Theorems · Theorem · order theory
Finset.inf_sup
∀ {α : Type u_1} {ι : Type u_2} [inst : DistribLattice α] [inst_1 : BoundedOrder α] [inst_2 : DecidableEq ι]
{κ : ι → Type u_3} (s : Finset ι) (t : (i : ι) → Finset (κ i)) (f : (i : ι) → κ i → α),
(s.inf fun i => (t i).sup (f i)) = (s.pi t).sup fun g => s.attach.inf fun i => f (↑i) (g ↑i ⋯)- Defined in
- Mathlib.Data.Finset.Lattice.Pi
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- Top.topproof · cited by 9,680
- Finset.imageproof · cited by 910
- Finset.supstatement and proof · cited by 530
- BoundedOrderstatement and proof · cited by 270
- Finset.infstatement and proof · cited by 219
- Finset.attachstatement and proof · cited by 168
- DistribLatticestatement and proof · cited by 150
- Finset.mem_insert_selfproof · cited by 128
- Finset.mem_insert_of_memproof · cited by 109
- Finset.inductionproof · cited by 108
- eq_of_forall_ge_iffproof · cited by 96
Cited by1
Results whose statement or proof uses this declaration.
- Finset.sup_infproof · cited by 0