Theorems · Theorem · order theory
partialSups_eq_ciSup_Iic
∀ {α : Type u_1} {ι : Type u_3} [inst : Preorder ι] [inst_1 : LocallyFiniteOrderBot ι]
[inst_2 : ConditionallyCompleteLattice α] (f : ι → α) (i : ι), (partialSups f) i = ⨆ i_1, f ↑i_1- Defined in
- Mathlib.Order.PartialSups
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- Set.Elemstatement and proof · cited by 7,166
- iSupstatement · cited by 2,415
- le_antisymmproof · cited by 2,068
- le_rflproof · cited by 1,558
- Set.Iicstatement and proof · cited by 1,111
- OrderHomstatement · cited by 934
- ConditionallyCompleteLatticestatement and proof · cited by 364
- LocallyFiniteOrderBotstatement and proof · cited by 286
- Finset.Iicproof · cited by 280
Cited by2
Results whose statement or proof uses this declaration.
- partialSups_eq_biSupproof · cited by 4
- ciSup_partialSups_eqproof · cited by 2