Theorems · Theorem · order theory
iInf_plift_down
∀ {α : Type u_1} {ι : Sort u_4} [inst : InfSet α] (f : ι → α), ⨅ i, f i.down = ⨅ i, f i- Defined in
- Mathlib.Order.CompleteLattice.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- InfSet
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- iInfstatement · cited by 1,690
- InfSetstatement and proof · cited by 145
- Function.Surjective.iInf_congrproof · cited by 11
- PLift.down_surjectiveproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- InfClosed.iInf_mem_of_nonemptyproof · cited by 3
- Set.iInter_plift_downproof · cited by 2
- Filter.iInf_principalproof · cited by 1