Theorems · Theorem · order theory
UpperSet.coe_iInf
∀ {α : Type u_1} {ι : Sort u_4} [inst : LE α] (f : ι → UpperSet α), ↑(⨅ i, f i) = ⋃ i, ↑(f i)- Defined in
- Mathlib.Order.UpperLower.CompleteLattice
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LE
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.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.iUnionstatement and proof · cited by 2,483
- iInfstatement · cited by 1,690
- Set.iUnion_congr_Propproof · cited by 374
- UpperSetstatement and proof · cited by 245
- Set.iUnion_existsproof · cited by 45
- Set.iUnion_iUnion_eq'proof · cited by 21
Cited by6
Results whose statement or proof uses this declaration.
- UpperSet.coe_iInf₂proof · cited by 3
- LowerSet.compl_iInfproof · cited by 1
- Topology.IsLower.isClosed_upperClosureproof · cited by 1
- UpperSet.compl_iInfproof · cited by 1
- UpperSet.mem_iInf_iffproof · cited by 0
- UpperSet.iInf_Iciproof · cited by 0