Theorems · Theorem · order theory
LowerSet.coe_iInf
∀ {α : Type u_1} {ι : Sort u_4} [inst : LE α] (f : ι → LowerSet α), ↑(⨅ i, f i) = ⋂ i, ↑(f i)- Defined in
- Mathlib.Order.UpperLower.CompleteLattice
- Cited by
- 4 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.
Cites9
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
- iInfstatement · cited by 1,690
- Set.iInterstatement and proof · cited by 1,084
- LowerSetstatement and proof · cited by 230
- Set.iInter_congr_Propproof · cited by 170
- Set.mem_rangeproof · cited by 102
- Set.iInter_existsproof · cited by 44
- Set.iInter_iInter_eq'proof · cited by 22
Cited by4
Results whose statement or proof uses this declaration.
- LowerSet.mem_iInf_iffproof · cited by 3
- LowerSet.coe_iInf₂proof · cited by 2
- LowerSet.compl_iInfproof · cited by 1
- UpperSet.compl_iInfproof · cited by 1