Theorems · Theorem · order theory
LowerSet.mem_iInf_iff
∀ {α : Type u_1} {ι : Sort u_4} [inst : LE α] {a : α} {f : ι → LowerSet α}, a ∈ ⨅ i, f i ↔ ∀ (i : ι), a ∈ f i- Defined in
- Mathlib.Order.UpperLower.CompleteLattice
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 63 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- iInfstatement · cited by 1,690
- SetLike.mem_coeproof · cited by 302
- LowerSetstatement and proof · cited by 230
- Set.mem_iInterproof · cited by 69
- LowerSet.coe_iInfproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- LowerSet.Iic_iInfproof · cited by 1
- LowerSet.Iic_sInfproof · cited by 0
- LowerSet.mem_iInf₂_iffproof · cited by 0