Theorems · Theorem · order theory
iSup_emptyset
∀ {α : Type u_1} {β : Type u_2} [inst : CompleteLattice α] {f : β → α}, ⨆ x ∈ ∅, f x = ⊥- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Bot.botstatement and proof · cited by 4,720
- iSupstatement and proof · cited by 2,415
- CompleteLatticestatement and proof · cited by 1,048
- iSup_congr_Propproof · cited by 247
- iSup_negproof · cited by 49
- iSup_botproof · cited by 29
Cited by2
Results whose statement or proof uses this declaration.
- Set.biUnion_emptyproof · cited by 12
- ExpGrowth.expGrowthSup_sumproof · cited by 0