Theorems · Theorem · order theory
iSup_plift_down
∀ {α : Type u_1} {ι : Sort u_4} [inst : SupSet α] (f : ι → α), ⨆ i, f i.down = ⨆ i, f i- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- SupSet
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iSupstatement · cited by 2,415
- SupSetstatement and proof · cited by 154
- Function.Surjective.iSup_congrproof · cited by 14
- PLift.down_surjectiveproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- Submodule.fg_iSupproof · cited by 3
- Subgroup.mem_iSup_of_directedproof · cited by 2
- AddSubgroup.mem_iSup_of_directedproof · cited by 2
- SupClosed.iSup_mem_of_nonemptyproof · cited by 2
- MeasureTheory.OuterMeasure.trim_iSupproof · cited by 1
- Set.iUnion_plift_downproof · cited by 1
- AddSubmonoid.FG.iSupproof · cited by 1
- Subgroup.FG.iSupproof · cited by 0
- AddSubgroup.FG.iSupproof · cited by 0
- Submonoid.FG.iSupproof · cited by 0