Theorems · Theorem · order theory
Finset.sup_inf
∀ {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.sup fun i => (t i).inf (f i)) = (s.pi t).inf fun g => s.attach.sup fun i => f (↑i) (g ↑i ⋯)- Defined in
- Mathlib.Data.Finset.Lattice.Pi
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites8
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
- Finset.supstatement · cited by 530
- BoundedOrderstatement and proof · cited by 270
- Finset.infstatement · cited by 219
- Finset.attachstatement · cited by 168
- DistribLatticestatement and proof · cited by 150
- Finset.pistatement · cited by 23
- Finset.inf_supproof · cited by 1
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