Theorems · Theorem · order theory
Finset.iInf_biUnion
∀ {α : Type u_2} {β : Type u_3} {γ : Type u_4} [inst : CompleteLattice β] [inst_1 : DecidableEq α] (s : Finset γ)
(t : γ → Finset α) (f : α → β), ⨅ y ∈ s.biUnion t, f y = ⨅ x ∈ s, ⨅ y ∈ t x, f y- Defined in
- Mathlib.Order.CompleteLattice.Finset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 75 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.
Cites9
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
- iInf_congr_Propproof · cited by 218
- Finset.biUnionstatement · cited by 217
- Finset.mem_biUnionproof · cited by 26
- iInf_andproof · cited by 15
- iInf_commproof · cited by 12
- iInf_existsproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Finset.set_biInter_biUnionproof · cited by 0