Theorems · Theorem · order theory
Finset.apply_inf_eq_inf_comp_of_linearOrder
∀ {α : Type u_2} {β : Type u_3} {ι : Type u_5} [inst : LinearOrder α] [inst_1 : OrderTop α] {s : Finset ι} {f : ι → α}
[inst_2 : SemilatticeInf β] [inst_3 : OrderTop β] (g : α → β), Monotone g → g ⊤ = ⊤ → g (s.inf f) = s.inf (g ∘ f)- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
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
- Top.topstatement and proof · cited by 9,680
- LinearOrderstatement and proof · cited by 8,572
- Monotonestatement and proof · cited by 1,397
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- Finset.infstatement · cited by 219
- Monotone.map_infproof · cited by 8
- Finset.apply_inf_eq_inf_compproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- Finset.comp_inf_eq_inf_comp_of_is_totalproof · cited by 0