Theorems · Theorem · order theory
Finset.inf_eq_iInf
∀ {α : Type u_2} {β : Type u_3} [inst : CompleteLattice β] (s : Finset α) (f : α → β), s.inf f = ⨅ a ∈ s, f a- Defined in
- Mathlib.Data.Finset.Lattice.Fold
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CompleteLattice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 · cited by 1,690
- CompleteLatticestatement and proof · cited by 1,048
- Finset.infstatement · cited by 219
- iInf_leproof · cited by 104
- le_iInfproof · cited by 102
- iInf_le_of_leproof · cited by 62
- ge_antisymmproof · cited by 51
- Finset.inf_leproof · cited by 23
- Finset.le_infproof · cited by 10
Cited by19
Results whose statement or proof uses this declaration.
- Finset.inf_id_eq_sInfproof · cited by 4
- partialSups_iff_forallproof · cited by 3
- IsDedekindDomain.inf_pow_eq_prod_of_primeproof · cited by 3
- Finset.inf_set_eq_iInterproof · cited by 3
- IsDedekindDomain.exists_sup_span_eqproof · cited by 2
- MeasureTheory.hahn_decompositionproof · cited by 2
- Submodule.isInternal_prime_power_torsion_of_is_torsion_by_idealproof · cited by 1
- ExpGrowth.expGrowthInf_biInfproof · cited by 1
- Set.map_finite_biInfproof · cited by 1
- Ideal.subset_union_prime'proof · cited by 1
- Submodule.comap_finsetInfproof · cited by 1
- LinearGrowth.linearGrowthInf_biInfproof · cited by 1