Theorems · Theorem · order theory
Finset.iInf_insert_update
∀ {α : Type u_2} {β : Type u_3} [inst : CompleteLattice β] [inst_1 : DecidableEq α] {x : α} {t : Finset α} (f : α → β)
{s : β}, x ∉ t → ⨅ i ∈ insert x t, Function.update f x s i = s ⊓ ⨅ i ∈ t, f i- Defined in
- Mathlib.Order.CompleteLattice.Finset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLatticeDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- iInfstatement and proof · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- Function.updatestatement and proof · cited by 502
- Finset.iInf_insertproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Finset.set_biInter_insert_updateproof · cited by 0