Theorems · Theorem · order theory
partialSups_bot
∀ {α : Type u_1} {ι : Type u_3} [inst : SemilatticeSup α] [inst_1 : PartialOrder ι] [inst_2 : LocallyFiniteOrder ι]
[inst_3 : OrderBot ι] (f : ι → α), (partialSups f) ⊥ = f ⊥- Defined in
- Mathlib.Order.PartialSups
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- PartialOrderstatement and proof · cited by 6,410
- Bot.botstatement and proof · cited by 4,720
- OrderBotstatement and proof · cited by 1,055
- OrderHomstatement · cited by 934
- SemilatticeSupstatement and proof · cited by 785
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Iicproof · cited by 280
- partialSupsstatement · cited by 67
- Finset.sup'_congrproof · cited by 38
- Finset.coe_Iicproof · cited by 36
- Finset.nonempty_Iicproof · cited by 18
Cited by2
Results whose statement or proof uses this declaration.
- partialSups_succ'proof · cited by 1
- partialSups_zeroproof · cited by 0