Theorems · Theorem · order theory
Monotone.partialSups_eq
∀ {α : Type u_1} {ι : Type u_3} [inst : SemilatticeSup α] [inst_1 : Preorder ι] [inst_2 : LocallyFiniteOrderBot ι]
{f : ι → α}, Monotone f → ⇑(partialSups f) = f- Defined in
- Mathlib.Order.PartialSups
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- le_antisymmproof · cited by 2,068
- Monotonestatement and proof · cited by 1,397
- OrderHomstatement · cited by 934
- SemilatticeSupstatement and proof · cited by 785
- LocallyFiniteOrderBotstatement and proof · cited by 286
- partialSupsstatement · cited by 67
- le_partialSupsproof · cited by 5
- partialSups_leproof · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.VectorMeasure.tendsto_vectorMeasure_iUnion_atTop_natproof · cited by 3
- Monotone.disjointed_succproof · cited by 2
- isCompact_setOfPred_finiteMeasure_mass_le_compl_isCompact_leproof · cited by 2
- Finset.sum_eq_sum_range_sdiffproof · cited by 1
- Monotone.disjointed_succ_supproof · cited by 1
- Finset.prod_eq_prod_range_sdiffproof · cited by 0