Theorems · Theorem · order theory
Finset.inf_empty
∀ {α : Type u_2} {β : Type u_3} [inst : SemilatticeInf α] [inst_1 : OrderTop α] {f : β → α}, ∅.inf f = ⊤- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Quot.sound
- Assumes
- SemilatticeInfOrderTop
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Top.topstatement · cited by 9,680
- SemilatticeInfstatement and proof · cited by 634
- OrderTopstatement and proof · cited by 493
- Finset.infstatement · cited by 219
- Finset.fold_emptyproof · cited by 3
Cited by15
Results whose statement or proof uses this declaration.
- Finset.inf_eq_top_iffproof · cited by 3
- Finset.inf_sup_distrib_leftproof · cited by 3
- PrimitiveSpectrum.hull_finsetInfproof · cited by 2
- Finset.inf_topproof · cited by 2
- Finset.inclusion_exclusion_sum_inf_complproof · cited by 1
- Topology.IsLocallyConstructible.finsetInfproof · cited by 1
- Submodule.coe_finsetInfproof · cited by 1
- CategoryTheory.Subobject.finset_inf_factorsproof · cited by 1
- Finset.sup_sdiff_leftproof · cited by 1
- Finset.inf_supproof · cited by 1
- IsRetrocompact.finsetInfproof · cited by 1
- Finset.le_inf_of_directed_leproof · cited by 0