto_limsup_innerproof · cited by 2
- ClosedSubmodule.toSubmodule_iSupproof · cited by 1
- AlgebraicGeometry.isCompact_basicOpenproof · cited by 1
- CompleteSublattice.coe_iSupproof · cited by 1
- OrderHom.iSup_applyproof · cited by 1
- Directed.iSup_inf_eqproof · cited by 1