Theorems · Theorem · order theory
iSup_le_iSup_of_partialSups_le_partialSups
∀ {α : Type u_1} {ι : Type u_3} [inst : Preorder ι] [inst_1 : LocallyFiniteOrderBot ι] [inst_2 : CompleteLattice α]
{f g : ι → α}, partialSups f ≤ partialSups g → ⨆ i, f i ≤ ⨆ i, g i- Defined in
- Mathlib.Order.PartialSups
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Preorderstatement and proof · cited by 7,952
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- OrderHomstatement · cited by 934
- LocallyFiniteOrderBotstatement and proof · cited by 286
- partialSupsstatement and proof · cited by 67
- iSup_monoproof · cited by 37
- iSup_partialSups_eqproof · cited by 3
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.