Theorems · Theorem · order theory
SupClosed.sSup_mem
∀ {α : Type u_3} [inst : CompleteLattice α] {s t : Set α}, SupClosed s → t.Finite → ⊥ ∈ s → t ⊆ s → sSup t ∈ s- Defined in
- Mathlib.Order.SupClosed
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Set.Elemproof · cited by 7,166
- Bot.botstatement and proof · cited by 4,720
- Finiteproof · cited by 3,029
- Set.Finitestatement and proof · cited by 1,814
- CompleteLatticestatement and proof · cited by 1,048
- SupSet.sSupstatement · cited by 954
- SupClosedstatement and proof · cited by 57
- Set.Finite.to_subtypeproof · cited by 44
- sSup_eq_iSup'proof · cited by 38
- SupClosed.iSup_memproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- SupClosed.biSup_memproof · cited by 3
- MeasureTheory.IsSetSemiring.mem_supClosure_iffproof · cited by 2
- BooleanSubalgebra.sSup_memproof · cited by 1
- IsRetrocompact.sUnionproof · cited by 0
- Topology.IsLocallyConstructible.sUnionproof · cited by 0