Theorems · Theorem · order theory
le_partialSups_of_le
∀ {α : Type u_1} {ι : Type u_3} [inst : SemilatticeSup α] [inst_1 : Preorder ι] [inst_2 : LocallyFiniteOrderBot ι]
(f : ι → α) {i j : ι}, i ≤ j → f i ≤ (partialSups f) j- Defined in
- Mathlib.Order.PartialSups
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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_rflproof · cited by 1,558
- OrderHomstatement · cited by 934
- SemilatticeSupstatement and proof · cited by 785
- LocallyFiniteOrderBotstatement and proof · cited by 286
- partialSupsstatement · cited by 67
- partialSups_le_iffproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- le_partialSupsproof · cited by 5
- partialSups_monotoneproof · cited by 1
- exists_partialSups_eqproof · cited by 0
- partialSups_monoproof · cited by 0